autograd API Reference

Python Library Documentation: function checkpoint in module autograd.differential_operators

checkpoint(fun)
    Returns a checkpointed version of `fun`, where intermediate values
    computed during the forward pass of `fun` are discarded and then recomputed
    for the backward pass. Useful to save memory, effectively trading off time
    and memory. See e.g. arxiv.org/abs/1604.06174.

Python Library Documentation: function deriv in module autograd.wrap_util

deriv(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    None

Python Library Documentation: class dict in module autograd.builtins

class dict(builtins.dict)
 |  dict(*args, **kwargs)
 |
 |  Method resolution order:
 |      dict
 |      builtins.dict
 |      builtins.object
 |
 |  Static methods defined here:
 |
 |  __new__(cls, *args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from builtins.dict:
 |
 |  __contains__(self, key, /)
 |      True if the dictionary has the specified key, else False.
 |
 |  __delitem__(self, key, /)
 |      Delete self[key].
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getattribute__(self, name, /)
 |      Return getattr(self, name).
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __init__(self, /, *args, **kwargs)
 |      Initialize self.  See help(type(self)) for accurate signature.
 |
 |  __ior__(self, value, /)
 |      Return self|=value.
 |
 |  __iter__(self, /)
 |      Implement iter(self).
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __reversed__(self, /)
 |      Return a reverse iterator over the dict keys.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __setitem__(self, key, value, /)
 |      Set self[key] to value.
 |
 |  __sizeof__(...)
 |      D.__sizeof__() -> size of D in memory, in bytes
 |
 |  clear(...)
 |      D.clear() -> None.  Remove all items from D.
 |
 |  copy(...)
 |      D.copy() -> a shallow copy of D
 |
 |  get(self, key, default=None, /)
 |      Return the value for key if key is in the dictionary, else default.
 |
 |  items(...)
 |      D.items() -> a set-like object providing a view on D's items
 |
 |  keys(...)
 |      D.keys() -> a set-like object providing a view on D's keys
 |
 |  pop(...)
 |      D.pop(k[,d]) -> v, remove specified key and return the corresponding value.
 |
 |      If the key is not found, return the default if given; otherwise,
 |      raise a KeyError.
 |
 |  popitem(self, /)
 |      Remove and return a (key, value) pair as a 2-tuple.
 |
 |      Pairs are returned in LIFO (last-in, first-out) order.
 |      Raises KeyError if the dict is empty.
 |
 |  setdefault(self, key, default=None, /)
 |      Insert key with a value of default if key is not in the dictionary.
 |
 |      Return the value for key if key is in the dictionary, else default.
 |
 |  update(...)
 |      D.update([E, ]**F) -> None.  Update D from dict/iterable E and F.
 |      If E is present and has a .keys() method, then does:  for k in E: D[k] = E[k]
 |      If E is present and lacks a .keys() method, then does:  for k, v in E: D[k] = v
 |      In either case, this is followed by: for k in F:  D[k] = F[k]
 |
 |  values(...)
 |      D.values() -> an object providing a view on D's values
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from builtins.dict:
 |
 |  __class_getitem__(...)
 |      See PEP 585
 |
 |  fromkeys(iterable, value=None, /)
 |      Create a new dictionary with keys from iterable and values set to value.
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes inherited from builtins.dict:
 |
 |  __hash__ = None

Python Library Documentation: function elementwise_grad in module autograd.wrap_util

elementwise_grad(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    Returns a function that computes the sum of each column of the Jacobian of
    `fun`, in one pass. If the Jacobian is diagonal, then this is the diagonal
    of the Jacobian.

Python Library Documentation: function grad in module autograd.wrap_util

grad(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    Returns a function which computes the gradient of `fun` with respect to
    positional argument number `argnum`. The returned function takes the same
    arguments as `fun`, but returns the gradient instead. The function `fun`
    should be scalar-valued. The gradient has the same type as the argument.

Python Library Documentation: function grad_and_aux in module autograd.wrap_util

grad_and_aux(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    Builds a function that returns the gradient of the first output and the
    (unmodified) second output of a function that returns two outputs.

Python Library Documentation: function grad_named in module autograd.differential_operators

grad_named(fun, argname)
    Takes gradients with respect to a named argument.
    Doesn't work on *args or **kwargs.

Python Library Documentation: function hessian in module autograd.wrap_util

hessian(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    Returns a function that computes the exact Hessian.

Python Library Documentation: function hessian_tensor_product in module autograd.differential_operators

hessian_tensor_product(fun, argnum=0)
    Builds a function that returns the exact Hessian-tensor product.
    The returned function has arguments (*args, tensor, **kwargs), and for
    vectors takes roughly 4x as long to evaluate as the original function.

Python Library Documentation: function hessian_tensor_product in module autograd.differential_operators

hessian_tensor_product(fun, argnum=0)
    Builds a function that returns the exact Hessian-tensor product.
    The returned function has arguments (*args, tensor, **kwargs), and for
    vectors takes roughly 4x as long to evaluate as the original function.

Python Library Documentation: function holomorphic_grad in module autograd.wrap_util

holomorphic_grad(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    None

Python Library Documentation: function isinstance in module autograd.tracer

isinstance(*args, **kwargs)
    Return whether an object is an instance of a class or of a subclass thereof.

    A tuple, as in ``isinstance(x, (A, B, ...))``, may be given as the target to
    check against. This is equivalent to ``isinstance(x, A) or isinstance(x, B)
    or ...`` etc.

Python Library Documentation: function jacobian in module autograd.wrap_util

jacobian(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    Returns a function which computes the Jacobian of `fun` with respect to
    positional argument number `argnum`, which must be a scalar or array. Unlike
    `grad` it is not restricted to scalar-output functions, but also it cannot
    take derivatives with respect to some argument types (like lists or dicts).
    If the input to `fun` has shape (in1, in2, ...) and the output has shape
    (out1, out2, ...) then the Jacobian has shape (out1, out2, ..., in1, in2, ...).

Python Library Documentation: class list in module autograd.builtins

class list(builtins.list)
 |  list(xs)
 |
 |  Method resolution order:
 |      list
 |      builtins.list
 |      builtins.object
 |
 |  Static methods defined here:
 |
 |  __new__(cls, xs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from builtins.list:
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __contains__(self, key, /)
 |      Return bool(key in self).
 |
 |  __delitem__(self, key, /)
 |      Delete self[key].
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getattribute__(self, name, /)
 |      Return getattr(self, name).
 |
 |  __getitem__(self, index, /)
 |      Return self[index].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __iadd__(self, value, /)
 |      Implement self+=value.
 |
 |  __imul__(self, value, /)
 |      Implement self*=value.
 |
 |  __init__(self, /, *args, **kwargs)
 |      Initialize self.  See help(type(self)) for accurate signature.
 |
 |  __iter__(self, /)
 |      Implement iter(self).
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __reversed__(self, /)
 |      Return a reverse iterator over the list.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __setitem__(self, key, value, /)
 |      Set self[key] to value.
 |
 |  __sizeof__(self, /)
 |      Return the size of the list in memory, in bytes.
 |
 |  append(self, object, /)
 |      Append object to the end of the list.
 |
 |  clear(self, /)
 |      Remove all items from list.
 |
 |  copy(self, /)
 |      Return a shallow copy of the list.
 |
 |  count(self, value, /)
 |      Return number of occurrences of value.
 |
 |  extend(self, iterable, /)
 |      Extend list by appending elements from the iterable.
 |
 |  index(self, value, start=0, stop=9223372036854775807, /)
 |      Return first index of value.
 |
 |      Raises ValueError if the value is not present.
 |
 |  insert(self, index, object, /)
 |      Insert object before index.
 |
 |  pop(self, index=-1, /)
 |      Remove and return item at index (default last).
 |
 |      Raises IndexError if list is empty or index is out of range.
 |
 |  remove(self, value, /)
 |      Remove first occurrence of value.
 |
 |      Raises ValueError if the value is not present.
 |
 |  reverse(self, /)
 |      Reverse *IN PLACE*.
 |
 |  sort(self, /, *, key=None, reverse=False)
 |      Sort the list in ascending order and return None.
 |
 |      The sort is in-place (i.e. the list itself is modified) and stable (i.e. the
 |      order of two equal elements is maintained).
 |
 |      If a key function is given, apply it once to each list item and sort them,
 |      ascending or descending, according to their function values.
 |
 |      The reverse flag can be set to sort in descending order.
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from builtins.list:
 |
 |  __class_getitem__(...)
 |      See PEP 585
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes inherited from builtins.list:
 |
 |  __hash__ = None

Python Library Documentation: function make_ggnvp in module autograd.differential_operators

make_ggnvp(f, g=<function <lambda> at 0x000001DD17CB1B20>, f_argnum=0)
    Builds a function for evaluating generalized-Gauss-Newton-vector products
    at a point. Slightly more expensive than mixed-mode.

Python Library Documentation: function make_hvp in module autograd.wrap_util

make_hvp(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    Builds a function for evaluating the Hessian-vector product at a point,
    which may be useful when evaluating many Hessian-vector products at the same
    point while caching the results of the forward pass.

Python Library Documentation: function make_jvp in module autograd.wrap_util

make_jvp(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    None

Python Library Documentation: function make_vjp in module autograd.wrap_util

make_vjp(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    None

Python Library Documentation: function multigrad_dict in module autograd.differential_operators

multigrad_dict(fun)
    Takes gradients wrt all arguments simultaneously,

Python Library Documentation: function primitive_with_deprecation_warnings in module autograd.core

primitive_with_deprecation_warnings(f_raw)

Python Library Documentation: function tensor_jacobian_product in module autograd.differential_operators

tensor_jacobian_product(fun, argnum=0)
    Builds a function that returns the exact tensor-Jacobian product, that
    is the Jacobian matrix left-multiplied by tensor. The returned function
    has arguments (*args, tensor, **kwargs).

Python Library Documentation: class tuple in module autograd.builtins

class tuple(builtins.tuple)
 |  tuple(xs)
 |
 |  Method resolution order:
 |      tuple
 |      builtins.tuple
 |      builtins.object
 |
 |  Static methods defined here:
 |
 |  __new__(cls, xs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from builtins.tuple:
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __contains__(self, key, /)
 |      Return bool(key in self).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getattribute__(self, name, /)
 |      Return getattr(self, name).
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __getnewargs__(self, /)
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __iter__(self, /)
 |      Implement iter(self).
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  count(self, value, /)
 |      Return number of occurrences of value.
 |
 |  index(self, value, start=0, stop=9223372036854775807, /)
 |      Return first index of value.
 |
 |      Raises ValueError if the value is not present.
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from builtins.tuple:
 |
 |  __class_getitem__(...)
 |      See PEP 585

Python Library Documentation: function type in module autograd.tracer

type(*args, **kwargs)
    type(object) -> the object's type
    type(name, bases, dict, **kwds) -> a new type

Python Library Documentation: function value_and_grad in module autograd.wrap_util

value_and_grad(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    Returns a function that returns both value and gradient. Suitable for use
    in scipy.optimize

Python Library Documentation: function tensor_jacobian_product in module autograd.differential_operators

tensor_jacobian_product(fun, argnum=0)
    Builds a function that returns the exact tensor-Jacobian product, that
    is the Jacobian matrix left-multiplied by tensor. The returned function
    has arguments (*args, tensor, **kwargs).

Python Library Documentation: class Box in module autograd.tracer

class Box(builtins.object)
 |  Box(value, trace, node)
 |
 |  Methods defined here:
 |
 |  __bool__(self)
 |
 |  __init__(self, value, trace, node)
 |      Initialize self.  See help(type(self)) for accurate signature.
 |
 |  __nonzero__ = __bool__(self)
 |
 |  __str__(self)
 |      Return str(self).
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  register(value_type)
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes defined here:
 |
 |  __array_priority__ = 90.0
 |
 |  type_mappings = {<class 'autograd.core.SparseObject'>: <class 'autogra...
 |
 |  types = {<class 'autograd.core.SparseBox'>, <class 'autograd.builtins....

Python Library Documentation: function absolute in module autograd.tracer

absolute(*args, called_by_autograd_dispatcher=False, **kwargs)
    absolute(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Calculate the absolute value element-wise.

    ``np.abs`` is a shorthand for this function.

    Parameters
    ----------
    x : array_like
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    absolute : ndarray
        An ndarray containing the absolute value of
        each element in `x`.  For complex input, ``a + ib``, the
        absolute value is :math:`\sqrt{ a^2 + b^2 }`.
        This is a scalar if `x` is a scalar.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([-1.2, 1.2])
    >>> np.absolute(x)
    array([ 1.2,  1.2])
    >>> np.absolute(1.2 + 1j)
    1.5620499351813308

    Plot the function over ``[-10, 10]``:

    >>> import matplotlib.pyplot as plt

    >>> x = np.linspace(start=-10, stop=10, num=101)
    >>> plt.plot(x, np.absolute(x))
    >>> plt.show()

    Plot the function over the complex plane:

    >>> xx = x + 1j * x[:, np.newaxis]
    >>> plt.imshow(np.abs(xx), extent=[-10, 10, -10, 10], cmap='gray')
    >>> plt.show()

    The `abs` function can be used as a shorthand for ``np.absolute`` on
    ndarrays.

    >>> x = np.array([-1.2, 1.2])
    >>> abs(x)
    array([1.2, 1.2])

Python Library Documentation: function absolute in module autograd.tracer

absolute(*args, called_by_autograd_dispatcher=False, **kwargs)
    absolute(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Calculate the absolute value element-wise.

    ``np.abs`` is a shorthand for this function.

    Parameters
    ----------
    x : array_like
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    absolute : ndarray
        An ndarray containing the absolute value of
        each element in `x`.  For complex input, ``a + ib``, the
        absolute value is :math:`\sqrt{ a^2 + b^2 }`.
        This is a scalar if `x` is a scalar.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([-1.2, 1.2])
    >>> np.absolute(x)
    array([ 1.2,  1.2])
    >>> np.absolute(1.2 + 1j)
    1.5620499351813308

    Plot the function over ``[-10, 10]``:

    >>> import matplotlib.pyplot as plt

    >>> x = np.linspace(start=-10, stop=10, num=101)
    >>> plt.plot(x, np.absolute(x))
    >>> plt.show()

    Plot the function over the complex plane:

    >>> xx = x + 1j * x[:, np.newaxis]
    >>> plt.imshow(np.abs(xx), extent=[-10, 10, -10, 10], cmap='gray')
    >>> plt.show()

    The `abs` function can be used as a shorthand for ``np.absolute`` on
    ndarrays.

    >>> x = np.array([-1.2, 1.2])
    >>> abs(x)
    array([1.2, 1.2])

Python Library Documentation: function arccos in module autograd.tracer

arccos(*args, called_by_autograd_dispatcher=False, **kwargs)
    arccos(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Trigonometric inverse cosine, element-wise.

    The inverse of `cos` so that, if ``y = cos(x)``, then ``x = arccos(y)``.

    Parameters
    ----------
    x : array_like
        `x`-coordinate on the unit circle.
        For real arguments, the domain is [-1, 1].
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    angle : ndarray
        The angle of the ray intersecting the unit circle at the given
        `x`-coordinate in radians [0, pi].
        This is a scalar if `x` is a scalar.

    See Also
    --------
    cos, arctan, arcsin, emath.arccos

    Notes
    -----
    `arccos` is a multivalued function: for each `x` there are infinitely
    many numbers `z` such that ``cos(z) = x``. The convention is to return
    the angle `z` whose real part lies in `[0, pi]`.

    For real-valued input data types, `arccos` always returns real output.
    For each value that cannot be expressed as a real number or infinity,
    it yields ``nan`` and sets the `invalid` floating point error flag.

    For complex-valued input, `arccos` is a complex analytic function that
    has branch cuts ``[-inf, -1]`` and `[1, inf]` and is continuous from
    above on the former and from below on the latter.

    The inverse `cos` is also known as `acos` or cos^-1.

    References
    ----------
    M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions",
    10th printing, 1964, pp. 79.
    https://personal.math.ubc.ca/~cbm/aands/page_79.htm

    Examples
    --------
    >>> import numpy as np

    We expect the arccos of 1 to be 0, and of -1 to be pi:

    >>> np.arccos([1, -1])
    array([ 0.        ,  3.14159265])

    Plot arccos:

    >>> import matplotlib.pyplot as plt
    >>> x = np.linspace(-1, 1, num=100)
    >>> plt.plot(x, np.arccos(x))
    >>> plt.axis('tight')
    >>> plt.show()

Python Library Documentation: function arccosh in module autograd.tracer

arccosh(*args, called_by_autograd_dispatcher=False, **kwargs)
    arccosh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Inverse hyperbolic cosine, element-wise.

    Parameters
    ----------
    x : array_like
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    arccosh : ndarray
        Array of the same shape as `x`.
        This is a scalar if `x` is a scalar.

    See Also
    --------

    cosh, arcsinh, sinh, arctanh, tanh

    Notes
    -----
    `arccosh` is a multivalued function: for each `x` there are infinitely
    many numbers `z` such that `cosh(z) = x`. The convention is to return the
    `z` whose imaginary part lies in ``[-pi, pi]`` and the real part in
    ``[0, inf]``.

    For real-valued input data types, `arccosh` always returns real output.
    For each value that cannot be expressed as a real number or infinity, it
    yields ``nan`` and sets the `invalid` floating point error flag.

    For complex-valued input, `arccosh` is a complex analytical function that
    has a branch cut `[-inf, 1]` and is continuous from above on it.

    References
    ----------
    .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions",
           10th printing, 1964, pp. 86.
           https://personal.math.ubc.ca/~cbm/aands/page_86.htm
    .. [2] Wikipedia, "Inverse hyperbolic function",
           https://en.wikipedia.org/wiki/Arccosh

    Examples
    --------
    >>> import numpy as np
    >>> np.arccosh([np.e, 10.0])
    array([ 1.65745445,  2.99322285])
    >>> np.arccosh(1)
    0.0

Python Library Documentation: function add in module autograd.tracer

add(*args, called_by_autograd_dispatcher=False, **kwargs)
    add(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Add arguments element-wise.

    Parameters
    ----------
    x1, x2 : array_like
        The arrays to be added.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    add : ndarray or scalar
        The sum of `x1` and `x2`, element-wise.
        This is a scalar if both `x1` and `x2` are scalars.

    Notes
    -----
    Equivalent to `x1` + `x2` in terms of array broadcasting.

    Examples
    --------
    >>> import numpy as np
    >>> np.add(1.0, 4.0)
    5.0
    >>> x1 = np.arange(9.0).reshape((3, 3))
    >>> x2 = np.arange(3.0)
    >>> np.add(x1, x2)
    array([[  0.,   2.,   4.],
           [  3.,   5.,   7.],
           [  6.,   8.,  10.]])

    The ``+`` operator can be used as a shorthand for ``np.add`` on ndarrays.

    >>> x1 = np.arange(9.0).reshape((3, 3))
    >>> x2 = np.arange(3.0)
    >>> x1 + x2
    array([[ 0.,  2.,  4.],
           [ 3.,  5.,  7.],
           [ 6.,  8., 10.]])

Python Library Documentation: function all in module autograd.tracer

all(*args, called_by_autograd_dispatcher=False, **kwargs)
    Test whether all array elements along a given axis evaluate to True.

    Parameters
    ----------
    a : array_like
        Input array or object that can be converted to an array.
    axis : None or int or tuple of ints, optional
        Axis or axes along which a logical AND reduction is performed.
        The default (``axis=None``) is to perform a logical AND over all
        the dimensions of the input array. `axis` may be negative, in
        which case it counts from the last to the first axis.

        .. versionadded:: 1.7.0

        If this is a tuple of ints, a reduction is performed on multiple
        axes, instead of a single axis or all the axes as before.
    out : ndarray, optional
        Alternate output array in which to place the result.
        It must have the same shape as the expected output and its
        type is preserved (e.g., if ``dtype(out)`` is float, the result
        will consist of 0.0's and 1.0's). See :ref:`ufuncs-output-type`
        for more details.

    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the input array.

        If the default value is passed, then `keepdims` will not be
        passed through to the `all` method of sub-classes of
        `ndarray`, however any non-default value will be.  If the
        sub-class' method does not implement `keepdims` any
        exceptions will be raised.

    where : array_like of bool, optional
        Elements to include in checking for all `True` values.
        See `~numpy.ufunc.reduce` for details.

        .. versionadded:: 1.20.0

    Returns
    -------
    all : ndarray, bool
        A new boolean or array is returned unless `out` is specified,
        in which case a reference to `out` is returned.

    See Also
    --------
    ndarray.all : equivalent method

    any : Test whether any element along a given axis evaluates to True.

    Notes
    -----
    Not a Number (NaN), positive infinity and negative infinity
    evaluate to `True` because these are not equal to zero.

    .. versionchanged:: 2.0
       Before NumPy 2.0, ``all`` did not return booleans for object dtype
       input arrays.
       This behavior is still available via ``np.logical_and.reduce``.

    Examples
    --------
    >>> import numpy as np
    >>> np.all([[True,False],[True,True]])
    False

    >>> np.all([[True,False],[True,True]], axis=0)
    array([ True, False])

    >>> np.all([-1, 4, 5])
    True

    >>> np.all([1.0, np.nan])
    True

    >>> np.all([[True, True], [False, True]], where=[[True], [False]])
    True

    >>> o=np.array(False)
    >>> z=np.all([-1, 4, 5], out=o)
    >>> id(z), id(o), z
    (28293632, 28293632, array(True)) # may vary

Python Library Documentation: function allclose in module autograd.tracer

allclose(*args, called_by_autograd_dispatcher=False, **kwargs)
    Returns True if two arrays are element-wise equal within a tolerance.

    The tolerance values are positive, typically very small numbers.  The
    relative difference (`rtol` * abs(`b`)) and the absolute difference
    `atol` are added together to compare against the absolute difference
    between `a` and `b`.

    .. warning:: The default `atol` is not appropriate for comparing numbers
                 with magnitudes much smaller than one (see Notes).

    NaNs are treated as equal if they are in the same place and if
    ``equal_nan=True``.  Infs are treated as equal if they are in the same
    place and of the same sign in both arrays.

    Parameters
    ----------
    a, b : array_like
        Input arrays to compare.
    rtol : array_like
        The relative tolerance parameter (see Notes).
    atol : array_like
        The absolute tolerance parameter (see Notes).
    equal_nan : bool
        Whether to compare NaN's as equal.  If True, NaN's in `a` will be
        considered equal to NaN's in `b` in the output array.

        .. versionadded:: 1.10.0

    Returns
    -------
    allclose : bool
        Returns True if the two arrays are equal within the given
        tolerance; False otherwise.

    See Also
    --------
    isclose, all, any, equal

    Notes
    -----
    If the following equation is element-wise True, then allclose returns
    True.::

     absolute(a - b) <= (atol + rtol * absolute(b))

    The above equation is not symmetric in `a` and `b`, so that
    ``allclose(a, b)`` might be different from ``allclose(b, a)`` in
    some rare cases.

    The default value of `atol` is not appropriate when the reference value
    `b` has magnitude smaller than one. For example, it is unlikely that
    ``a = 1e-9`` and ``b = 2e-9`` should be considered "close", yet
    ``allclose(1e-9, 2e-9)`` is ``True`` with default settings. Be sure
    to select `atol` for the use case at hand, especially for defining the
    threshold below which a non-zero value in `a` will be considered "close"
    to a very small or zero value in `b`.

    The comparison of `a` and `b` uses standard broadcasting, which
    means that `a` and `b` need not have the same shape in order for
    ``allclose(a, b)`` to evaluate to True.  The same is true for
    `equal` but not `array_equal`.

    `allclose` is not defined for non-numeric data types.
    `bool` is considered a numeric data-type for this purpose.

    Examples
    --------
    >>> import numpy as np
    >>> np.allclose([1e10,1e-7], [1.00001e10,1e-8])
    False

    >>> np.allclose([1e10,1e-8], [1.00001e10,1e-9])
    True

    >>> np.allclose([1e10,1e-8], [1.0001e10,1e-9])
    False

    >>> np.allclose([1.0, np.nan], [1.0, np.nan])
    False

    >>> np.allclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)
    True

Python Library Documentation: function amax in module autograd.tracer

amax(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the maximum of an array or maximum along an axis.

    `amax` is an alias of `~numpy.max`.

    See Also
    --------
    max : alias of this function
    ndarray.max : equivalent method

Python Library Documentation: function amin in module autograd.tracer

amin(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the minimum of an array or minimum along an axis.

    `amin` is an alias of `~numpy.min`.

    See Also
    --------
    min : alias of this function
    ndarray.min : equivalent method

Python Library Documentation: function angle in module autograd.tracer

angle(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the angle of the complex argument.

    Parameters
    ----------
    z : array_like
        A complex number or sequence of complex numbers.
    deg : bool, optional
        Return angle in degrees if True, radians if False (default).

    Returns
    -------
    angle : ndarray or scalar
        The counterclockwise angle from the positive real axis on the complex
        plane in the range ``(-pi, pi]``, with dtype as numpy.float64.

        .. versionchanged:: 1.16.0
            This function works on subclasses of ndarray like `ma.array`.

    See Also
    --------
    arctan2
    absolute

    Notes
    -----
    This function passes the imaginary and real parts of the argument to
    `arctan2` to compute the result; consequently, it follows the convention
    of `arctan2` when the magnitude of the argument is zero. See example.

    Examples
    --------
    >>> import numpy as np
    >>> np.angle([1.0, 1.0j, 1+1j])               # in radians
    array([ 0.        ,  1.57079633,  0.78539816]) # may vary
    >>> np.angle(1+1j, deg=True)                  # in degrees
    45.0
    >>> np.angle([0., -0., complex(0., -0.), complex(-0., -0.)])  # convention
    array([ 0.        ,  3.14159265, -0.        , -3.14159265])

Python Library Documentation: function any in module autograd.tracer

any(*args, called_by_autograd_dispatcher=False, **kwargs)
    Test whether any array element along a given axis evaluates to True.

    Returns single boolean if `axis` is ``None``

    Parameters
    ----------
    a : array_like
        Input array or object that can be converted to an array.
    axis : None or int or tuple of ints, optional
        Axis or axes along which a logical OR reduction is performed.
        The default (``axis=None``) is to perform a logical OR over all
        the dimensions of the input array. `axis` may be negative, in
        which case it counts from the last to the first axis.

        .. versionadded:: 1.7.0

        If this is a tuple of ints, a reduction is performed on multiple
        axes, instead of a single axis or all the axes as before.
    out : ndarray, optional
        Alternate output array in which to place the result.  It must have
        the same shape as the expected output and its type is preserved
        (e.g., if it is of type float, then it will remain so, returning
        1.0 for True and 0.0 for False, regardless of the type of `a`).
        See :ref:`ufuncs-output-type` for more details.

    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the input array.

        If the default value is passed, then `keepdims` will not be
        passed through to the `any` method of sub-classes of
        `ndarray`, however any non-default value will be.  If the
        sub-class' method does not implement `keepdims` any
        exceptions will be raised.

    where : array_like of bool, optional
        Elements to include in checking for any `True` values.
        See `~numpy.ufunc.reduce` for details.

        .. versionadded:: 1.20.0

    Returns
    -------
    any : bool or ndarray
        A new boolean or `ndarray` is returned unless `out` is specified,
        in which case a reference to `out` is returned.

    See Also
    --------
    ndarray.any : equivalent method

    all : Test whether all elements along a given axis evaluate to True.

    Notes
    -----
    Not a Number (NaN), positive infinity and negative infinity evaluate
    to `True` because these are not equal to zero.

    .. versionchanged:: 2.0
       Before NumPy 2.0, ``any`` did not return booleans for object dtype
       input arrays.
       This behavior is still available via ``np.logical_or.reduce``.

    Examples
    --------
    >>> import numpy as np
    >>> np.any([[True, False], [True, True]])
    True

    >>> np.any([[True,  False, True ],
    ...         [False, False, False]], axis=0)
    array([ True, False, True])

    >>> np.any([-1, 0, 5])
    True

    >>> np.any([[np.nan], [np.inf]], axis=1, keepdims=True)
    array([[ True],
           [ True]])

    >>> np.any([[True, False], [False, False]], where=[[False], [True]])
    False

    >>> a = np.array([[1, 0, 0],
    ...               [0, 0, 1],
    ...               [0, 0, 0]])
    >>> np.any(a, axis=0)
    array([ True, False,  True])
    >>> np.any(a, axis=1)
    array([ True,  True, False])

    >>> o=np.array(False)
    >>> z=np.any([-1, 4, 5], out=o)
    >>> z, o
    (array(True), array(True))
    >>> # Check now that z is a reference to o
    >>> z is o
    True
    >>> id(z), id(o) # identity of z and o              # doctest: +SKIP
    (191614240, 191614240)

Python Library Documentation: function append in module autograd.numpy.numpy_wrapper

append(arr, values, axis=None)

Python Library Documentation: function apply_along_axis in module autograd.tracer

apply_along_axis(*args, called_by_autograd_dispatcher=False, **kwargs)
    Apply a function to 1-D slices along the given axis.

    Execute `func1d(a, *args, **kwargs)` where `func1d` operates on 1-D arrays
    and `a` is a 1-D slice of `arr` along `axis`.

    This is equivalent to (but faster than) the following use of `ndindex` and
    `s_`, which sets each of ``ii``, ``jj``, and ``kk`` to a tuple of indices::

        Ni, Nk = a.shape[:axis], a.shape[axis+1:]
        for ii in ndindex(Ni):
            for kk in ndindex(Nk):
                f = func1d(arr[ii + s_[:,] + kk])
                Nj = f.shape
                for jj in ndindex(Nj):
                    out[ii + jj + kk] = f[jj]

    Equivalently, eliminating the inner loop, this can be expressed as::

        Ni, Nk = a.shape[:axis], a.shape[axis+1:]
        for ii in ndindex(Ni):
            for kk in ndindex(Nk):
                out[ii + s_[...,] + kk] = func1d(arr[ii + s_[:,] + kk])

    Parameters
    ----------
    func1d : function (M,) -> (Nj...)
        This function should accept 1-D arrays. It is applied to 1-D
        slices of `arr` along the specified axis.
    axis : integer
        Axis along which `arr` is sliced.
    arr : ndarray (Ni..., M, Nk...)
        Input array.
    args : any
        Additional arguments to `func1d`.
    kwargs : any
        Additional named arguments to `func1d`.

        .. versionadded:: 1.9.0


    Returns
    -------
    out : ndarray  (Ni..., Nj..., Nk...)
        The output array. The shape of `out` is identical to the shape of
        `arr`, except along the `axis` dimension. This axis is removed, and
        replaced with new dimensions equal to the shape of the return value
        of `func1d`. So if `func1d` returns a scalar `out` will have one
        fewer dimensions than `arr`.

    See Also
    --------
    apply_over_axes : Apply a function repeatedly over multiple axes.

    Examples
    --------
    >>> import numpy as np
    >>> def my_func(a):
    ...     """Average first and last element of a 1-D array"""
    ...     return (a[0] + a[-1]) * 0.5
    >>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])
    >>> np.apply_along_axis(my_func, 0, b)
    array([4., 5., 6.])
    >>> np.apply_along_axis(my_func, 1, b)
    array([2.,  5.,  8.])

    For a function that returns a 1D array, the number of dimensions in
    `outarr` is the same as `arr`.

    >>> b = np.array([[8,1,7], [4,3,9], [5,2,6]])
    >>> np.apply_along_axis(sorted, 1, b)
    array([[1, 7, 8],
           [3, 4, 9],
           [2, 5, 6]])

    For a function that returns a higher dimensional array, those dimensions
    are inserted in place of the `axis` dimension.

    >>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])
    >>> np.apply_along_axis(np.diag, -1, b)
    array([[[1, 0, 0],
            [0, 2, 0],
            [0, 0, 3]],
           [[4, 0, 0],
            [0, 5, 0],
            [0, 0, 6]],
           [[7, 0, 0],
            [0, 8, 0],
            [0, 0, 9]]])

Python Library Documentation: function apply_over_axes in module autograd.tracer

apply_over_axes(*args, called_by_autograd_dispatcher=False, **kwargs)
    Apply a function repeatedly over multiple axes.

    `func` is called as `res = func(a, axis)`, where `axis` is the first
    element of `axes`.  The result `res` of the function call must have
    either the same dimensions as `a` or one less dimension.  If `res`
    has one less dimension than `a`, a dimension is inserted before
    `axis`.  The call to `func` is then repeated for each axis in `axes`,
    with `res` as the first argument.

    Parameters
    ----------
    func : function
        This function must take two arguments, `func(a, axis)`.
    a : array_like
        Input array.
    axes : array_like
        Axes over which `func` is applied; the elements must be integers.

    Returns
    -------
    apply_over_axis : ndarray
        The output array.  The number of dimensions is the same as `a`,
        but the shape can be different.  This depends on whether `func`
        changes the shape of its output with respect to its input.

    See Also
    --------
    apply_along_axis :
        Apply a function to 1-D slices of an array along the given axis.

    Notes
    -----
    This function is equivalent to tuple axis arguments to reorderable ufuncs
    with keepdims=True. Tuple axis arguments to ufuncs have been available since
    version 1.7.0.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.arange(24).reshape(2,3,4)
    >>> a
    array([[[ 0,  1,  2,  3],
            [ 4,  5,  6,  7],
            [ 8,  9, 10, 11]],
           [[12, 13, 14, 15],
            [16, 17, 18, 19],
            [20, 21, 22, 23]]])

    Sum over axes 0 and 2. The result has same number of dimensions
    as the original array:

    >>> np.apply_over_axes(np.sum, a, [0,2])
    array([[[ 60],
            [ 92],
            [124]]])

    Tuple axis arguments to ufuncs are equivalent:

    >>> np.sum(a, axis=(0,2), keepdims=True)
    array([[[ 60],
            [ 92],
            [124]]])

Python Library Documentation: function arange in module autograd.tracer

arange(*args, called_by_autograd_dispatcher=False, **kwargs)
    arange([start,] stop[, step,], dtype=None, *, device=None, like=None)

    Return evenly spaced values within a given interval.

    ``arange`` can be called with a varying number of positional arguments:

    * ``arange(stop)``: Values are generated within the half-open interval
      ``[0, stop)`` (in other words, the interval including `start` but
      excluding `stop`).
    * ``arange(start, stop)``: Values are generated within the half-open
      interval ``[start, stop)``.
    * ``arange(start, stop, step)`` Values are generated within the half-open
      interval ``[start, stop)``, with spacing between values given by
      ``step``.

    For integer arguments the function is roughly equivalent to the Python
    built-in :py:class:`range`, but returns an ndarray rather than a ``range``
    instance.

    When using a non-integer step, such as 0.1, it is often better to use
    `numpy.linspace`.

    See the Warning sections below for more information.

    Parameters
    ----------
    start : integer or real, optional
        Start of interval.  The interval includes this value.  The default
        start value is 0.
    stop : integer or real
        End of interval.  The interval does not include this value, except
        in some cases where `step` is not an integer and floating point
        round-off affects the length of `out`.
    step : integer or real, optional
        Spacing between values.  For any output `out`, this is the distance
        between two adjacent values, ``out[i+1] - out[i]``.  The default
        step size is 1.  If `step` is specified as a position argument,
        `start` must also be given.
    dtype : dtype, optional
        The type of the output array.  If `dtype` is not given, infer the data
        type from the other input arguments.
    device : str, optional
        The device on which to place the created array. Default: ``None``.
        For Array-API interoperability only, so must be ``"cpu"`` if passed.

        .. versionadded:: 2.0.0
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    arange : ndarray
        Array of evenly spaced values.

        For floating point arguments, the length of the result is
        ``ceil((stop - start)/step)``.  Because of floating point overflow,
        this rule may result in the last element of `out` being greater
        than `stop`.

    Warnings
    --------
    The length of the output might not be numerically stable.

    Another stability issue is due to the internal implementation of
    `numpy.arange`.
    The actual step value used to populate the array is
    ``dtype(start + step) - dtype(start)`` and not `step`. Precision loss
    can occur here, due to casting or due to using floating points when
    `start` is much larger than `step`. This can lead to unexpected
    behaviour. For example::

      >>> np.arange(0, 5, 0.5, dtype=int)
      array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
      >>> np.arange(-3, 3, 0.5, dtype=int)
      array([-3, -2, -1,  0,  1,  2,  3,  4,  5,  6,  7,  8])

    In such cases, the use of `numpy.linspace` should be preferred.

    The built-in :py:class:`range` generates :std:doc:`Python built-in integers
    that have arbitrary size <python:c-api/long>`, while `numpy.arange`
    produces `numpy.int32` or `numpy.int64` numbers. This may result in
    incorrect results for large integer values::

      >>> power = 40
      >>> modulo = 10000
      >>> x1 = [(n ** power) % modulo for n in range(8)]
      >>> x2 = [(n ** power) % modulo for n in np.arange(8)]
      >>> print(x1)
      [0, 1, 7776, 8801, 6176, 625, 6576, 4001]  # correct
      >>> print(x2)
      [0, 1, 7776, 7185, 0, 5969, 4816, 3361]  # incorrect

    See Also
    --------
    numpy.linspace : Evenly spaced numbers with careful handling of endpoints.
    numpy.ogrid: Arrays of evenly spaced numbers in N-dimensions.
    numpy.mgrid: Grid-shaped arrays of evenly spaced numbers in N-dimensions.
    :ref:`how-to-partition`

    Examples
    --------
    >>> import numpy as np
    >>> np.arange(3)
    array([0, 1, 2])
    >>> np.arange(3.0)
    array([ 0.,  1.,  2.])
    >>> np.arange(3,7)
    array([3, 4, 5, 6])
    >>> np.arange(3,7,2)
    array([3, 5])

Python Library Documentation: function arccos in module autograd.tracer

arccos(*args, called_by_autograd_dispatcher=False, **kwargs)
    arccos(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Trigonometric inverse cosine, element-wise.

    The inverse of `cos` so that, if ``y = cos(x)``, then ``x = arccos(y)``.

    Parameters
    ----------
    x : array_like
        `x`-coordinate on the unit circle.
        For real arguments, the domain is [-1, 1].
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    angle : ndarray
        The angle of the ray intersecting the unit circle at the given
        `x`-coordinate in radians [0, pi].
        This is a scalar if `x` is a scalar.

    See Also
    --------
    cos, arctan, arcsin, emath.arccos

    Notes
    -----
    `arccos` is a multivalued function: for each `x` there are infinitely
    many numbers `z` such that ``cos(z) = x``. The convention is to return
    the angle `z` whose real part lies in `[0, pi]`.

    For real-valued input data types, `arccos` always returns real output.
    For each value that cannot be expressed as a real number or infinity,
    it yields ``nan`` and sets the `invalid` floating point error flag.

    For complex-valued input, `arccos` is a complex analytic function that
    has branch cuts ``[-inf, -1]`` and `[1, inf]` and is continuous from
    above on the former and from below on the latter.

    The inverse `cos` is also known as `acos` or cos^-1.

    References
    ----------
    M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions",
    10th printing, 1964, pp. 79.
    https://personal.math.ubc.ca/~cbm/aands/page_79.htm

    Examples
    --------
    >>> import numpy as np

    We expect the arccos of 1 to be 0, and of -1 to be pi:

    >>> np.arccos([1, -1])
    array([ 0.        ,  3.14159265])

    Plot arccos:

    >>> import matplotlib.pyplot as plt
    >>> x = np.linspace(-1, 1, num=100)
    >>> plt.plot(x, np.arccos(x))
    >>> plt.axis('tight')
    >>> plt.show()

Python Library Documentation: function arccosh in module autograd.tracer

arccosh(*args, called_by_autograd_dispatcher=False, **kwargs)
    arccosh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Inverse hyperbolic cosine, element-wise.

    Parameters
    ----------
    x : array_like
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    arccosh : ndarray
        Array of the same shape as `x`.
        This is a scalar if `x` is a scalar.

    See Also
    --------

    cosh, arcsinh, sinh, arctanh, tanh

    Notes
    -----
    `arccosh` is a multivalued function: for each `x` there are infinitely
    many numbers `z` such that `cosh(z) = x`. The convention is to return the
    `z` whose imaginary part lies in ``[-pi, pi]`` and the real part in
    ``[0, inf]``.

    For real-valued input data types, `arccosh` always returns real output.
    For each value that cannot be expressed as a real number or infinity, it
    yields ``nan`` and sets the `invalid` floating point error flag.

    For complex-valued input, `arccosh` is a complex analytical function that
    has a branch cut `[-inf, 1]` and is continuous from above on it.

    References
    ----------
    .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions",
           10th printing, 1964, pp. 86.
           https://personal.math.ubc.ca/~cbm/aands/page_86.htm
    .. [2] Wikipedia, "Inverse hyperbolic function",
           https://en.wikipedia.org/wiki/Arccosh

    Examples
    --------
    >>> import numpy as np
    >>> np.arccosh([np.e, 10.0])
    array([ 1.65745445,  2.99322285])
    >>> np.arccosh(1)
    0.0

Python Library Documentation: function arcsin in module autograd.tracer

arcsin(*args, called_by_autograd_dispatcher=False, **kwargs)
    arcsin(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Inverse sine, element-wise.

    Parameters
    ----------
    x : array_like
        `y`-coordinate on the unit circle.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    angle : ndarray
        The inverse sine of each element in `x`, in radians and in the
        closed interval ``[-pi/2, pi/2]``.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    sin, cos, arccos, tan, arctan, arctan2, emath.arcsin

    Notes
    -----
    `arcsin` is a multivalued function: for each `x` there are infinitely
    many numbers `z` such that :math:`sin(z) = x`.  The convention is to
    return the angle `z` whose real part lies in [-pi/2, pi/2].

    For real-valued input data types, *arcsin* always returns real output.
    For each value that cannot be expressed as a real number or infinity,
    it yields ``nan`` and sets the `invalid` floating point error flag.

    For complex-valued input, `arcsin` is a complex analytic function that
    has, by convention, the branch cuts [-inf, -1] and [1, inf]  and is
    continuous from above on the former and from below on the latter.

    The inverse sine is also known as `asin` or sin^{-1}.

    References
    ----------
    Abramowitz, M. and Stegun, I. A., *Handbook of Mathematical Functions*,
    10th printing, New York: Dover, 1964, pp. 79ff.
    https://personal.math.ubc.ca/~cbm/aands/page_79.htm

    Examples
    --------
    >>> import numpy as np
    >>> np.arcsin(1)     # pi/2
    1.5707963267948966
    >>> np.arcsin(-1)    # -pi/2
    -1.5707963267948966
    >>> np.arcsin(0)
    0.0

Python Library Documentation: function arcsinh in module autograd.tracer

arcsinh(*args, called_by_autograd_dispatcher=False, **kwargs)
    arcsinh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Inverse hyperbolic sine element-wise.

    Parameters
    ----------
    x : array_like
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Array of the same shape as `x`.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    `arcsinh` is a multivalued function: for each `x` there are infinitely
    many numbers `z` such that `sinh(z) = x`. The convention is to return the
    `z` whose imaginary part lies in `[-pi/2, pi/2]`.

    For real-valued input data types, `arcsinh` always returns real output.
    For each value that cannot be expressed as a real number or infinity, it
    returns ``nan`` and sets the `invalid` floating point error flag.

    For complex-valued input, `arcsinh` is a complex analytical function that
    has branch cuts `[1j, infj]` and `[-1j, -infj]` and is continuous from
    the right on the former and from the left on the latter.

    The inverse hyperbolic sine is also known as `asinh` or ``sinh^-1``.

    References
    ----------
    .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions",
           10th printing, 1964, pp. 86.
           https://personal.math.ubc.ca/~cbm/aands/page_86.htm
    .. [2] Wikipedia, "Inverse hyperbolic function",
           https://en.wikipedia.org/wiki/Arcsinh

    Examples
    --------
    >>> import numpy as np
    >>> np.arcsinh(np.array([np.e, 10.0]))
    array([ 1.72538256,  2.99822295])

Python Library Documentation: function arctan in module autograd.tracer

arctan(*args, called_by_autograd_dispatcher=False, **kwargs)
    arctan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Trigonometric inverse tangent, element-wise.

    The inverse of tan, so that if ``y = tan(x)`` then ``x = arctan(y)``.

    Parameters
    ----------
    x : array_like
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Out has the same shape as `x`.  Its real part is in
        ``[-pi/2, pi/2]`` (``arctan(+/-inf)`` returns ``+/-pi/2``).
        This is a scalar if `x` is a scalar.

    See Also
    --------
    arctan2 : The "four quadrant" arctan of the angle formed by (`x`, `y`)
        and the positive `x`-axis.
    angle : Argument of complex values.

    Notes
    -----
    `arctan` is a multi-valued function: for each `x` there are infinitely
    many numbers `z` such that tan(`z`) = `x`.  The convention is to return
    the angle `z` whose real part lies in [-pi/2, pi/2].

    For real-valued input data types, `arctan` always returns real output.
    For each value that cannot be expressed as a real number or infinity,
    it yields ``nan`` and sets the `invalid` floating point error flag.

    For complex-valued input, `arctan` is a complex analytic function that
    has [``1j, infj``] and [``-1j, -infj``] as branch cuts, and is continuous
    from the left on the former and from the right on the latter.

    The inverse tangent is also known as `atan` or tan^{-1}.

    References
    ----------
    Abramowitz, M. and Stegun, I. A., *Handbook of Mathematical Functions*,
    10th printing, New York: Dover, 1964, pp. 79.
    https://personal.math.ubc.ca/~cbm/aands/page_79.htm

    Examples
    --------
    We expect the arctan of 0 to be 0, and of 1 to be pi/4:

    >>> import numpy as np

    >>> np.arctan([0, 1])
    array([ 0.        ,  0.78539816])

    >>> np.pi/4
    0.78539816339744828

    Plot arctan:

    >>> import matplotlib.pyplot as plt
    >>> x = np.linspace(-10, 10)
    >>> plt.plot(x, np.arctan(x))
    >>> plt.axis('tight')
    >>> plt.show()

Python Library Documentation: function arctan2 in module autograd.tracer

arctan2(*args, called_by_autograd_dispatcher=False, **kwargs)
    arctan2(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Element-wise arc tangent of ``x1/x2`` choosing the quadrant correctly.

    The quadrant (i.e., branch) is chosen so that ``arctan2(x1, x2)`` is
    the signed angle in radians between the ray ending at the origin and
    passing through the point (1,0), and the ray ending at the origin and
    passing through the point (`x2`, `x1`).  (Note the role reversal: the
    "`y`-coordinate" is the first function parameter, the "`x`-coordinate"
    is the second.)  By IEEE convention, this function is defined for
    `x2` = +/-0 and for either or both of `x1` and `x2` = +/-inf (see
    Notes for specific values).

    This function is not defined for complex-valued arguments; for the
    so-called argument of complex values, use `angle`.

    Parameters
    ----------
    x1 : array_like, real-valued
        `y`-coordinates.
    x2 : array_like, real-valued
        `x`-coordinates.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    angle : ndarray
        Array of angles in radians, in the range ``[-pi, pi]``.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    arctan, tan, angle

    Notes
    -----
    *arctan2* is identical to the `atan2` function of the underlying
    C library.  The following special values are defined in the C
    standard: [1]_

    ====== ====== ================
    `x1`   `x2`   `arctan2(x1,x2)`
    ====== ====== ================
    +/- 0  +0     +/- 0
    +/- 0  -0     +/- pi
     > 0   +/-inf +0 / +pi
     < 0   +/-inf -0 / -pi
    +/-inf +inf   +/- (pi/4)
    +/-inf -inf   +/- (3*pi/4)
    ====== ====== ================

    Note that +0 and -0 are distinct floating point numbers, as are +inf
    and -inf.

    References
    ----------
    .. [1] ISO/IEC standard 9899:1999, "Programming language C."

    Examples
    --------
    Consider four points in different quadrants:

    >>> import numpy as np

    >>> x = np.array([-1, +1, +1, -1])
    >>> y = np.array([-1, -1, +1, +1])
    >>> np.arctan2(y, x) * 180 / np.pi
    array([-135.,  -45.,   45.,  135.])

    Note the order of the parameters. `arctan2` is defined also when `x2` = 0
    and at several other special points, obtaining values in
    the range ``[-pi, pi]``:

    >>> np.arctan2([1., -1.], [0., 0.])
    array([ 1.57079633, -1.57079633])
    >>> np.arctan2([0., 0., np.inf], [+0., -0., np.inf])
    array([0.        , 3.14159265, 0.78539816])

Python Library Documentation: function arctanh in module autograd.tracer

arctanh(*args, called_by_autograd_dispatcher=False, **kwargs)
    arctanh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Inverse hyperbolic tangent element-wise.

    Parameters
    ----------
    x : array_like
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Array of the same shape as `x`.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    emath.arctanh

    Notes
    -----
    `arctanh` is a multivalued function: for each `x` there are infinitely
    many numbers `z` such that ``tanh(z) = x``. The convention is to return
    the `z` whose imaginary part lies in `[-pi/2, pi/2]`.

    For real-valued input data types, `arctanh` always returns real output.
    For each value that cannot be expressed as a real number or infinity,
    it yields ``nan`` and sets the `invalid` floating point error flag.

    For complex-valued input, `arctanh` is a complex analytical function
    that has branch cuts `[-1, -inf]` and `[1, inf]` and is continuous from
    above on the former and from below on the latter.

    The inverse hyperbolic tangent is also known as `atanh` or ``tanh^-1``.

    References
    ----------
    .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions",
           10th printing, 1964, pp. 86.
           https://personal.math.ubc.ca/~cbm/aands/page_86.htm
    .. [2] Wikipedia, "Inverse hyperbolic function",
           https://en.wikipedia.org/wiki/Arctanh

    Examples
    --------
    >>> import numpy as np
    >>> np.arctanh([0, -0.5])
    array([ 0.        , -0.54930614])

Python Library Documentation: function argmax in module autograd.tracer

argmax(*args, called_by_autograd_dispatcher=False, **kwargs)
    Returns the indices of the maximum values along an axis.

    Parameters
    ----------
    a : array_like
        Input array.
    axis : int, optional
        By default, the index is into the flattened array, otherwise
        along the specified axis.
    out : array, optional
        If provided, the result will be inserted into this array. It should
        be of the appropriate shape and dtype.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the array.

        .. versionadded:: 1.22.0

    Returns
    -------
    index_array : ndarray of ints
        Array of indices into the array. It has the same shape as ``a.shape``
        with the dimension along `axis` removed. If `keepdims` is set to True,
        then the size of `axis` will be 1 with the resulting array having same
        shape as ``a.shape``.

    See Also
    --------
    ndarray.argmax, argmin
    amax : The maximum value along a given axis.
    unravel_index : Convert a flat index into an index tuple.
    take_along_axis : Apply ``np.expand_dims(index_array, axis)``
                      from argmax to an array as if by calling max.

    Notes
    -----
    In case of multiple occurrences of the maximum values, the indices
    corresponding to the first occurrence are returned.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.arange(6).reshape(2,3) + 10
    >>> a
    array([[10, 11, 12],
           [13, 14, 15]])
    >>> np.argmax(a)
    5
    >>> np.argmax(a, axis=0)
    array([1, 1, 1])
    >>> np.argmax(a, axis=1)
    array([2, 2])

    Indexes of the maximal elements of a N-dimensional array:

    >>> ind = np.unravel_index(np.argmax(a, axis=None), a.shape)
    >>> ind
    (1, 2)
    >>> a[ind]
    15

    >>> b = np.arange(6)
    >>> b[1] = 5
    >>> b
    array([0, 5, 2, 3, 4, 5])
    >>> np.argmax(b)  # Only the first occurrence is returned.
    1

    >>> x = np.array([[4,2,3], [1,0,3]])
    >>> index_array = np.argmax(x, axis=-1)
    >>> # Same as np.amax(x, axis=-1, keepdims=True)
    >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1)
    array([[4],
           [3]])
    >>> # Same as np.amax(x, axis=-1)
    >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1),
    ...     axis=-1).squeeze(axis=-1)
    array([4, 3])

    Setting `keepdims` to `True`,

    >>> x = np.arange(24).reshape((2, 3, 4))
    >>> res = np.argmax(x, axis=1, keepdims=True)
    >>> res.shape
    (2, 1, 4)

Python Library Documentation: function argmin in module autograd.tracer

argmin(*args, called_by_autograd_dispatcher=False, **kwargs)
    Returns the indices of the minimum values along an axis.

    Parameters
    ----------
    a : array_like
        Input array.
    axis : int, optional
        By default, the index is into the flattened array, otherwise
        along the specified axis.
    out : array, optional
        If provided, the result will be inserted into this array. It should
        be of the appropriate shape and dtype.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the array.

        .. versionadded:: 1.22.0

    Returns
    -------
    index_array : ndarray of ints
        Array of indices into the array. It has the same shape as `a.shape`
        with the dimension along `axis` removed. If `keepdims` is set to True,
        then the size of `axis` will be 1 with the resulting array having same
        shape as `a.shape`.

    See Also
    --------
    ndarray.argmin, argmax
    amin : The minimum value along a given axis.
    unravel_index : Convert a flat index into an index tuple.
    take_along_axis : Apply ``np.expand_dims(index_array, axis)``
                      from argmin to an array as if by calling min.

    Notes
    -----
    In case of multiple occurrences of the minimum values, the indices
    corresponding to the first occurrence are returned.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.arange(6).reshape(2,3) + 10
    >>> a
    array([[10, 11, 12],
           [13, 14, 15]])
    >>> np.argmin(a)
    0
    >>> np.argmin(a, axis=0)
    array([0, 0, 0])
    >>> np.argmin(a, axis=1)
    array([0, 0])

    Indices of the minimum elements of a N-dimensional array:

    >>> ind = np.unravel_index(np.argmin(a, axis=None), a.shape)
    >>> ind
    (0, 0)
    >>> a[ind]
    10

    >>> b = np.arange(6) + 10
    >>> b[4] = 10
    >>> b
    array([10, 11, 12, 13, 10, 15])
    >>> np.argmin(b)  # Only the first occurrence is returned.
    0

    >>> x = np.array([[4,2,3], [1,0,3]])
    >>> index_array = np.argmin(x, axis=-1)
    >>> # Same as np.amin(x, axis=-1, keepdims=True)
    >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1)
    array([[2],
           [0]])
    >>> # Same as np.amax(x, axis=-1)
    >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1),
    ...     axis=-1).squeeze(axis=-1)
    array([2, 0])

    Setting `keepdims` to `True`,

    >>> x = np.arange(24).reshape((2, 3, 4))
    >>> res = np.argmin(x, axis=1, keepdims=True)
    >>> res.shape
    (2, 1, 4)

Python Library Documentation: function argpartition in module autograd.tracer

argpartition(*args, called_by_autograd_dispatcher=False, **kwargs)
    Perform an indirect partition along the given axis using the
    algorithm specified by the `kind` keyword. It returns an array of
    indices of the same shape as `a` that index data along the given
    axis in partitioned order.

    .. versionadded:: 1.8.0

    Parameters
    ----------
    a : array_like
        Array to sort.
    kth : int or sequence of ints
        Element index to partition by. The k-th element will be in its
        final sorted position and all smaller elements will be moved
        before it and all larger elements behind it. The order of all
        elements in the partitions is undefined. If provided with a
        sequence of k-th it will partition all of them into their sorted
        position at once.

        .. deprecated:: 1.22.0
            Passing booleans as index is deprecated.
    axis : int or None, optional
        Axis along which to sort. The default is -1 (the last axis). If
        None, the flattened array is used.
    kind : {'introselect'}, optional
        Selection algorithm. Default is 'introselect'
    order : str or list of str, optional
        When `a` is an array with fields defined, this argument
        specifies which fields to compare first, second, etc. A single
        field can be specified as a string, and not all fields need be
        specified, but unspecified fields will still be used, in the
        order in which they come up in the dtype, to break ties.

    Returns
    -------
    index_array : ndarray, int
        Array of indices that partition `a` along the specified axis.
        If `a` is one-dimensional, ``a[index_array]`` yields a partitioned `a`.
        More generally, ``np.take_along_axis(a, index_array, axis=axis)``
        always yields the partitioned `a`, irrespective of dimensionality.

    See Also
    --------
    partition : Describes partition algorithms used.
    ndarray.partition : Inplace partition.
    argsort : Full indirect sort.
    take_along_axis : Apply ``index_array`` from argpartition
                      to an array as if by calling partition.

    Notes
    -----
    The returned indices are not guaranteed to be sorted according to
    the values. Furthermore, the default selection algorithm ``introselect``
    is unstable, and hence the returned indices are not guaranteed
    to be the earliest/latest occurrence of the element.

    `argpartition` works for real/complex inputs with nan values,
    see `partition` for notes on the enhanced sort order and
    different selection algorithms.

    Examples
    --------
    One dimensional array:

    >>> import numpy as np
    >>> x = np.array([3, 4, 2, 1])
    >>> x[np.argpartition(x, 3)]
    array([2, 1, 3, 4]) # may vary
    >>> x[np.argpartition(x, (1, 3))]
    array([1, 2, 3, 4]) # may vary

    >>> x = [3, 4, 2, 1]
    >>> np.array(x)[np.argpartition(x, 3)]
    array([2, 1, 3, 4]) # may vary

    Multi-dimensional array:

    >>> x = np.array([[3, 4, 2], [1, 3, 1]])
    >>> index_array = np.argpartition(x, kth=1, axis=-1)
    >>> # below is the same as np.partition(x, kth=1)
    >>> np.take_along_axis(x, index_array, axis=-1)
    array([[2, 3, 4],
           [1, 1, 3]])

Python Library Documentation: function argsort in module autograd.tracer

argsort(*args, called_by_autograd_dispatcher=False, **kwargs)
    Returns the indices that would sort an array.

    Perform an indirect sort along the given axis using the algorithm specified
    by the `kind` keyword. It returns an array of indices of the same shape as
    `a` that index data along the given axis in sorted order.

    Parameters
    ----------
    a : array_like
        Array to sort.
    axis : int or None, optional
        Axis along which to sort.  The default is -1 (the last axis). If None,
        the flattened array is used.
    kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
        Sorting algorithm. The default is 'quicksort'. Note that both 'stable'
        and 'mergesort' use timsort under the covers and, in general, the
        actual implementation will vary with data type. The 'mergesort' option
        is retained for backwards compatibility.

        .. versionchanged:: 1.15.0.
           The 'stable' option was added.
    order : str or list of str, optional
        When `a` is an array with fields defined, this argument specifies
        which fields to compare first, second, etc.  A single field can
        be specified as a string, and not all fields need be specified,
        but unspecified fields will still be used, in the order in which
        they come up in the dtype, to break ties.
    stable : bool, optional
        Sort stability. If ``True``, the returned array will maintain
        the relative order of ``a`` values which compare as equal.
        If ``False`` or ``None``, this is not guaranteed. Internally,
        this option selects ``kind='stable'``. Default: ``None``.

        .. versionadded:: 2.0.0

    Returns
    -------
    index_array : ndarray, int
        Array of indices that sort `a` along the specified `axis`.
        If `a` is one-dimensional, ``a[index_array]`` yields a sorted `a`.
        More generally, ``np.take_along_axis(a, index_array, axis=axis)``
        always yields the sorted `a`, irrespective of dimensionality.

    See Also
    --------
    sort : Describes sorting algorithms used.
    lexsort : Indirect stable sort with multiple keys.
    ndarray.sort : Inplace sort.
    argpartition : Indirect partial sort.
    take_along_axis : Apply ``index_array`` from argsort
                      to an array as if by calling sort.

    Notes
    -----
    See `sort` for notes on the different sorting algorithms.

    As of NumPy 1.4.0 `argsort` works with real/complex arrays containing
    nan values. The enhanced sort order is documented in `sort`.

    Examples
    --------
    One dimensional array:

    >>> import numpy as np
    >>> x = np.array([3, 1, 2])
    >>> np.argsort(x)
    array([1, 2, 0])

    Two-dimensional array:

    >>> x = np.array([[0, 3], [2, 2]])
    >>> x
    array([[0, 3],
           [2, 2]])

    >>> ind = np.argsort(x, axis=0)  # sorts along first axis (down)
    >>> ind
    array([[0, 1],
           [1, 0]])
    >>> np.take_along_axis(x, ind, axis=0)  # same as np.sort(x, axis=0)
    array([[0, 2],
           [2, 3]])

    >>> ind = np.argsort(x, axis=1)  # sorts along last axis (across)
    >>> ind
    array([[0, 1],
           [0, 1]])
    >>> np.take_along_axis(x, ind, axis=1)  # same as np.sort(x, axis=1)
    array([[0, 3],
           [2, 2]])

    Indices of the sorted elements of a N-dimensional array:

    >>> ind = np.unravel_index(np.argsort(x, axis=None), x.shape)
    >>> ind
    (array([0, 1, 1, 0]), array([0, 0, 1, 1]))
    >>> x[ind]  # same as np.sort(x, axis=None)
    array([0, 2, 2, 3])

    Sorting with keys:

    >>> x = np.array([(1, 0), (0, 1)], dtype=[('x', '<i4'), ('y', '<i4')])
    >>> x
    array([(1, 0), (0, 1)],
          dtype=[('x', '<i4'), ('y', '<i4')])

    >>> np.argsort(x, order=('x','y'))
    array([1, 0])

    >>> np.argsort(x, order=('y','x'))
    array([0, 1])

Python Library Documentation: function argwhere in module autograd.tracer

argwhere(*args, called_by_autograd_dispatcher=False, **kwargs)
    Find the indices of array elements that are non-zero, grouped by element.

    Parameters
    ----------
    a : array_like
        Input data.

    Returns
    -------
    index_array : (N, a.ndim) ndarray
        Indices of elements that are non-zero. Indices are grouped by element.
        This array will have shape ``(N, a.ndim)`` where ``N`` is the number of
        non-zero items.

    See Also
    --------
    where, nonzero

    Notes
    -----
    ``np.argwhere(a)`` is almost the same as ``np.transpose(np.nonzero(a))``,
    but produces a result of the correct shape for a 0D array.

    The output of ``argwhere`` is not suitable for indexing arrays.
    For this purpose use ``nonzero(a)`` instead.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.arange(6).reshape(2,3)
    >>> x
    array([[0, 1, 2],
           [3, 4, 5]])
    >>> np.argwhere(x>1)
    array([[0, 2],
           [1, 0],
           [1, 1],
           [1, 2]])

Python Library Documentation: function around in module autograd.tracer

around(*args, called_by_autograd_dispatcher=False, **kwargs)
    Round an array to the given number of decimals.

    `around` is an alias of `~numpy.round`.

    See Also
    --------
    ndarray.round : equivalent method
    round : alias for this function
    ceil, fix, floor, rint, trunc

Python Library Documentation: function array in module autograd.numpy.numpy_wrapper

array(A, *args, **kwargs)

Python Library Documentation: function array2string in module autograd.tracer

array2string(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return a string representation of an array.

    Parameters
    ----------
    a : ndarray
        Input array.
    max_line_width : int, optional
        Inserts newlines if text is longer than `max_line_width`.
        Defaults to ``numpy.get_printoptions()['linewidth']``.
    precision : int or None, optional
        Floating point precision.
        Defaults to ``numpy.get_printoptions()['precision']``.
    suppress_small : bool, optional
        Represent numbers "very close" to zero as zero; default is False.
        Very close is defined by precision: if the precision is 8, e.g.,
        numbers smaller (in absolute value) than 5e-9 are represented as
        zero.
        Defaults to ``numpy.get_printoptions()['suppress']``.
    separator : str, optional
        Inserted between elements.
    prefix : str, optional
    suffix : str, optional
        The length of the prefix and suffix strings are used to respectively
        align and wrap the output. An array is typically printed as::

          prefix + array2string(a) + suffix

        The output is left-padded by the length of the prefix string, and
        wrapping is forced at the column ``max_line_width - len(suffix)``.
        It should be noted that the content of prefix and suffix strings are
        not included in the output.
    style : _NoValue, optional
        Has no effect, do not use.

        .. deprecated:: 1.14.0
    formatter : dict of callables, optional
        If not None, the keys should indicate the type(s) that the respective
        formatting function applies to.  Callables should return a string.
        Types that are not specified (by their corresponding keys) are handled
        by the default formatters.  Individual types for which a formatter
        can be set are:

        - 'bool'
        - 'int'
        - 'timedelta' : a `numpy.timedelta64`
        - 'datetime' : a `numpy.datetime64`
        - 'float'
        - 'longfloat' : 128-bit floats
        - 'complexfloat'
        - 'longcomplexfloat' : composed of two 128-bit floats
        - 'void' : type `numpy.void`
        - 'numpystr' : types `numpy.bytes_` and `numpy.str_`

        Other keys that can be used to set a group of types at once are:

        - 'all' : sets all types
        - 'int_kind' : sets 'int'
        - 'float_kind' : sets 'float' and 'longfloat'
        - 'complex_kind' : sets 'complexfloat' and 'longcomplexfloat'
        - 'str_kind' : sets 'numpystr'
    threshold : int, optional
        Total number of array elements which trigger summarization
        rather than full repr.
        Defaults to ``numpy.get_printoptions()['threshold']``.
    edgeitems : int, optional
        Number of array items in summary at beginning and end of
        each dimension.
        Defaults to ``numpy.get_printoptions()['edgeitems']``.
    sign : string, either '-', '+', or ' ', optional
        Controls printing of the sign of floating-point types. If '+', always
        print the sign of positive values. If ' ', always prints a space
        (whitespace character) in the sign position of positive values.  If
        '-', omit the sign character of positive values.
        Defaults to ``numpy.get_printoptions()['sign']``.

        .. versionchanged:: 2.0
             The sign parameter can now be an integer type, previously
             types were floating-point types.

    floatmode : str, optional
        Controls the interpretation of the `precision` option for
        floating-point types.
        Defaults to ``numpy.get_printoptions()['floatmode']``.
        Can take the following values:

        - 'fixed': Always print exactly `precision` fractional digits,
          even if this would print more or fewer digits than
          necessary to specify the value uniquely.
        - 'unique': Print the minimum number of fractional digits necessary
          to represent each value uniquely. Different elements may
          have a different number of digits.  The value of the
          `precision` option is ignored.
        - 'maxprec': Print at most `precision` fractional digits, but if
          an element can be uniquely represented with fewer digits
          only print it with that many.
        - 'maxprec_equal': Print at most `precision` fractional digits,
          but if every element in the array can be uniquely
          represented with an equal number of fewer digits, use that
          many digits for all elements.
    legacy : string or `False`, optional
        If set to the string ``'1.13'`` enables 1.13 legacy printing mode. This
        approximates numpy 1.13 print output by including a space in the sign
        position of floats and different behavior for 0d arrays. If set to
        `False`, disables legacy mode. Unrecognized strings will be ignored
        with a warning for forward compatibility.

        .. versionadded:: 1.14.0

    Returns
    -------
    array_str : str
        String representation of the array.

    Raises
    ------
    TypeError
        if a callable in `formatter` does not return a string.

    See Also
    --------
    array_str, array_repr, set_printoptions, get_printoptions

    Notes
    -----
    If a formatter is specified for a certain type, the `precision` keyword is
    ignored for that type.

    This is a very flexible function; `array_repr` and `array_str` are using
    `array2string` internally so keywords with the same name should work
    identically in all three functions.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([1e-16,1,2,3])
    >>> np.array2string(x, precision=2, separator=',',
    ...                       suppress_small=True)
    '[0.,1.,2.,3.]'

    >>> x  = np.arange(3.)
    >>> np.array2string(x, formatter={'float_kind':lambda x: "%.2f" % x})
    '[0.00 1.00 2.00]'

    >>> x  = np.arange(3)
    >>> np.array2string(x, formatter={'int':lambda x: hex(x)})
    '[0x0 0x1 0x2]'

Python Library Documentation: function array_equal in module autograd.tracer

array_equal(*args, called_by_autograd_dispatcher=False, **kwargs)
    True if two arrays have the same shape and elements, False otherwise.

    Parameters
    ----------
    a1, a2 : array_like
        Input arrays.
    equal_nan : bool
        Whether to compare NaN's as equal. If the dtype of a1 and a2 is
        complex, values will be considered equal if either the real or the
        imaginary component of a given value is ``nan``.

        .. versionadded:: 1.19.0

    Returns
    -------
    b : bool
        Returns True if the arrays are equal.

    See Also
    --------
    allclose: Returns True if two arrays are element-wise equal within a
              tolerance.
    array_equiv: Returns True if input arrays are shape consistent and all
                 elements equal.

    Examples
    --------
    >>> import numpy as np

    >>> np.array_equal([1, 2], [1, 2])
    True

    >>> np.array_equal(np.array([1, 2]), np.array([1, 2]))
    True

    >>> np.array_equal([1, 2], [1, 2, 3])
    False

    >>> np.array_equal([1, 2], [1, 4])
    False

    >>> a = np.array([1, np.nan])
    >>> np.array_equal(a, a)
    False

    >>> np.array_equal(a, a, equal_nan=True)
    True

    When ``equal_nan`` is True, complex values with nan components are
    considered equal if either the real *or* the imaginary components are nan.

    >>> a = np.array([1 + 1j])
    >>> b = a.copy()
    >>> a.real = np.nan
    >>> b.imag = np.nan
    >>> np.array_equal(a, b, equal_nan=True)
    True

Python Library Documentation: function array_equiv in module autograd.tracer

array_equiv(*args, called_by_autograd_dispatcher=False, **kwargs)
    Returns True if input arrays are shape consistent and all elements equal.

    Shape consistent means they are either the same shape, or one input array
    can be broadcasted to create the same shape as the other one.

    Parameters
    ----------
    a1, a2 : array_like
        Input arrays.

    Returns
    -------
    out : bool
        True if equivalent, False otherwise.

    Examples
    --------
    >>> import numpy as np
    >>> np.array_equiv([1, 2], [1, 2])
    True
    >>> np.array_equiv([1, 2], [1, 3])
    False

    Showing the shape equivalence:

    >>> np.array_equiv([1, 2], [[1, 2], [1, 2]])
    True
    >>> np.array_equiv([1, 2], [[1, 2, 1, 2], [1, 2, 1, 2]])
    False

    >>> np.array_equiv([1, 2], [[1, 2], [1, 3]])
    False

Python Library Documentation: function array_from_args in module autograd.tracer

array_from_args(*args, called_by_autograd_dispatcher=False, **kwargs)
    None

Python Library Documentation: function array_repr in module autograd.tracer

array_repr(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the string representation of an array.

    Parameters
    ----------
    arr : ndarray
        Input array.
    max_line_width : int, optional
        Inserts newlines if text is longer than `max_line_width`.
        Defaults to ``numpy.get_printoptions()['linewidth']``.
    precision : int, optional
        Floating point precision.
        Defaults to ``numpy.get_printoptions()['precision']``.
    suppress_small : bool, optional
        Represent numbers "very close" to zero as zero; default is False.
        Very close is defined by precision: if the precision is 8, e.g.,
        numbers smaller (in absolute value) than 5e-9 are represented as
        zero.
        Defaults to ``numpy.get_printoptions()['suppress']``.

    Returns
    -------
    string : str
      The string representation of an array.

    See Also
    --------
    array_str, array2string, set_printoptions

    Examples
    --------
    >>> import numpy as np
    >>> np.array_repr(np.array([1,2]))
    'array([1, 2])'
    >>> np.array_repr(np.ma.array([0.]))
    'MaskedArray([0.])'
    >>> np.array_repr(np.array([], np.int32))
    'array([], dtype=int32)'

    >>> x = np.array([1e-6, 4e-7, 2, 3])
    >>> np.array_repr(x, precision=6, suppress_small=True)
    'array([0.000001,  0.      ,  2.      ,  3.      ])'

Python Library Documentation: function array_split in module autograd.tracer

array_split(*args, called_by_autograd_dispatcher=False, **kwargs)
    Split an array into multiple sub-arrays.

    Please refer to the ``split`` documentation.  The only difference
    between these functions is that ``array_split`` allows
    `indices_or_sections` to be an integer that does *not* equally
    divide the axis. For an array of length l that should be split
    into n sections, it returns l % n sub-arrays of size l//n + 1
    and the rest of size l//n.

    See Also
    --------
    split : Split array into multiple sub-arrays of equal size.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.arange(8.0)
    >>> np.array_split(x, 3)
    [array([0.,  1.,  2.]), array([3.,  4.,  5.]), array([6.,  7.])]

    >>> x = np.arange(9)
    >>> np.array_split(x, 4)
    [array([0, 1, 2]), array([3, 4]), array([5, 6]), array([7, 8])]

Python Library Documentation: function array_str in module autograd.tracer

array_str(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return a string representation of the data in an array.

    The data in the array is returned as a single string.  This function is
    similar to `array_repr`, the difference being that `array_repr` also
    returns information on the kind of array and its data type.

    Parameters
    ----------
    a : ndarray
        Input array.
    max_line_width : int, optional
        Inserts newlines if text is longer than `max_line_width`.
        Defaults to ``numpy.get_printoptions()['linewidth']``.
    precision : int, optional
        Floating point precision.
        Defaults to ``numpy.get_printoptions()['precision']``.
    suppress_small : bool, optional
        Represent numbers "very close" to zero as zero; default is False.
        Very close is defined by precision: if the precision is 8, e.g.,
        numbers smaller (in absolute value) than 5e-9 are represented as
        zero.
        Defaults to ``numpy.get_printoptions()['suppress']``.

    See Also
    --------
    array2string, array_repr, set_printoptions

    Examples
    --------
    >>> import numpy as np
    >>> np.array_str(np.arange(3))
    '[0 1 2]'

Python Library Documentation: function asanyarray in module autograd.tracer

asanyarray(*args, called_by_autograd_dispatcher=False, **kwargs)
    asanyarray(a, dtype=None, order=None, *, like=None)

    Convert the input to an ndarray, but pass ndarray subclasses through.

    Parameters
    ----------
    a : array_like
        Input data, in any form that can be converted to an array.  This
        includes scalars, lists, lists of tuples, tuples, tuples of tuples,
        tuples of lists, and ndarrays.
    dtype : data-type, optional
        By default, the data-type is inferred from the input data.
    order : {'C', 'F', 'A', 'K'}, optional
        Memory layout.  'A' and 'K' depend on the order of input array a.
        'C' row-major (C-style),
        'F' column-major (Fortran-style) memory representation.
        'A' (any) means 'F' if `a` is Fortran contiguous, 'C' otherwise
        'K' (keep) preserve input order
        Defaults to 'C'.
    device : str, optional
        The device on which to place the created array. Default: ``None``.
        For Array-API interoperability only, so must be ``"cpu"`` if passed.

        .. versionadded:: 2.1.0

    copy : bool, optional
        If ``True``, then the object is copied. If ``None`` then the object is
        copied only if needed, i.e. if ``__array__`` returns a copy, if obj
        is a nested sequence, or if a copy is needed to satisfy any of
        the other requirements (``dtype``, ``order``, etc.).
        For ``False`` it raises a ``ValueError`` if a copy cannot be avoided.
        Default: ``None``.

        .. versionadded:: 2.1.0

    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    out : ndarray or an ndarray subclass
        Array interpretation of `a`.  If `a` is an ndarray or a subclass
        of ndarray, it is returned as-is and no copy is performed.

    See Also
    --------
    asarray : Similar function which always returns ndarrays.
    ascontiguousarray : Convert input to a contiguous array.
    asfortranarray : Convert input to an ndarray with column-major
                     memory order.
    asarray_chkfinite : Similar function which checks input for NaNs and
                        Infs.
    fromiter : Create an array from an iterator.
    fromfunction : Construct an array by executing a function on grid
                   positions.

    Examples
    --------
    Convert a list into an array:

    >>> a = [1, 2]
    >>> import numpy as np
    >>> np.asanyarray(a)
    array([1, 2])

    Instances of `ndarray` subclasses are passed through as-is:

    >>> a = np.array([(1., 2), (3., 4)], dtype='f4,i4').view(np.recarray)
    >>> np.asanyarray(a) is a
    True

Python Library Documentation: function asarray in module autograd.tracer

asarray(*args, called_by_autograd_dispatcher=False, **kwargs)
    asarray(a, dtype=None, order=None, *, device=None, copy=None, like=None)

    Convert the input to an array.

    Parameters
    ----------
    a : array_like
        Input data, in any form that can be converted to an array.  This
        includes lists, lists of tuples, tuples, tuples of tuples, tuples
        of lists and ndarrays.
    dtype : data-type, optional
        By default, the data-type is inferred from the input data.
    order : {'C', 'F', 'A', 'K'}, optional
        Memory layout.  'A' and 'K' depend on the order of input array a.
        'C' row-major (C-style),
        'F' column-major (Fortran-style) memory representation.
        'A' (any) means 'F' if `a` is Fortran contiguous, 'C' otherwise
        'K' (keep) preserve input order
        Defaults to 'K'.
    device : str, optional
        The device on which to place the created array. Default: ``None``.
        For Array-API interoperability only, so must be ``"cpu"`` if passed.

        .. versionadded:: 2.0.0
    copy : bool, optional
        If ``True``, then the object is copied. If ``None`` then the object is
        copied only if needed, i.e. if ``__array__`` returns a copy, if obj
        is a nested sequence, or if a copy is needed to satisfy any of
        the other requirements (``dtype``, ``order``, etc.).
        For ``False`` it raises a ``ValueError`` if a copy cannot be avoided.
        Default: ``None``.

        .. versionadded:: 2.0.0
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    out : ndarray
        Array interpretation of ``a``.  No copy is performed if the input
        is already an ndarray with matching dtype and order.  If ``a`` is a
        subclass of ndarray, a base class ndarray is returned.

    See Also
    --------
    asanyarray : Similar function which passes through subclasses.
    ascontiguousarray : Convert input to a contiguous array.
    asfortranarray : Convert input to an ndarray with column-major
                     memory order.
    asarray_chkfinite : Similar function which checks input for NaNs and Infs.
    fromiter : Create an array from an iterator.
    fromfunction : Construct an array by executing a function on grid
                   positions.

    Examples
    --------
    Convert a list into an array:

    >>> a = [1, 2]
    >>> import numpy as np
    >>> np.asarray(a)
    array([1, 2])

    Existing arrays are not copied:

    >>> a = np.array([1, 2])
    >>> np.asarray(a) is a
    True

    If `dtype` is set, array is copied only if dtype does not match:

    >>> a = np.array([1, 2], dtype=np.float32)
    >>> np.shares_memory(np.asarray(a, dtype=np.float32), a)
    True
    >>> np.shares_memory(np.asarray(a, dtype=np.float64), a)
    False

    Contrary to `asanyarray`, ndarray subclasses are not passed through:

    >>> issubclass(np.recarray, np.ndarray)
    True
    >>> a = np.array([(1., 2), (3., 4)], dtype='f4,i4').view(np.recarray)
    >>> np.asarray(a) is a
    False
    >>> np.asanyarray(a) is a
    True

Python Library Documentation: function asarray_chkfinite in module autograd.tracer

asarray_chkfinite(*args, called_by_autograd_dispatcher=False, **kwargs)
    Convert the input to an array, checking for NaNs or Infs.

    Parameters
    ----------
    a : array_like
        Input data, in any form that can be converted to an array.  This
        includes lists, lists of tuples, tuples, tuples of tuples, tuples
        of lists and ndarrays.  Success requires no NaNs or Infs.
    dtype : data-type, optional
        By default, the data-type is inferred from the input data.
    order : {'C', 'F', 'A', 'K'}, optional
        Memory layout.  'A' and 'K' depend on the order of input array a.
        'C' row-major (C-style),
        'F' column-major (Fortran-style) memory representation.
        'A' (any) means 'F' if `a` is Fortran contiguous, 'C' otherwise
        'K' (keep) preserve input order
        Defaults to 'C'.

    Returns
    -------
    out : ndarray
        Array interpretation of `a`.  No copy is performed if the input
        is already an ndarray.  If `a` is a subclass of ndarray, a base
        class ndarray is returned.

    Raises
    ------
    ValueError
        Raises ValueError if `a` contains NaN (Not a Number) or Inf (Infinity).

    See Also
    --------
    asarray : Create and array.
    asanyarray : Similar function which passes through subclasses.
    ascontiguousarray : Convert input to a contiguous array.
    asfortranarray : Convert input to an ndarray with column-major
                     memory order.
    fromiter : Create an array from an iterator.
    fromfunction : Construct an array by executing a function on grid
                   positions.

    Examples
    --------
    >>> import numpy as np

    Convert a list into an array. If all elements are finite, then
    ``asarray_chkfinite`` is identical to ``asarray``.

    >>> a = [1, 2]
    >>> np.asarray_chkfinite(a, dtype=float)
    array([1., 2.])

    Raises ValueError if array_like contains Nans or Infs.

    >>> a = [1, 2, np.inf]
    >>> try:
    ...     np.asarray_chkfinite(a)
    ... except ValueError:
    ...     print('ValueError')
    ...
    ValueError

Python Library Documentation: function ascontiguousarray in module autograd.tracer

ascontiguousarray(*args, called_by_autograd_dispatcher=False, **kwargs)
    ascontiguousarray(a, dtype=None, *, like=None)

    Return a contiguous array (ndim >= 1) in memory (C order).

    Parameters
    ----------
    a : array_like
        Input array.
    dtype : str or dtype object, optional
        Data-type of returned array.
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    out : ndarray
        Contiguous array of same shape and content as `a`, with type `dtype`
        if specified.

    See Also
    --------
    asfortranarray : Convert input to an ndarray with column-major
                     memory order.
    require : Return an ndarray that satisfies requirements.
    ndarray.flags : Information about the memory layout of the array.

    Examples
    --------
    Starting with a Fortran-contiguous array:

    >>> import numpy as np
    >>> x = np.ones((2, 3), order='F')
    >>> x.flags['F_CONTIGUOUS']
    True

    Calling ``ascontiguousarray`` makes a C-contiguous copy:

    >>> y = np.ascontiguousarray(x)
    >>> y.flags['C_CONTIGUOUS']
    True
    >>> np.may_share_memory(x, y)
    False

    Now, starting with a C-contiguous array:

    >>> x = np.ones((2, 3), order='C')
    >>> x.flags['C_CONTIGUOUS']
    True

    Then, calling ``ascontiguousarray`` returns the same object:

    >>> y = np.ascontiguousarray(x)
    >>> x is y
    True

    Note: This function returns an array with at least one-dimension (1-d)
    so it will not preserve 0-d arrays.

Python Library Documentation: function asfortranarray in module autograd.tracer

asfortranarray(*args, called_by_autograd_dispatcher=False, **kwargs)
    asfortranarray(a, dtype=None, *, like=None)

    Return an array (ndim >= 1) laid out in Fortran order in memory.

    Parameters
    ----------
    a : array_like
        Input array.
    dtype : str or dtype object, optional
        By default, the data-type is inferred from the input data.
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    out : ndarray
        The input `a` in Fortran, or column-major, order.

    See Also
    --------
    ascontiguousarray : Convert input to a contiguous (C order) array.
    asanyarray : Convert input to an ndarray with either row or
        column-major memory order.
    require : Return an ndarray that satisfies requirements.
    ndarray.flags : Information about the memory layout of the array.

    Examples
    --------
    Starting with a C-contiguous array:

    >>> import numpy as np
    >>> x = np.ones((2, 3), order='C')
    >>> x.flags['C_CONTIGUOUS']
    True

    Calling ``asfortranarray`` makes a Fortran-contiguous copy:

    >>> y = np.asfortranarray(x)
    >>> y.flags['F_CONTIGUOUS']
    True
    >>> np.may_share_memory(x, y)
    False

    Now, starting with a Fortran-contiguous array:

    >>> x = np.ones((2, 3), order='F')
    >>> x.flags['F_CONTIGUOUS']
    True

    Then, calling ``asfortranarray`` returns the same object:

    >>> y = np.asfortranarray(x)
    >>> x is y
    True

    Note: This function returns an array with at least one-dimension (1-d)
    so it will not preserve 0-d arrays.

Python Library Documentation: function arcsin in module autograd.tracer

arcsin(*args, called_by_autograd_dispatcher=False, **kwargs)
    arcsin(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Inverse sine, element-wise.

    Parameters
    ----------
    x : array_like
        `y`-coordinate on the unit circle.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    angle : ndarray
        The inverse sine of each element in `x`, in radians and in the
        closed interval ``[-pi/2, pi/2]``.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    sin, cos, arccos, tan, arctan, arctan2, emath.arcsin

    Notes
    -----
    `arcsin` is a multivalued function: for each `x` there are infinitely
    many numbers `z` such that :math:`sin(z) = x`.  The convention is to
    return the angle `z` whose real part lies in [-pi/2, pi/2].

    For real-valued input data types, *arcsin* always returns real output.
    For each value that cannot be expressed as a real number or infinity,
    it yields ``nan`` and sets the `invalid` floating point error flag.

    For complex-valued input, `arcsin` is a complex analytic function that
    has, by convention, the branch cuts [-inf, -1] and [1, inf]  and is
    continuous from above on the former and from below on the latter.

    The inverse sine is also known as `asin` or sin^{-1}.

    References
    ----------
    Abramowitz, M. and Stegun, I. A., *Handbook of Mathematical Functions*,
    10th printing, New York: Dover, 1964, pp. 79ff.
    https://personal.math.ubc.ca/~cbm/aands/page_79.htm

    Examples
    --------
    >>> import numpy as np
    >>> np.arcsin(1)     # pi/2
    1.5707963267948966
    >>> np.arcsin(-1)    # -pi/2
    -1.5707963267948966
    >>> np.arcsin(0)
    0.0

Python Library Documentation: function arcsinh in module autograd.tracer

arcsinh(*args, called_by_autograd_dispatcher=False, **kwargs)
    arcsinh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Inverse hyperbolic sine element-wise.

    Parameters
    ----------
    x : array_like
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Array of the same shape as `x`.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    `arcsinh` is a multivalued function: for each `x` there are infinitely
    many numbers `z` such that `sinh(z) = x`. The convention is to return the
    `z` whose imaginary part lies in `[-pi/2, pi/2]`.

    For real-valued input data types, `arcsinh` always returns real output.
    For each value that cannot be expressed as a real number or infinity, it
    returns ``nan`` and sets the `invalid` floating point error flag.

    For complex-valued input, `arcsinh` is a complex analytical function that
    has branch cuts `[1j, infj]` and `[-1j, -infj]` and is continuous from
    the right on the former and from the left on the latter.

    The inverse hyperbolic sine is also known as `asinh` or ``sinh^-1``.

    References
    ----------
    .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions",
           10th printing, 1964, pp. 86.
           https://personal.math.ubc.ca/~cbm/aands/page_86.htm
    .. [2] Wikipedia, "Inverse hyperbolic function",
           https://en.wikipedia.org/wiki/Arcsinh

    Examples
    --------
    >>> import numpy as np
    >>> np.arcsinh(np.array([np.e, 10.0]))
    array([ 1.72538256,  2.99822295])

Python Library Documentation: function asmatrix in module autograd.tracer

asmatrix(*args, called_by_autograd_dispatcher=False, **kwargs)
    Interpret the input as a matrix.

    Unlike `matrix`, `asmatrix` does not make a copy if the input is already
    a matrix or an ndarray.  Equivalent to ``matrix(data, copy=False)``.

    Parameters
    ----------
    data : array_like
        Input data.
    dtype : data-type
       Data-type of the output matrix.

    Returns
    -------
    mat : matrix
        `data` interpreted as a matrix.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([[1, 2], [3, 4]])

    >>> m = np.asmatrix(x)

    >>> x[0,0] = 5

    >>> m
    matrix([[5, 2],
            [3, 4]])

Python Library Documentation: function astype in module autograd.tracer

astype(*args, called_by_autograd_dispatcher=False, **kwargs)
    Copies an array to a specified data type.

    This function is an Array API compatible alternative to
    `numpy.ndarray.astype`.

    Parameters
    ----------
    x : ndarray
        Input NumPy array to cast. ``array_likes`` are explicitly not
        supported here.
    dtype : dtype
        Data type of the result.
    copy : bool, optional
        Specifies whether to copy an array when the specified dtype matches
        the data type of the input array ``x``. If ``True``, a newly allocated
        array must always be returned. If ``False`` and the specified dtype
        matches the data type of the input array, the input array must be
        returned; otherwise, a newly allocated array must be returned.
        Defaults to ``True``.
    device : str, optional
        The device on which to place the returned array. Default: None.
        For Array-API interoperability only, so must be ``"cpu"`` if passed.

        .. versionadded:: 2.1.0

    Returns
    -------
    out : ndarray
        An array having the specified data type.

    See Also
    --------
    ndarray.astype

    Examples
    --------
    >>> import numpy as np
    >>> arr = np.array([1, 2, 3]); arr
    array([1, 2, 3])
    >>> np.astype(arr, np.float64)
    array([1., 2., 3.])

    Non-copy case:

    >>> arr = np.array([1, 2, 3])
    >>> arr_noncpy = np.astype(arr, arr.dtype, copy=False)
    >>> np.shares_memory(arr, arr_noncpy)
    True

Python Library Documentation: function arctan in module autograd.tracer

arctan(*args, called_by_autograd_dispatcher=False, **kwargs)
    arctan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Trigonometric inverse tangent, element-wise.

    The inverse of tan, so that if ``y = tan(x)`` then ``x = arctan(y)``.

    Parameters
    ----------
    x : array_like
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Out has the same shape as `x`.  Its real part is in
        ``[-pi/2, pi/2]`` (``arctan(+/-inf)`` returns ``+/-pi/2``).
        This is a scalar if `x` is a scalar.

    See Also
    --------
    arctan2 : The "four quadrant" arctan of the angle formed by (`x`, `y`)
        and the positive `x`-axis.
    angle : Argument of complex values.

    Notes
    -----
    `arctan` is a multi-valued function: for each `x` there are infinitely
    many numbers `z` such that tan(`z`) = `x`.  The convention is to return
    the angle `z` whose real part lies in [-pi/2, pi/2].

    For real-valued input data types, `arctan` always returns real output.
    For each value that cannot be expressed as a real number or infinity,
    it yields ``nan`` and sets the `invalid` floating point error flag.

    For complex-valued input, `arctan` is a complex analytic function that
    has [``1j, infj``] and [``-1j, -infj``] as branch cuts, and is continuous
    from the left on the former and from the right on the latter.

    The inverse tangent is also known as `atan` or tan^{-1}.

    References
    ----------
    Abramowitz, M. and Stegun, I. A., *Handbook of Mathematical Functions*,
    10th printing, New York: Dover, 1964, pp. 79.
    https://personal.math.ubc.ca/~cbm/aands/page_79.htm

    Examples
    --------
    We expect the arctan of 0 to be 0, and of 1 to be pi/4:

    >>> import numpy as np

    >>> np.arctan([0, 1])
    array([ 0.        ,  0.78539816])

    >>> np.pi/4
    0.78539816339744828

    Plot arctan:

    >>> import matplotlib.pyplot as plt
    >>> x = np.linspace(-10, 10)
    >>> plt.plot(x, np.arctan(x))
    >>> plt.axis('tight')
    >>> plt.show()

Python Library Documentation: function arctan2 in module autograd.tracer

arctan2(*args, called_by_autograd_dispatcher=False, **kwargs)
    arctan2(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Element-wise arc tangent of ``x1/x2`` choosing the quadrant correctly.

    The quadrant (i.e., branch) is chosen so that ``arctan2(x1, x2)`` is
    the signed angle in radians between the ray ending at the origin and
    passing through the point (1,0), and the ray ending at the origin and
    passing through the point (`x2`, `x1`).  (Note the role reversal: the
    "`y`-coordinate" is the first function parameter, the "`x`-coordinate"
    is the second.)  By IEEE convention, this function is defined for
    `x2` = +/-0 and for either or both of `x1` and `x2` = +/-inf (see
    Notes for specific values).

    This function is not defined for complex-valued arguments; for the
    so-called argument of complex values, use `angle`.

    Parameters
    ----------
    x1 : array_like, real-valued
        `y`-coordinates.
    x2 : array_like, real-valued
        `x`-coordinates.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    angle : ndarray
        Array of angles in radians, in the range ``[-pi, pi]``.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    arctan, tan, angle

    Notes
    -----
    *arctan2* is identical to the `atan2` function of the underlying
    C library.  The following special values are defined in the C
    standard: [1]_

    ====== ====== ================
    `x1`   `x2`   `arctan2(x1,x2)`
    ====== ====== ================
    +/- 0  +0     +/- 0
    +/- 0  -0     +/- pi
     > 0   +/-inf +0 / +pi
     < 0   +/-inf -0 / -pi
    +/-inf +inf   +/- (pi/4)
    +/-inf -inf   +/- (3*pi/4)
    ====== ====== ================

    Note that +0 and -0 are distinct floating point numbers, as are +inf
    and -inf.

    References
    ----------
    .. [1] ISO/IEC standard 9899:1999, "Programming language C."

    Examples
    --------
    Consider four points in different quadrants:

    >>> import numpy as np

    >>> x = np.array([-1, +1, +1, -1])
    >>> y = np.array([-1, -1, +1, +1])
    >>> np.arctan2(y, x) * 180 / np.pi
    array([-135.,  -45.,   45.,  135.])

    Note the order of the parameters. `arctan2` is defined also when `x2` = 0
    and at several other special points, obtaining values in
    the range ``[-pi, pi]``:

    >>> np.arctan2([1., -1.], [0., 0.])
    array([ 1.57079633, -1.57079633])
    >>> np.arctan2([0., 0., np.inf], [+0., -0., np.inf])
    array([0.        , 3.14159265, 0.78539816])

Python Library Documentation: function arctanh in module autograd.tracer

arctanh(*args, called_by_autograd_dispatcher=False, **kwargs)
    arctanh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Inverse hyperbolic tangent element-wise.

    Parameters
    ----------
    x : array_like
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Array of the same shape as `x`.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    emath.arctanh

    Notes
    -----
    `arctanh` is a multivalued function: for each `x` there are infinitely
    many numbers `z` such that ``tanh(z) = x``. The convention is to return
    the `z` whose imaginary part lies in `[-pi/2, pi/2]`.

    For real-valued input data types, `arctanh` always returns real output.
    For each value that cannot be expressed as a real number or infinity,
    it yields ``nan`` and sets the `invalid` floating point error flag.

    For complex-valued input, `arctanh` is a complex analytical function
    that has branch cuts `[-1, -inf]` and `[1, inf]` and is continuous from
    above on the former and from below on the latter.

    The inverse hyperbolic tangent is also known as `atanh` or ``tanh^-1``.

    References
    ----------
    .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions",
           10th printing, 1964, pp. 86.
           https://personal.math.ubc.ca/~cbm/aands/page_86.htm
    .. [2] Wikipedia, "Inverse hyperbolic function",
           https://en.wikipedia.org/wiki/Arctanh

    Examples
    --------
    >>> import numpy as np
    >>> np.arctanh([0, -0.5])
    array([ 0.        , -0.54930614])

Python Library Documentation: function atleast_1d in module autograd.tracer

atleast_1d(*args, called_by_autograd_dispatcher=False, **kwargs)
    Convert inputs to arrays with at least one dimension.

    Scalar inputs are converted to 1-dimensional arrays, whilst
    higher-dimensional inputs are preserved.

    Parameters
    ----------
    arys1, arys2, ... : array_like
        One or more input arrays.

    Returns
    -------
    ret : ndarray
        An array, or tuple of arrays, each with ``a.ndim >= 1``.
        Copies are made only if necessary.

    See Also
    --------
    atleast_2d, atleast_3d

    Examples
    --------
    >>> import numpy as np
    >>> np.atleast_1d(1.0)
    array([1.])

    >>> x = np.arange(9.0).reshape(3,3)
    >>> np.atleast_1d(x)
    array([[0., 1., 2.],
           [3., 4., 5.],
           [6., 7., 8.]])
    >>> np.atleast_1d(x) is x
    True

    >>> np.atleast_1d(1, [3, 4])
    (array([1]), array([3, 4]))

Python Library Documentation: function atleast_2d in module autograd.tracer

atleast_2d(*args, called_by_autograd_dispatcher=False, **kwargs)
    View inputs as arrays with at least two dimensions.

    Parameters
    ----------
    arys1, arys2, ... : array_like
        One or more array-like sequences.  Non-array inputs are converted
        to arrays.  Arrays that already have two or more dimensions are
        preserved.

    Returns
    -------
    res, res2, ... : ndarray
        An array, or tuple of arrays, each with ``a.ndim >= 2``.
        Copies are avoided where possible, and views with two or more
        dimensions are returned.

    See Also
    --------
    atleast_1d, atleast_3d

    Examples
    --------
    >>> import numpy as np
    >>> np.atleast_2d(3.0)
    array([[3.]])

    >>> x = np.arange(3.0)
    >>> np.atleast_2d(x)
    array([[0., 1., 2.]])
    >>> np.atleast_2d(x).base is x
    True

    >>> np.atleast_2d(1, [1, 2], [[1, 2]])
    (array([[1]]), array([[1, 2]]), array([[1, 2]]))

Python Library Documentation: function atleast_3d in module autograd.tracer

atleast_3d(*args, called_by_autograd_dispatcher=False, **kwargs)
    View inputs as arrays with at least three dimensions.

    Parameters
    ----------
    arys1, arys2, ... : array_like
        One or more array-like sequences.  Non-array inputs are converted to
        arrays.  Arrays that already have three or more dimensions are
        preserved.

    Returns
    -------
    res1, res2, ... : ndarray
        An array, or tuple of arrays, each with ``a.ndim >= 3``.  Copies are
        avoided where possible, and views with three or more dimensions are
        returned.  For example, a 1-D array of shape ``(N,)`` becomes a view
        of shape ``(1, N, 1)``, and a 2-D array of shape ``(M, N)`` becomes a
        view of shape ``(M, N, 1)``.

    See Also
    --------
    atleast_1d, atleast_2d

    Examples
    --------
    >>> import numpy as np
    >>> np.atleast_3d(3.0)
    array([[[3.]]])

    >>> x = np.arange(3.0)
    >>> np.atleast_3d(x).shape
    (1, 3, 1)

    >>> x = np.arange(12.0).reshape(4,3)
    >>> np.atleast_3d(x).shape
    (4, 3, 1)
    >>> np.atleast_3d(x).base is x.base  # x is a reshape, so not base itself
    True

    >>> for arr in np.atleast_3d([1, 2], [[1, 2]], [[[1, 2]]]):
    ...     print(arr, arr.shape) # doctest: +SKIP
    ...
    [[[1]
      [2]]] (1, 2, 1)
    [[[1]
      [2]]] (1, 2, 1)
    [[[1 2]]] (1, 1, 2)

Python Library Documentation: function average in module autograd.tracer

average(*args, called_by_autograd_dispatcher=False, **kwargs)
    Compute the weighted average along the specified axis.

    Parameters
    ----------
    a : array_like
        Array containing data to be averaged. If `a` is not an array, a
        conversion is attempted.
    axis : None or int or tuple of ints, optional
        Axis or axes along which to average `a`.  The default,
        `axis=None`, will average over all of the elements of the input array.
        If axis is negative it counts from the last to the first axis.

        .. versionadded:: 1.7.0

        If axis is a tuple of ints, averaging is performed on all of the axes
        specified in the tuple instead of a single axis or all the axes as
        before.
    weights : array_like, optional
        An array of weights associated with the values in `a`. Each value in
        `a` contributes to the average according to its associated weight.
        The array of weights must be the same shape as `a` if no axis is
        specified, otherwise the weights must have dimensions and shape
        consistent with `a` along the specified axis.
        If `weights=None`, then all data in `a` are assumed to have a
        weight equal to one.
        The calculation is::

            avg = sum(a * weights) / sum(weights)

        where the sum is over all included elements.
        The only constraint on the values of `weights` is that `sum(weights)`
        must not be 0.
    returned : bool, optional
        Default is `False`. If `True`, the tuple (`average`, `sum_of_weights`)
        is returned, otherwise only the average is returned.
        If `weights=None`, `sum_of_weights` is equivalent to the number of
        elements over which the average is taken.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the original `a`.
        *Note:* `keepdims` will not work with instances of `numpy.matrix`
        or other classes whose methods do not support `keepdims`.

        .. versionadded:: 1.23.0

    Returns
    -------
    retval, [sum_of_weights] : array_type or double
        Return the average along the specified axis. When `returned` is `True`,
        return a tuple with the average as the first element and the sum
        of the weights as the second element. `sum_of_weights` is of the
        same type as `retval`. The result dtype follows a general pattern.
        If `weights` is None, the result dtype will be that of `a` , or ``float64``
        if `a` is integral. Otherwise, if `weights` is not None and `a` is non-
        integral, the result type will be the type of lowest precision capable of
        representing values of both `a` and `weights`. If `a` happens to be
        integral, the previous rules still applies but the result dtype will
        at least be ``float64``.

    Raises
    ------
    ZeroDivisionError
        When all weights along axis are zero. See `numpy.ma.average` for a
        version robust to this type of error.
    TypeError
        When `weights` does not have the same shape as `a`, and `axis=None`.
    ValueError
        When `weights` does not have dimensions and shape consistent with `a`
        along specified `axis`.

    See Also
    --------
    mean

    ma.average : average for masked arrays -- useful if your data contains
                 "missing" values
    numpy.result_type : Returns the type that results from applying the
                        numpy type promotion rules to the arguments.

    Examples
    --------
    >>> import numpy as np
    >>> data = np.arange(1, 5)
    >>> data
    array([1, 2, 3, 4])
    >>> np.average(data)
    2.5
    >>> np.average(np.arange(1, 11), weights=np.arange(10, 0, -1))
    4.0

    >>> data = np.arange(6).reshape((3, 2))
    >>> data
    array([[0, 1],
           [2, 3],
           [4, 5]])
    >>> np.average(data, axis=1, weights=[1./4, 3./4])
    array([0.75, 2.75, 4.75])
    >>> np.average(data, weights=[1./4, 3./4])
    Traceback (most recent call last):
        ...
    TypeError: Axis must be specified when shapes of a and weights differ.

    With ``keepdims=True``, the following result has shape (3, 1).

    >>> np.average(data, axis=1, keepdims=True)
    array([[0.5],
           [2.5],
           [4.5]])

    >>> data = np.arange(8).reshape((2, 2, 2))
    >>> data
    array([[[0, 1],
            [2, 3]],
           [[4, 5],
            [6, 7]]])
    >>> np.average(data, axis=(0, 1), weights=[[1./4, 3./4], [1., 1./2]])
    array([3.4, 4.4])
    >>> np.average(data, axis=0, weights=[[1./4, 3./4], [1., 1./2]])
    Traceback (most recent call last):
        ...
    ValueError: Shape of weights must be consistent
    with shape of a along specified axis.

Python Library Documentation: function bartlett in module autograd.tracer

bartlett(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the Bartlett window.

    The Bartlett window is very similar to a triangular window, except
    that the end points are at zero.  It is often used in signal
    processing for tapering a signal, without generating too much
    ripple in the frequency domain.

    Parameters
    ----------
    M : int
        Number of points in the output window. If zero or less, an
        empty array is returned.

    Returns
    -------
    out : array
        The triangular window, with the maximum value normalized to one
        (the value one appears only if the number of samples is odd), with
        the first and last samples equal to zero.

    See Also
    --------
    blackman, hamming, hanning, kaiser

    Notes
    -----
    The Bartlett window is defined as

    .. math:: w(n) = \frac{2}{M-1} \left(
              \frac{M-1}{2} - \left|n - \frac{M-1}{2}\right|
              \right)

    Most references to the Bartlett window come from the signal processing
    literature, where it is used as one of many windowing functions for
    smoothing values.  Note that convolution with this window produces linear
    interpolation.  It is also known as an apodization (which means "removing
    the foot", i.e. smoothing discontinuities at the beginning and end of the
    sampled signal) or tapering function. The Fourier transform of the
    Bartlett window is the product of two sinc functions. Note the excellent
    discussion in Kanasewich [2]_.

    References
    ----------
    .. [1] M.S. Bartlett, "Periodogram Analysis and Continuous Spectra",
           Biometrika 37, 1-16, 1950.
    .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics",
           The University of Alberta Press, 1975, pp. 109-110.
    .. [3] A.V. Oppenheim and R.W. Schafer, "Discrete-Time Signal
           Processing", Prentice-Hall, 1999, pp. 468-471.
    .. [4] Wikipedia, "Window function",
           https://en.wikipedia.org/wiki/Window_function
    .. [5] W.H. Press,  B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
           "Numerical Recipes", Cambridge University Press, 1986, page 429.

    Examples
    --------
    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> np.bartlett(12)
    array([ 0.        ,  0.18181818,  0.36363636,  0.54545455,  0.72727273, # may vary
            0.90909091,  0.90909091,  0.72727273,  0.54545455,  0.36363636,
            0.18181818,  0.        ])

    Plot the window and its frequency response (requires SciPy and matplotlib).

    .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from numpy.fft import fft, fftshift
        window = np.bartlett(51)
        plt.plot(window)
        plt.title("Bartlett window")
        plt.ylabel("Amplitude")
        plt.xlabel("Sample")
        plt.show()
        plt.figure()
        A = fft(window, 2048) / 25.5
        mag = np.abs(fftshift(A))
        freq = np.linspace(-0.5, 0.5, len(A))
        with np.errstate(divide='ignore', invalid='ignore'):
            response = 20 * np.log10(mag)
        response = np.clip(response, -100, 100)
        plt.plot(freq, response)
        plt.title("Frequency response of Bartlett window")
        plt.ylabel("Magnitude [dB]")
        plt.xlabel("Normalized frequency [cycles per sample]")
        plt.axis('tight')
        plt.show()

Python Library Documentation: function base_repr in module autograd.tracer

base_repr(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return a string representation of a number in the given base system.

    Parameters
    ----------
    number : int
        The value to convert. Positive and negative values are handled.
    base : int, optional
        Convert `number` to the `base` number system. The valid range is 2-36,
        the default value is 2.
    padding : int, optional
        Number of zeros padded on the left. Default is 0 (no padding).

    Returns
    -------
    out : str
        String representation of `number` in `base` system.

    See Also
    --------
    binary_repr : Faster version of `base_repr` for base 2.

    Examples
    --------
    >>> import numpy as np
    >>> np.base_repr(5)
    '101'
    >>> np.base_repr(6, 5)
    '11'
    >>> np.base_repr(7, base=5, padding=3)
    '00012'

    >>> np.base_repr(10, base=16)
    'A'
    >>> np.base_repr(32, base=16)
    '20'

Python Library Documentation: function binary_repr in module autograd.tracer

binary_repr(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the binary representation of the input number as a string.

    For negative numbers, if width is not given, a minus sign is added to the
    front. If width is given, the two's complement of the number is
    returned, with respect to that width.

    In a two's-complement system negative numbers are represented by the two's
    complement of the absolute value. This is the most common method of
    representing signed integers on computers [1]_. A N-bit two's-complement
    system can represent every integer in the range
    :math:`-2^{N-1}` to :math:`+2^{N-1}-1`.

    Parameters
    ----------
    num : int
        Only an integer decimal number can be used.
    width : int, optional
        The length of the returned string if `num` is positive, or the length
        of the two's complement if `num` is negative, provided that `width` is
        at least a sufficient number of bits for `num` to be represented in
        the designated form. If the `width` value is insufficient, an error is
        raised.

    Returns
    -------
    bin : str
        Binary representation of `num` or two's complement of `num`.

    See Also
    --------
    base_repr: Return a string representation of a number in the given base
               system.
    bin: Python's built-in binary representation generator of an integer.

    Notes
    -----
    `binary_repr` is equivalent to using `base_repr` with base 2, but about 25x
    faster.

    References
    ----------
    .. [1] Wikipedia, "Two's complement",
        https://en.wikipedia.org/wiki/Two's_complement

    Examples
    --------
    >>> import numpy as np
    >>> np.binary_repr(3)
    '11'
    >>> np.binary_repr(-3)
    '-11'
    >>> np.binary_repr(3, width=4)
    '0011'

    The two's complement is returned when the input number is negative and
    width is specified:

    >>> np.binary_repr(-3, width=3)
    '101'
    >>> np.binary_repr(-3, width=5)
    '11101'

Python Library Documentation: function bincount in module autograd.tracer

bincount(*args, called_by_autograd_dispatcher=False, **kwargs)
    bincount(x, /, weights=None, minlength=0)

    Count number of occurrences of each value in array of non-negative ints.

    The number of bins (of size 1) is one larger than the largest value in
    `x`. If `minlength` is specified, there will be at least this number
    of bins in the output array (though it will be longer if necessary,
    depending on the contents of `x`).
    Each bin gives the number of occurrences of its index value in `x`.
    If `weights` is specified the input array is weighted by it, i.e. if a
    value ``n`` is found at position ``i``, ``out[n] += weight[i]`` instead
    of ``out[n] += 1``.

    Parameters
    ----------
    x : array_like, 1 dimension, nonnegative ints
        Input array.
    weights : array_like, optional
        Weights, array of the same shape as `x`.
    minlength : int, optional
        A minimum number of bins for the output array.

        .. versionadded:: 1.6.0

    Returns
    -------
    out : ndarray of ints
        The result of binning the input array.
        The length of `out` is equal to ``np.amax(x)+1``.

    Raises
    ------
    ValueError
        If the input is not 1-dimensional, or contains elements with negative
        values, or if `minlength` is negative.
    TypeError
        If the type of the input is float or complex.

    See Also
    --------
    histogram, digitize, unique

    Examples
    --------
    >>> import numpy as np
    >>> np.bincount(np.arange(5))
    array([1, 1, 1, 1, 1])
    >>> np.bincount(np.array([0, 1, 1, 3, 2, 1, 7]))
    array([1, 3, 1, 1, 0, 0, 0, 1])

    >>> x = np.array([0, 1, 1, 3, 2, 1, 7, 23])
    >>> np.bincount(x).size == np.amax(x)+1
    True

    The input array needs to be of integer dtype, otherwise a
    TypeError is raised:

    >>> np.bincount(np.arange(5, dtype=float))
    Traceback (most recent call last):
      ...
    TypeError: Cannot cast array data from dtype('float64') to dtype('int64')
    according to the rule 'safe'

    A possible use of ``bincount`` is to perform sums over
    variable-size chunks of an array, using the ``weights`` keyword.

    >>> w = np.array([0.3, 0.5, 0.2, 0.7, 1., -0.6]) # weights
    >>> x = np.array([0, 1, 1, 2, 2, 2])
    >>> np.bincount(x,  weights=w)
    array([ 0.3,  0.7,  1.1])

Python Library Documentation: function bitwise_and in module autograd.tracer

bitwise_and(*args, called_by_autograd_dispatcher=False, **kwargs)
    bitwise_and(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Compute the bit-wise AND of two arrays element-wise.

    Computes the bit-wise AND of the underlying binary representation of
    the integers in the input arrays. This ufunc implements the C/Python
    operator ``&``.

    Parameters
    ----------
    x1, x2 : array_like
        Only integer and boolean types are handled.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Result.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    logical_and
    bitwise_or
    bitwise_xor
    binary_repr :
        Return the binary representation of the input number as a string.

    Examples
    --------
    >>> import numpy as np

    The number 13 is represented by ``00001101``.  Likewise, 17 is
    represented by ``00010001``.  The bit-wise AND of 13 and 17 is
    therefore ``000000001``, or 1:

    >>> np.bitwise_and(13, 17)
    1

    >>> np.bitwise_and(14, 13)
    12
    >>> np.binary_repr(12)
    '1100'
    >>> np.bitwise_and([14,3], 13)
    array([12,  1])

    >>> np.bitwise_and([11,7], [4,25])
    array([0, 1])
    >>> np.bitwise_and(np.array([2,5,255]), np.array([3,14,16]))
    array([ 2,  4, 16])
    >>> np.bitwise_and([True, True], [False, True])
    array([False,  True])

    The ``&`` operator can be used as a shorthand for ``np.bitwise_and`` on
    ndarrays.

    >>> x1 = np.array([2, 5, 255])
    >>> x2 = np.array([3, 14, 16])
    >>> x1 & x2
    array([ 2,  4, 16])

Python Library Documentation: function bitwise_count in module autograd.tracer

bitwise_count(*args, called_by_autograd_dispatcher=False, **kwargs)
    bitwise_count(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Computes the number of 1-bits in the absolute value of ``x``.
    Analogous to the builtin `int.bit_count` or ``popcount`` in C++.

    Parameters
    ----------
    x : array_like, unsigned int
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The corresponding number of 1-bits in the input.
        Returns uint8 for all integer types
        This is a scalar if `x` is a scalar.

    References
    ----------
    .. [1] https://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetParallel

    .. [2] Wikipedia, "Hamming weight",
           https://en.wikipedia.org/wiki/Hamming_weight

    .. [3] http://aggregate.ee.engr.uky.edu/MAGIC/#Population%20Count%20(Ones%20Count)

    Examples
    --------
    >>> import numpy as np
    >>> np.bitwise_count(1023)
    10
    >>> a = np.array([2**i - 1 for i in range(16)])
    >>> np.bitwise_count(a)
    array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15],
          dtype=uint8)

Python Library Documentation: function invert in module autograd.tracer

invert(*args, called_by_autograd_dispatcher=False, **kwargs)
    invert(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Compute bit-wise inversion, or bit-wise NOT, element-wise.

    Computes the bit-wise NOT of the underlying binary representation of
    the integers in the input arrays. This ufunc implements the C/Python
    operator ``~``.

    For signed integer inputs, the bit-wise NOT of the absolute value is
    returned. In a two's-complement system, this operation effectively flips
    all the bits, resulting in a representation that corresponds to the
    negative of the input plus one. This is the most common method of
    representing signed integers on computers [1]_. A N-bit two's-complement
    system can represent every integer in the range :math:`-2^{N-1}` to
    :math:`+2^{N-1}-1`.

    Parameters
    ----------
    x : array_like
        Only integer and boolean types are handled.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Result.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    bitwise_and, bitwise_or, bitwise_xor
    logical_not
    binary_repr :
        Return the binary representation of the input number as a string.

    Notes
    -----
    ``numpy.bitwise_not`` is an alias for `invert`:

    >>> np.bitwise_not is np.invert
    True

    References
    ----------
    .. [1] Wikipedia, "Two's complement",
        https://en.wikipedia.org/wiki/Two's_complement

    Examples
    --------
    >>> import numpy as np

    We've seen that 13 is represented by ``00001101``.
    The invert or bit-wise NOT of 13 is then:

    >>> x = np.invert(np.array(13, dtype=np.uint8))
    >>> x
    242
    >>> np.binary_repr(x, width=8)
    '11110010'

    The result depends on the bit-width:

    >>> x = np.invert(np.array(13, dtype=np.uint16))
    >>> x
    65522
    >>> np.binary_repr(x, width=16)
    '1111111111110010'

    When using signed integer types, the result is the bit-wise NOT of
    the unsigned type, interpreted as a signed integer:

    >>> np.invert(np.array([13], dtype=np.int8))
    array([-14], dtype=int8)
    >>> np.binary_repr(-14, width=8)
    '11110010'

    Booleans are accepted as well:

    >>> np.invert(np.array([True, False]))
    array([False,  True])

    The ``~`` operator can be used as a shorthand for ``np.invert`` on
    ndarrays.

    >>> x1 = np.array([True, False])
    >>> ~x1
    array([False,  True])

Python Library Documentation: function left_shift in module autograd.tracer

left_shift(*args, called_by_autograd_dispatcher=False, **kwargs)
    left_shift(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Shift the bits of an integer to the left.

    Bits are shifted to the left by appending `x2` 0s at the right of `x1`.
    Since the internal representation of numbers is in binary format, this
    operation is equivalent to multiplying `x1` by ``2**x2``.

    Parameters
    ----------
    x1 : array_like of integer type
        Input values.
    x2 : array_like of integer type
        Number of zeros to append to `x1`. Has to be non-negative.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : array of integer type
        Return `x1` with bits shifted `x2` times to the left.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    right_shift : Shift the bits of an integer to the right.
    binary_repr : Return the binary representation of the input number
        as a string.

    Examples
    --------
    >>> import numpy as np
    >>> np.binary_repr(5)
    '101'
    >>> np.left_shift(5, 2)
    20
    >>> np.binary_repr(20)
    '10100'

    >>> np.left_shift(5, [1,2,3])
    array([10, 20, 40])

    Note that the dtype of the second argument may change the dtype of the
    result and can lead to unexpected results in some cases (see
    :ref:`Casting Rules <ufuncs.casting>`):

    >>> a = np.left_shift(np.uint8(255), np.int64(1))  # Expect 254
    >>> print(a, type(a)) # Unexpected result due to upcasting
    510 <class 'numpy.int64'>
    >>> b = np.left_shift(np.uint8(255), np.uint8(1))
    >>> print(b, type(b))
    254 <class 'numpy.uint8'>

    The ``<<`` operator can be used as a shorthand for ``np.left_shift`` on
    ndarrays.

    >>> x1 = 5
    >>> x2 = np.array([1, 2, 3])
    >>> x1 << x2
    array([10, 20, 40])

Python Library Documentation: function invert in module autograd.tracer

invert(*args, called_by_autograd_dispatcher=False, **kwargs)
    invert(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Compute bit-wise inversion, or bit-wise NOT, element-wise.

    Computes the bit-wise NOT of the underlying binary representation of
    the integers in the input arrays. This ufunc implements the C/Python
    operator ``~``.

    For signed integer inputs, the bit-wise NOT of the absolute value is
    returned. In a two's-complement system, this operation effectively flips
    all the bits, resulting in a representation that corresponds to the
    negative of the input plus one. This is the most common method of
    representing signed integers on computers [1]_. A N-bit two's-complement
    system can represent every integer in the range :math:`-2^{N-1}` to
    :math:`+2^{N-1}-1`.

    Parameters
    ----------
    x : array_like
        Only integer and boolean types are handled.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Result.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    bitwise_and, bitwise_or, bitwise_xor
    logical_not
    binary_repr :
        Return the binary representation of the input number as a string.

    Notes
    -----
    ``numpy.bitwise_not`` is an alias for `invert`:

    >>> np.bitwise_not is np.invert
    True

    References
    ----------
    .. [1] Wikipedia, "Two's complement",
        https://en.wikipedia.org/wiki/Two's_complement

    Examples
    --------
    >>> import numpy as np

    We've seen that 13 is represented by ``00001101``.
    The invert or bit-wise NOT of 13 is then:

    >>> x = np.invert(np.array(13, dtype=np.uint8))
    >>> x
    242
    >>> np.binary_repr(x, width=8)
    '11110010'

    The result depends on the bit-width:

    >>> x = np.invert(np.array(13, dtype=np.uint16))
    >>> x
    65522
    >>> np.binary_repr(x, width=16)
    '1111111111110010'

    When using signed integer types, the result is the bit-wise NOT of
    the unsigned type, interpreted as a signed integer:

    >>> np.invert(np.array([13], dtype=np.int8))
    array([-14], dtype=int8)
    >>> np.binary_repr(-14, width=8)
    '11110010'

    Booleans are accepted as well:

    >>> np.invert(np.array([True, False]))
    array([False,  True])

    The ``~`` operator can be used as a shorthand for ``np.invert`` on
    ndarrays.

    >>> x1 = np.array([True, False])
    >>> ~x1
    array([False,  True])

Python Library Documentation: function bitwise_or in module autograd.tracer

bitwise_or(*args, called_by_autograd_dispatcher=False, **kwargs)
    bitwise_or(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Compute the bit-wise OR of two arrays element-wise.

    Computes the bit-wise OR of the underlying binary representation of
    the integers in the input arrays. This ufunc implements the C/Python
    operator ``|``.

    Parameters
    ----------
    x1, x2 : array_like
        Only integer and boolean types are handled.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Result.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    logical_or
    bitwise_and
    bitwise_xor
    binary_repr :
        Return the binary representation of the input number as a string.

    Examples
    --------
    >>> import numpy as np

    The number 13 has the binary representation ``00001101``. Likewise,
    16 is represented by ``00010000``.  The bit-wise OR of 13 and 16 is
    then ``00011101``, or 29:

    >>> np.bitwise_or(13, 16)
    29
    >>> np.binary_repr(29)
    '11101'

    >>> np.bitwise_or(32, 2)
    34
    >>> np.bitwise_or([33, 4], 1)
    array([33,  5])
    >>> np.bitwise_or([33, 4], [1, 2])
    array([33,  6])

    >>> np.bitwise_or(np.array([2, 5, 255]), np.array([4, 4, 4]))
    array([  6,   5, 255])
    >>> np.array([2, 5, 255]) | np.array([4, 4, 4])
    array([  6,   5, 255])
    >>> np.bitwise_or(np.array([2, 5, 255, 2147483647], dtype=np.int32),
    ...               np.array([4, 4, 4, 2147483647], dtype=np.int32))
    array([         6,          5,        255, 2147483647])
    >>> np.bitwise_or([True, True], [False, True])
    array([ True,  True])

    The ``|`` operator can be used as a shorthand for ``np.bitwise_or`` on
    ndarrays.

    >>> x1 = np.array([2, 5, 255])
    >>> x2 = np.array([4, 4, 4])
    >>> x1 | x2
    array([  6,   5, 255])

Python Library Documentation: function right_shift in module autograd.tracer

right_shift(*args, called_by_autograd_dispatcher=False, **kwargs)
    right_shift(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Shift the bits of an integer to the right.

    Bits are shifted to the right `x2`.  Because the internal
    representation of numbers is in binary format, this operation is
    equivalent to dividing `x1` by ``2**x2``.

    Parameters
    ----------
    x1 : array_like, int
        Input values.
    x2 : array_like, int
        Number of bits to remove at the right of `x1`.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray, int
        Return `x1` with bits shifted `x2` times to the right.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    left_shift : Shift the bits of an integer to the left.
    binary_repr : Return the binary representation of the input number
        as a string.

    Examples
    --------
    >>> import numpy as np
    >>> np.binary_repr(10)
    '1010'
    >>> np.right_shift(10, 1)
    5
    >>> np.binary_repr(5)
    '101'

    >>> np.right_shift(10, [1,2,3])
    array([5, 2, 1])

    The ``>>`` operator can be used as a shorthand for ``np.right_shift`` on
    ndarrays.

    >>> x1 = 10
    >>> x2 = np.array([1,2,3])
    >>> x1 >> x2
    array([5, 2, 1])

Python Library Documentation: function bitwise_xor in module autograd.tracer

bitwise_xor(*args, called_by_autograd_dispatcher=False, **kwargs)
    bitwise_xor(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Compute the bit-wise XOR of two arrays element-wise.

    Computes the bit-wise XOR of the underlying binary representation of
    the integers in the input arrays. This ufunc implements the C/Python
    operator ``^``.

    Parameters
    ----------
    x1, x2 : array_like
        Only integer and boolean types are handled.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Result.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    logical_xor
    bitwise_and
    bitwise_or
    binary_repr :
        Return the binary representation of the input number as a string.

    Examples
    --------
    >>> import numpy as np

    The number 13 is represented by ``00001101``. Likewise, 17 is
    represented by ``00010001``.  The bit-wise XOR of 13 and 17 is
    therefore ``00011100``, or 28:

    >>> np.bitwise_xor(13, 17)
    28
    >>> np.binary_repr(28)
    '11100'

    >>> np.bitwise_xor(31, 5)
    26
    >>> np.bitwise_xor([31,3], 5)
    array([26,  6])

    >>> np.bitwise_xor([31,3], [5,6])
    array([26,  5])
    >>> np.bitwise_xor([True, True], [False, True])
    array([ True, False])

    The ``^`` operator can be used as a shorthand for ``np.bitwise_xor`` on
    ndarrays.

    >>> x1 = np.array([True, True])
    >>> x2 = np.array([False, True])
    >>> x1 ^ x2
    array([ True, False])

Python Library Documentation: function blackman in module autograd.tracer

blackman(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the Blackman window.

    The Blackman window is a taper formed by using the first three
    terms of a summation of cosines. It was designed to have close to the
    minimal leakage possible.  It is close to optimal, only slightly worse
    than a Kaiser window.

    Parameters
    ----------
    M : int
        Number of points in the output window. If zero or less, an empty
        array is returned.

    Returns
    -------
    out : ndarray
        The window, with the maximum value normalized to one (the value one
        appears only if the number of samples is odd).

    See Also
    --------
    bartlett, hamming, hanning, kaiser

    Notes
    -----
    The Blackman window is defined as

    .. math::  w(n) = 0.42 - 0.5 \cos(2\pi n/M) + 0.08 \cos(4\pi n/M)

    Most references to the Blackman window come from the signal processing
    literature, where it is used as one of many windowing functions for
    smoothing values.  It is also known as an apodization (which means
    "removing the foot", i.e. smoothing discontinuities at the beginning
    and end of the sampled signal) or tapering function. It is known as a
    "near optimal" tapering function, almost as good (by some measures)
    as the kaiser window.

    References
    ----------
    Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra,
    Dover Publications, New York.

    Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing.
    Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471.

    Examples
    --------
    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> np.blackman(12)
    array([-1.38777878e-17,   3.26064346e-02,   1.59903635e-01, # may vary
            4.14397981e-01,   7.36045180e-01,   9.67046769e-01,
            9.67046769e-01,   7.36045180e-01,   4.14397981e-01,
            1.59903635e-01,   3.26064346e-02,  -1.38777878e-17])

    Plot the window and the frequency response.

    .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from numpy.fft import fft, fftshift
        window = np.blackman(51)
        plt.plot(window)
        plt.title("Blackman window")
        plt.ylabel("Amplitude")
        plt.xlabel("Sample")
        plt.show()  # doctest: +SKIP

        plt.figure()
        A = fft(window, 2048) / 25.5
        mag = np.abs(fftshift(A))
        freq = np.linspace(-0.5, 0.5, len(A))
        with np.errstate(divide='ignore', invalid='ignore'):
            response = 20 * np.log10(mag)
        response = np.clip(response, -100, 100)
        plt.plot(freq, response)
        plt.title("Frequency response of Blackman window")
        plt.ylabel("Magnitude [dB]")
        plt.xlabel("Normalized frequency [cycles per sample]")
        plt.axis('tight')
        plt.show()

Python Library Documentation: function block in module autograd.tracer

block(*args, called_by_autograd_dispatcher=False, **kwargs)
    Assemble an nd-array from nested lists of blocks.

    Blocks in the innermost lists are concatenated (see `concatenate`) along
    the last dimension (-1), then these are concatenated along the
    second-last dimension (-2), and so on until the outermost list is reached.

    Blocks can be of any dimension, but will not be broadcasted using
    the normal rules. Instead, leading axes of size 1 are inserted,
    to make ``block.ndim`` the same for all blocks. This is primarily useful
    for working with scalars, and means that code like ``np.block([v, 1])``
    is valid, where ``v.ndim == 1``.

    When the nested list is two levels deep, this allows block matrices to be
    constructed from their components.

    .. versionadded:: 1.13.0

    Parameters
    ----------
    arrays : nested list of array_like or scalars (but not tuples)
        If passed a single ndarray or scalar (a nested list of depth 0), this
        is returned unmodified (and not copied).

        Elements shapes must match along the appropriate axes (without
        broadcasting), but leading 1s will be prepended to the shape as
        necessary to make the dimensions match.

    Returns
    -------
    block_array : ndarray
        The array assembled from the given blocks.

        The dimensionality of the output is equal to the greatest of:

        * the dimensionality of all the inputs
        * the depth to which the input list is nested

    Raises
    ------
    ValueError
        * If list depths are mismatched - for instance, ``[[a, b], c]`` is
          illegal, and should be spelt ``[[a, b], [c]]``
        * If lists are empty - for instance, ``[[a, b], []]``

    See Also
    --------
    concatenate : Join a sequence of arrays along an existing axis.
    stack : Join a sequence of arrays along a new axis.
    vstack : Stack arrays in sequence vertically (row wise).
    hstack : Stack arrays in sequence horizontally (column wise).
    dstack : Stack arrays in sequence depth wise (along third axis).
    column_stack : Stack 1-D arrays as columns into a 2-D array.
    vsplit : Split an array into multiple sub-arrays vertically (row-wise).
    unstack : Split an array into a tuple of sub-arrays along an axis.

    Notes
    -----

    When called with only scalars, ``np.block`` is equivalent to an ndarray
    call. So ``np.block([[1, 2], [3, 4]])`` is equivalent to
    ``np.array([[1, 2], [3, 4]])``.

    This function does not enforce that the blocks lie on a fixed grid.
    ``np.block([[a, b], [c, d]])`` is not restricted to arrays of the form::

        AAAbb
        AAAbb
        cccDD

    But is also allowed to produce, for some ``a, b, c, d``::

        AAAbb
        AAAbb
        cDDDD

    Since concatenation happens along the last axis first, `block` is *not*
    capable of producing the following directly::

        AAAbb
        cccbb
        cccDD

    Matlab's "square bracket stacking", ``[A, B, ...; p, q, ...]``, is
    equivalent to ``np.block([[A, B, ...], [p, q, ...]])``.

    Examples
    --------
    The most common use of this function is to build a block matrix:

    >>> import numpy as np
    >>> A = np.eye(2) * 2
    >>> B = np.eye(3) * 3
    >>> np.block([
    ...     [A,               np.zeros((2, 3))],
    ...     [np.ones((3, 2)), B               ]
    ... ])
    array([[2., 0., 0., 0., 0.],
           [0., 2., 0., 0., 0.],
           [1., 1., 3., 0., 0.],
           [1., 1., 0., 3., 0.],
           [1., 1., 0., 0., 3.]])

    With a list of depth 1, `block` can be used as `hstack`:

    >>> np.block([1, 2, 3])              # hstack([1, 2, 3])
    array([1, 2, 3])

    >>> a = np.array([1, 2, 3])
    >>> b = np.array([4, 5, 6])
    >>> np.block([a, b, 10])             # hstack([a, b, 10])
    array([ 1,  2,  3,  4,  5,  6, 10])

    >>> A = np.ones((2, 2), int)
    >>> B = 2 * A
    >>> np.block([A, B])                 # hstack([A, B])
    array([[1, 1, 2, 2],
           [1, 1, 2, 2]])

    With a list of depth 2, `block` can be used in place of `vstack`:

    >>> a = np.array([1, 2, 3])
    >>> b = np.array([4, 5, 6])
    >>> np.block([[a], [b]])             # vstack([a, b])
    array([[1, 2, 3],
           [4, 5, 6]])

    >>> A = np.ones((2, 2), int)
    >>> B = 2 * A
    >>> np.block([[A], [B]])             # vstack([A, B])
    array([[1, 1],
           [1, 1],
           [2, 2],
           [2, 2]])

    It can also be used in place of `atleast_1d` and `atleast_2d`:

    >>> a = np.array(0)
    >>> b = np.array([1])
    >>> np.block([a])                    # atleast_1d(a)
    array([0])
    >>> np.block([b])                    # atleast_1d(b)
    array([1])

    >>> np.block([[a]])                  # atleast_2d(a)
    array([[0]])
    >>> np.block([[b]])                  # atleast_2d(b)
    array([[1]])

Python Library Documentation: function bmat in module autograd.tracer

bmat(*args, called_by_autograd_dispatcher=False, **kwargs)
    Build a matrix object from a string, nested sequence, or array.

    Parameters
    ----------
    obj : str or array_like
        Input data. If a string, variables in the current scope may be
        referenced by name.
    ldict : dict, optional
        A dictionary that replaces local operands in current frame.
        Ignored if `obj` is not a string or `gdict` is None.
    gdict : dict, optional
        A dictionary that replaces global operands in current frame.
        Ignored if `obj` is not a string.

    Returns
    -------
    out : matrix
        Returns a matrix object, which is a specialized 2-D array.

    See Also
    --------
    block :
        A generalization of this function for N-d arrays, that returns normal
        ndarrays.

    Examples
    --------
    >>> import numpy as np
    >>> A = np.asmatrix('1 1; 1 1')
    >>> B = np.asmatrix('2 2; 2 2')
    >>> C = np.asmatrix('3 4; 5 6')
    >>> D = np.asmatrix('7 8; 9 0')

    All the following expressions construct the same block matrix:

    >>> np.bmat([[A, B], [C, D]])
    matrix([[1, 1, 2, 2],
            [1, 1, 2, 2],
            [3, 4, 7, 8],
            [5, 6, 9, 0]])
    >>> np.bmat(np.r_[np.c_[A, B], np.c_[C, D]])
    matrix([[1, 1, 2, 2],
            [1, 1, 2, 2],
            [3, 4, 7, 8],
            [5, 6, 9, 0]])
    >>> np.bmat('A,B; C,D')
    matrix([[1, 1, 2, 2],
            [1, 1, 2, 2],
            [3, 4, 7, 8],
            [5, 6, 9, 0]])

Python Library Documentation: class bool in module numpy

class bool(generic)
 |  Boolean type (True or False), stored as a byte.
 |
 |  .. warning::
 |
 |     The :class:`bool` type is not a subclass of the :class:`int_` type
 |     (the :class:`bool` is not even a number type). This is different
 |     than Python's default implementation of :class:`bool` as a
 |     sub-class of :class:`int`.
 |
 |  :Character code: ``'?'``
 |
 |  Method resolution order:
 |      bool
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class bool in module numpy

class bool(generic)
 |  Boolean type (True or False), stored as a byte.
 |
 |  .. warning::
 |
 |     The :class:`bool` type is not a subclass of the :class:`int_` type
 |     (the :class:`bool` is not even a number type). This is different
 |     than Python's default implementation of :class:`bool` as a
 |     sub-class of :class:`int`.
 |
 |  :Character code: ``'?'``
 |
 |  Method resolution order:
 |      bool
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class broadcast in module numpy

class broadcast(builtins.object)
 |  Produce an object that mimics broadcasting.
 |
 |  Parameters
 |  ----------
 |  in1, in2, ... : array_like
 |      Input parameters.
 |
 |  Returns
 |  -------
 |  b : broadcast object
 |      Broadcast the input parameters against one another, and
 |      return an object that encapsulates the result.
 |      Amongst others, it has ``shape`` and ``nd`` properties, and
 |      may be used as an iterator.
 |
 |  See Also
 |  --------
 |  broadcast_arrays
 |  broadcast_to
 |  broadcast_shapes
 |
 |  Examples
 |  --------
 |
 |  Manually adding two vectors, using broadcasting:
 |
 |  >>> import numpy as np
 |  >>> x = np.array([[1], [2], [3]])
 |  >>> y = np.array([4, 5, 6])
 |  >>> b = np.broadcast(x, y)
 |
 |  >>> out = np.empty(b.shape)
 |  >>> out.flat = [u+v for (u,v) in b]
 |  >>> out
 |  array([[5.,  6.,  7.],
 |         [6.,  7.,  8.],
 |         [7.,  8.,  9.]])
 |
 |  Compare against built-in broadcasting:
 |
 |  >>> x + y
 |  array([[5, 6, 7],
 |         [6, 7, 8],
 |         [7, 8, 9]])
 |
 |  Methods defined here:
 |
 |  __iter__(self, /)
 |      Implement iter(self).
 |
 |  __next__(self, /)
 |      Implement next(self).
 |
 |  reset(...)
 |      reset()
 |
 |      Reset the broadcasted result's iterator(s).
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      None
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 3])
 |      >>> y = np.array([[4], [5], [6]])
 |      >>> b = np.broadcast(x, y)
 |      >>> b.index
 |      0
 |      >>> next(b), next(b), next(b)
 |      ((1, 4), (2, 4), (3, 4))
 |      >>> b.index
 |      3
 |      >>> b.reset()
 |      >>> b.index
 |      0
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  index
 |      current index in broadcasted result
 |
 |      Examples
 |      --------
 |
 |      >>> import numpy as np
 |      >>> x = np.array([[1], [2], [3]])
 |      >>> y = np.array([4, 5, 6])
 |      >>> b = np.broadcast(x, y)
 |      >>> b.index
 |      0
 |      >>> next(b), next(b), next(b)
 |      ((1, 4), (1, 5), (1, 6))
 |      >>> b.index
 |      3
 |
 |  iters
 |      tuple of iterators along ``self``'s "components."
 |
 |      Returns a tuple of `numpy.flatiter` objects, one for each "component"
 |      of ``self``.
 |
 |      See Also
 |      --------
 |      numpy.flatiter
 |
 |      Examples
 |      --------
 |
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 3])
 |      >>> y = np.array([[4], [5], [6]])
 |      >>> b = np.broadcast(x, y)
 |      >>> row, col = b.iters
 |      >>> next(row), next(col)
 |      (1, 4)
 |
 |  nd
 |      Number of dimensions of broadcasted result. For code intended for NumPy
 |      1.12.0 and later the more consistent `ndim` is preferred.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 3])
 |      >>> y = np.array([[4], [5], [6]])
 |      >>> b = np.broadcast(x, y)
 |      >>> b.nd
 |      2
 |
 |  ndim
 |      Number of dimensions of broadcasted result. Alias for `nd`.
 |
 |      .. versionadded:: 1.12.0
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 3])
 |      >>> y = np.array([[4], [5], [6]])
 |      >>> b = np.broadcast(x, y)
 |      >>> b.ndim
 |      2
 |
 |  numiter
 |      Number of iterators possessed by the broadcasted result.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 3])
 |      >>> y = np.array([[4], [5], [6]])
 |      >>> b = np.broadcast(x, y)
 |      >>> b.numiter
 |      2
 |
 |  shape
 |      Shape of broadcasted result.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 3])
 |      >>> y = np.array([[4], [5], [6]])
 |      >>> b = np.broadcast(x, y)
 |      >>> b.shape
 |      (3, 3)
 |
 |  size
 |      Total size of broadcasted result.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 3])
 |      >>> y = np.array([[4], [5], [6]])
 |      >>> b = np.broadcast(x, y)
 |      >>> b.size
 |      9

Python Library Documentation: function broadcast_arrays in module autograd.tracer

broadcast_arrays(*args, called_by_autograd_dispatcher=False, **kwargs)
    Broadcast any number of arrays against each other.

    Parameters
    ----------
    *args : array_likes
        The arrays to broadcast.

    subok : bool, optional
        If True, then sub-classes will be passed-through, otherwise
        the returned arrays will be forced to be a base-class array (default).

    Returns
    -------
    broadcasted : tuple of arrays
        These arrays are views on the original arrays.  They are typically
        not contiguous.  Furthermore, more than one element of a
        broadcasted array may refer to a single memory location. If you need
        to write to the arrays, make copies first. While you can set the
        ``writable`` flag True, writing to a single output value may end up
        changing more than one location in the output array.

        .. deprecated:: 1.17
            The output is currently marked so that if written to, a deprecation
            warning will be emitted. A future version will set the
            ``writable`` flag False so writing to it will raise an error.

    See Also
    --------
    broadcast
    broadcast_to
    broadcast_shapes

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([[1,2,3]])
    >>> y = np.array([[4],[5]])
    >>> np.broadcast_arrays(x, y)
    (array([[1, 2, 3],
            [1, 2, 3]]),
     array([[4, 4, 4],
            [5, 5, 5]]))

    Here is a useful idiom for getting contiguous copies instead of
    non-contiguous views.

    >>> [np.array(a) for a in np.broadcast_arrays(x, y)]
    [array([[1, 2, 3],
            [1, 2, 3]]),
     array([[4, 4, 4],
            [5, 5, 5]])]

Python Library Documentation: function broadcast_shapes in module autograd.tracer

broadcast_shapes(*args, called_by_autograd_dispatcher=False, **kwargs)
    Broadcast the input shapes into a single shape.

    :ref:`Learn more about broadcasting here <basics.broadcasting>`.

    .. versionadded:: 1.20.0

    Parameters
    ----------
    *args : tuples of ints, or ints
        The shapes to be broadcast against each other.

    Returns
    -------
    tuple
        Broadcasted shape.

    Raises
    ------
    ValueError
        If the shapes are not compatible and cannot be broadcast according
        to NumPy's broadcasting rules.

    See Also
    --------
    broadcast
    broadcast_arrays
    broadcast_to

    Examples
    --------
    >>> import numpy as np
    >>> np.broadcast_shapes((1, 2), (3, 1), (3, 2))
    (3, 2)

    >>> np.broadcast_shapes((6, 7), (5, 6, 1), (7,), (5, 1, 7))
    (5, 6, 7)

Python Library Documentation: function broadcast_to in module autograd.tracer

broadcast_to(*args, called_by_autograd_dispatcher=False, **kwargs)
    Broadcast an array to a new shape.

    Parameters
    ----------
    array : array_like
        The array to broadcast.
    shape : tuple or int
        The shape of the desired array. A single integer ``i`` is interpreted
        as ``(i,)``.
    subok : bool, optional
        If True, then sub-classes will be passed-through, otherwise
        the returned array will be forced to be a base-class array (default).

    Returns
    -------
    broadcast : array
        A readonly view on the original array with the given shape. It is
        typically not contiguous. Furthermore, more than one element of a
        broadcasted array may refer to a single memory location.

    Raises
    ------
    ValueError
        If the array is not compatible with the new shape according to NumPy's
        broadcasting rules.

    See Also
    --------
    broadcast
    broadcast_arrays
    broadcast_shapes

    Notes
    -----
    .. versionadded:: 1.10.0

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([1, 2, 3])
    >>> np.broadcast_to(x, (3, 3))
    array([[1, 2, 3],
           [1, 2, 3],
           [1, 2, 3]])

Python Library Documentation: function busday_count in module autograd.tracer

busday_count(*args, called_by_autograd_dispatcher=False, **kwargs)
    busday_count(
        begindates,
        enddates,
        weekmask='1111100',
        holidays=[],
        busdaycal=None,
        out=None
    )

    Counts the number of valid days between `begindates` and
    `enddates`, not including the day of `enddates`.

    If ``enddates`` specifies a date value that is earlier than the
    corresponding ``begindates`` date value, the count will be negative.

    .. versionadded:: 1.7.0

    Parameters
    ----------
    begindates : array_like of datetime64[D]
        The array of the first dates for counting.
    enddates : array_like of datetime64[D]
        The array of the end dates for counting, which are excluded
        from the count themselves.
    weekmask : str or array_like of bool, optional
        A seven-element array indicating which of Monday through Sunday are
        valid days. May be specified as a length-seven list or array, like
        [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string
        like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for
        weekdays, optionally separated by white space. Valid abbreviations
        are: Mon Tue Wed Thu Fri Sat Sun
    holidays : array_like of datetime64[D], optional
        An array of dates to consider as invalid dates.  They may be
        specified in any order, and NaT (not-a-time) dates are ignored.
        This list is saved in a normalized form that is suited for
        fast calculations of valid days.
    busdaycal : busdaycalendar, optional
        A `busdaycalendar` object which specifies the valid days. If this
        parameter is provided, neither weekmask nor holidays may be
        provided.
    out : array of int, optional
        If provided, this array is filled with the result.

    Returns
    -------
    out : array of int
        An array with a shape from broadcasting ``begindates`` and ``enddates``
        together, containing the number of valid days between
        the begin and end dates.

    See Also
    --------
    busdaycalendar : An object that specifies a custom set of valid days.
    is_busday : Returns a boolean array indicating valid days.
    busday_offset : Applies an offset counted in valid days.

    Examples
    --------
    >>> import numpy as np
    >>> # Number of weekdays in January 2011
    ... np.busday_count('2011-01', '2011-02')
    21
    >>> # Number of weekdays in 2011
    >>> np.busday_count('2011', '2012')
    260
    >>> # Number of Saturdays in 2011
    ... np.busday_count('2011', '2012', weekmask='Sat')
    53

Python Library Documentation: function busday_offset in module autograd.tracer

busday_offset(*args, called_by_autograd_dispatcher=False, **kwargs)
    busday_offset(
        dates,
        offsets,
        roll='raise',
        weekmask='1111100',
        holidays=None,
        busdaycal=None,
        out=None
    )

    First adjusts the date to fall on a valid day according to
    the ``roll`` rule, then applies offsets to the given dates
    counted in valid days.

    .. versionadded:: 1.7.0

    Parameters
    ----------
    dates : array_like of datetime64[D]
        The array of dates to process.
    offsets : array_like of int
        The array of offsets, which is broadcast with ``dates``.
    roll : {'raise', 'nat', 'forward', 'following', 'backward', 'preceding',         'modifiedfollowing', 'modifiedpreceding'}, optional
        How to treat dates that do not fall on a valid day. The default
        is 'raise'.

        * 'raise' means to raise an exception for an invalid day.
        * 'nat' means to return a NaT (not-a-time) for an invalid day.
        * 'forward' and 'following' mean to take the first valid day
          later in time.
        * 'backward' and 'preceding' mean to take the first valid day
          earlier in time.
        * 'modifiedfollowing' means to take the first valid day
          later in time unless it is across a Month boundary, in which
          case to take the first valid day earlier in time.
        * 'modifiedpreceding' means to take the first valid day
          earlier in time unless it is across a Month boundary, in which
          case to take the first valid day later in time.
    weekmask : str or array_like of bool, optional
        A seven-element array indicating which of Monday through Sunday are
        valid days. May be specified as a length-seven list or array, like
        [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string
        like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for
        weekdays, optionally separated by white space. Valid abbreviations
        are: Mon Tue Wed Thu Fri Sat Sun
    holidays : array_like of datetime64[D], optional
        An array of dates to consider as invalid dates.  They may be
        specified in any order, and NaT (not-a-time) dates are ignored.
        This list is saved in a normalized form that is suited for
        fast calculations of valid days.
    busdaycal : busdaycalendar, optional
        A `busdaycalendar` object which specifies the valid days. If this
        parameter is provided, neither weekmask nor holidays may be
        provided.
    out : array of datetime64[D], optional
        If provided, this array is filled with the result.

    Returns
    -------
    out : array of datetime64[D]
        An array with a shape from broadcasting ``dates`` and ``offsets``
        together, containing the dates with offsets applied.

    See Also
    --------
    busdaycalendar : An object that specifies a custom set of valid days.
    is_busday : Returns a boolean array indicating valid days.
    busday_count : Counts how many valid days are in a half-open date range.

    Examples
    --------
    >>> import numpy as np
    >>> # First business day in October 2011 (not accounting for holidays)
    ... np.busday_offset('2011-10', 0, roll='forward')
    np.datetime64('2011-10-03')
    >>> # Last business day in February 2012 (not accounting for holidays)
    ... np.busday_offset('2012-03', -1, roll='forward')
    np.datetime64('2012-02-29')
    >>> # Third Wednesday in January 2011
    ... np.busday_offset('2011-01', 2, roll='forward', weekmask='Wed')
    np.datetime64('2011-01-19')
    >>> # 2012 Mother's Day in Canada and the U.S.
    ... np.busday_offset('2012-05', 1, roll='forward', weekmask='Sun')
    np.datetime64('2012-05-13')

    >>> # First business day on or after a date
    ... np.busday_offset('2011-03-20', 0, roll='forward')
    np.datetime64('2011-03-21')
    >>> np.busday_offset('2011-03-22', 0, roll='forward')
    np.datetime64('2011-03-22')
    >>> # First business day after a date
    ... np.busday_offset('2011-03-20', 1, roll='backward')
    np.datetime64('2011-03-21')
    >>> np.busday_offset('2011-03-22', 1, roll='backward')
    np.datetime64('2011-03-23')

Python Library Documentation: class busdaycalendar in module numpy

class busdaycalendar(builtins.object)
 |  busdaycalendar(weekmask='1111100', holidays=None)
 |
 |  A business day calendar object that efficiently stores information
 |  defining valid days for the busday family of functions.
 |
 |  The default valid days are Monday through Friday ("business days").
 |  A busdaycalendar object can be specified with any set of weekly
 |  valid days, plus an optional "holiday" dates that always will be invalid.
 |
 |  Once a busdaycalendar object is created, the weekmask and holidays
 |  cannot be modified.
 |
 |  .. versionadded:: 1.7.0
 |
 |  Parameters
 |  ----------
 |  weekmask : str or array_like of bool, optional
 |      A seven-element array indicating which of Monday through Sunday are
 |      valid days. May be specified as a length-seven list or array, like
 |      [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string
 |      like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for
 |      weekdays, optionally separated by white space. Valid abbreviations
 |      are: Mon Tue Wed Thu Fri Sat Sun
 |  holidays : array_like of datetime64[D], optional
 |      An array of dates to consider as invalid dates, no matter which
 |      weekday they fall upon.  Holiday dates may be specified in any
 |      order, and NaT (not-a-time) dates are ignored.  This list is
 |      saved in a normalized form that is suited for fast calculations
 |      of valid days.
 |
 |  Returns
 |  -------
 |  out : busdaycalendar
 |      A business day calendar object containing the specified
 |      weekmask and holidays values.
 |
 |  See Also
 |  --------
 |  is_busday : Returns a boolean array indicating valid days.
 |  busday_offset : Applies an offset counted in valid days.
 |  busday_count : Counts how many valid days are in a half-open date range.
 |
 |  Attributes
 |  ----------
 |  weekmask : (copy) seven-element array of bool
 |  holidays : (copy) sorted array of datetime64[D]
 |
 |  Notes
 |  -----
 |  Once a busdaycalendar object is created, you cannot modify the
 |  weekmask or holidays.  The attributes return copies of internal data.
 |
 |  Examples
 |  --------
 |  >>> import numpy as np
 |  >>> # Some important days in July
 |  ... bdd = np.busdaycalendar(
 |  ...             holidays=['2011-07-01', '2011-07-04', '2011-07-17'])
 |  >>> # Default is Monday to Friday weekdays
 |  ... bdd.weekmask
 |  array([ True,  True,  True,  True,  True, False, False])
 |  >>> # Any holidays already on the weekend are removed
 |  ... bdd.holidays
 |  array(['2011-07-01', '2011-07-04'], dtype='datetime64[D]')
 |
 |  Methods defined here:
 |
 |  __init__(self, /, *args, **kwargs)
 |      Initialize self.  See help(type(self)) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  holidays
 |      A copy of the holiday array indicating additional invalid days.
 |
 |  weekmask
 |      A copy of the seven-element boolean mask indicating valid days.

Python Library Documentation: class IntdtypeSubclass in module autograd.numpy.numpy_wrapper

class IntdtypeSubclass(numpy.int8)
 |  IntdtypeSubclass(*args, **kwargs)
 |
 |  Method resolution order:
 |      IntdtypeSubclass
 |      numpy.int8
 |      numpy.signedinteger
 |      numpy.integer
 |      numpy.number
 |      numpy.generic
 |      builtins.object
 |
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs) from autograd.tracer.notrace_primitive.<locals>
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.int8:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      int8.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.int8(127).bit_count()
 |      7
 |      >>> np.int8(-127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from numpy.int8:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class bytes_ in module numpy

class bytes_(builtins.bytes, character)
 |  A byte string.
 |
 |  When used in arrays, this type strips trailing null bytes.
 |
 |  :Character code: ``'S'``
 |
 |  Method resolution order:
 |      bytes_
 |      builtins.bytes
 |      character
 |      flexible
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from builtins.bytes:
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __bytes__(self, /)
 |      Convert this value to exact type bytes.
 |
 |  __contains__(self, key, /)
 |      Return bool(key in self).
 |
 |  __getattribute__(self, name, /)
 |      Return getattr(self, name).
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __getnewargs__(...)
 |
 |  __iter__(self, /)
 |      Implement iter(self).
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  capitalize(...)
 |      B.capitalize() -> copy of B
 |
 |      Return a copy of B with only its first character capitalized (ASCII)
 |      and the rest lower-cased.
 |
 |  center(self, width, fillchar=b' ', /)
 |      Return a centered string of length width.
 |
 |      Padding is done using the specified fill character.
 |
 |  count(...)
 |      B.count(sub[, start[, end]]) -> int
 |
 |      Return the number of non-overlapping occurrences of subsection sub in
 |      bytes B[start:end].  Optional arguments start and end are interpreted
 |      as in slice notation.
 |
 |  decode(self, /, encoding='utf-8', errors='strict')
 |      Decode the bytes using the codec registered for encoding.
 |
 |      encoding
 |        The encoding with which to decode the bytes.
 |      errors
 |        The error handling scheme to use for the handling of decoding errors.
 |        The default is 'strict' meaning that decoding errors raise a
 |        UnicodeDecodeError. Other possible values are 'ignore' and 'replace'
 |        as well as any other name registered with codecs.register_error that
 |        can handle UnicodeDecodeErrors.
 |
 |  endswith(...)
 |      B.endswith(suffix[, start[, end]]) -> bool
 |
 |      Return True if B ends with the specified suffix, False otherwise.
 |      With optional start, test B beginning at that position.
 |      With optional end, stop comparing B at that position.
 |      suffix can also be a tuple of bytes to try.
 |
 |  expandtabs(self, /, tabsize=8)
 |      Return a copy where all tab characters are expanded using spaces.
 |
 |      If tabsize is not given, a tab size of 8 characters is assumed.
 |
 |  find(...)
 |      B.find(sub[, start[, end]]) -> int
 |
 |      Return the lowest index in B where subsection sub is found,
 |      such that sub is contained within B[start,end].  Optional
 |      arguments start and end are interpreted as in slice notation.
 |
 |      Return -1 on failure.
 |
 |  hex(...)
 |      Create a string of hexadecimal numbers from a bytes object.
 |
 |        sep
 |          An optional single character or byte to separate hex bytes.
 |        bytes_per_sep
 |          How many bytes between separators.  Positive values count from the
 |          right, negative values count from the left.
 |
 |      Example:
 |      >>> value = b'\xb9\x01\xef'
 |      >>> value.hex()
 |      'b901ef'
 |      >>> value.hex(':')
 |      'b9:01:ef'
 |      >>> value.hex(':', 2)
 |      'b9:01ef'
 |      >>> value.hex(':', -2)
 |      'b901:ef'
 |
 |  index(...)
 |      B.index(sub[, start[, end]]) -> int
 |
 |      Return the lowest index in B where subsection sub is found,
 |      such that sub is contained within B[start,end].  Optional
 |      arguments start and end are interpreted as in slice notation.
 |
 |      Raises ValueError when the subsection is not found.
 |
 |  isalnum(...)
 |      B.isalnum() -> bool
 |
 |      Return True if all characters in B are alphanumeric
 |      and there is at least one character in B, False otherwise.
 |
 |  isalpha(...)
 |      B.isalpha() -> bool
 |
 |      Return True if all characters in B are alphabetic
 |      and there is at least one character in B, False otherwise.
 |
 |  isascii(...)
 |      B.isascii() -> bool
 |
 |      Return True if B is empty or all characters in B are ASCII,
 |      False otherwise.
 |
 |  isdigit(...)
 |      B.isdigit() -> bool
 |
 |      Return True if all characters in B are digits
 |      and there is at least one character in B, False otherwise.
 |
 |  islower(...)
 |      B.islower() -> bool
 |
 |      Return True if all cased characters in B are lowercase and there is
 |      at least one cased character in B, False otherwise.
 |
 |  isspace(...)
 |      B.isspace() -> bool
 |
 |      Return True if all characters in B are whitespace
 |      and there is at least one character in B, False otherwise.
 |
 |  istitle(...)
 |      B.istitle() -> bool
 |
 |      Return True if B is a titlecased string and there is at least one
 |      character in B, i.e. uppercase characters may only follow uncased
 |      characters and lowercase characters only cased ones. Return False
 |      otherwise.
 |
 |  isupper(...)
 |      B.isupper() -> bool
 |
 |      Return True if all cased characters in B are uppercase and there is
 |      at least one cased character in B, False otherwise.
 |
 |  join(self, iterable_of_bytes, /)
 |      Concatenate any number of bytes objects.
 |
 |      The bytes whose method is called is inserted in between each pair.
 |
 |      The result is returned as a new bytes object.
 |
 |      Example: b'.'.join([b'ab', b'pq', b'rs']) -> b'ab.pq.rs'.
 |
 |  ljust(self, width, fillchar=b' ', /)
 |      Return a left-justified string of length width.
 |
 |      Padding is done using the specified fill character.
 |
 |  lower(...)
 |      B.lower() -> copy of B
 |
 |      Return a copy of B with all ASCII characters converted to lowercase.
 |
 |  lstrip(self, bytes=None, /)
 |      Strip leading bytes contained in the argument.
 |
 |      If the argument is omitted or None, strip leading  ASCII whitespace.
 |
 |  partition(self, sep, /)
 |      Partition the bytes into three parts using the given separator.
 |
 |      This will search for the separator sep in the bytes. If the separator is found,
 |      returns a 3-tuple containing the part before the separator, the separator
 |      itself, and the part after it.
 |
 |      If the separator is not found, returns a 3-tuple containing the original bytes
 |      object and two empty bytes objects.
 |
 |  removeprefix(self, prefix, /)
 |      Return a bytes object with the given prefix string removed if present.
 |
 |      If the bytes starts with the prefix string, return bytes[len(prefix):].
 |      Otherwise, return a copy of the original bytes.
 |
 |  removesuffix(self, suffix, /)
 |      Return a bytes object with the given suffix string removed if present.
 |
 |      If the bytes ends with the suffix string and that suffix is not empty,
 |      return bytes[:-len(prefix)].  Otherwise, return a copy of the original
 |      bytes.
 |
 |  replace(self, old, new, count=-1, /)
 |      Return a copy with all occurrences of substring old replaced by new.
 |
 |        count
 |          Maximum number of occurrences to replace.
 |          -1 (the default value) means replace all occurrences.
 |
 |      If the optional argument count is given, only the first count occurrences are
 |      replaced.
 |
 |  rfind(...)
 |      B.rfind(sub[, start[, end]]) -> int
 |
 |      Return the highest index in B where subsection sub is found,
 |      such that sub is contained within B[start,end].  Optional
 |      arguments start and end are interpreted as in slice notation.
 |
 |      Return -1 on failure.
 |
 |  rindex(...)
 |      B.rindex(sub[, start[, end]]) -> int
 |
 |      Return the highest index in B where subsection sub is found,
 |      such that sub is contained within B[start,end].  Optional
 |      arguments start and end are interpreted as in slice notation.
 |
 |      Raise ValueError when the subsection is not found.
 |
 |  rjust(self, width, fillchar=b' ', /)
 |      Return a right-justified string of length width.
 |
 |      Padding is done using the specified fill character.
 |
 |  rpartition(self, sep, /)
 |      Partition the bytes into three parts using the given separator.
 |
 |      This will search for the separator sep in the bytes, starting at the end. If
 |      the separator is found, returns a 3-tuple containing the part before the
 |      separator, the separator itself, and the part after it.
 |
 |      If the separator is not found, returns a 3-tuple containing two empty bytes
 |      objects and the original bytes object.
 |
 |  rsplit(self, /, sep=None, maxsplit=-1)
 |      Return a list of the sections in the bytes, using sep as the delimiter.
 |
 |        sep
 |          The delimiter according which to split the bytes.
 |          None (the default value) means split on ASCII whitespace characters
 |          (space, tab, return, newline, formfeed, vertical tab).
 |        maxsplit
 |          Maximum number of splits to do.
 |          -1 (the default value) means no limit.
 |
 |      Splitting is done starting at the end of the bytes and working to the front.
 |
 |  rstrip(self, bytes=None, /)
 |      Strip trailing bytes contained in the argument.
 |
 |      If the argument is omitted or None, strip trailing ASCII whitespace.
 |
 |  split(self, /, sep=None, maxsplit=-1)
 |      Return a list of the sections in the bytes, using sep as the delimiter.
 |
 |      sep
 |        The delimiter according which to split the bytes.
 |        None (the default value) means split on ASCII whitespace characters
 |        (space, tab, return, newline, formfeed, vertical tab).
 |      maxsplit
 |        Maximum number of splits to do.
 |        -1 (the default value) means no limit.
 |
 |  splitlines(self, /, keepends=False)
 |      Return a list of the lines in the bytes, breaking at line boundaries.
 |
 |      Line breaks are not included in the resulting list unless keepends is given and
 |      true.
 |
 |  startswith(...)
 |      B.startswith(prefix[, start[, end]]) -> bool
 |
 |      Return True if B starts with the specified prefix, False otherwise.
 |      With optional start, test B beginning at that position.
 |      With optional end, stop comparing B at that position.
 |      prefix can also be a tuple of bytes to try.
 |
 |  strip(self, bytes=None, /)
 |      Strip leading and trailing bytes contained in the argument.
 |
 |      If the argument is omitted or None, strip leading and trailing ASCII whitespace.
 |
 |  swapcase(...)
 |      B.swapcase() -> copy of B
 |
 |      Return a copy of B with uppercase ASCII characters converted
 |      to lowercase ASCII and vice versa.
 |
 |  title(...)
 |      B.title() -> copy of B
 |
 |      Return a titlecased version of B, i.e. ASCII words start with uppercase
 |      characters, all remaining cased characters have lowercase.
 |
 |  translate(self, table, /, delete=b'')
 |      Return a copy with each character mapped by the given translation table.
 |
 |        table
 |          Translation table, which must be a bytes object of length 256.
 |
 |      All characters occurring in the optional argument delete are removed.
 |      The remaining characters are mapped through the given translation table.
 |
 |  upper(...)
 |      B.upper() -> copy of B
 |
 |      Return a copy of B with all ASCII characters converted to uppercase.
 |
 |  zfill(self, width, /)
 |      Pad a numeric string with zeros on the left, to fill a field of the given width.
 |
 |      The original string is never truncated.
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from builtins.bytes:
 |
 |  fromhex(string, /)
 |      Create a bytes object from a string of hexadecimal numbers.
 |
 |      Spaces between two numbers are accepted.
 |      Example: bytes.fromhex('B9 01EF') -> b'\\xb9\\x01\\xef'.
 |
 |  ----------------------------------------------------------------------
 |  Static methods inherited from builtins.bytes:
 |
 |  maketrans(frm, to, /)
 |      Return a translation table useable for the bytes or bytearray translate method.
 |
 |      The returned table will be one where each byte in frm is mapped to the byte at
 |      the same position in to.
 |
 |      The bytes objects frm and to must be of the same length.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: c_class in module autograd.numpy.numpy_wrapper object

class c_class(builtins.object)
 |  Methods defined here:
 |
 |  __getitem__(self, args)
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object

Python Library Documentation: class c_class in module autograd.numpy.numpy_wrapper

class c_class(builtins.object)
 |  Methods defined here:
 |
 |  __getitem__(self, args)
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object

Python Library Documentation: function can_cast in module autograd.tracer

can_cast(*args, called_by_autograd_dispatcher=False, **kwargs)
    can_cast(from_, to, casting='safe')

    Returns True if cast between data types can occur according to the
    casting rule.

    Parameters
    ----------
    from_ : dtype, dtype specifier, NumPy scalar, or array
        Data type, NumPy scalar, or array to cast from.
    to : dtype or dtype specifier
        Data type to cast to.
    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
        Controls what kind of data casting may occur.

        * 'no' means the data types should not be cast at all.
        * 'equiv' means only byte-order changes are allowed.
        * 'safe' means only casts which can preserve values are allowed.
        * 'same_kind' means only safe casts or casts within a kind,
          like float64 to float32, are allowed.
        * 'unsafe' means any data conversions may be done.

    Returns
    -------
    out : bool
        True if cast can occur according to the casting rule.

    Notes
    -----
    .. versionchanged:: 1.17.0
       Casting between a simple data type and a structured one is possible only
       for "unsafe" casting.  Casting to multiple fields is allowed, but
       casting from multiple fields is not.

    .. versionchanged:: 1.9.0
       Casting from numeric to string types in 'safe' casting mode requires
       that the string dtype length is long enough to store the maximum
       integer/float value converted.

    .. versionchanged:: 2.0
       This function does not support Python scalars anymore and does not
       apply any value-based logic for 0-D arrays and NumPy scalars.

    See also
    --------
    dtype, result_type

    Examples
    --------
    Basic examples

    >>> import numpy as np
    >>> np.can_cast(np.int32, np.int64)
    True
    >>> np.can_cast(np.float64, complex)
    True
    >>> np.can_cast(complex, float)
    False

    >>> np.can_cast('i8', 'f8')
    True
    >>> np.can_cast('i8', 'f4')
    False
    >>> np.can_cast('i4', 'S4')
    False

Python Library Documentation: function cbrt in module autograd.tracer

cbrt(*args, called_by_autograd_dispatcher=False, **kwargs)
    cbrt(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the cube-root of an array, element-wise.

    .. versionadded:: 1.10.0

    Parameters
    ----------
    x : array_like
        The values whose cube-roots are required.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        An array of the same shape as `x`, containing the
        cube root of each element in `x`.
        If `out` was provided, `y` is a reference to it.
        This is a scalar if `x` is a scalar.


    Examples
    --------
    >>> import numpy as np
    >>> np.cbrt([1,8,27])
    array([ 1.,  2.,  3.])

Python Library Documentation: class complex128 in module numpy

class complex128(complexfloating, builtins.complex)
 |  complex128(real=0, imag=0)
 |
 |  Complex number type composed of two double-precision floating-point
 |  numbers, compatible with Python :class:`complex`.
 |
 |  :Character code: ``'D'``
 |  :Canonical name: `numpy.cdouble`
 |  :Alias on this platform (win32 AMD64): `numpy.complex128`: Complex number type composed of 2 64-bit-precision floating-point numbers.
 |
 |  Method resolution order:
 |      complex128
 |      complexfloating
 |      inexact
 |      number
 |      generic
 |      builtins.complex
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from complexfloating:
 |
 |  __round__(...)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from builtins.complex:
 |
 |  __complex__(self, /)
 |      Convert this value to exact type complex.
 |
 |  __getattribute__(self, name, /)
 |      Return getattr(self, name).
 |
 |  __getnewargs__(self, /)

Python Library Documentation: function ceil in module autograd.tracer

ceil(*args, called_by_autograd_dispatcher=False, **kwargs)
    ceil(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the ceiling of the input, element-wise.

    The ceil of the scalar `x` is the smallest integer `i`, such that
    ``i >= x``.  It is often denoted as :math:`\lceil x \rceil`.

    Parameters
    ----------
    x : array_like
        Input data.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray or scalar
        The ceiling of each element in `x`.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    floor, trunc, rint, fix

    Examples
    --------
    >>> import numpy as np

    >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
    >>> np.ceil(a)
    array([-1., -1., -0.,  1.,  2.,  2.,  2.])

Python Library Documentation: class character in module numpy

class character(flexible)
 |  Abstract base class of all character string scalar types.
 |
 |  Method resolution order:
 |      character
 |      flexible
 |      generic
 |      builtins.object
 |
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes inherited from generic:
 |
 |  __hash__ = None

Python Library Documentation: function choose in module autograd.tracer

choose(*args, called_by_autograd_dispatcher=False, **kwargs)
    Construct an array from an index array and a list of arrays to choose from.

    First of all, if confused or uncertain, definitely look at the Examples -
    in its full generality, this function is less simple than it might
    seem from the following code description (below ndi =
    `numpy.lib.index_tricks`):

    ``np.choose(a,c) == np.array([c[a[I]][I] for I in ndi.ndindex(a.shape)])``.

    But this omits some subtleties.  Here is a fully general summary:

    Given an "index" array (`a`) of integers and a sequence of ``n`` arrays
    (`choices`), `a` and each choice array are first broadcast, as necessary,
    to arrays of a common shape; calling these *Ba* and *Bchoices[i], i =
    0,...,n-1* we have that, necessarily, ``Ba.shape == Bchoices[i].shape``
    for each ``i``.  Then, a new array with shape ``Ba.shape`` is created as
    follows:

    * if ``mode='raise'`` (the default), then, first of all, each element of
      ``a`` (and thus ``Ba``) must be in the range ``[0, n-1]``; now, suppose
      that ``i`` (in that range) is the value at the ``(j0, j1, ..., jm)``
      position in ``Ba`` - then the value at the same position in the new array
      is the value in ``Bchoices[i]`` at that same position;

    * if ``mode='wrap'``, values in `a` (and thus `Ba`) may be any (signed)
      integer; modular arithmetic is used to map integers outside the range
      `[0, n-1]` back into that range; and then the new array is constructed
      as above;

    * if ``mode='clip'``, values in `a` (and thus ``Ba``) may be any (signed)
      integer; negative integers are mapped to 0; values greater than ``n-1``
      are mapped to ``n-1``; and then the new array is constructed as above.

    Parameters
    ----------
    a : int array
        This array must contain integers in ``[0, n-1]``, where ``n`` is the
        number of choices, unless ``mode=wrap`` or ``mode=clip``, in which
        cases any integers are permissible.
    choices : sequence of arrays
        Choice arrays. `a` and all of the choices must be broadcastable to the
        same shape.  If `choices` is itself an array (not recommended), then
        its outermost dimension (i.e., the one corresponding to
        ``choices.shape[0]``) is taken as defining the "sequence".
    out : array, optional
        If provided, the result will be inserted into this array. It should
        be of the appropriate shape and dtype. Note that `out` is always
        buffered if ``mode='raise'``; use other modes for better performance.
    mode : {'raise' (default), 'wrap', 'clip'}, optional
        Specifies how indices outside ``[0, n-1]`` will be treated:

        * 'raise' : an exception is raised
        * 'wrap' : value becomes value mod ``n``
        * 'clip' : values < 0 are mapped to 0, values > n-1 are mapped to n-1

    Returns
    -------
    merged_array : array
        The merged result.

    Raises
    ------
    ValueError: shape mismatch
        If `a` and each choice array are not all broadcastable to the same
        shape.

    See Also
    --------
    ndarray.choose : equivalent method
    numpy.take_along_axis : Preferable if `choices` is an array

    Notes
    -----
    To reduce the chance of misinterpretation, even though the following
    "abuse" is nominally supported, `choices` should neither be, nor be
    thought of as, a single array, i.e., the outermost sequence-like container
    should be either a list or a tuple.

    Examples
    --------

    >>> import numpy as np
    >>> choices = [[0, 1, 2, 3], [10, 11, 12, 13],
    ...   [20, 21, 22, 23], [30, 31, 32, 33]]
    >>> np.choose([2, 3, 1, 0], choices
    ... # the first element of the result will be the first element of the
    ... # third (2+1) "array" in choices, namely, 20; the second element
    ... # will be the second element of the fourth (3+1) choice array, i.e.,
    ... # 31, etc.
    ... )
    array([20, 31, 12,  3])
    >>> np.choose([2, 4, 1, 0], choices, mode='clip') # 4 goes to 3 (4-1)
    array([20, 31, 12,  3])
    >>> # because there are 4 choice arrays
    >>> np.choose([2, 4, 1, 0], choices, mode='wrap') # 4 goes to (4 mod 4)
    array([20,  1, 12,  3])
    >>> # i.e., 0

    A couple examples illustrating how choose broadcasts:

    >>> a = [[1, 0, 1], [0, 1, 0], [1, 0, 1]]
    >>> choices = [-10, 10]
    >>> np.choose(a, choices)
    array([[ 10, -10,  10],
           [-10,  10, -10],
           [ 10, -10,  10]])

    >>> # With thanks to Anne Archibald
    >>> a = np.array([0, 1]).reshape((2,1,1))
    >>> c1 = np.array([1, 2, 3]).reshape((1,3,1))
    >>> c2 = np.array([-1, -2, -3, -4, -5]).reshape((1,1,5))
    >>> np.choose(a, (c1, c2)) # result is 2x3x5, res[0,:,:]=c1, res[1,:,:]=c2
    array([[[ 1,  1,  1,  1,  1],
            [ 2,  2,  2,  2,  2],
            [ 3,  3,  3,  3,  3]],
           [[-1, -2, -3, -4, -5],
            [-1, -2, -3, -4, -5],
            [-1, -2, -3, -4, -5]]])

Python Library Documentation: function clip in module autograd.tracer

clip(*args, called_by_autograd_dispatcher=False, **kwargs)
    Clip (limit) the values in an array.

    Given an interval, values outside the interval are clipped to
    the interval edges.  For example, if an interval of ``[0, 1]``
    is specified, values smaller than 0 become 0, and values larger
    than 1 become 1.

    Equivalent to but faster than ``np.minimum(a_max, np.maximum(a, a_min))``.

    No check is performed to ensure ``a_min < a_max``.

    Parameters
    ----------
    a : array_like
        Array containing elements to clip.
    a_min, a_max : array_like or None
        Minimum and maximum value. If ``None``, clipping is not performed on
        the corresponding edge. If both ``a_min`` and ``a_max`` are ``None``,
        the elements of the returned array stay the same. Both are broadcasted
        against ``a``.
    out : ndarray, optional
        The results will be placed in this array. It may be the input
        array for in-place clipping.  `out` must be of the right shape
        to hold the output.  Its type is preserved.
    min, max : array_like or None
        Array API compatible alternatives for ``a_min`` and ``a_max``
        arguments. Either ``a_min`` and ``a_max`` or ``min`` and ``max``
        can be passed at the same time. Default: ``None``.

        .. versionadded:: 2.1.0
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

        .. versionadded:: 1.17.0

    Returns
    -------
    clipped_array : ndarray
        An array with the elements of `a`, but where values
        < `a_min` are replaced with `a_min`, and those > `a_max`
        with `a_max`.

    See Also
    --------
    :ref:`ufuncs-output-type`

    Notes
    -----
    When `a_min` is greater than `a_max`, `clip` returns an
    array in which all values are equal to `a_max`,
    as shown in the second example.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.arange(10)
    >>> a
    array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
    >>> np.clip(a, 1, 8)
    array([1, 1, 2, 3, 4, 5, 6, 7, 8, 8])
    >>> np.clip(a, 8, 1)
    array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])
    >>> np.clip(a, 3, 6, out=a)
    array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6])
    >>> a
    array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6])
    >>> a = np.arange(10)
    >>> a
    array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
    >>> np.clip(a, [3, 4, 1, 1, 1, 4, 4, 4, 4, 4], 8)
    array([3, 4, 2, 3, 4, 5, 6, 7, 8, 8])

Python Library Documentation: class clongdouble in module numpy

class clongdouble(complexfloating)
 |  Complex number type composed of two extended-precision floating-point
 |  numbers.
 |
 |  :Character code: ``'G'``
 |
 |  Method resolution order:
 |      clongdouble
 |      complexfloating
 |      inexact
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __complex__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from complexfloating:
 |
 |  __round__(...)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: function column_stack in module autograd.numpy.numpy_wrapper

column_stack(tup)

Python Library Documentation: function common_type in module autograd.tracer

common_type(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return a scalar type which is common to the input arrays.

    The return type will always be an inexact (i.e. floating point) scalar
    type, even if all the arrays are integer arrays. If one of the inputs is
    an integer array, the minimum precision type that is returned is a
    64-bit floating point dtype.

    All input arrays except int64 and uint64 can be safely cast to the
    returned dtype without loss of information.

    Parameters
    ----------
    array1, array2, ... : ndarrays
        Input arrays.

    Returns
    -------
    out : data type code
        Data type code.

    See Also
    --------
    dtype, mintypecode

    Examples
    --------
    >>> np.common_type(np.arange(2, dtype=np.float32))
    <class 'numpy.float32'>
    >>> np.common_type(np.arange(2, dtype=np.float32), np.arange(2))
    <class 'numpy.float64'>
    >>> np.common_type(np.arange(4), np.array([45, 6.j]), np.array([45.0]))
    <class 'numpy.complex128'>

Python Library Documentation: class complex128 in module numpy

class complex128(complexfloating, builtins.complex)
 |  complex128(real=0, imag=0)
 |
 |  Complex number type composed of two double-precision floating-point
 |  numbers, compatible with Python :class:`complex`.
 |
 |  :Character code: ``'D'``
 |  :Canonical name: `numpy.cdouble`
 |  :Alias on this platform (win32 AMD64): `numpy.complex128`: Complex number type composed of 2 64-bit-precision floating-point numbers.
 |
 |  Method resolution order:
 |      complex128
 |      complexfloating
 |      inexact
 |      number
 |      generic
 |      builtins.complex
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from complexfloating:
 |
 |  __round__(...)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from builtins.complex:
 |
 |  __complex__(self, /)
 |      Convert this value to exact type complex.
 |
 |  __getattribute__(self, name, /)
 |      Return getattr(self, name).
 |
 |  __getnewargs__(self, /)

Python Library Documentation: class complex64 in module numpy

class complex64(complexfloating)
 |  Complex number type composed of two single-precision floating-point
 |  numbers.
 |
 |  :Character code: ``'F'``
 |  :Canonical name: `numpy.csingle`
 |  :Alias on this platform (win32 AMD64): `numpy.complex64`: Complex number type composed of 2 32-bit-precision floating-point numbers.
 |
 |  Method resolution order:
 |      complex64
 |      complexfloating
 |      inexact
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __complex__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from complexfloating:
 |
 |  __round__(...)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class complexfloating in module numpy

class complexfloating(inexact)
 |  Abstract base class of all complex number scalar types that are made up of
 |  floating-point numbers.
 |
 |  Method resolution order:
 |      complexfloating
 |      inexact
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __round__(...)
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from number:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes inherited from generic:
 |
 |  __hash__ = None

Python Library Documentation: function compress in module autograd.tracer

compress(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return selected slices of an array along given axis.

    When working along a given axis, a slice along that axis is returned in
    `output` for each index where `condition` evaluates to True. When
    working on a 1-D array, `compress` is equivalent to `extract`.

    Parameters
    ----------
    condition : 1-D array of bools
        Array that selects which entries to return. If len(condition)
        is less than the size of `a` along the given axis, then output is
        truncated to the length of the condition array.
    a : array_like
        Array from which to extract a part.
    axis : int, optional
        Axis along which to take slices. If None (default), work on the
        flattened array.
    out : ndarray, optional
        Output array.  Its type is preserved and it must be of the right
        shape to hold the output.

    Returns
    -------
    compressed_array : ndarray
        A copy of `a` without the slices along axis for which `condition`
        is false.

    See Also
    --------
    take, choose, diag, diagonal, select
    ndarray.compress : Equivalent method in ndarray
    extract : Equivalent method when working on 1-D arrays
    :ref:`ufuncs-output-type`

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[1, 2], [3, 4], [5, 6]])
    >>> a
    array([[1, 2],
           [3, 4],
           [5, 6]])
    >>> np.compress([0, 1], a, axis=0)
    array([[3, 4]])
    >>> np.compress([False, True, True], a, axis=0)
    array([[3, 4],
           [5, 6]])
    >>> np.compress([False, True], a, axis=1)
    array([[2],
           [4],
           [6]])

    Working on the flattened array does not return slices along an axis but
    selects elements.

    >>> np.compress([False, True], a)
    array([2])

Python Library Documentation: function concatenate in module autograd.tracer

concatenate(*args, called_by_autograd_dispatcher=False, **kwargs)
    concatenate(
        (a1, a2, ...),
        axis=0,
        out=None,
        dtype=None,
        casting="same_kind"
    )

    Join a sequence of arrays along an existing axis.

    Parameters
    ----------
    a1, a2, ... : sequence of array_like
        The arrays must have the same shape, except in the dimension
        corresponding to `axis` (the first, by default).
    axis : int, optional
        The axis along which the arrays will be joined.  If axis is None,
        arrays are flattened before use.  Default is 0.
    out : ndarray, optional
        If provided, the destination to place the result. The shape must be
        correct, matching that of what concatenate would have returned if no
        out argument were specified.
    dtype : str or dtype
        If provided, the destination array will have this dtype. Cannot be
        provided together with `out`.

        .. versionadded:: 1.20.0

    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
        Controls what kind of data casting may occur. Defaults to 'same_kind'.
        For a description of the options, please see :term:`casting`.

        .. versionadded:: 1.20.0

    Returns
    -------
    res : ndarray
        The concatenated array.

    See Also
    --------
    ma.concatenate : Concatenate function that preserves input masks.
    array_split : Split an array into multiple sub-arrays of equal or
                  near-equal size.
    split : Split array into a list of multiple sub-arrays of equal size.
    hsplit : Split array into multiple sub-arrays horizontally (column wise).
    vsplit : Split array into multiple sub-arrays vertically (row wise).
    dsplit : Split array into multiple sub-arrays along the 3rd axis (depth).
    stack : Stack a sequence of arrays along a new axis.
    block : Assemble arrays from blocks.
    hstack : Stack arrays in sequence horizontally (column wise).
    vstack : Stack arrays in sequence vertically (row wise).
    dstack : Stack arrays in sequence depth wise (along third dimension).
    column_stack : Stack 1-D arrays as columns into a 2-D array.

    Notes
    -----
    When one or more of the arrays to be concatenated is a MaskedArray,
    this function will return a MaskedArray object instead of an ndarray,
    but the input masks are *not* preserved. In cases where a MaskedArray
    is expected as input, use the ma.concatenate function from the masked
    array module instead.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[1, 2], [3, 4]])
    >>> b = np.array([[5, 6]])
    >>> np.concatenate((a, b), axis=0)
    array([[1, 2],
           [3, 4],
           [5, 6]])
    >>> np.concatenate((a, b.T), axis=1)
    array([[1, 2, 5],
           [3, 4, 6]])
    >>> np.concatenate((a, b), axis=None)
    array([1, 2, 3, 4, 5, 6])

    This function will not preserve masking of MaskedArray inputs.

    >>> a = np.ma.arange(3)
    >>> a[1] = np.ma.masked
    >>> b = np.arange(2, 5)
    >>> a
    masked_array(data=[0, --, 2],
                 mask=[False,  True, False],
           fill_value=999999)
    >>> b
    array([2, 3, 4])
    >>> np.concatenate([a, b])
    masked_array(data=[0, 1, 2, 2, 3, 4],
                 mask=False,
           fill_value=999999)
    >>> np.ma.concatenate([a, b])
    masked_array(data=[0, --, 2, 2, 3, 4],
                 mask=[False,  True, False, False, False, False],
           fill_value=999999)

Python Library Documentation: function <lambda> in module autograd.numpy.numpy_wrapper

<lambda> lambda arr_list, axis=0

Python Library Documentation: function concatenate_args in module autograd.tracer

concatenate_args(*args, called_by_autograd_dispatcher=False, **kwargs)
    None

Python Library Documentation: function conjugate in module autograd.tracer

conjugate(*args, called_by_autograd_dispatcher=False, **kwargs)
    conjugate(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the complex conjugate, element-wise.

    The complex conjugate of a complex number is obtained by changing the
    sign of its imaginary part.

    Parameters
    ----------
    x : array_like
        Input value.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The complex conjugate of `x`, with same dtype as `y`.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    `conj` is an alias for `conjugate`:

    >>> np.conj is np.conjugate
    True

    Examples
    --------
    >>> import numpy as np
    >>> np.conjugate(1+2j)
    (1-2j)

    >>> x = np.eye(2) + 1j * np.eye(2)
    >>> np.conjugate(x)
    array([[ 1.-1.j,  0.-0.j],
           [ 0.-0.j,  1.-1.j]])

Python Library Documentation: function conjugate in module autograd.tracer

conjugate(*args, called_by_autograd_dispatcher=False, **kwargs)
    conjugate(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the complex conjugate, element-wise.

    The complex conjugate of a complex number is obtained by changing the
    sign of its imaginary part.

    Parameters
    ----------
    x : array_like
        Input value.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The complex conjugate of `x`, with same dtype as `y`.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    `conj` is an alias for `conjugate`:

    >>> np.conj is np.conjugate
    True

    Examples
    --------
    >>> import numpy as np
    >>> np.conjugate(1+2j)
    (1-2j)

    >>> x = np.eye(2) + 1j * np.eye(2)
    >>> np.conjugate(x)
    array([[ 1.-1.j,  0.-0.j],
           [ 0.-0.j,  1.-1.j]])

Python Library Documentation: function convolve in module autograd.tracer

convolve(*args, called_by_autograd_dispatcher=False, **kwargs)
    Returns the discrete, linear convolution of two one-dimensional sequences.

    The convolution operator is often seen in signal processing, where it
    models the effect of a linear time-invariant system on a signal [1]_.  In
    probability theory, the sum of two independent random variables is
    distributed according to the convolution of their individual
    distributions.

    If `v` is longer than `a`, the arrays are swapped before computation.

    Parameters
    ----------
    a : (N,) array_like
        First one-dimensional input array.
    v : (M,) array_like
        Second one-dimensional input array.
    mode : {'full', 'valid', 'same'}, optional
        'full':
          By default, mode is 'full'.  This returns the convolution
          at each point of overlap, with an output shape of (N+M-1,). At
          the end-points of the convolution, the signals do not overlap
          completely, and boundary effects may be seen.

        'same':
          Mode 'same' returns output of length ``max(M, N)``.  Boundary
          effects are still visible.

        'valid':
          Mode 'valid' returns output of length
          ``max(M, N) - min(M, N) + 1``.  The convolution product is only given
          for points where the signals overlap completely.  Values outside
          the signal boundary have no effect.

    Returns
    -------
    out : ndarray
        Discrete, linear convolution of `a` and `v`.

    See Also
    --------
    scipy.signal.fftconvolve : Convolve two arrays using the Fast Fourier
                               Transform.
    scipy.linalg.toeplitz : Used to construct the convolution operator.
    polymul : Polynomial multiplication. Same output as convolve, but also
              accepts poly1d objects as input.

    Notes
    -----
    The discrete convolution operation is defined as

    .. math:: (a * v)_n = \sum_{m = -\infty}^{\infty} a_m v_{n - m}

    It can be shown that a convolution :math:`x(t) * y(t)` in time/space
    is equivalent to the multiplication :math:`X(f) Y(f)` in the Fourier
    domain, after appropriate padding (padding is necessary to prevent
    circular convolution).  Since multiplication is more efficient (faster)
    than convolution, the function `scipy.signal.fftconvolve` exploits the
    FFT to calculate the convolution of large data-sets.

    References
    ----------
    .. [1] Wikipedia, "Convolution",
        https://en.wikipedia.org/wiki/Convolution

    Examples
    --------
    Note how the convolution operator flips the second array
    before "sliding" the two across one another:

    >>> import numpy as np
    >>> np.convolve([1, 2, 3], [0, 1, 0.5])
    array([0. , 1. , 2.5, 4. , 1.5])

    Only return the middle values of the convolution.
    Contains boundary effects, where zeros are taken
    into account:

    >>> np.convolve([1,2,3],[0,1,0.5], 'same')
    array([1. ,  2.5,  4. ])

    The two arrays are of the same length, so there
    is only one position where they completely overlap:

    >>> np.convolve([1,2,3],[0,1,0.5], 'valid')
    array([2.5])

Python Library Documentation: function copy in module autograd.tracer

copy(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return an array copy of the given object.

    Parameters
    ----------
    a : array_like
        Input data.
    order : {'C', 'F', 'A', 'K'}, optional
        Controls the memory layout of the copy. 'C' means C-order,
        'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
        'C' otherwise. 'K' means match the layout of `a` as closely
        as possible. (Note that this function and :meth:`ndarray.copy` are very
        similar, but have different default values for their order=
        arguments.)
    subok : bool, optional
        If True, then sub-classes will be passed-through, otherwise the
        returned array will be forced to be a base-class array (defaults to False).

        .. versionadded:: 1.19.0

    Returns
    -------
    arr : ndarray
        Array interpretation of `a`.

    See Also
    --------
    ndarray.copy : Preferred method for creating an array copy

    Notes
    -----
    This is equivalent to:

    >>> np.array(a, copy=True)  #doctest: +SKIP

    The copy made of the data is shallow, i.e., for arrays with object dtype,
    the new array will point to the same objects.
    See Examples from `ndarray.copy`.

    Examples
    --------
    >>> import numpy as np

    Create an array x, with a reference y and a copy z:

    >>> x = np.array([1, 2, 3])
    >>> y = x
    >>> z = np.copy(x)

    Note that, when we modify x, y changes, but not z:

    >>> x[0] = 10
    >>> x[0] == y[0]
    True
    >>> x[0] == z[0]
    False

    Note that, np.copy clears previously set WRITEABLE=False flag.

    >>> a = np.array([1, 2, 3])
    >>> a.flags["WRITEABLE"] = False
    >>> b = np.copy(a)
    >>> b.flags["WRITEABLE"]
    True
    >>> b[0] = 3
    >>> b
    array([3, 2, 3])

Python Library Documentation: function copysign in module autograd.tracer

copysign(*args, called_by_autograd_dispatcher=False, **kwargs)
    copysign(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Change the sign of x1 to that of x2, element-wise.

    If `x2` is a scalar, its sign will be copied to all elements of `x1`.

    Parameters
    ----------
    x1 : array_like
        Values to change the sign of.
    x2 : array_like
        The sign of `x2` is copied to `x1`.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        The values of `x1` with the sign of `x2`.
        This is a scalar if both `x1` and `x2` are scalars.

    Examples
    --------
    >>> import numpy as np
    >>> np.copysign(1.3, -1)
    -1.3
    >>> 1/np.copysign(0, 1)
    inf
    >>> 1/np.copysign(0, -1)
    -inf

    >>> np.copysign([-1, 0, 1], -1.1)
    array([-1., -0., -1.])
    >>> np.copysign([-1, 0, 1], np.arange(3)-1)
    array([-1.,  0.,  1.])

Python Library Documentation: function copyto in module autograd.tracer

copyto(*args, called_by_autograd_dispatcher=False, **kwargs)
    copyto(dst, src, casting='same_kind', where=True)

    Copies values from one array to another, broadcasting as necessary.

    Raises a TypeError if the `casting` rule is violated, and if
    `where` is provided, it selects which elements to copy.

    .. versionadded:: 1.7.0

    Parameters
    ----------
    dst : ndarray
        The array into which values are copied.
    src : array_like
        The array from which values are copied.
    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
        Controls what kind of data casting may occur when copying.

        * 'no' means the data types should not be cast at all.
        * 'equiv' means only byte-order changes are allowed.
        * 'safe' means only casts which can preserve values are allowed.
        * 'same_kind' means only safe casts or casts within a kind,
          like float64 to float32, are allowed.
        * 'unsafe' means any data conversions may be done.
    where : array_like of bool, optional
        A boolean array which is broadcasted to match the dimensions
        of `dst`, and selects elements to copy from `src` to `dst`
        wherever it contains the value True.

    Examples
    --------
    >>> import numpy as np
    >>> A = np.array([4, 5, 6])
    >>> B = [1, 2, 3]
    >>> np.copyto(A, B)
    >>> A
    array([1, 2, 3])

    >>> A = np.array([[1, 2, 3], [4, 5, 6]])
    >>> B = [[4, 5, 6], [7, 8, 9]]
    >>> np.copyto(A, B)
    >>> A
    array([[4, 5, 6],
           [7, 8, 9]])

Python Library Documentation: function corrcoef in module autograd.tracer

corrcoef(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return Pearson product-moment correlation coefficients.

    Please refer to the documentation for `cov` for more detail.  The
    relationship between the correlation coefficient matrix, `R`, and the
    covariance matrix, `C`, is

    .. math:: R_{ij} = \frac{ C_{ij} } { \sqrt{ C_{ii} C_{jj} } }

    The values of `R` are between -1 and 1, inclusive.

    Parameters
    ----------
    x : array_like
        A 1-D or 2-D array containing multiple variables and observations.
        Each row of `x` represents a variable, and each column a single
        observation of all those variables. Also see `rowvar` below.
    y : array_like, optional
        An additional set of variables and observations. `y` has the same
        shape as `x`.
    rowvar : bool, optional
        If `rowvar` is True (default), then each row represents a
        variable, with observations in the columns. Otherwise, the relationship
        is transposed: each column represents a variable, while the rows
        contain observations.
    bias : _NoValue, optional
        Has no effect, do not use.

        .. deprecated:: 1.10.0
    ddof : _NoValue, optional
        Has no effect, do not use.

        .. deprecated:: 1.10.0
    dtype : data-type, optional
        Data-type of the result. By default, the return data-type will have
        at least `numpy.float64` precision.

        .. versionadded:: 1.20

    Returns
    -------
    R : ndarray
        The correlation coefficient matrix of the variables.

    See Also
    --------
    cov : Covariance matrix

    Notes
    -----
    Due to floating point rounding the resulting array may not be Hermitian,
    the diagonal elements may not be 1, and the elements may not satisfy the
    inequality abs(a) <= 1. The real and imaginary parts are clipped to the
    interval [-1,  1] in an attempt to improve on that situation but is not
    much help in the complex case.

    This function accepts but discards arguments `bias` and `ddof`.  This is
    for backwards compatibility with previous versions of this function.  These
    arguments had no effect on the return values of the function and can be
    safely ignored in this and previous versions of numpy.

    Examples
    --------
    >>> import numpy as np

    In this example we generate two random arrays, ``xarr`` and ``yarr``, and
    compute the row-wise and column-wise Pearson correlation coefficients,
    ``R``. Since ``rowvar`` is  true by  default, we first find the row-wise
    Pearson correlation coefficients between the variables of ``xarr``.

    >>> import numpy as np
    >>> rng = np.random.default_rng(seed=42)
    >>> xarr = rng.random((3, 3))
    >>> xarr
    array([[0.77395605, 0.43887844, 0.85859792],
           [0.69736803, 0.09417735, 0.97562235],
           [0.7611397 , 0.78606431, 0.12811363]])
    >>> R1 = np.corrcoef(xarr)
    >>> R1
    array([[ 1.        ,  0.99256089, -0.68080986],
           [ 0.99256089,  1.        , -0.76492172],
           [-0.68080986, -0.76492172,  1.        ]])

    If we add another set of variables and observations ``yarr``, we can
    compute the row-wise Pearson correlation coefficients between the
    variables in ``xarr`` and ``yarr``.

    >>> yarr = rng.random((3, 3))
    >>> yarr
    array([[0.45038594, 0.37079802, 0.92676499],
           [0.64386512, 0.82276161, 0.4434142 ],
           [0.22723872, 0.55458479, 0.06381726]])
    >>> R2 = np.corrcoef(xarr, yarr)
    >>> R2
    array([[ 1.        ,  0.99256089, -0.68080986,  0.75008178, -0.934284  ,
            -0.99004057],
           [ 0.99256089,  1.        , -0.76492172,  0.82502011, -0.97074098,
            -0.99981569],
           [-0.68080986, -0.76492172,  1.        , -0.99507202,  0.89721355,
             0.77714685],
           [ 0.75008178,  0.82502011, -0.99507202,  1.        , -0.93657855,
            -0.83571711],
           [-0.934284  , -0.97074098,  0.89721355, -0.93657855,  1.        ,
             0.97517215],
           [-0.99004057, -0.99981569,  0.77714685, -0.83571711,  0.97517215,
             1.        ]])

    Finally if we use the option ``rowvar=False``, the columns are now
    being treated as the variables and we will find the column-wise Pearson
    correlation coefficients between variables in ``xarr`` and ``yarr``.

    >>> R3 = np.corrcoef(xarr, yarr, rowvar=False)
    >>> R3
    array([[ 1.        ,  0.77598074, -0.47458546, -0.75078643, -0.9665554 ,
             0.22423734],
           [ 0.77598074,  1.        , -0.92346708, -0.99923895, -0.58826587,
            -0.44069024],
           [-0.47458546, -0.92346708,  1.        ,  0.93773029,  0.23297648,
             0.75137473],
           [-0.75078643, -0.99923895,  0.93773029,  1.        ,  0.55627469,
             0.47536961],
           [-0.9665554 , -0.58826587,  0.23297648,  0.55627469,  1.        ,
            -0.46666491],
           [ 0.22423734, -0.44069024,  0.75137473,  0.47536961, -0.46666491,
             1.        ]])

Python Library Documentation: function correlate in module autograd.tracer

correlate(*args, called_by_autograd_dispatcher=False, **kwargs)
    Cross-correlation of two 1-dimensional sequences.

    This function computes the correlation as generally defined in signal
    processing texts [1]_:

    .. math:: c_k = \sum_n a_{n+k} \cdot \overline{v}_n

    with a and v sequences being zero-padded where necessary and
    :math:`\overline v` denoting complex conjugation.

    Parameters
    ----------
    a, v : array_like
        Input sequences.
    mode : {'valid', 'same', 'full'}, optional
        Refer to the `convolve` docstring.  Note that the default
        is 'valid', unlike `convolve`, which uses 'full'.

    Returns
    -------
    out : ndarray
        Discrete cross-correlation of `a` and `v`.

    See Also
    --------
    convolve : Discrete, linear convolution of two one-dimensional sequences.
    scipy.signal.correlate : uses FFT which has superior performance
        on large arrays.

    Notes
    -----
    The definition of correlation above is not unique and sometimes
    correlation may be defined differently. Another common definition is [1]_:

    .. math:: c'_k = \sum_n a_{n} \cdot \overline{v_{n+k}}

    which is related to :math:`c_k` by :math:`c'_k = c_{-k}`.

    `numpy.correlate` may perform slowly in large arrays (i.e. n = 1e5)
    because it does not use the FFT to compute the convolution; in that case,
    `scipy.signal.correlate` might be preferable.

    References
    ----------
    .. [1] Wikipedia, "Cross-correlation",
           https://en.wikipedia.org/wiki/Cross-correlation

    Examples
    --------
    >>> import numpy as np
    >>> np.correlate([1, 2, 3], [0, 1, 0.5])
    array([3.5])
    >>> np.correlate([1, 2, 3], [0, 1, 0.5], "same")
    array([2. ,  3.5,  3. ])
    >>> np.correlate([1, 2, 3], [0, 1, 0.5], "full")
    array([0.5,  2. ,  3.5,  3. ,  0. ])

    Using complex sequences:

    >>> np.correlate([1+1j, 2, 3-1j], [0, 1, 0.5j], 'full')
    array([ 0.5-0.5j,  1.0+0.j ,  1.5-1.5j,  3.0-1.j ,  0.0+0.j ])

    Note that you get the time reversed, complex conjugated result
    (:math:`\overline{c_{-k}}`) when the two input sequences a and v change
    places:

    >>> np.correlate([0, 1, 0.5j], [1+1j, 2, 3-1j], 'full')
    array([ 0.0+0.j ,  3.0+1.j ,  1.5+1.5j,  1.0+0.j ,  0.5+0.5j])

Python Library Documentation: function cos in module autograd.tracer

cos(*args, called_by_autograd_dispatcher=False, **kwargs)
    cos(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Cosine element-wise.

    Parameters
    ----------
    x : array_like
        Input array in radians.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The corresponding cosine values.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    If `out` is provided, the function writes the result into it,
    and returns a reference to `out`.  (See Examples)

    References
    ----------
    M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions.
    New York, NY: Dover, 1972.

    Examples
    --------
    >>> import numpy as np
    >>> np.cos(np.array([0, np.pi/2, np.pi]))
    array([  1.00000000e+00,   6.12303177e-17,  -1.00000000e+00])
    >>>
    >>> # Example of providing the optional output parameter
    >>> out1 = np.array([0], dtype='d')
    >>> out2 = np.cos([0.1], out1)
    >>> out2 is out1
    True
    >>>
    >>> # Example of ValueError due to provision of shape mis-matched `out`
    >>> np.cos(np.zeros((3,3)),np.zeros((2,2)))
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ValueError: operands could not be broadcast together with shapes (3,3) (2,2)

Python Library Documentation: function cosh in module autograd.tracer

cosh(*args, called_by_autograd_dispatcher=False, **kwargs)
    cosh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Hyperbolic cosine, element-wise.

    Equivalent to ``1/2 * (np.exp(x) + np.exp(-x))`` and ``np.cos(1j*x)``.

    Parameters
    ----------
    x : array_like
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Output array of same shape as `x`.
        This is a scalar if `x` is a scalar.

    Examples
    --------
    >>> import numpy as np
    >>> np.cosh(0)
    1.0

    The hyperbolic cosine describes the shape of a hanging cable:

    >>> import matplotlib.pyplot as plt
    >>> x = np.linspace(-4, 4, 1000)
    >>> plt.plot(x, np.cosh(x))
    >>> plt.show()

Python Library Documentation: function count_nonzero in module autograd.tracer

count_nonzero(*args, called_by_autograd_dispatcher=False, **kwargs)
    Counts the number of non-zero values in the array ``a``.

    The word "non-zero" is in reference to the Python 2.x
    built-in method ``__nonzero__()`` (renamed ``__bool__()``
    in Python 3.x) of Python objects that tests an object's
    "truthfulness". For example, any number is considered
    truthful if it is nonzero, whereas any string is considered
    truthful if it is not the empty string. Thus, this function
    (recursively) counts how many elements in ``a`` (and in
    sub-arrays thereof) have their ``__nonzero__()`` or ``__bool__()``
    method evaluated to ``True``.

    Parameters
    ----------
    a : array_like
        The array for which to count non-zeros.
    axis : int or tuple, optional
        Axis or tuple of axes along which to count non-zeros.
        Default is None, meaning that non-zeros will be counted
        along a flattened version of ``a``.

        .. versionadded:: 1.12.0

    keepdims : bool, optional
        If this is set to True, the axes that are counted are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the input array.

        .. versionadded:: 1.19.0

    Returns
    -------
    count : int or array of int
        Number of non-zero values in the array along a given axis.
        Otherwise, the total number of non-zero values in the array
        is returned.

    See Also
    --------
    nonzero : Return the coordinates of all the non-zero values.

    Examples
    --------
    >>> import numpy as np
    >>> np.count_nonzero(np.eye(4))
    4
    >>> a = np.array([[0, 1, 7, 0],
    ...               [3, 0, 2, 19]])
    >>> np.count_nonzero(a)
    5
    >>> np.count_nonzero(a, axis=0)
    array([1, 1, 2, 1])
    >>> np.count_nonzero(a, axis=1)
    array([2, 3])
    >>> np.count_nonzero(a, axis=1, keepdims=True)
    array([[2],
           [3]])

Python Library Documentation: function cov in module autograd.tracer

cov(*args, called_by_autograd_dispatcher=False, **kwargs)
    Estimate a covariance matrix, given data and weights.

    Covariance indicates the level to which two variables vary together.
    If we examine N-dimensional samples, :math:`X = [x_1, x_2, ... x_N]^T`,
    then the covariance matrix element :math:`C_{ij}` is the covariance of
    :math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance
    of :math:`x_i`.

    See the notes for an outline of the algorithm.

    Parameters
    ----------
    m : array_like
        A 1-D or 2-D array containing multiple variables and observations.
        Each row of `m` represents a variable, and each column a single
        observation of all those variables. Also see `rowvar` below.
    y : array_like, optional
        An additional set of variables and observations. `y` has the same form
        as that of `m`.
    rowvar : bool, optional
        If `rowvar` is True (default), then each row represents a
        variable, with observations in the columns. Otherwise, the relationship
        is transposed: each column represents a variable, while the rows
        contain observations.
    bias : bool, optional
        Default normalization (False) is by ``(N - 1)``, where ``N`` is the
        number of observations given (unbiased estimate). If `bias` is True,
        then normalization is by ``N``. These values can be overridden by using
        the keyword ``ddof`` in numpy versions >= 1.5.
    ddof : int, optional
        If not ``None`` the default value implied by `bias` is overridden.
        Note that ``ddof=1`` will return the unbiased estimate, even if both
        `fweights` and `aweights` are specified, and ``ddof=0`` will return
        the simple average. See the notes for the details. The default value
        is ``None``.

        .. versionadded:: 1.5
    fweights : array_like, int, optional
        1-D array of integer frequency weights; the number of times each
        observation vector should be repeated.

        .. versionadded:: 1.10
    aweights : array_like, optional
        1-D array of observation vector weights. These relative weights are
        typically large for observations considered "important" and smaller for
        observations considered less "important". If ``ddof=0`` the array of
        weights can be used to assign probabilities to observation vectors.

        .. versionadded:: 1.10
    dtype : data-type, optional
        Data-type of the result. By default, the return data-type will have
        at least `numpy.float64` precision.

        .. versionadded:: 1.20

    Returns
    -------
    out : ndarray
        The covariance matrix of the variables.

    See Also
    --------
    corrcoef : Normalized covariance matrix

    Notes
    -----
    Assume that the observations are in the columns of the observation
    array `m` and let ``f = fweights`` and ``a = aweights`` for brevity. The
    steps to compute the weighted covariance are as follows::

        >>> m = np.arange(10, dtype=np.float64)
        >>> f = np.arange(10) * 2
        >>> a = np.arange(10) ** 2.
        >>> ddof = 1
        >>> w = f * a
        >>> v1 = np.sum(w)
        >>> v2 = np.sum(w * a)
        >>> m -= np.sum(m * w, axis=None, keepdims=True) / v1
        >>> cov = np.dot(m * w, m.T) * v1 / (v1**2 - ddof * v2)

    Note that when ``a == 1``, the normalization factor
    ``v1 / (v1**2 - ddof * v2)`` goes over to ``1 / (np.sum(f) - ddof)``
    as it should.

    Examples
    --------
    >>> import numpy as np

    Consider two variables, :math:`x_0` and :math:`x_1`, which
    correlate perfectly, but in opposite directions:

    >>> x = np.array([[0, 2], [1, 1], [2, 0]]).T
    >>> x
    array([[0, 1, 2],
           [2, 1, 0]])

    Note how :math:`x_0` increases while :math:`x_1` decreases. The covariance
    matrix shows this clearly:

    >>> np.cov(x)
    array([[ 1., -1.],
           [-1.,  1.]])

    Note that element :math:`C_{0,1}`, which shows the correlation between
    :math:`x_0` and :math:`x_1`, is negative.

    Further, note how `x` and `y` are combined:

    >>> x = [-2.1, -1,  4.3]
    >>> y = [3,  1.1,  0.12]
    >>> X = np.stack((x, y), axis=0)
    >>> np.cov(X)
    array([[11.71      , -4.286     ], # may vary
           [-4.286     ,  2.144133]])
    >>> np.cov(x, y)
    array([[11.71      , -4.286     ], # may vary
           [-4.286     ,  2.144133]])
    >>> np.cov(x)
    array(11.71)

Python Library Documentation: function cross in module autograd.tracer

cross(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the cross product of two (arrays of) vectors.

    The cross product of `a` and `b` in :math:`R^3` is a vector perpendicular
    to both `a` and `b`.  If `a` and `b` are arrays of vectors, the vectors
    are defined by the last axis of `a` and `b` by default, and these axes
    can have dimensions 2 or 3.  Where the dimension of either `a` or `b` is
    2, the third component of the input vector is assumed to be zero and the
    cross product calculated accordingly.  In cases where both input vectors
    have dimension 2, the z-component of the cross product is returned.

    Parameters
    ----------
    a : array_like
        Components of the first vector(s).
    b : array_like
        Components of the second vector(s).
    axisa : int, optional
        Axis of `a` that defines the vector(s).  By default, the last axis.
    axisb : int, optional
        Axis of `b` that defines the vector(s).  By default, the last axis.
    axisc : int, optional
        Axis of `c` containing the cross product vector(s).  Ignored if
        both input vectors have dimension 2, as the return is scalar.
        By default, the last axis.
    axis : int, optional
        If defined, the axis of `a`, `b` and `c` that defines the vector(s)
        and cross product(s).  Overrides `axisa`, `axisb` and `axisc`.

    Returns
    -------
    c : ndarray
        Vector cross product(s).

    Raises
    ------
    ValueError
        When the dimension of the vector(s) in `a` and/or `b` does not
        equal 2 or 3.

    See Also
    --------
    inner : Inner product
    outer : Outer product.
    linalg.cross : An Array API compatible variation of ``np.cross``,
                   which accepts (arrays of) 3-element vectors only.
    ix_ : Construct index arrays.

    Notes
    -----
    .. versionadded:: 1.9.0

    Supports full broadcasting of the inputs.

    Dimension-2 input arrays were deprecated in 2.0.0. If you do need this
    functionality, you can use::

        def cross2d(x, y):
            return x[..., 0] * y[..., 1] - x[..., 1] * y[..., 0]

    Examples
    --------
    Vector cross-product.

    >>> import numpy as np
    >>> x = [1, 2, 3]
    >>> y = [4, 5, 6]
    >>> np.cross(x, y)
    array([-3,  6, -3])

    One vector with dimension 2.

    >>> x = [1, 2]
    >>> y = [4, 5, 6]
    >>> np.cross(x, y)
    array([12, -6, -3])

    Equivalently:

    >>> x = [1, 2, 0]
    >>> y = [4, 5, 6]
    >>> np.cross(x, y)
    array([12, -6, -3])

    Both vectors with dimension 2.

    >>> x = [1,2]
    >>> y = [4,5]
    >>> np.cross(x, y)
    array(-3)

    Multiple vector cross-products. Note that the direction of the cross
    product vector is defined by the *right-hand rule*.

    >>> x = np.array([[1,2,3], [4,5,6]])
    >>> y = np.array([[4,5,6], [1,2,3]])
    >>> np.cross(x, y)
    array([[-3,  6, -3],
           [ 3, -6,  3]])

    The orientation of `c` can be changed using the `axisc` keyword.

    >>> np.cross(x, y, axisc=0)
    array([[-3,  3],
           [ 6, -6],
           [-3,  3]])

    Change the vector definition of `x` and `y` using `axisa` and `axisb`.

    >>> x = np.array([[1,2,3], [4,5,6], [7, 8, 9]])
    >>> y = np.array([[7, 8, 9], [4,5,6], [1,2,3]])
    >>> np.cross(x, y)
    array([[ -6,  12,  -6],
           [  0,   0,   0],
           [  6, -12,   6]])
    >>> np.cross(x, y, axisa=0, axisb=0)
    array([[-24,  48, -24],
           [-30,  60, -30],
           [-36,  72, -36]])

Python Library Documentation: class complex64 in module numpy

class complex64(complexfloating)
 |  Complex number type composed of two single-precision floating-point
 |  numbers.
 |
 |  :Character code: ``'F'``
 |  :Canonical name: `numpy.csingle`
 |  :Alias on this platform (win32 AMD64): `numpy.complex64`: Complex number type composed of 2 32-bit-precision floating-point numbers.
 |
 |  Method resolution order:
 |      complex64
 |      complexfloating
 |      inexact
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __complex__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from complexfloating:
 |
 |  __round__(...)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: function cumprod in module autograd.tracer

cumprod(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the cumulative product of elements along a given axis.

    Parameters
    ----------
    a : array_like
        Input array.
    axis : int, optional
        Axis along which the cumulative product is computed.  By default
        the input is flattened.
    dtype : dtype, optional
        Type of the returned array, as well as of the accumulator in which
        the elements are multiplied.  If *dtype* is not specified, it
        defaults to the dtype of `a`, unless `a` has an integer dtype with
        a precision less than that of the default platform integer.  In
        that case, the default platform integer is used instead.
    out : ndarray, optional
        Alternative output array in which to place the result. It must
        have the same shape and buffer length as the expected output
        but the type of the resulting values will be cast if necessary.

    Returns
    -------
    cumprod : ndarray
        A new array holding the result is returned unless `out` is
        specified, in which case a reference to out is returned.

    See Also
    --------
    cumulative_prod : Array API compatible alternative for ``cumprod``.
    :ref:`ufuncs-output-type`

    Notes
    -----
    Arithmetic is modular when using integer types, and no error is
    raised on overflow.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([1,2,3])
    >>> np.cumprod(a) # intermediate results 1, 1*2
    ...               # total product 1*2*3 = 6
    array([1, 2, 6])
    >>> a = np.array([[1, 2, 3], [4, 5, 6]])
    >>> np.cumprod(a, dtype=float) # specify type of output
    array([   1.,    2.,    6.,   24.,  120.,  720.])

    The cumulative product for each column (i.e., over the rows) of `a`:

    >>> np.cumprod(a, axis=0)
    array([[ 1,  2,  3],
           [ 4, 10, 18]])

    The cumulative product for each row (i.e. over the columns) of `a`:

    >>> np.cumprod(a,axis=1)
    array([[  1,   2,   6],
           [  4,  20, 120]])

Python Library Documentation: function cumsum in module autograd.tracer

cumsum(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the cumulative sum of the elements along a given axis.

    Parameters
    ----------
    a : array_like
        Input array.
    axis : int, optional
        Axis along which the cumulative sum is computed. The default
        (None) is to compute the cumsum over the flattened array.
    dtype : dtype, optional
        Type of the returned array and of the accumulator in which the
        elements are summed.  If `dtype` is not specified, it defaults
        to the dtype of `a`, unless `a` has an integer dtype with a
        precision less than that of the default platform integer.  In
        that case, the default platform integer is used.
    out : ndarray, optional
        Alternative output array in which to place the result. It must
        have the same shape and buffer length as the expected output
        but the type will be cast if necessary. See :ref:`ufuncs-output-type`
        for more details.

    Returns
    -------
    cumsum_along_axis : ndarray.
        A new array holding the result is returned unless `out` is
        specified, in which case a reference to `out` is returned. The
        result has the same size as `a`, and the same shape as `a` if
        `axis` is not None or `a` is a 1-d array.

    See Also
    --------
    cumulative_sum : Array API compatible alternative for ``cumsum``.
    sum : Sum array elements.
    trapezoid : Integration of array values using composite trapezoidal rule.
    diff : Calculate the n-th discrete difference along given axis.

    Notes
    -----
    Arithmetic is modular when using integer types, and no error is
    raised on overflow.

    ``cumsum(a)[-1]`` may not be equal to ``sum(a)`` for floating-point
    values since ``sum`` may use a pairwise summation routine, reducing
    the roundoff-error. See `sum` for more information.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[1,2,3], [4,5,6]])
    >>> a
    array([[1, 2, 3],
           [4, 5, 6]])
    >>> np.cumsum(a)
    array([ 1,  3,  6, 10, 15, 21])
    >>> np.cumsum(a, dtype=float)     # specifies type of output value(s)
    array([  1.,   3.,   6.,  10.,  15.,  21.])

    >>> np.cumsum(a,axis=0)      # sum over rows for each of the 3 columns
    array([[1, 2, 3],
           [5, 7, 9]])
    >>> np.cumsum(a,axis=1)      # sum over columns for each of the 2 rows
    array([[ 1,  3,  6],
           [ 4,  9, 15]])

    ``cumsum(b)[-1]`` may not be equal to ``sum(b)``

    >>> b = np.array([1, 2e-9, 3e-9] * 1000000)
    >>> b.cumsum()[-1]
    1000000.0050045159
    >>> b.sum()
    1000000.0050000029

Python Library Documentation: function cumulative_prod in module autograd.tracer

cumulative_prod(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the cumulative product of elements along a given axis.

    This function is an Array API compatible alternative to `numpy.cumprod`.

    Parameters
    ----------
    x : array_like
        Input array.
    axis : int, optional
        Axis along which the cumulative product is computed. The default
        (None) is only allowed for one-dimensional arrays. For arrays
        with more than one dimension ``axis`` is required.
    dtype : dtype, optional
        Type of the returned array, as well as of the accumulator in which
        the elements are multiplied.  If ``dtype`` is not specified, it
        defaults to the dtype of ``x``, unless ``x`` has an integer dtype
        with a precision less than that of the default platform integer.
        In that case, the default platform integer is used instead.
    out : ndarray, optional
        Alternative output array in which to place the result. It must
        have the same shape and buffer length as the expected output
        but the type of the resulting values will be cast if necessary.
        See :ref:`ufuncs-output-type` for more details.
    include_initial : bool, optional
        Boolean indicating whether to include the initial value (ones) as
        the first value in the output. With ``include_initial=True``
        the shape of the output is different than the shape of the input.
        Default: ``False``.

    Returns
    -------
    cumulative_prod_along_axis : ndarray
        A new array holding the result is returned unless ``out`` is
        specified, in which case a reference to ``out`` is returned. The
        result has the same shape as ``x`` if ``include_initial=False``.

    Notes
    -----
    Arithmetic is modular when using integer types, and no error is
    raised on overflow.

    Examples
    --------
    >>> a = np.array([1, 2, 3])
    >>> np.cumulative_prod(a)  # intermediate results 1, 1*2
    ...                        # total product 1*2*3 = 6
    array([1, 2, 6])
    >>> a = np.array([1, 2, 3, 4, 5, 6])
    >>> np.cumulative_prod(a, dtype=float) # specify type of output
    array([   1.,    2.,    6.,   24.,  120.,  720.])

    The cumulative product for each column (i.e., over the rows) of ``b``:

    >>> b = np.array([[1, 2, 3], [4, 5, 6]])
    >>> np.cumulative_prod(b, axis=0)
    array([[ 1,  2,  3],
           [ 4, 10, 18]])

    The cumulative product for each row (i.e. over the columns) of ``b``:

    >>> np.cumulative_prod(b, axis=1)
    array([[  1,   2,   6],
           [  4,  20, 120]])

Python Library Documentation: function cumulative_sum in module autograd.tracer

cumulative_sum(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the cumulative sum of the elements along a given axis.

    This function is an Array API compatible alternative to `numpy.cumsum`.

    Parameters
    ----------
    x : array_like
        Input array.
    axis : int, optional
        Axis along which the cumulative sum is computed. The default
        (None) is only allowed for one-dimensional arrays. For arrays
        with more than one dimension ``axis`` is required.
    dtype : dtype, optional
        Type of the returned array and of the accumulator in which the
        elements are summed.  If ``dtype`` is not specified, it defaults
        to the dtype of ``x``, unless ``x`` has an integer dtype with
        a precision less than that of the default platform integer.
        In that case, the default platform integer is used.
    out : ndarray, optional
        Alternative output array in which to place the result. It must
        have the same shape and buffer length as the expected output
        but the type will be cast if necessary. See :ref:`ufuncs-output-type`
        for more details.
    include_initial : bool, optional
        Boolean indicating whether to include the initial value (ones) as
        the first value in the output. With ``include_initial=True``
        the shape of the output is different than the shape of the input.
        Default: ``False``.

    Returns
    -------
    cumulative_sum_along_axis : ndarray
        A new array holding the result is returned unless ``out`` is
        specified, in which case a reference to ``out`` is returned. The
        result has the same shape as ``x`` if ``include_initial=False``.

    See Also
    --------
    sum : Sum array elements.
    trapezoid : Integration of array values using composite trapezoidal rule.
    diff : Calculate the n-th discrete difference along given axis.

    Notes
    -----
    Arithmetic is modular when using integer types, and no error is
    raised on overflow.

    ``cumulative_sum(a)[-1]`` may not be equal to ``sum(a)`` for
    floating-point values since ``sum`` may use a pairwise summation routine,
    reducing the roundoff-error. See `sum` for more information.

    Examples
    --------
    >>> a = np.array([1, 2, 3, 4, 5, 6])
    >>> a
    array([1, 2, 3, 4, 5, 6])
    >>> np.cumulative_sum(a)
    array([ 1,  3,  6, 10, 15, 21])
    >>> np.cumulative_sum(a, dtype=float)  # specifies type of output value(s)
    array([  1.,   3.,   6.,  10.,  15.,  21.])

    >>> b = np.array([[1, 2, 3], [4, 5, 6]])
    >>> np.cumulative_sum(b,axis=0)  # sum over rows for each of the 3 columns
    array([[1, 2, 3],
           [5, 7, 9]])
    >>> np.cumulative_sum(b,axis=1)  # sum over columns for each of the 2 rows
    array([[ 1,  3,  6],
           [ 4,  9, 15]])

    ``cumulative_sum(c)[-1]`` may not be equal to ``sum(c)``

    >>> c = np.array([1, 2e-9, 3e-9] * 1000000)
    >>> np.cumulative_sum(c)[-1]
    1000000.0050045159
    >>> c.sum()
    1000000.0050000029

Python Library Documentation: function custom_where in module autograd.numpy

custom_where(condition, *args, **kwargs)

Python Library Documentation: class datetime64 in module numpy

class datetime64(generic)
 |  If created from a 64-bit integer, it represents an offset from
 |  ``1970-01-01T00:00:00``.
 |  If created from string, the string can be in ISO 8601 date
 |  or datetime format.
 |
 |  When parsing a string to create a datetime object, if the string contains
 |  a trailing timezone (A 'Z' or a timezone offset), the timezone will be
 |  dropped and a User Warning is given.
 |
 |  Datetime64 objects should be considered to be UTC and therefore have an
 |  offset of +0000.
 |
 |  >>> np.datetime64(10, 'Y')
 |  np.datetime64('1980')
 |  >>> np.datetime64('1980', 'Y')
 |  np.datetime64('1980')
 |  >>> np.datetime64(10, 'D')
 |  np.datetime64('1970-01-11')
 |
 |  See :ref:`arrays.datetime` for more information.
 |
 |  :Character code: ``'M'``
 |
 |  Method resolution order:
 |      datetime64
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: function datetime_as_string in module autograd.tracer

datetime_as_string(*args, called_by_autograd_dispatcher=False, **kwargs)
    datetime_as_string(arr, unit=None, timezone='naive', casting='same_kind')

    Convert an array of datetimes into an array of strings.

    Parameters
    ----------
    arr : array_like of datetime64
        The array of UTC timestamps to format.
    unit : str
        One of None, 'auto', or
        a :ref:`datetime unit <arrays.dtypes.dateunits>`.
    timezone : {'naive', 'UTC', 'local'} or tzinfo
        Timezone information to use when displaying the datetime. If 'UTC',
        end with a Z to indicate UTC time. If 'local', convert to the local
        timezone first, and suffix with a +-#### timezone offset. If a tzinfo
        object, then do as with 'local', but use the specified timezone.
    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}
        Casting to allow when changing between datetime units.

    Returns
    -------
    str_arr : ndarray
        An array of strings the same shape as `arr`.

    Examples
    --------
    >>> import numpy as np
    >>> import pytz
    >>> d = np.arange('2002-10-27T04:30', 4*60, 60, dtype='M8[m]')
    >>> d
    array(['2002-10-27T04:30', '2002-10-27T05:30', '2002-10-27T06:30',
           '2002-10-27T07:30'], dtype='datetime64[m]')

    Setting the timezone to UTC shows the same information, but with a Z suffix

    >>> np.datetime_as_string(d, timezone='UTC')
    array(['2002-10-27T04:30Z', '2002-10-27T05:30Z', '2002-10-27T06:30Z',
           '2002-10-27T07:30Z'], dtype='<U35')

    Note that we picked datetimes that cross a DST boundary. Passing in a
    ``pytz`` timezone object will print the appropriate offset

    >>> np.datetime_as_string(d, timezone=pytz.timezone('US/Eastern'))
    array(['2002-10-27T00:30-0400', '2002-10-27T01:30-0400',
           '2002-10-27T01:30-0500', '2002-10-27T02:30-0500'], dtype='<U39')

    Passing in a unit will change the precision

    >>> np.datetime_as_string(d, unit='h')
    array(['2002-10-27T04', '2002-10-27T05', '2002-10-27T06', '2002-10-27T07'],
          dtype='<U32')
    >>> np.datetime_as_string(d, unit='s')
    array(['2002-10-27T04:30:00', '2002-10-27T05:30:00', '2002-10-27T06:30:00',
           '2002-10-27T07:30:00'], dtype='<U38')

    'casting' can be used to specify whether precision can be changed

    >>> np.datetime_as_string(d, unit='h', casting='safe')
    Traceback (most recent call last):
        ...
    TypeError: Cannot create a datetime string as units 'h' from a NumPy
    datetime with units 'm' according to the rule 'safe'

Python Library Documentation: function datetime_data in module autograd.tracer

datetime_data(*args, called_by_autograd_dispatcher=False, **kwargs)
    datetime_data(dtype, /)

    Get information about the step size of a date or time type.

    The returned tuple can be passed as the second argument of `numpy.datetime64` and
    `numpy.timedelta64`.

    Parameters
    ----------
    dtype : dtype
        The dtype object, which must be a `datetime64` or `timedelta64` type.

    Returns
    -------
    unit : str
        The :ref:`datetime unit <arrays.dtypes.dateunits>` on which this dtype
        is based.
    count : int
        The number of base units in a step.

    Examples
    --------
    >>> import numpy as np
    >>> dt_25s = np.dtype('timedelta64[25s]')
    >>> np.datetime_data(dt_25s)
    ('s', 25)
    >>> np.array(10, dt_25s).astype('timedelta64[s]')
    array(250, dtype='timedelta64[s]')

    The result can be used to construct a datetime that uses the same units
    as a timedelta

    >>> np.datetime64('2010', np.datetime_data(dt_25s))
    np.datetime64('2010-01-01T00:00:00','25s')

Python Library Documentation: function deg2rad in module autograd.tracer

deg2rad(*args, called_by_autograd_dispatcher=False, **kwargs)
    deg2rad(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Convert angles from degrees to radians.

    Parameters
    ----------
    x : array_like
        Angles in degrees.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The corresponding angle in radians.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    rad2deg : Convert angles from radians to degrees.
    unwrap : Remove large jumps in angle by wrapping.

    Notes
    -----
    .. versionadded:: 1.3.0

    ``deg2rad(x)`` is ``x * pi / 180``.

    Examples
    --------
    >>> import numpy as np
    >>> np.deg2rad(180)
    3.1415926535897931

Python Library Documentation: function degrees in module autograd.tracer

degrees(*args, called_by_autograd_dispatcher=False, **kwargs)
    degrees(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Convert angles from radians to degrees.

    Parameters
    ----------
    x : array_like
        Input array in radians.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray of floats
        The corresponding degree values; if `out` was supplied this is a
        reference to it.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    rad2deg : equivalent function

    Examples
    --------
    Convert a radian array to degrees

    >>> import numpy as np

    >>> rad = np.arange(12.)*np.pi/6
    >>> np.degrees(rad)
    array([   0.,   30.,   60.,   90.,  120.,  150.,  180.,  210.,  240.,
            270.,  300.,  330.])

    >>> out = np.zeros((rad.shape))
    >>> r = np.degrees(rad, out)
    >>> np.all(r == out)
    True

Python Library Documentation: function delete in module autograd.tracer

delete(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return a new array with sub-arrays along an axis deleted. For a one
    dimensional array, this returns those entries not returned by
    `arr[obj]`.

    Parameters
    ----------
    arr : array_like
        Input array.
    obj : slice, int or array of ints
        Indicate indices of sub-arrays to remove along the specified axis.

        .. versionchanged:: 1.19.0
            Boolean indices are now treated as a mask of elements to remove,
            rather than being cast to the integers 0 and 1.

    axis : int, optional
        The axis along which to delete the subarray defined by `obj`.
        If `axis` is None, `obj` is applied to the flattened array.

    Returns
    -------
    out : ndarray
        A copy of `arr` with the elements specified by `obj` removed. Note
        that `delete` does not occur in-place. If `axis` is None, `out` is
        a flattened array.

    See Also
    --------
    insert : Insert elements into an array.
    append : Append elements at the end of an array.

    Notes
    -----
    Often it is preferable to use a boolean mask. For example:

    >>> arr = np.arange(12) + 1
    >>> mask = np.ones(len(arr), dtype=bool)
    >>> mask[[0,2,4]] = False
    >>> result = arr[mask,...]

    Is equivalent to ``np.delete(arr, [0,2,4], axis=0)``, but allows further
    use of `mask`.

    Examples
    --------
    >>> import numpy as np
    >>> arr = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])
    >>> arr
    array([[ 1,  2,  3,  4],
           [ 5,  6,  7,  8],
           [ 9, 10, 11, 12]])
    >>> np.delete(arr, 1, 0)
    array([[ 1,  2,  3,  4],
           [ 9, 10, 11, 12]])

    >>> np.delete(arr, np.s_[::2], 1)
    array([[ 2,  4],
           [ 6,  8],
           [10, 12]])
    >>> np.delete(arr, [1,3,5], None)
    array([ 1,  3,  5,  7,  8,  9, 10, 11, 12])

Python Library Documentation: function diag in module autograd.tracer

diag(*args, called_by_autograd_dispatcher=False, **kwargs)
    Extract a diagonal or construct a diagonal array.

    See the more detailed documentation for ``numpy.diagonal`` if you use this
    function to extract a diagonal and wish to write to the resulting array;
    whether it returns a copy or a view depends on what version of numpy you
    are using.

    Parameters
    ----------
    v : array_like
        If `v` is a 2-D array, return a copy of its `k`-th diagonal.
        If `v` is a 1-D array, return a 2-D array with `v` on the `k`-th
        diagonal.
    k : int, optional
        Diagonal in question. The default is 0. Use `k>0` for diagonals
        above the main diagonal, and `k<0` for diagonals below the main
        diagonal.

    Returns
    -------
    out : ndarray
        The extracted diagonal or constructed diagonal array.

    See Also
    --------
    diagonal : Return specified diagonals.
    diagflat : Create a 2-D array with the flattened input as a diagonal.
    trace : Sum along diagonals.
    triu : Upper triangle of an array.
    tril : Lower triangle of an array.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.arange(9).reshape((3,3))
    >>> x
    array([[0, 1, 2],
           [3, 4, 5],
           [6, 7, 8]])

    >>> np.diag(x)
    array([0, 4, 8])
    >>> np.diag(x, k=1)
    array([1, 5])
    >>> np.diag(x, k=-1)
    array([3, 7])

    >>> np.diag(np.diag(x))
    array([[0, 0, 0],
           [0, 4, 0],
           [0, 0, 8]])

Python Library Documentation: function diag_indices in module autograd.tracer

diag_indices(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the indices to access the main diagonal of an array.

    This returns a tuple of indices that can be used to access the main
    diagonal of an array `a` with ``a.ndim >= 2`` dimensions and shape
    (n, n, ..., n). For ``a.ndim = 2`` this is the usual diagonal, for
    ``a.ndim > 2`` this is the set of indices to access ``a[i, i, ..., i]``
    for ``i = [0..n-1]``.

    Parameters
    ----------
    n : int
      The size, along each dimension, of the arrays for which the returned
      indices can be used.

    ndim : int, optional
      The number of dimensions.

    See Also
    --------
    diag_indices_from

    Notes
    -----
    .. versionadded:: 1.4.0

    Examples
    --------
    >>> import numpy as np

    Create a set of indices to access the diagonal of a (4, 4) array:

    >>> di = np.diag_indices(4)
    >>> di
    (array([0, 1, 2, 3]), array([0, 1, 2, 3]))
    >>> a = np.arange(16).reshape(4, 4)
    >>> a
    array([[ 0,  1,  2,  3],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11],
           [12, 13, 14, 15]])
    >>> a[di] = 100
    >>> a
    array([[100,   1,   2,   3],
           [  4, 100,   6,   7],
           [  8,   9, 100,  11],
           [ 12,  13,  14, 100]])

    Now, we create indices to manipulate a 3-D array:

    >>> d3 = np.diag_indices(2, 3)
    >>> d3
    (array([0, 1]), array([0, 1]), array([0, 1]))

    And use it to set the diagonal of an array of zeros to 1:

    >>> a = np.zeros((2, 2, 2), dtype=int)
    >>> a[d3] = 1
    >>> a
    array([[[1, 0],
            [0, 0]],
           [[0, 0],
            [0, 1]]])

Python Library Documentation: function diag_indices_from in module autograd.tracer

diag_indices_from(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the indices to access the main diagonal of an n-dimensional array.

    See `diag_indices` for full details.

    Parameters
    ----------
    arr : array, at least 2-D

    See Also
    --------
    diag_indices

    Notes
    -----
    .. versionadded:: 1.4.0

    Examples
    --------
    >>> import numpy as np

    Create a 4 by 4 array.

    >>> a = np.arange(16).reshape(4, 4)
    >>> a
    array([[ 0,  1,  2,  3],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11],
           [12, 13, 14, 15]])

    Get the indices of the diagonal elements.

    >>> di = np.diag_indices_from(a)
    >>> di
    (array([0, 1, 2, 3]), array([0, 1, 2, 3]))

    >>> a[di]
    array([ 0,  5, 10, 15])

    This is simply syntactic sugar for diag_indices.

    >>> np.diag_indices(a.shape[0])
    (array([0, 1, 2, 3]), array([0, 1, 2, 3]))

Python Library Documentation: function diagflat in module autograd.tracer

diagflat(*args, called_by_autograd_dispatcher=False, **kwargs)
    Create a two-dimensional array with the flattened input as a diagonal.

    Parameters
    ----------
    v : array_like
        Input data, which is flattened and set as the `k`-th
        diagonal of the output.
    k : int, optional
        Diagonal to set; 0, the default, corresponds to the "main" diagonal,
        a positive (negative) `k` giving the number of the diagonal above
        (below) the main.

    Returns
    -------
    out : ndarray
        The 2-D output array.

    See Also
    --------
    diag : MATLAB work-alike for 1-D and 2-D arrays.
    diagonal : Return specified diagonals.
    trace : Sum along diagonals.

    Examples
    --------
    >>> import numpy as np
    >>> np.diagflat([[1,2], [3,4]])
    array([[1, 0, 0, 0],
           [0, 2, 0, 0],
           [0, 0, 3, 0],
           [0, 0, 0, 4]])

    >>> np.diagflat([1,2], 1)
    array([[0, 1, 0],
           [0, 0, 2],
           [0, 0, 0]])

Python Library Documentation: function diagonal in module autograd.tracer

diagonal(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return specified diagonals.

    If `a` is 2-D, returns the diagonal of `a` with the given offset,
    i.e., the collection of elements of the form ``a[i, i+offset]``.  If
    `a` has more than two dimensions, then the axes specified by `axis1`
    and `axis2` are used to determine the 2-D sub-array whose diagonal is
    returned.  The shape of the resulting array can be determined by
    removing `axis1` and `axis2` and appending an index to the right equal
    to the size of the resulting diagonals.

    In versions of NumPy prior to 1.7, this function always returned a new,
    independent array containing a copy of the values in the diagonal.

    In NumPy 1.7 and 1.8, it continues to return a copy of the diagonal,
    but depending on this fact is deprecated. Writing to the resulting
    array continues to work as it used to, but a FutureWarning is issued.

    Starting in NumPy 1.9 it returns a read-only view on the original array.
    Attempting to write to the resulting array will produce an error.

    In some future release, it will return a read/write view and writing to
    the returned array will alter your original array.  The returned array
    will have the same type as the input array.

    If you don't write to the array returned by this function, then you can
    just ignore all of the above.

    If you depend on the current behavior, then we suggest copying the
    returned array explicitly, i.e., use ``np.diagonal(a).copy()`` instead
    of just ``np.diagonal(a)``. This will work with both past and future
    versions of NumPy.

    Parameters
    ----------
    a : array_like
        Array from which the diagonals are taken.
    offset : int, optional
        Offset of the diagonal from the main diagonal.  Can be positive or
        negative.  Defaults to main diagonal (0).
    axis1 : int, optional
        Axis to be used as the first axis of the 2-D sub-arrays from which
        the diagonals should be taken.  Defaults to first axis (0).
    axis2 : int, optional
        Axis to be used as the second axis of the 2-D sub-arrays from
        which the diagonals should be taken. Defaults to second axis (1).

    Returns
    -------
    array_of_diagonals : ndarray
        If `a` is 2-D, then a 1-D array containing the diagonal and of the
        same type as `a` is returned unless `a` is a `matrix`, in which case
        a 1-D array rather than a (2-D) `matrix` is returned in order to
        maintain backward compatibility.

        If ``a.ndim > 2``, then the dimensions specified by `axis1` and `axis2`
        are removed, and a new axis inserted at the end corresponding to the
        diagonal.

    Raises
    ------
    ValueError
        If the dimension of `a` is less than 2.

    See Also
    --------
    diag : MATLAB work-a-like for 1-D and 2-D arrays.
    diagflat : Create diagonal arrays.
    trace : Sum along diagonals.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.arange(4).reshape(2,2)
    >>> a
    array([[0, 1],
           [2, 3]])
    >>> a.diagonal()
    array([0, 3])
    >>> a.diagonal(1)
    array([1])

    A 3-D example:

    >>> a = np.arange(8).reshape(2,2,2); a
    array([[[0, 1],
            [2, 3]],
           [[4, 5],
            [6, 7]]])
    >>> a.diagonal(0,  # Main diagonals of two arrays created by skipping
    ...            0,  # across the outer(left)-most axis last and
    ...            1)  # the "middle" (row) axis first.
    array([[0, 6],
           [1, 7]])

    The sub-arrays whose main diagonals we just obtained; note that each
    corresponds to fixing the right-most (column) axis, and that the
    diagonals are "packed" in rows.

    >>> a[:,:,0]  # main diagonal is [0 6]
    array([[0, 2],
           [4, 6]])
    >>> a[:,:,1]  # main diagonal is [1 7]
    array([[1, 3],
           [5, 7]])

    The anti-diagonal can be obtained by reversing the order of elements
    using either `numpy.flipud` or `numpy.fliplr`.

    >>> a = np.arange(9).reshape(3, 3)
    >>> a
    array([[0, 1, 2],
           [3, 4, 5],
           [6, 7, 8]])
    >>> np.fliplr(a).diagonal()  # Horizontal flip
    array([2, 4, 6])
    >>> np.flipud(a).diagonal()  # Vertical flip
    array([6, 4, 2])

    Note that the order in which the diagonal is retrieved varies depending
    on the flip function.

Python Library Documentation: function diff in module autograd.tracer

diff(*args, called_by_autograd_dispatcher=False, **kwargs)
    Calculate the n-th discrete difference along the given axis.

    The first difference is given by ``out[i] = a[i+1] - a[i]`` along
    the given axis, higher differences are calculated by using `diff`
    recursively.

    Parameters
    ----------
    a : array_like
        Input array
    n : int, optional
        The number of times values are differenced. If zero, the input
        is returned as-is.
    axis : int, optional
        The axis along which the difference is taken, default is the
        last axis.
    prepend, append : array_like, optional
        Values to prepend or append to `a` along axis prior to
        performing the difference.  Scalar values are expanded to
        arrays with length 1 in the direction of axis and the shape
        of the input array in along all other axes.  Otherwise the
        dimension and shape must match `a` except along axis.

        .. versionadded:: 1.16.0

    Returns
    -------
    diff : ndarray
        The n-th differences. The shape of the output is the same as `a`
        except along `axis` where the dimension is smaller by `n`. The
        type of the output is the same as the type of the difference
        between any two elements of `a`. This is the same as the type of
        `a` in most cases. A notable exception is `datetime64`, which
        results in a `timedelta64` output array.

    See Also
    --------
    gradient, ediff1d, cumsum

    Notes
    -----
    Type is preserved for boolean arrays, so the result will contain
    `False` when consecutive elements are the same and `True` when they
    differ.

    For unsigned integer arrays, the results will also be unsigned. This
    should not be surprising, as the result is consistent with
    calculating the difference directly:

    >>> u8_arr = np.array([1, 0], dtype=np.uint8)
    >>> np.diff(u8_arr)
    array([255], dtype=uint8)
    >>> u8_arr[1,...] - u8_arr[0,...]
    255

    If this is not desirable, then the array should be cast to a larger
    integer type first:

    >>> i16_arr = u8_arr.astype(np.int16)
    >>> np.diff(i16_arr)
    array([-1], dtype=int16)

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([1, 2, 4, 7, 0])
    >>> np.diff(x)
    array([ 1,  2,  3, -7])
    >>> np.diff(x, n=2)
    array([  1,   1, -10])

    >>> x = np.array([[1, 3, 6, 10], [0, 5, 6, 8]])
    >>> np.diff(x)
    array([[2, 3, 4],
           [5, 1, 2]])
    >>> np.diff(x, axis=0)
    array([[-1,  2,  0, -2]])

    >>> x = np.arange('1066-10-13', '1066-10-16', dtype=np.datetime64)
    >>> np.diff(x)
    array([1, 1], dtype='timedelta64[D]')

Python Library Documentation: function digitize in module autograd.tracer

digitize(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the indices of the bins to which each value in input array belongs.

    =========  =============  ============================
    `right`    order of bins  returned index `i` satisfies
    =========  =============  ============================
    ``False``  increasing     ``bins[i-1] <= x < bins[i]``
    ``True``   increasing     ``bins[i-1] < x <= bins[i]``
    ``False``  decreasing     ``bins[i-1] > x >= bins[i]``
    ``True``   decreasing     ``bins[i-1] >= x > bins[i]``
    =========  =============  ============================

    If values in `x` are beyond the bounds of `bins`, 0 or ``len(bins)`` is
    returned as appropriate.

    Parameters
    ----------
    x : array_like
        Input array to be binned. Prior to NumPy 1.10.0, this array had to
        be 1-dimensional, but can now have any shape.
    bins : array_like
        Array of bins. It has to be 1-dimensional and monotonic.
    right : bool, optional
        Indicating whether the intervals include the right or the left bin
        edge. Default behavior is (right==False) indicating that the interval
        does not include the right edge. The left bin end is open in this
        case, i.e., bins[i-1] <= x < bins[i] is the default behavior for
        monotonically increasing bins.

    Returns
    -------
    indices : ndarray of ints
        Output array of indices, of same shape as `x`.

    Raises
    ------
    ValueError
        If `bins` is not monotonic.
    TypeError
        If the type of the input is complex.

    See Also
    --------
    bincount, histogram, unique, searchsorted

    Notes
    -----
    If values in `x` are such that they fall outside the bin range,
    attempting to index `bins` with the indices that `digitize` returns
    will result in an IndexError.

    .. versionadded:: 1.10.0

    `numpy.digitize` is  implemented in terms of `numpy.searchsorted`.
    This means that a binary search is used to bin the values, which scales
    much better for larger number of bins than the previous linear search.
    It also removes the requirement for the input array to be 1-dimensional.

    For monotonically *increasing* `bins`, the following are equivalent::

        np.digitize(x, bins, right=True)
        np.searchsorted(bins, x, side='left')

    Note that as the order of the arguments are reversed, the side must be too.
    The `searchsorted` call is marginally faster, as it does not do any
    monotonicity checks. Perhaps more importantly, it supports all dtypes.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([0.2, 6.4, 3.0, 1.6])
    >>> bins = np.array([0.0, 1.0, 2.5, 4.0, 10.0])
    >>> inds = np.digitize(x, bins)
    >>> inds
    array([1, 4, 3, 2])
    >>> for n in range(x.size):
    ...   print(bins[inds[n]-1], "<=", x[n], "<", bins[inds[n]])
    ...
    0.0 <= 0.2 < 1.0
    4.0 <= 6.4 < 10.0
    2.5 <= 3.0 < 4.0
    1.0 <= 1.6 < 2.5

    >>> x = np.array([1.2, 10.0, 12.4, 15.5, 20.])
    >>> bins = np.array([0, 5, 10, 15, 20])
    >>> np.digitize(x,bins,right=True)
    array([1, 2, 3, 4, 4])
    >>> np.digitize(x,bins,right=False)
    array([1, 3, 3, 4, 5])

Python Library Documentation: function divide in module autograd.tracer

divide(*args, called_by_autograd_dispatcher=False, **kwargs)
    divide(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Divide arguments element-wise.

    Parameters
    ----------
    x1 : array_like
        Dividend array.
    x2 : array_like
        Divisor array.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray or scalar
        The quotient ``x1/x2``, element-wise.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    seterr : Set whether to raise or warn on overflow, underflow and
             division by zero.

    Notes
    -----
    Equivalent to ``x1`` / ``x2`` in terms of array-broadcasting.

    The ``true_divide(x1, x2)`` function is an alias for
    ``divide(x1, x2)``.

    Examples
    --------
    >>> import numpy as np
    >>> np.divide(2.0, 4.0)
    0.5
    >>> x1 = np.arange(9.0).reshape((3, 3))
    >>> x2 = np.arange(3.0)
    >>> np.divide(x1, x2)
    array([[nan, 1. , 1. ],
           [inf, 4. , 2.5],
           [inf, 7. , 4. ]])

    The ``/`` operator can be used as a shorthand for ``np.divide`` on
    ndarrays.

    >>> x1 = np.arange(9.0).reshape((3, 3))
    >>> x2 = 2 * np.ones(3)
    >>> x1 / x2
    array([[0. , 0.5, 1. ],
           [1.5, 2. , 2.5],
           [3. , 3.5, 4. ]])

Python Library Documentation: function divmod in module autograd.tracer

divmod(*args, called_by_autograd_dispatcher=False, **kwargs)
    divmod(x1, x2[, out1, out2], / [, out=(None, None)], *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return element-wise quotient and remainder simultaneously.

    .. versionadded:: 1.13.0

    ``np.divmod(x, y)`` is equivalent to ``(x // y, x % y)``, but faster
    because it avoids redundant work. It is used to implement the Python
    built-in function ``divmod`` on NumPy arrays.

    Parameters
    ----------
    x1 : array_like
        Dividend array.
    x2 : array_like
        Divisor array.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out1 : ndarray
        Element-wise quotient resulting from floor division.
        This is a scalar if both `x1` and `x2` are scalars.
    out2 : ndarray
        Element-wise remainder from floor division.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    floor_divide : Equivalent to Python's ``//`` operator.
    remainder : Equivalent to Python's ``%`` operator.
    modf : Equivalent to ``divmod(x, 1)`` for positive ``x`` with the return
           values switched.

    Examples
    --------
    >>> import numpy as np
    >>> np.divmod(np.arange(5), 3)
    (array([0, 0, 0, 1, 1]), array([0, 1, 2, 0, 1]))

    The `divmod` function can be used as a shorthand for ``np.divmod`` on
    ndarrays.

    >>> x = np.arange(5)
    >>> divmod(x, 3)
    (array([0, 0, 0, 1, 1]), array([0, 1, 2, 0, 1]))

Python Library Documentation: function dot in module autograd.tracer

dot(*args, called_by_autograd_dispatcher=False, **kwargs)
    dot(a, b, out=None)

    Dot product of two arrays. Specifically,

    - If both `a` and `b` are 1-D arrays, it is inner product of vectors
      (without complex conjugation).

    - If both `a` and `b` are 2-D arrays, it is matrix multiplication,
      but using :func:`matmul` or ``a @ b`` is preferred.

    - If either `a` or `b` is 0-D (scalar), it is equivalent to
      :func:`multiply` and using ``numpy.multiply(a, b)`` or ``a * b`` is
      preferred.

    - If `a` is an N-D array and `b` is a 1-D array, it is a sum product over
      the last axis of `a` and `b`.

    - If `a` is an N-D array and `b` is an M-D array (where ``M>=2``), it is a
      sum product over the last axis of `a` and the second-to-last axis of
      `b`::

        dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])

    It uses an optimized BLAS library when possible (see `numpy.linalg`).

    Parameters
    ----------
    a : array_like
        First argument.
    b : array_like
        Second argument.
    out : ndarray, optional
        Output argument. This must have the exact kind that would be returned
        if it was not used. In particular, it must have the right type, must be
        C-contiguous, and its dtype must be the dtype that would be returned
        for `dot(a,b)`. This is a performance feature. Therefore, if these
        conditions are not met, an exception is raised, instead of attempting
        to be flexible.

    Returns
    -------
    output : ndarray
        Returns the dot product of `a` and `b`.  If `a` and `b` are both
        scalars or both 1-D arrays then a scalar is returned; otherwise
        an array is returned.
        If `out` is given, then it is returned.

    Raises
    ------
    ValueError
        If the last dimension of `a` is not the same size as
        the second-to-last dimension of `b`.

    See Also
    --------
    vdot : Complex-conjugating dot product.
    tensordot : Sum products over arbitrary axes.
    einsum : Einstein summation convention.
    matmul : '@' operator as method with out parameter.
    linalg.multi_dot : Chained dot product.

    Examples
    --------
    >>> import numpy as np
    >>> np.dot(3, 4)
    12

    Neither argument is complex-conjugated:

    >>> np.dot([2j, 3j], [2j, 3j])
    (-13+0j)

    For 2-D arrays it is the matrix product:

    >>> a = [[1, 0], [0, 1]]
    >>> b = [[4, 1], [2, 2]]
    >>> np.dot(a, b)
    array([[4, 1],
           [2, 2]])

    >>> a = np.arange(3*4*5*6).reshape((3,4,5,6))
    >>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3))
    >>> np.dot(a, b)[2,3,2,1,2,2]
    499128
    >>> sum(a[2,3,2,:] * b[1,2,:,2])
    499128

Python Library Documentation: class float64 in module numpy

class float64(floating, builtins.float)
 |  float64(x=0, /)
 |
 |  Double-precision floating-point number type, compatible with Python
 |  :class:`float` and C ``double``.
 |
 |  :Character code: ``'d'``
 |  :Canonical name: `numpy.double`
 |  :Alias on this platform (win32 AMD64): `numpy.float64`: 64-bit precision floating-point number type: sign bit, 11 bits exponent, 52 bits mantissa.
 |
 |  Method resolution order:
 |      float64
 |      floating
 |      inexact
 |      number
 |      generic
 |      builtins.float
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  as_integer_ratio(...)
 |      double.as_integer_ratio() -> (int, int)
 |
 |      Return a pair of integers, whose ratio is exactly equal to the original
 |      floating point number, and with a positive denominator.
 |      Raise `OverflowError` on infinities and a `ValueError` on NaNs.
 |
 |      >>> np.double(10.0).as_integer_ratio()
 |      (10, 1)
 |      >>> np.double(0.0).as_integer_ratio()
 |      (0, 1)
 |      >>> np.double(-.25).as_integer_ratio()
 |      (-1, 4)
 |
 |  is_integer(...)
 |      double.is_integer() -> bool
 |
 |      Return ``True`` if the floating point number is finite with integral
 |      value, and ``False`` otherwise.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> np.double(-2.0).is_integer()
 |      True
 |      >>> np.double(3.2).is_integer()
 |      False
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from floating:
 |
 |  __round__(...)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from builtins.float:
 |
 |  __ceil__(self, /)
 |      Return the ceiling as an Integral.
 |
 |  __floor__(self, /)
 |      Return the floor as an Integral.
 |
 |  __getnewargs__(self, /)
 |
 |  __trunc__(self, /)
 |      Return the Integral closest to x between 0 and x.
 |
 |  hex(self, /)
 |      Return a hexadecimal representation of a floating-point number.
 |
 |      >>> (-0.1).hex()
 |      '-0x1.999999999999ap-4'
 |      >>> 3.14159.hex()
 |      '0x1.921f9f01b866ep+1'
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from builtins.float:
 |
 |  __getformat__(typestr, /)
 |      You probably don't want to use this function.
 |
 |        typestr
 |          Must be 'double' or 'float'.
 |
 |      It exists mainly to be used in Python's test suite.
 |
 |      This function returns whichever of 'unknown', 'IEEE, big-endian' or 'IEEE,
 |      little-endian' best describes the format of floating-point numbers used by the
 |      C type named by typestr.
 |
 |  fromhex(string, /)
 |      Create a floating-point number from a hexadecimal string.
 |
 |      >>> float.fromhex('0x1.ffffp10')
 |      2047.984375
 |      >>> float.fromhex('-0x1p-1074')
 |      -5e-324

Python Library Documentation: function dsplit in module autograd.tracer

dsplit(*args, called_by_autograd_dispatcher=False, **kwargs)
    Split array into multiple sub-arrays along the 3rd axis (depth).

    Please refer to the `split` documentation.  `dsplit` is equivalent
    to `split` with ``axis=2``, the array is always split along the third
    axis provided the array dimension is greater than or equal to 3.

    See Also
    --------
    split : Split an array into multiple sub-arrays of equal size.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.arange(16.0).reshape(2, 2, 4)
    >>> x
    array([[[ 0.,   1.,   2.,   3.],
            [ 4.,   5.,   6.,   7.]],
           [[ 8.,   9.,  10.,  11.],
            [12.,  13.,  14.,  15.]]])
    >>> np.dsplit(x, 2)
    [array([[[ 0.,  1.],
            [ 4.,  5.]],
           [[ 8.,  9.],
            [12., 13.]]]), array([[[ 2.,  3.],
            [ 6.,  7.]],
           [[10., 11.],
            [14., 15.]]])]
    >>> np.dsplit(x, np.array([3, 6]))
    [array([[[ 0.,   1.,   2.],
            [ 4.,   5.,   6.]],
           [[ 8.,   9.,  10.],
            [12.,  13.,  14.]]]),
     array([[[ 3.],
            [ 7.]],
           [[11.],
            [15.]]]),
    array([], shape=(2, 2, 0), dtype=float64)]

Python Library Documentation: function dstack in module autograd.tracer

dstack(*args, called_by_autograd_dispatcher=False, **kwargs)
    Stack arrays in sequence depth wise (along third axis).

    This is equivalent to concatenation along the third axis after 2-D arrays
    of shape `(M,N)` have been reshaped to `(M,N,1)` and 1-D arrays of shape
    `(N,)` have been reshaped to `(1,N,1)`. Rebuilds arrays divided by
    `dsplit`.

    This function makes most sense for arrays with up to 3 dimensions. For
    instance, for pixel-data with a height (first axis), width (second axis),
    and r/g/b channels (third axis). The functions `concatenate`, `stack` and
    `block` provide more general stacking and concatenation operations.

    Parameters
    ----------
    tup : sequence of arrays
        The arrays must have the same shape along all but the third axis.
        1-D or 2-D arrays must have the same shape.

    Returns
    -------
    stacked : ndarray
        The array formed by stacking the given arrays, will be at least 3-D.

    See Also
    --------
    concatenate : Join a sequence of arrays along an existing axis.
    stack : Join a sequence of arrays along a new axis.
    block : Assemble an nd-array from nested lists of blocks.
    vstack : Stack arrays in sequence vertically (row wise).
    hstack : Stack arrays in sequence horizontally (column wise).
    column_stack : Stack 1-D arrays as columns into a 2-D array.
    dsplit : Split array along third axis.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array((1,2,3))
    >>> b = np.array((2,3,4))
    >>> np.dstack((a,b))
    array([[[1, 2],
            [2, 3],
            [3, 4]]])

    >>> a = np.array([[1],[2],[3]])
    >>> b = np.array([[2],[3],[4]])
    >>> np.dstack((a,b))
    array([[[1, 2]],
           [[2, 3]],
           [[3, 4]]])

Python Library Documentation: function dtype in module autograd.tracer

dtype(*args, called_by_autograd_dispatcher=False, **kwargs)
    dtype(dtype, align=False, copy=False, [metadata])

    Create a data type object.

    A numpy array is homogeneous, and contains elements described by a
    dtype object. A dtype object can be constructed from different
    combinations of fundamental numeric types.

    Parameters
    ----------
    dtype
        Object to be converted to a data type object.
    align : bool, optional
        Add padding to the fields to match what a C compiler would output
        for a similar C-struct. Can be ``True`` only if `obj` is a dictionary
        or a comma-separated string. If a struct dtype is being created,
        this also sets a sticky alignment flag ``isalignedstruct``.
    copy : bool, optional
        Make a new copy of the data-type object. If ``False``, the result
        may just be a reference to a built-in data-type object.
    metadata : dict, optional
        An optional dictionary with dtype metadata.

    See also
    --------
    result_type

    Examples
    --------
    Using array-scalar type:

    >>> import numpy as np
    >>> np.dtype(np.int16)
    dtype('int16')

    Structured type, one field name 'f1', containing int16:

    >>> np.dtype([('f1', np.int16)])
    dtype([('f1', '<i2')])

    Structured type, one field named 'f1', in itself containing a structured
    type with one field:

    >>> np.dtype([('f1', [('f1', np.int16)])])
    dtype([('f1', [('f1', '<i2')])])

    Structured type, two fields: the first field contains an unsigned int, the
    second an int32:

    >>> np.dtype([('f1', np.uint64), ('f2', np.int32)])
    dtype([('f1', '<u8'), ('f2', '<i4')])

    Using array-protocol type strings:

    >>> np.dtype([('a','f8'),('b','S10')])
    dtype([('a', '<f8'), ('b', 'S10')])

    Using comma-separated field formats.  The shape is (2,3):

    >>> np.dtype("i4, (2,3)f8")
    dtype([('f0', '<i4'), ('f1', '<f8', (2, 3))])

    Using tuples.  ``int`` is a fixed type, 3 the field's shape.  ``void``
    is a flexible type, here of size 10:

    >>> np.dtype([('hello',(np.int64,3)),('world',np.void,10)])
    dtype([('hello', '<i8', (3,)), ('world', 'V10')])

    Subdivide ``int16`` into 2 ``int8``'s, called x and y.  0 and 1 are
    the offsets in bytes:

    >>> np.dtype((np.int16, {'x':(np.int8,0), 'y':(np.int8,1)}))
    dtype((numpy.int16, [('x', 'i1'), ('y', 'i1')]))

    Using dictionaries.  Two fields named 'gender' and 'age':

    >>> np.dtype({'names':['gender','age'], 'formats':['S1',np.uint8]})
    dtype([('gender', 'S1'), ('age', 'u1')])

    Offsets in bytes, here 0 and 25:

    >>> np.dtype({'surname':('S25',0),'age':(np.uint8,25)})
    dtype([('surname', 'S25'), ('age', 'u1')])

Python Library Documentation: float object

class float(object)
 |  float(x=0, /)
 |
 |  Convert a string or number to a floating-point number, if possible.
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __ceil__(self, /)
 |      Return the ceiling as an Integral.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floor__(self, /)
 |      Return the floor as an Integral.
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(self, format_spec, /)
 |      Formats the float according to format_spec.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getnewargs__(self, /)
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __round__(self, ndigits=None, /)
 |      Return the Integral closest to x, rounding half toward even.
 |
 |      When an argument is passed, work like built-in round(x, ndigits).
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __trunc__(self, /)
 |      Return the Integral closest to x between 0 and x.
 |
 |  as_integer_ratio(self, /)
 |      Return a pair of integers, whose ratio is exactly equal to the original float.
 |
 |      The ratio is in lowest terms and has a positive denominator.  Raise
 |      OverflowError on infinities and a ValueError on NaNs.
 |
 |      >>> (10.0).as_integer_ratio()
 |      (10, 1)
 |      >>> (0.0).as_integer_ratio()
 |      (0, 1)
 |      >>> (-.25).as_integer_ratio()
 |      (-1, 4)
 |
 |  conjugate(self, /)
 |      Return self, the complex conjugate of any float.
 |
 |  hex(self, /)
 |      Return a hexadecimal representation of a floating-point number.
 |
 |      >>> (-0.1).hex()
 |      '-0x1.999999999999ap-4'
 |      >>> 3.14159.hex()
 |      '0x1.921f9f01b866ep+1'
 |
 |  is_integer(self, /)
 |      Return True if the float is an integer.
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __getformat__(typestr, /)
 |      You probably don't want to use this function.
 |
 |        typestr
 |          Must be 'double' or 'float'.
 |
 |      It exists mainly to be used in Python's test suite.
 |
 |      This function returns whichever of 'unknown', 'IEEE, big-endian' or 'IEEE,
 |      little-endian' best describes the format of floating-point numbers used by the
 |      C type named by typestr.
 |
 |  fromhex(string, /)
 |      Create a floating-point number from a hexadecimal string.
 |
 |      >>> float.fromhex('0x1.ffffp10')
 |      2047.984375
 |      >>> float.fromhex('-0x1p-1074')
 |      -5e-324
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  imag
 |      the imaginary part of a complex number
 |
 |  real
 |      the real part of a complex number

Python Library Documentation: function ediff1d in module autograd.tracer

ediff1d(*args, called_by_autograd_dispatcher=False, **kwargs)
    The differences between consecutive elements of an array.

    Parameters
    ----------
    ary : array_like
        If necessary, will be flattened before the differences are taken.
    to_end : array_like, optional
        Number(s) to append at the end of the returned differences.
    to_begin : array_like, optional
        Number(s) to prepend at the beginning of the returned differences.

    Returns
    -------
    ediff1d : ndarray
        The differences. Loosely, this is ``ary.flat[1:] - ary.flat[:-1]``.

    See Also
    --------
    diff, gradient

    Notes
    -----
    When applied to masked arrays, this function drops the mask information
    if the `to_begin` and/or `to_end` parameters are used.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([1, 2, 4, 7, 0])
    >>> np.ediff1d(x)
    array([ 1,  2,  3, -7])

    >>> np.ediff1d(x, to_begin=-99, to_end=np.array([88, 99]))
    array([-99,   1,   2, ...,  -7,  88,  99])

    The returned array is always 1D.

    >>> y = [[1, 2, 4], [1, 6, 24]]
    >>> np.ediff1d(y)
    array([ 1,  2, -3,  5, 18])

Python Library Documentation: function einsum in module autograd.tracer

einsum(*args, called_by_autograd_dispatcher=False, **kwargs)
    einsum(subscripts, *operands, out=None, dtype=None, order='K',
           casting='safe', optimize=False)

    Evaluates the Einstein summation convention on the operands.

    Using the Einstein summation convention, many common multi-dimensional,
    linear algebraic array operations can be represented in a simple fashion.
    In *implicit* mode `einsum` computes these values.

    In *explicit* mode, `einsum` provides further flexibility to compute
    other array operations that might not be considered classical Einstein
    summation operations, by disabling, or forcing summation over specified
    subscript labels.

    See the notes and examples for clarification.

    Parameters
    ----------
    subscripts : str
        Specifies the subscripts for summation as comma separated list of
        subscript labels. An implicit (classical Einstein summation)
        calculation is performed unless the explicit indicator '->' is
        included as well as subscript labels of the precise output form.
    operands : list of array_like
        These are the arrays for the operation.
    out : ndarray, optional
        If provided, the calculation is done into this array.
    dtype : {data-type, None}, optional
        If provided, forces the calculation to use the data type specified.
        Note that you may have to also give a more liberal `casting`
        parameter to allow the conversions. Default is None.
    order : {'C', 'F', 'A', 'K'}, optional
        Controls the memory layout of the output. 'C' means it should
        be C contiguous. 'F' means it should be Fortran contiguous,
        'A' means it should be 'F' if the inputs are all 'F', 'C' otherwise.
        'K' means it should be as close to the layout as the inputs as
        is possible, including arbitrarily permuted axes.
        Default is 'K'.
    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
        Controls what kind of data casting may occur.  Setting this to
        'unsafe' is not recommended, as it can adversely affect accumulations.

        * 'no' means the data types should not be cast at all.
        * 'equiv' means only byte-order changes are allowed.
        * 'safe' means only casts which can preserve values are allowed.
        * 'same_kind' means only safe casts or casts within a kind,
          like float64 to float32, are allowed.
        * 'unsafe' means any data conversions may be done.

        Default is 'safe'.
    optimize : {False, True, 'greedy', 'optimal'}, optional
        Controls if intermediate optimization should occur. No optimization
        will occur if False and True will default to the 'greedy' algorithm.
        Also accepts an explicit contraction list from the ``np.einsum_path``
        function. See ``np.einsum_path`` for more details. Defaults to False.

    Returns
    -------
    output : ndarray
        The calculation based on the Einstein summation convention.

    See Also
    --------
    einsum_path, dot, inner, outer, tensordot, linalg.multi_dot
    einsum:
        Similar verbose interface is provided by the
        `einops <https://github.com/arogozhnikov/einops>`_ package to cover
        additional operations: transpose, reshape/flatten, repeat/tile,
        squeeze/unsqueeze and reductions.
        The `opt_einsum <https://optimized-einsum.readthedocs.io/en/stable/>`_
        optimizes contraction order for einsum-like expressions
        in backend-agnostic manner.

    Notes
    -----
    .. versionadded:: 1.6.0

    The Einstein summation convention can be used to compute
    many multi-dimensional, linear algebraic array operations. `einsum`
    provides a succinct way of representing these.

    A non-exhaustive list of these operations,
    which can be computed by `einsum`, is shown below along with examples:

    * Trace of an array, :py:func:`numpy.trace`.
    * Return a diagonal, :py:func:`numpy.diag`.
    * Array axis summations, :py:func:`numpy.sum`.
    * Transpositions and permutations, :py:func:`numpy.transpose`.
    * Matrix multiplication and dot product, :py:func:`numpy.matmul`
        :py:func:`numpy.dot`.
    * Vector inner and outer products, :py:func:`numpy.inner`
        :py:func:`numpy.outer`.
    * Broadcasting, element-wise and scalar multiplication,
        :py:func:`numpy.multiply`.
    * Tensor contractions, :py:func:`numpy.tensordot`.
    * Chained array operations, in efficient calculation order,
        :py:func:`numpy.einsum_path`.

    The subscripts string is a comma-separated list of subscript labels,
    where each label refers to a dimension of the corresponding operand.
    Whenever a label is repeated it is summed, so ``np.einsum('i,i', a, b)``
    is equivalent to :py:func:`np.inner(a,b) <numpy.inner>`. If a label
    appears only once, it is not summed, so ``np.einsum('i', a)``
    produces a view of ``a`` with no changes. A further example
    ``np.einsum('ij,jk', a, b)`` describes traditional matrix multiplication
    and is equivalent to :py:func:`np.matmul(a,b) <numpy.matmul>`.
    Repeated subscript labels in one operand take the diagonal.
    For example, ``np.einsum('ii', a)`` is equivalent to
    :py:func:`np.trace(a) <numpy.trace>`.

    In *implicit mode*, the chosen subscripts are important
    since the axes of the output are reordered alphabetically.  This
    means that ``np.einsum('ij', a)`` doesn't affect a 2D array, while
    ``np.einsum('ji', a)`` takes its transpose. Additionally,
    ``np.einsum('ij,jk', a, b)`` returns a matrix multiplication, while,
    ``np.einsum('ij,jh', a, b)`` returns the transpose of the
    multiplication since subscript 'h' precedes subscript 'i'.

    In *explicit mode* the output can be directly controlled by
    specifying output subscript labels.  This requires the
    identifier '->' as well as the list of output subscript labels.
    This feature increases the flexibility of the function since
    summing can be disabled or forced when required. The call
    ``np.einsum('i->', a)`` is like :py:func:`np.sum(a) <numpy.sum>`
    if ``a`` is a 1-D array, and ``np.einsum('ii->i', a)``
    is like :py:func:`np.diag(a) <numpy.diag>` if ``a`` is a square 2-D array.
    The difference is that `einsum` does not allow broadcasting by default.
    Additionally ``np.einsum('ij,jh->ih', a, b)`` directly specifies the
    order of the output subscript labels and therefore returns matrix
    multiplication, unlike the example above in implicit mode.

    To enable and control broadcasting, use an ellipsis.  Default
    NumPy-style broadcasting is done by adding an ellipsis
    to the left of each term, like ``np.einsum('...ii->...i', a)``.
    ``np.einsum('...i->...', a)`` is like
    :py:func:`np.sum(a, axis=-1) <numpy.sum>` for array ``a`` of any shape.
    To take the trace along the first and last axes,
    you can do ``np.einsum('i...i', a)``, or to do a matrix-matrix
    product with the left-most indices instead of rightmost, one can do
    ``np.einsum('ij...,jk...->ik...', a, b)``.

    When there is only one operand, no axes are summed, and no output
    parameter is provided, a view into the operand is returned instead
    of a new array.  Thus, taking the diagonal as ``np.einsum('ii->i', a)``
    produces a view (changed in version 1.10.0).

    `einsum` also provides an alternative way to provide the subscripts and
    operands as ``einsum(op0, sublist0, op1, sublist1, ..., [sublistout])``.
    If the output shape is not provided in this format `einsum` will be
    calculated in implicit mode, otherwise it will be performed explicitly.
    The examples below have corresponding `einsum` calls with the two
    parameter methods.

    .. versionadded:: 1.10.0

    Views returned from einsum are now writeable whenever the input array
    is writeable. For example, ``np.einsum('ijk...->kji...', a)`` will now
    have the same effect as :py:func:`np.swapaxes(a, 0, 2) <numpy.swapaxes>`
    and ``np.einsum('ii->i', a)`` will return a writeable view of the diagonal
    of a 2D array.

    .. versionadded:: 1.12.0

    Added the ``optimize`` argument which will optimize the contraction order
    of an einsum expression. For a contraction with three or more operands
    this can greatly increase the computational efficiency at the cost of
    a larger memory footprint during computation.

    Typically a 'greedy' algorithm is applied which empirical tests have shown
    returns the optimal path in the majority of cases. In some cases 'optimal'
    will return the superlative path through a more expensive, exhaustive
    search. For iterative calculations it may be advisable to calculate
    the optimal path once and reuse that path by supplying it as an argument.
    An example is given below.

    See :py:func:`numpy.einsum_path` for more details.

    Examples
    --------
    >>> a = np.arange(25).reshape(5,5)
    >>> b = np.arange(5)
    >>> c = np.arange(6).reshape(2,3)

    Trace of a matrix:

    >>> np.einsum('ii', a)
    60
    >>> np.einsum(a, [0,0])
    60
    >>> np.trace(a)
    60

    Extract the diagonal (requires explicit form):

    >>> np.einsum('ii->i', a)
    array([ 0,  6, 12, 18, 24])
    >>> np.einsum(a, [0,0], [0])
    array([ 0,  6, 12, 18, 24])
    >>> np.diag(a)
    array([ 0,  6, 12, 18, 24])

    Sum over an axis (requires explicit form):

    >>> np.einsum('ij->i', a)
    array([ 10,  35,  60,  85, 110])
    >>> np.einsum(a, [0,1], [0])
    array([ 10,  35,  60,  85, 110])
    >>> np.sum(a, axis=1)
    array([ 10,  35,  60,  85, 110])

    For higher dimensional arrays summing a single axis can be done
    with ellipsis:

    >>> np.einsum('...j->...', a)
    array([ 10,  35,  60,  85, 110])
    >>> np.einsum(a, [Ellipsis,1], [Ellipsis])
    array([ 10,  35,  60,  85, 110])

    Compute a matrix transpose, or reorder any number of axes:

    >>> np.einsum('ji', c)
    array([[0, 3],
           [1, 4],
           [2, 5]])
    >>> np.einsum('ij->ji', c)
    array([[0, 3],
           [1, 4],
           [2, 5]])
    >>> np.einsum(c, [1,0])
    array([[0, 3],
           [1, 4],
           [2, 5]])
    >>> np.transpose(c)
    array([[0, 3],
           [1, 4],
           [2, 5]])

    Vector inner products:

    >>> np.einsum('i,i', b, b)
    30
    >>> np.einsum(b, [0], b, [0])
    30
    >>> np.inner(b,b)
    30

    Matrix vector multiplication:

    >>> np.einsum('ij,j', a, b)
    array([ 30,  80, 130, 180, 230])
    >>> np.einsum(a, [0,1], b, [1])
    array([ 30,  80, 130, 180, 230])
    >>> np.dot(a, b)
    array([ 30,  80, 130, 180, 230])
    >>> np.einsum('...j,j', a, b)
    array([ 30,  80, 130, 180, 230])

    Broadcasting and scalar multiplication:

    >>> np.einsum('..., ...', 3, c)
    array([[ 0,  3,  6],
           [ 9, 12, 15]])
    >>> np.einsum(',ij', 3, c)
    array([[ 0,  3,  6],
           [ 9, 12, 15]])
    >>> np.einsum(3, [Ellipsis], c, [Ellipsis])
    array([[ 0,  3,  6],
           [ 9, 12, 15]])
    >>> np.multiply(3, c)
    array([[ 0,  3,  6],
           [ 9, 12, 15]])

    Vector outer product:

    >>> np.einsum('i,j', np.arange(2)+1, b)
    array([[0, 1, 2, 3, 4],
           [0, 2, 4, 6, 8]])
    >>> np.einsum(np.arange(2)+1, [0], b, [1])
    array([[0, 1, 2, 3, 4],
           [0, 2, 4, 6, 8]])
    >>> np.outer(np.arange(2)+1, b)
    array([[0, 1, 2, 3, 4],
           [0, 2, 4, 6, 8]])

    Tensor contraction:

    >>> a = np.arange(60.).reshape(3,4,5)
    >>> b = np.arange(24.).reshape(4,3,2)
    >>> np.einsum('ijk,jil->kl', a, b)
    array([[4400., 4730.],
           [4532., 4874.],
           [4664., 5018.],
           [4796., 5162.],
           [4928., 5306.]])
    >>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3])
    array([[4400., 4730.],
           [4532., 4874.],
           [4664., 5018.],
           [4796., 5162.],
           [4928., 5306.]])
    >>> np.tensordot(a,b, axes=([1,0],[0,1]))
    array([[4400., 4730.],
           [4532., 4874.],
           [4664., 5018.],
           [4796., 5162.],
           [4928., 5306.]])

    Writeable returned arrays (since version 1.10.0):

    >>> a = np.zeros((3, 3))
    >>> np.einsum('ii->i', a)[:] = 1
    >>> a
    array([[1., 0., 0.],
           [0., 1., 0.],
           [0., 0., 1.]])

    Example of ellipsis use:

    >>> a = np.arange(6).reshape((3,2))
    >>> b = np.arange(12).reshape((4,3))
    >>> np.einsum('ki,jk->ij', a, b)
    array([[10, 28, 46, 64],
           [13, 40, 67, 94]])
    >>> np.einsum('ki,...k->i...', a, b)
    array([[10, 28, 46, 64],
           [13, 40, 67, 94]])
    >>> np.einsum('k...,jk', a, b)
    array([[10, 28, 46, 64],
           [13, 40, 67, 94]])

    Chained array operations. For more complicated contractions, speed ups
    might be achieved by repeatedly computing a 'greedy' path or pre-computing
    the 'optimal' path and repeatedly applying it, using an `einsum_path`
    insertion (since version 1.12.0). Performance improvements can be
    particularly significant with larger arrays:

    >>> a = np.ones(64).reshape(2,4,8)

    Basic `einsum`: ~1520ms  (benchmarked on 3.1GHz Intel i5.)

    >>> for iteration in range(500):
    ...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a)

    Sub-optimal `einsum` (due to repeated path calculation time): ~330ms

    >>> for iteration in range(500):
    ...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a,
    ...         optimize='optimal')

    Greedy `einsum` (faster optimal path approximation): ~160ms

    >>> for iteration in range(500):
    ...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='greedy')

    Optimal `einsum` (best usage pattern in some use cases): ~110ms

    >>> path = np.einsum_path('ijk,ilm,njm,nlk,abc->',a,a,a,a,a,
    ...     optimize='optimal')[0]
    >>> for iteration in range(500):
    ...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize=path)

Python Library Documentation: function einsum_path in module autograd.tracer

einsum_path(*args, called_by_autograd_dispatcher=False, **kwargs)
    einsum_path(subscripts, *operands, optimize='greedy')

    Evaluates the lowest cost contraction order for an einsum expression by
    considering the creation of intermediate arrays.

    Parameters
    ----------
    subscripts : str
        Specifies the subscripts for summation.
    *operands : list of array_like
        These are the arrays for the operation.
    optimize : {bool, list, tuple, 'greedy', 'optimal'}
        Choose the type of path. If a tuple is provided, the second argument is
        assumed to be the maximum intermediate size created. If only a single
        argument is provided the largest input or output array size is used
        as a maximum intermediate size.

        * if a list is given that starts with ``einsum_path``, uses this as the
          contraction path
        * if False no optimization is taken
        * if True defaults to the 'greedy' algorithm
        * 'optimal' An algorithm that combinatorially explores all possible
          ways of contracting the listed tensors and chooses the least costly
          path. Scales exponentially with the number of terms in the
          contraction.
        * 'greedy' An algorithm that chooses the best pair contraction
          at each step. Effectively, this algorithm searches the largest inner,
          Hadamard, and then outer products at each step. Scales cubically with
          the number of terms in the contraction. Equivalent to the 'optimal'
          path for most contractions.

        Default is 'greedy'.

    Returns
    -------
    path : list of tuples
        A list representation of the einsum path.
    string_repr : str
        A printable representation of the einsum path.

    Notes
    -----
    The resulting path indicates which terms of the input contraction should be
    contracted first, the result of this contraction is then appended to the
    end of the contraction list. This list can then be iterated over until all
    intermediate contractions are complete.

    See Also
    --------
    einsum, linalg.multi_dot

    Examples
    --------

    We can begin with a chain dot example. In this case, it is optimal to
    contract the ``b`` and ``c`` tensors first as represented by the first
    element of the path ``(1, 2)``. The resulting tensor is added to the end
    of the contraction and the remaining contraction ``(0, 1)`` is then
    completed.

    >>> np.random.seed(123)
    >>> a = np.random.rand(2, 2)
    >>> b = np.random.rand(2, 5)
    >>> c = np.random.rand(5, 2)
    >>> path_info = np.einsum_path('ij,jk,kl->il', a, b, c, optimize='greedy')
    >>> print(path_info[0])
    ['einsum_path', (1, 2), (0, 1)]
    >>> print(path_info[1])
      Complete contraction:  ij,jk,kl->il # may vary
             Naive scaling:  4
         Optimized scaling:  3
          Naive FLOP count:  1.600e+02
      Optimized FLOP count:  5.600e+01
       Theoretical speedup:  2.857
      Largest intermediate:  4.000e+00 elements
    -------------------------------------------------------------------------
    scaling                  current                                remaining
    -------------------------------------------------------------------------
       3                   kl,jk->jl                                ij,jl->il
       3                   jl,ij->il                                   il->il


    A more complex index transformation example.

    >>> I = np.random.rand(10, 10, 10, 10)
    >>> C = np.random.rand(10, 10)
    >>> path_info = np.einsum_path('ea,fb,abcd,gc,hd->efgh', C, C, I, C, C,
    ...                            optimize='greedy')

    >>> print(path_info[0])
    ['einsum_path', (0, 2), (0, 3), (0, 2), (0, 1)]
    >>> print(path_info[1])
      Complete contraction:  ea,fb,abcd,gc,hd->efgh # may vary
             Naive scaling:  8
         Optimized scaling:  5
          Naive FLOP count:  8.000e+08
      Optimized FLOP count:  8.000e+05
       Theoretical speedup:  1000.000
      Largest intermediate:  1.000e+04 elements
    --------------------------------------------------------------------------
    scaling                  current                                remaining
    --------------------------------------------------------------------------
       5               abcd,ea->bcde                      fb,gc,hd,bcde->efgh
       5               bcde,fb->cdef                         gc,hd,cdef->efgh
       5               cdef,gc->defg                            hd,defg->efgh
       5               defg,hd->efgh                               efgh->efgh

Python Library Documentation: function empty in module autograd.tracer

empty(*args, called_by_autograd_dispatcher=False, **kwargs)
    empty(shape, dtype=float, order='C', *, device=None, like=None)

    Return a new array of given shape and type, without initializing entries.

    Parameters
    ----------
    shape : int or tuple of int
        Shape of the empty array, e.g., ``(2, 3)`` or ``2``.
    dtype : data-type, optional
        Desired output data-type for the array, e.g, `numpy.int8`. Default is
        `numpy.float64`.
    order : {'C', 'F'}, optional, default: 'C'
        Whether to store multi-dimensional data in row-major
        (C-style) or column-major (Fortran-style) order in
        memory.
    device : str, optional
        The device on which to place the created array. Default: ``None``.
        For Array-API interoperability only, so must be ``"cpu"`` if passed.

        .. versionadded:: 2.0.0
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    out : ndarray
        Array of uninitialized (arbitrary) data of the given shape, dtype, and
        order.  Object arrays will be initialized to None.

    See Also
    --------
    empty_like : Return an empty array with shape and type of input.
    ones : Return a new array setting values to one.
    zeros : Return a new array setting values to zero.
    full : Return a new array of given shape filled with value.

    Notes
    -----
    Unlike other array creation functions (e.g. `zeros`, `ones`, `full`),
    `empty` does not initialize the values of the array, and may therefore be
    marginally faster. However, the values stored in the newly allocated array
    are arbitrary. For reproducible behavior, be sure to set each element of
    the array before reading.

    Examples
    --------
    >>> import numpy as np
    >>> np.empty([2, 2])
    array([[ -9.74499359e+001,   6.69583040e-309],
           [  2.13182611e-314,   3.06959433e-309]])         #uninitialized

    >>> np.empty([2, 2], dtype=int)
    array([[-1073741821, -1067949133],
           [  496041986,    19249760]])                     #uninitialized

Python Library Documentation: function empty_like in module autograd.tracer

empty_like(*args, called_by_autograd_dispatcher=False, **kwargs)
    empty_like(prototype, dtype=None, order='K', subok=True, shape=None, *,
               device=None)

    Return a new array with the same shape and type as a given array.

    Parameters
    ----------
    prototype : array_like
        The shape and data-type of `prototype` define these same attributes
        of the returned array.
    dtype : data-type, optional
        Overrides the data type of the result.

        .. versionadded:: 1.6.0
    order : {'C', 'F', 'A', or 'K'}, optional
        Overrides the memory layout of the result. 'C' means C-order,
        'F' means F-order, 'A' means 'F' if `prototype` is Fortran
        contiguous, 'C' otherwise. 'K' means match the layout of `prototype`
        as closely as possible.

        .. versionadded:: 1.6.0
    subok : bool, optional.
        If True, then the newly created array will use the sub-class
        type of `prototype`, otherwise it will be a base-class array. Defaults
        to True.
    shape : int or sequence of ints, optional.
        Overrides the shape of the result. If order='K' and the number of
        dimensions is unchanged, will try to keep order, otherwise,
        order='C' is implied.

        .. versionadded:: 1.17.0
    device : str, optional
        The device on which to place the created array. Default: None.
        For Array-API interoperability only, so must be ``"cpu"`` if passed.

        .. versionadded:: 2.0.0

    Returns
    -------
    out : ndarray
        Array of uninitialized (arbitrary) data with the same
        shape and type as `prototype`.

    See Also
    --------
    ones_like : Return an array of ones with shape and type of input.
    zeros_like : Return an array of zeros with shape and type of input.
    full_like : Return a new array with shape of input filled with value.
    empty : Return a new uninitialized array.

    Notes
    -----
    Unlike other array creation functions (e.g. `zeros_like`, `ones_like`,
    `full_like`), `empty_like` does not initialize the values of the array,
    and may therefore be marginally faster. However, the values stored in the
    newly allocated array are arbitrary. For reproducible behavior, be sure
    to set each element of the array before reading.

    Examples
    --------
    >>> import numpy as np
    >>> a = ([1,2,3], [4,5,6])                         # a is array-like
    >>> np.empty_like(a)
    array([[-1073741821, -1073741821,           3],    # uninitialized
           [          0,           0, -1073741821]])
    >>> a = np.array([[1., 2., 3.],[4.,5.,6.]])
    >>> np.empty_like(a)
    array([[ -2.00000715e+000,   1.48219694e-323,  -2.00000572e+000], # uninitialized
           [  4.38791518e-305,  -2.00000715e+000,   4.17269252e-309]])

Python Library Documentation: function equal in module autograd.tracer

equal(*args, called_by_autograd_dispatcher=False, **kwargs)
    equal(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return (x1 == x2) element-wise.

    Parameters
    ----------
    x1, x2 : array_like
        Input arrays.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Output array, element-wise comparison of `x1` and `x2`.
        Typically of type bool, unless ``dtype=object`` is passed.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    not_equal, greater_equal, less_equal, greater, less

    Examples
    --------
    >>> import numpy as np
    >>> np.equal([0, 1, 3], np.arange(3))
    array([ True,  True, False])

    What is compared are values, not types. So an int (1) and an array of
    length one can evaluate as True:

    >>> np.equal(1, np.ones(1))
    array([ True])

    The ``==`` operator can be used as a shorthand for ``np.equal`` on
    ndarrays.

    >>> a = np.array([2, 4, 6])
    >>> b = np.array([2, 4, 2])
    >>> a == b
    array([ True,  True, False])

Python Library Documentation: class errstate in module numpy

class errstate(builtins.object)
 |  errstate(*, call=<numpy._core._ufunc_config._unspecified object at 0x000001DD1619E810>, all=None, divide=None, over=None, under=None, invalid=None)
 |
 |  errstate(**kwargs)
 |
 |  Context manager for floating-point error handling.
 |
 |  Using an instance of `errstate` as a context manager allows statements in
 |  that context to execute with a known error handling behavior. Upon entering
 |  the context the error handling is set with `seterr` and `seterrcall`, and
 |  upon exiting it is reset to what it was before.
 |
 |  ..  versionchanged:: 1.17.0
 |      `errstate` is also usable as a function decorator, saving
 |      a level of indentation if an entire function is wrapped.
 |
 |  .. versionchanged:: 2.0
 |      `errstate` is now fully thread and asyncio safe, but may not be
 |      entered more than once.
 |      It is not safe to decorate async functions using ``errstate``.
 |
 |  Parameters
 |  ----------
 |  kwargs : {divide, over, under, invalid}
 |      Keyword arguments. The valid keywords are the possible floating-point
 |      exceptions. Each keyword should have a string value that defines the
 |      treatment for the particular error. Possible values are
 |      {'ignore', 'warn', 'raise', 'call', 'print', 'log'}.
 |
 |  See Also
 |  --------
 |  seterr, geterr, seterrcall, geterrcall
 |
 |  Notes
 |  -----
 |  For complete documentation of the types of floating-point exceptions and
 |  treatment options, see `seterr`.
 |
 |  Examples
 |  --------
 |  >>> import numpy as np
 |  >>> olderr = np.seterr(all='ignore')  # Set error handling to known state.
 |
 |  >>> np.arange(3) / 0.
 |  array([nan, inf, inf])
 |  >>> with np.errstate(divide='ignore'):
 |  ...     np.arange(3) / 0.
 |  array([nan, inf, inf])
 |
 |  >>> np.sqrt(-1)
 |  np.float64(nan)
 |  >>> with np.errstate(invalid='raise'):
 |  ...     np.sqrt(-1)
 |  Traceback (most recent call last):
 |    File "<stdin>", line 2, in <module>
 |  FloatingPointError: invalid value encountered in sqrt
 |
 |  Outside the context the error handling behavior has not changed:
 |
 |  >>> np.geterr()
 |  {'divide': 'ignore', 'over': 'ignore', 'under': 'ignore', 'invalid': 'ignore'}
 |  >>> olderr = np.seterr(**olderr)  # restore original state
 |
 |  Methods defined here:
 |
 |  __call__(self, func) from numpy._core._ufunc_config.errstate
 |      Call self as a function.
 |
 |  __enter__(self) from numpy._core._ufunc_config.errstate
 |
 |  __exit__(self, *exc_info) from numpy._core._ufunc_config.errstate
 |
 |  __init__(self, *, call=<numpy._core._ufunc_config._unspecified object at 0x000001DD1619E810>, all=None, divide=None, over=None, under=None, invalid=None) from numpy._core._ufunc_config.errstate
 |      Initialize self.  See help(type(self)) for accurate signature.

Python Library Documentation: float object

class float(object)
 |  float(x=0, /)
 |
 |  Convert a string or number to a floating-point number, if possible.
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __ceil__(self, /)
 |      Return the ceiling as an Integral.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floor__(self, /)
 |      Return the floor as an Integral.
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(self, format_spec, /)
 |      Formats the float according to format_spec.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getnewargs__(self, /)
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __round__(self, ndigits=None, /)
 |      Return the Integral closest to x, rounding half toward even.
 |
 |      When an argument is passed, work like built-in round(x, ndigits).
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __trunc__(self, /)
 |      Return the Integral closest to x between 0 and x.
 |
 |  as_integer_ratio(self, /)
 |      Return a pair of integers, whose ratio is exactly equal to the original float.
 |
 |      The ratio is in lowest terms and has a positive denominator.  Raise
 |      OverflowError on infinities and a ValueError on NaNs.
 |
 |      >>> (10.0).as_integer_ratio()
 |      (10, 1)
 |      >>> (0.0).as_integer_ratio()
 |      (0, 1)
 |      >>> (-.25).as_integer_ratio()
 |      (-1, 4)
 |
 |  conjugate(self, /)
 |      Return self, the complex conjugate of any float.
 |
 |  hex(self, /)
 |      Return a hexadecimal representation of a floating-point number.
 |
 |      >>> (-0.1).hex()
 |      '-0x1.999999999999ap-4'
 |      >>> 3.14159.hex()
 |      '0x1.921f9f01b866ep+1'
 |
 |  is_integer(self, /)
 |      Return True if the float is an integer.
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __getformat__(typestr, /)
 |      You probably don't want to use this function.
 |
 |        typestr
 |          Must be 'double' or 'float'.
 |
 |      It exists mainly to be used in Python's test suite.
 |
 |      This function returns whichever of 'unknown', 'IEEE, big-endian' or 'IEEE,
 |      little-endian' best describes the format of floating-point numbers used by the
 |      C type named by typestr.
 |
 |  fromhex(string, /)
 |      Create a floating-point number from a hexadecimal string.
 |
 |      >>> float.fromhex('0x1.ffffp10')
 |      2047.984375
 |      >>> float.fromhex('-0x1p-1074')
 |      -5e-324
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  imag
 |      the imaginary part of a complex number
 |
 |  real
 |      the real part of a complex number

Python Library Documentation: function exp in module autograd.tracer

exp(*args, called_by_autograd_dispatcher=False, **kwargs)
    exp(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Calculate the exponential of all elements in the input array.

    Parameters
    ----------
    x : array_like
        Input values.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Output array, element-wise exponential of `x`.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    expm1 : Calculate ``exp(x) - 1`` for all elements in the array.
    exp2  : Calculate ``2**x`` for all elements in the array.

    Notes
    -----
    The irrational number ``e`` is also known as Euler's number.  It is
    approximately 2.718281, and is the base of the natural logarithm,
    ``ln`` (this means that, if :math:`x = \ln y = \log_e y`,
    then :math:`e^x = y`. For real input, ``exp(x)`` is always positive.

    For complex arguments, ``x = a + ib``, we can write
    :math:`e^x = e^a e^{ib}`.  The first term, :math:`e^a`, is already
    known (it is the real argument, described above).  The second term,
    :math:`e^{ib}`, is :math:`\cos b + i \sin b`, a function with
    magnitude 1 and a periodic phase.

    References
    ----------
    .. [1] Wikipedia, "Exponential function",
           https://en.wikipedia.org/wiki/Exponential_function
    .. [2] M. Abramovitz and I. A. Stegun, "Handbook of Mathematical Functions
           with Formulas, Graphs, and Mathematical Tables," Dover, 1964, p. 69,
           https://personal.math.ubc.ca/~cbm/aands/page_69.htm

    Examples
    --------
    Plot the magnitude and phase of ``exp(x)`` in the complex plane:

    >>> import numpy as np

    >>> import matplotlib.pyplot as plt

    >>> x = np.linspace(-2*np.pi, 2*np.pi, 100)
    >>> xx = x + 1j * x[:, np.newaxis] # a + ib over complex plane
    >>> out = np.exp(xx)

    >>> plt.subplot(121)
    >>> plt.imshow(np.abs(out),
    ...            extent=[-2*np.pi, 2*np.pi, -2*np.pi, 2*np.pi], cmap='gray')
    >>> plt.title('Magnitude of exp(x)')

    >>> plt.subplot(122)
    >>> plt.imshow(np.angle(out),
    ...            extent=[-2*np.pi, 2*np.pi, -2*np.pi, 2*np.pi], cmap='hsv')
    >>> plt.title('Phase (angle) of exp(x)')
    >>> plt.show()

Python Library Documentation: function exp2 in module autograd.tracer

exp2(*args, called_by_autograd_dispatcher=False, **kwargs)
    exp2(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Calculate `2**p` for all `p` in the input array.

    Parameters
    ----------
    x : array_like
        Input values.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Element-wise 2 to the power `x`.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    power

    Notes
    -----
    .. versionadded:: 1.3.0



    Examples
    --------
    >>> import numpy as np
    >>> np.exp2([2, 3])
    array([ 4.,  8.])

Python Library Documentation: function expand_dims in module autograd.tracer

expand_dims(*args, called_by_autograd_dispatcher=False, **kwargs)
    Expand the shape of an array.

    Insert a new axis that will appear at the `axis` position in the expanded
    array shape.

    Parameters
    ----------
    a : array_like
        Input array.
    axis : int or tuple of ints
        Position in the expanded axes where the new axis (or axes) is placed.

        .. deprecated:: 1.13.0
            Passing an axis where ``axis > a.ndim`` will be treated as
            ``axis == a.ndim``, and passing ``axis < -a.ndim - 1`` will
            be treated as ``axis == 0``. This behavior is deprecated.

        .. versionchanged:: 1.18.0
            A tuple of axes is now supported.  Out of range axes as
            described above are now forbidden and raise an
            `~exceptions.AxisError`.

    Returns
    -------
    result : ndarray
        View of `a` with the number of dimensions increased.

    See Also
    --------
    squeeze : The inverse operation, removing singleton dimensions
    reshape : Insert, remove, and combine dimensions, and resize existing ones
    atleast_1d, atleast_2d, atleast_3d

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([1, 2])
    >>> x.shape
    (2,)

    The following is equivalent to ``x[np.newaxis, :]`` or ``x[np.newaxis]``:

    >>> y = np.expand_dims(x, axis=0)
    >>> y
    array([[1, 2]])
    >>> y.shape
    (1, 2)

    The following is equivalent to ``x[:, np.newaxis]``:

    >>> y = np.expand_dims(x, axis=1)
    >>> y
    array([[1],
           [2]])
    >>> y.shape
    (2, 1)

    ``axis`` may also be a tuple:

    >>> y = np.expand_dims(x, axis=(0, 1))
    >>> y
    array([[[1, 2]]])

    >>> y = np.expand_dims(x, axis=(2, 0))
    >>> y
    array([[[1],
            [2]]])

    Note that some examples may use ``None`` instead of ``np.newaxis``.  These
    are the same objects:

    >>> np.newaxis is None
    True

Python Library Documentation: function expm1 in module autograd.tracer

expm1(*args, called_by_autograd_dispatcher=False, **kwargs)
    expm1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Calculate ``exp(x) - 1`` for all elements in the array.

    Parameters
    ----------
    x : array_like
        Input values.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Element-wise exponential minus one: ``out = exp(x) - 1``.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    log1p : ``log(1 + x)``, the inverse of expm1.


    Notes
    -----
    This function provides greater precision than ``exp(x) - 1``
    for small values of ``x``.

    Examples
    --------
    The true value of ``exp(1e-10) - 1`` is ``1.00000000005e-10`` to
    about 32 significant digits. This example shows the superiority of
    expm1 in this case.

    >>> import numpy as np

    >>> np.expm1(1e-10)
    1.00000000005e-10
    >>> np.exp(1e-10) - 1
    1.000000082740371e-10

Python Library Documentation: function extract in module autograd.tracer

extract(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the elements of an array that satisfy some condition.

    This is equivalent to ``np.compress(ravel(condition), ravel(arr))``.  If
    `condition` is boolean ``np.extract`` is equivalent to ``arr[condition]``.

    Note that `place` does the exact opposite of `extract`.

    Parameters
    ----------
    condition : array_like
        An array whose nonzero or True entries indicate the elements of `arr`
        to extract.
    arr : array_like
        Input array of the same size as `condition`.

    Returns
    -------
    extract : ndarray
        Rank 1 array of values from `arr` where `condition` is True.

    See Also
    --------
    take, put, copyto, compress, place

    Examples
    --------
    >>> import numpy as np
    >>> arr = np.arange(12).reshape((3, 4))
    >>> arr
    array([[ 0,  1,  2,  3],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11]])
    >>> condition = np.mod(arr, 3)==0
    >>> condition
    array([[ True, False, False,  True],
           [False, False,  True, False],
           [False,  True, False, False]])
    >>> np.extract(condition, arr)
    array([0, 3, 6, 9])


    If `condition` is boolean:

    >>> arr[condition]
    array([0, 3, 6, 9])

Python Library Documentation: function eye in module autograd.tracer

eye(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return a 2-D array with ones on the diagonal and zeros elsewhere.

    Parameters
    ----------
    N : int
      Number of rows in the output.
    M : int, optional
      Number of columns in the output. If None, defaults to `N`.
    k : int, optional
      Index of the diagonal: 0 (the default) refers to the main diagonal,
      a positive value refers to an upper diagonal, and a negative value
      to a lower diagonal.
    dtype : data-type, optional
      Data-type of the returned array.
    order : {'C', 'F'}, optional
        Whether the output should be stored in row-major (C-style) or
        column-major (Fortran-style) order in memory.

        .. versionadded:: 1.14.0
    device : str, optional
        The device on which to place the created array. Default: None.
        For Array-API interoperability only, so must be ``"cpu"`` if passed.

        .. versionadded:: 2.0.0
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    I : ndarray of shape (N,M)
      An array where all elements are equal to zero, except for the `k`-th
      diagonal, whose values are equal to one.

    See Also
    --------
    identity : (almost) equivalent function
    diag : diagonal 2-D array from a 1-D array specified by the user.

    Examples
    --------
    >>> import numpy as np
    >>> np.eye(2, dtype=int)
    array([[1, 0],
           [0, 1]])
    >>> np.eye(3, k=1)
    array([[0.,  1.,  0.],
           [0.,  0.,  1.],
           [0.,  0.,  0.]])

Python Library Documentation: function fabs in module autograd.tracer

fabs(*args, called_by_autograd_dispatcher=False, **kwargs)
    fabs(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Compute the absolute values element-wise.

    This function returns the absolute values (positive magnitude) of the
    data in `x`. Complex values are not handled, use `absolute` to find the
    absolute values of complex data.

    Parameters
    ----------
    x : array_like
        The array of numbers for which the absolute values are required. If
        `x` is a scalar, the result `y` will also be a scalar.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray or scalar
        The absolute values of `x`, the returned values are always floats.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    absolute : Absolute values including `complex` types.

    Examples
    --------
    >>> import numpy as np
    >>> np.fabs(-1)
    1.0
    >>> np.fabs([-1.2, 1.2])
    array([ 1.2,  1.2])

Python Library Documentation: function fill_diagonal in module autograd.tracer

fill_diagonal(*args, called_by_autograd_dispatcher=False, **kwargs)
    Fill the main diagonal of the given array of any dimensionality.

    For an array `a` with ``a.ndim >= 2``, the diagonal is the list of
    values ``a[i, ..., i]`` with indices ``i`` all identical.  This function
    modifies the input array in-place without returning a value.

    Parameters
    ----------
    a : array, at least 2-D.
      Array whose diagonal is to be filled in-place.
    val : scalar or array_like
      Value(s) to write on the diagonal. If `val` is scalar, the value is
      written along the diagonal. If array-like, the flattened `val` is
      written along the diagonal, repeating if necessary to fill all
      diagonal entries.

    wrap : bool
      For tall matrices in NumPy version up to 1.6.2, the
      diagonal "wrapped" after N columns. You can have this behavior
      with this option. This affects only tall matrices.

    See also
    --------
    diag_indices, diag_indices_from

    Notes
    -----
    .. versionadded:: 1.4.0

    This functionality can be obtained via `diag_indices`, but internally
    this version uses a much faster implementation that never constructs the
    indices and uses simple slicing.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.zeros((3, 3), int)
    >>> np.fill_diagonal(a, 5)
    >>> a
    array([[5, 0, 0],
           [0, 5, 0],
           [0, 0, 5]])

    The same function can operate on a 4-D array:

    >>> a = np.zeros((3, 3, 3, 3), int)
    >>> np.fill_diagonal(a, 4)

    We only show a few blocks for clarity:

    >>> a[0, 0]
    array([[4, 0, 0],
           [0, 0, 0],
           [0, 0, 0]])
    >>> a[1, 1]
    array([[0, 0, 0],
           [0, 4, 0],
           [0, 0, 0]])
    >>> a[2, 2]
    array([[0, 0, 0],
           [0, 0, 0],
           [0, 0, 4]])

    The wrap option affects only tall matrices:

    >>> # tall matrices no wrap
    >>> a = np.zeros((5, 3), int)
    >>> np.fill_diagonal(a, 4)
    >>> a
    array([[4, 0, 0],
           [0, 4, 0],
           [0, 0, 4],
           [0, 0, 0],
           [0, 0, 0]])

    >>> # tall matrices wrap
    >>> a = np.zeros((5, 3), int)
    >>> np.fill_diagonal(a, 4, wrap=True)
    >>> a
    array([[4, 0, 0],
           [0, 4, 0],
           [0, 0, 4],
           [0, 0, 0],
           [4, 0, 0]])

    >>> # wide matrices
    >>> a = np.zeros((3, 5), int)
    >>> np.fill_diagonal(a, 4, wrap=True)
    >>> a
    array([[4, 0, 0, 0, 0],
           [0, 4, 0, 0, 0],
           [0, 0, 4, 0, 0]])

    The anti-diagonal can be filled by reversing the order of elements
    using either `numpy.flipud` or `numpy.fliplr`.

    >>> a = np.zeros((3, 3), int);
    >>> np.fill_diagonal(np.fliplr(a), [1,2,3])  # Horizontal flip
    >>> a
    array([[0, 0, 1],
           [0, 2, 0],
           [3, 0, 0]])
    >>> np.fill_diagonal(np.flipud(a), [1,2,3])  # Vertical flip
    >>> a
    array([[0, 0, 3],
           [0, 2, 0],
           [1, 0, 0]])

    Note that the order in which the diagonal is filled varies depending
    on the flip function.

Python Library Documentation: class finfo in module numpy

class finfo(builtins.object)
 |  finfo(dtype)
 |
 |  finfo(dtype)
 |
 |  Machine limits for floating point types.
 |
 |  Attributes
 |  ----------
 |  bits : int
 |      The number of bits occupied by the type.
 |  dtype : dtype
 |      Returns the dtype for which `finfo` returns information. For complex
 |      input, the returned dtype is the associated ``float*`` dtype for its
 |      real and complex components.
 |  eps : float
 |      The difference between 1.0 and the next smallest representable float
 |      larger than 1.0. For example, for 64-bit binary floats in the IEEE-754
 |      standard, ``eps = 2**-52``, approximately 2.22e-16.
 |  epsneg : float
 |      The difference between 1.0 and the next smallest representable float
 |      less than 1.0. For example, for 64-bit binary floats in the IEEE-754
 |      standard, ``epsneg = 2**-53``, approximately 1.11e-16.
 |  iexp : int
 |      The number of bits in the exponent portion of the floating point
 |      representation.
 |  machep : int
 |      The exponent that yields `eps`.
 |  max : floating point number of the appropriate type
 |      The largest representable number.
 |  maxexp : int
 |      The smallest positive power of the base (2) that causes overflow.
 |  min : floating point number of the appropriate type
 |      The smallest representable number, typically ``-max``.
 |  minexp : int
 |      The most negative power of the base (2) consistent with there
 |      being no leading 0's in the mantissa.
 |  negep : int
 |      The exponent that yields `epsneg`.
 |  nexp : int
 |      The number of bits in the exponent including its sign and bias.
 |  nmant : int
 |      The number of bits in the mantissa.
 |  precision : int
 |      The approximate number of decimal digits to which this kind of
 |      float is precise.
 |  resolution : floating point number of the appropriate type
 |      The approximate decimal resolution of this type, i.e.,
 |      ``10**-precision``.
 |  tiny : float
 |      An alias for `smallest_normal`, kept for backwards compatibility.
 |  smallest_normal : float
 |      The smallest positive floating point number with 1 as leading bit in
 |      the mantissa following IEEE-754 (see Notes).
 |  smallest_subnormal : float
 |      The smallest positive floating point number with 0 as leading bit in
 |      the mantissa following IEEE-754.
 |
 |  Parameters
 |  ----------
 |  dtype : float, dtype, or instance
 |      Kind of floating point or complex floating point
 |      data-type about which to get information.
 |
 |  See Also
 |  --------
 |  iinfo : The equivalent for integer data types.
 |  spacing : The distance between a value and the nearest adjacent number
 |  nextafter : The next floating point value after x1 towards x2
 |
 |  Notes
 |  -----
 |  For developers of NumPy: do not instantiate this at the module level.
 |  The initial calculation of these parameters is expensive and negatively
 |  impacts import times.  These objects are cached, so calling ``finfo()``
 |  repeatedly inside your functions is not a problem.
 |
 |  Note that ``smallest_normal`` is not actually the smallest positive
 |  representable value in a NumPy floating point type. As in the IEEE-754
 |  standard [1]_, NumPy floating point types make use of subnormal numbers to
 |  fill the gap between 0 and ``smallest_normal``. However, subnormal numbers
 |  may have significantly reduced precision [2]_.
 |
 |  This function can also be used for complex data types as well. If used,
 |  the output will be the same as the corresponding real float type
 |  (e.g. numpy.finfo(numpy.csingle) is the same as numpy.finfo(numpy.single)).
 |  However, the output is true for the real and imaginary components.
 |
 |  References
 |  ----------
 |  .. [1] IEEE Standard for Floating-Point Arithmetic, IEEE Std 754-2008,
 |         pp.1-70, 2008, https://doi.org/10.1109/IEEESTD.2008.4610935
 |  .. [2] Wikipedia, "Denormal Numbers",
 |         https://en.wikipedia.org/wiki/Denormal_number
 |
 |  Examples
 |  --------
 |  >>> import numpy as np
 |  >>> np.finfo(np.float64).dtype
 |  dtype('float64')
 |  >>> np.finfo(np.complex64).dtype
 |  dtype('float32')
 |
 |  Methods defined here:
 |
 |  __repr__(self) from numpy._core.getlimits.finfo
 |      Return repr(self).
 |
 |  __str__(self) from numpy._core.getlimits.finfo
 |      Return str(self).
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(cls, dtype) from numpy._core.getlimits.finfo
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Readonly properties defined here:
 |
 |  smallest_normal
 |      Return the value for the smallest normal.
 |
 |      Returns
 |      -------
 |      smallest_normal : float
 |          Value for the smallest normal.
 |
 |      Warns
 |      -----
 |      UserWarning
 |          If the calculated value for the smallest normal is requested for
 |          double-double.
 |
 |  tiny
 |      Return the value for tiny, alias of smallest_normal.
 |
 |      Returns
 |      -------
 |      tiny : float
 |          Value for the smallest normal, alias of smallest_normal.
 |
 |      Warns
 |      -----
 |      UserWarning
 |          If the calculated value for the smallest normal is requested for
 |          double-double.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object

Python Library Documentation: function fix in module autograd.tracer

fix(*args, called_by_autograd_dispatcher=False, **kwargs)
    Round to nearest integer towards zero.

    Round an array of floats element-wise to nearest integer towards zero.
    The rounded values have the same data-type as the input.

    Parameters
    ----------
    x : array_like
        An array to be rounded
    out : ndarray, optional
        A location into which the result is stored. If provided, it must have
        a shape that the input broadcasts to. If not provided or None, a
        freshly-allocated array is returned.

    Returns
    -------
    out : ndarray of floats
        An array with the same dimensions and data-type as the input.
        If second argument is not supplied then a new array is returned
        with the rounded values.

        If a second argument is supplied the result is stored there.
        The return value ``out`` is then a reference to that array.

    See Also
    --------
    rint, trunc, floor, ceil
    around : Round to given number of decimals

    Examples
    --------
    >>> import numpy as np
    >>> np.fix(3.14)
    3.0
    >>> np.fix(3)
    3
    >>> np.fix([2.1, 2.9, -2.1, -2.9])
    array([ 2.,  2., -2., -2.])

Python Library Documentation: class flatiter in module numpy

class flatiter(builtins.object)
 |  Flat iterator object to iterate over arrays.
 |
 |  A `flatiter` iterator is returned by ``x.flat`` for any array `x`.
 |  It allows iterating over the array as if it were a 1-D array,
 |  either in a for-loop or by calling its `next` method.
 |
 |  Iteration is done in row-major, C-style order (the last
 |  index varying the fastest). The iterator can also be indexed using
 |  basic slicing or advanced indexing.
 |
 |  See Also
 |  --------
 |  ndarray.flat : Return a flat iterator over an array.
 |  ndarray.flatten : Returns a flattened copy of an array.
 |
 |  Notes
 |  -----
 |  A `flatiter` iterator can not be constructed directly from Python code
 |  by calling the `flatiter` constructor.
 |
 |  Examples
 |  --------
 |  >>> import numpy as np
 |  >>> x = np.arange(6).reshape(2, 3)
 |  >>> fl = x.flat
 |  >>> type(fl)
 |  <class 'numpy.flatiter'>
 |  >>> for item in fl:
 |  ...     print(item)
 |  ...
 |  0
 |  1
 |  2
 |  3
 |  4
 |  5
 |
 |  >>> fl[2:4]
 |  array([2, 3])
 |
 |  Methods defined here:
 |
 |  __array__(...)
 |      __array__(type=None) Get array from iterator
 |
 |  __delitem__(self, key, /)
 |      Delete self[key].
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __iter__(self, /)
 |      Implement iter(self).
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __next__(self, /)
 |      Implement next(self).
 |
 |  __setitem__(self, key, value, /)
 |      Set self[key] to value.
 |
 |  copy(...)
 |      copy()
 |
 |      Get a copy of the iterator as a 1-D array.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.arange(6).reshape(2, 3)
 |      >>> x
 |      array([[0, 1, 2],
 |             [3, 4, 5]])
 |      >>> fl = x.flat
 |      >>> fl.copy()
 |      array([0, 1, 2, 3, 4, 5])
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  base
 |      A reference to the array that is iterated over.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.arange(5)
 |      >>> fl = x.flat
 |      >>> fl.base is x
 |      True
 |
 |  coords
 |      An N-dimensional tuple of current coordinates.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.arange(6).reshape(2, 3)
 |      >>> fl = x.flat
 |      >>> fl.coords
 |      (0, 0)
 |      >>> next(fl)
 |      0
 |      >>> fl.coords
 |      (0, 1)
 |
 |  index
 |      Current flat index into the array.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.arange(6).reshape(2, 3)
 |      >>> fl = x.flat
 |      >>> fl.index
 |      0
 |      >>> next(fl)
 |      0
 |      >>> fl.index
 |      1
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes defined here:
 |
 |  __hash__ = None

Python Library Documentation: function flatnonzero in module autograd.tracer

flatnonzero(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return indices that are non-zero in the flattened version of a.

    This is equivalent to ``np.nonzero(np.ravel(a))[0]``.

    Parameters
    ----------
    a : array_like
        Input data.

    Returns
    -------
    res : ndarray
        Output array, containing the indices of the elements of ``a.ravel()``
        that are non-zero.

    See Also
    --------
    nonzero : Return the indices of the non-zero elements of the input array.
    ravel : Return a 1-D array containing the elements of the input array.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.arange(-2, 3)
    >>> x
    array([-2, -1,  0,  1,  2])
    >>> np.flatnonzero(x)
    array([0, 1, 3, 4])

    Use the indices of the non-zero elements as an index array to extract
    these elements:

    >>> x.ravel()[np.flatnonzero(x)]
    array([-2, -1,  1,  2])

Python Library Documentation: class flexible in module numpy

class flexible(generic)
 |  Abstract base class of all scalar types without predefined length.
 |  The actual size of these types depends on the specific `numpy.dtype`
 |  instantiation.
 |
 |  Method resolution order:
 |      flexible
 |      generic
 |      builtins.object
 |
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes inherited from generic:
 |
 |  __hash__ = None

Python Library Documentation: function flip in module autograd.tracer

flip(*args, called_by_autograd_dispatcher=False, **kwargs)
    Reverse the order of elements in an array along the given axis.

    The shape of the array is preserved, but the elements are reordered.

    .. versionadded:: 1.12.0

    Parameters
    ----------
    m : array_like
        Input array.
    axis : None or int or tuple of ints, optional
         Axis or axes along which to flip over. The default,
         axis=None, will flip over all of the axes of the input array.
         If axis is negative it counts from the last to the first axis.

         If axis is a tuple of ints, flipping is performed on all of the axes
         specified in the tuple.

         .. versionchanged:: 1.15.0
            None and tuples of axes are supported

    Returns
    -------
    out : array_like
        A view of `m` with the entries of axis reversed.  Since a view is
        returned, this operation is done in constant time.

    See Also
    --------
    flipud : Flip an array vertically (axis=0).
    fliplr : Flip an array horizontally (axis=1).

    Notes
    -----
    flip(m, 0) is equivalent to flipud(m).

    flip(m, 1) is equivalent to fliplr(m).

    flip(m, n) corresponds to ``m[...,::-1,...]`` with ``::-1`` at position n.

    flip(m) corresponds to ``m[::-1,::-1,...,::-1]`` with ``::-1`` at all
    positions.

    flip(m, (0, 1)) corresponds to ``m[::-1,::-1,...]`` with ``::-1`` at
    position 0 and position 1.

    Examples
    --------
    >>> import numpy as np
    >>> A = np.arange(8).reshape((2,2,2))
    >>> A
    array([[[0, 1],
            [2, 3]],
           [[4, 5],
            [6, 7]]])
    >>> np.flip(A, 0)
    array([[[4, 5],
            [6, 7]],
           [[0, 1],
            [2, 3]]])
    >>> np.flip(A, 1)
    array([[[2, 3],
            [0, 1]],
           [[6, 7],
            [4, 5]]])
    >>> np.flip(A)
    array([[[7, 6],
            [5, 4]],
           [[3, 2],
            [1, 0]]])
    >>> np.flip(A, (0, 2))
    array([[[5, 4],
            [7, 6]],
           [[1, 0],
            [3, 2]]])
    >>> rng = np.random.default_rng()
    >>> A = rng.normal(size=(3,4,5))
    >>> np.all(np.flip(A,2) == A[:,:,::-1,...])
    True

Python Library Documentation: function fliplr in module autograd.tracer

fliplr(*args, called_by_autograd_dispatcher=False, **kwargs)
    Reverse the order of elements along axis 1 (left/right).

    For a 2-D array, this flips the entries in each row in the left/right
    direction. Columns are preserved, but appear in a different order than
    before.

    Parameters
    ----------
    m : array_like
        Input array, must be at least 2-D.

    Returns
    -------
    f : ndarray
        A view of `m` with the columns reversed.  Since a view
        is returned, this operation is :math:`\mathcal O(1)`.

    See Also
    --------
    flipud : Flip array in the up/down direction.
    flip : Flip array in one or more dimensions.
    rot90 : Rotate array counterclockwise.

    Notes
    -----
    Equivalent to ``m[:,::-1]`` or ``np.flip(m, axis=1)``.
    Requires the array to be at least 2-D.

    Examples
    --------
    >>> import numpy as np
    >>> A = np.diag([1.,2.,3.])
    >>> A
    array([[1.,  0.,  0.],
           [0.,  2.,  0.],
           [0.,  0.,  3.]])
    >>> np.fliplr(A)
    array([[0.,  0.,  1.],
           [0.,  2.,  0.],
           [3.,  0.,  0.]])

    >>> rng = np.random.default_rng()
    >>> A = rng.normal(size=(2,3,5))
    >>> np.all(np.fliplr(A) == A[:,::-1,...])
    True

Python Library Documentation: function flipud in module autograd.tracer

flipud(*args, called_by_autograd_dispatcher=False, **kwargs)
    Reverse the order of elements along axis 0 (up/down).

    For a 2-D array, this flips the entries in each column in the up/down
    direction. Rows are preserved, but appear in a different order than before.

    Parameters
    ----------
    m : array_like
        Input array.

    Returns
    -------
    out : array_like
        A view of `m` with the rows reversed.  Since a view is
        returned, this operation is :math:`\mathcal O(1)`.

    See Also
    --------
    fliplr : Flip array in the left/right direction.
    flip : Flip array in one or more dimensions.
    rot90 : Rotate array counterclockwise.

    Notes
    -----
    Equivalent to ``m[::-1, ...]`` or ``np.flip(m, axis=0)``.
    Requires the array to be at least 1-D.

    Examples
    --------
    >>> import numpy as np
    >>> A = np.diag([1.0, 2, 3])
    >>> A
    array([[1.,  0.,  0.],
           [0.,  2.,  0.],
           [0.,  0.,  3.]])
    >>> np.flipud(A)
    array([[0.,  0.,  3.],
           [0.,  2.,  0.],
           [1.,  0.,  0.]])

    >>> rng = np.random.default_rng()
    >>> A = rng.normal(size=(2,3,5))
    >>> np.all(np.flipud(A) == A[::-1,...])
    True

    >>> np.flipud([1,2])
    array([2, 1])

Python Library Documentation: class float16 in module numpy

class float16(floating)
 |  Half-precision floating-point number type.
 |
 |  :Character code: ``'e'``
 |  :Canonical name: `numpy.half`
 |  :Alias on this platform (win32 AMD64): `numpy.float16`: 16-bit-precision floating-point number type: sign bit, 5 bits exponent, 10 bits mantissa.
 |
 |  Method resolution order:
 |      float16
 |      floating
 |      inexact
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  as_integer_ratio(...)
 |      half.as_integer_ratio() -> (int, int)
 |
 |      Return a pair of integers, whose ratio is exactly equal to the original
 |      floating point number, and with a positive denominator.
 |      Raise `OverflowError` on infinities and a `ValueError` on NaNs.
 |
 |      >>> np.half(10.0).as_integer_ratio()
 |      (10, 1)
 |      >>> np.half(0.0).as_integer_ratio()
 |      (0, 1)
 |      >>> np.half(-.25).as_integer_ratio()
 |      (-1, 4)
 |
 |  is_integer(...)
 |      half.is_integer() -> bool
 |
 |      Return ``True`` if the floating point number is finite with integral
 |      value, and ``False`` otherwise.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> np.half(-2.0).is_integer()
 |      True
 |      >>> np.half(3.2).is_integer()
 |      False
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from floating:
 |
 |  __round__(...)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class float32 in module numpy

class float32(floating)
 |  Single-precision floating-point number type, compatible with C ``float``.
 |
 |  :Character code: ``'f'``
 |  :Canonical name: `numpy.single`
 |  :Alias on this platform (win32 AMD64): `numpy.float32`: 32-bit-precision floating-point number type: sign bit, 8 bits exponent, 23 bits mantissa.
 |
 |  Method resolution order:
 |      float32
 |      floating
 |      inexact
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  as_integer_ratio(...)
 |      single.as_integer_ratio() -> (int, int)
 |
 |      Return a pair of integers, whose ratio is exactly equal to the original
 |      floating point number, and with a positive denominator.
 |      Raise `OverflowError` on infinities and a `ValueError` on NaNs.
 |
 |      >>> np.single(10.0).as_integer_ratio()
 |      (10, 1)
 |      >>> np.single(0.0).as_integer_ratio()
 |      (0, 1)
 |      >>> np.single(-.25).as_integer_ratio()
 |      (-1, 4)
 |
 |  is_integer(...)
 |      single.is_integer() -> bool
 |
 |      Return ``True`` if the floating point number is finite with integral
 |      value, and ``False`` otherwise.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> np.single(-2.0).is_integer()
 |      True
 |      >>> np.single(3.2).is_integer()
 |      False
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from floating:
 |
 |  __round__(...)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class float64 in module numpy

class float64(floating, builtins.float)
 |  float64(x=0, /)
 |
 |  Double-precision floating-point number type, compatible with Python
 |  :class:`float` and C ``double``.
 |
 |  :Character code: ``'d'``
 |  :Canonical name: `numpy.double`
 |  :Alias on this platform (win32 AMD64): `numpy.float64`: 64-bit precision floating-point number type: sign bit, 11 bits exponent, 52 bits mantissa.
 |
 |  Method resolution order:
 |      float64
 |      floating
 |      inexact
 |      number
 |      generic
 |      builtins.float
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  as_integer_ratio(...)
 |      double.as_integer_ratio() -> (int, int)
 |
 |      Return a pair of integers, whose ratio is exactly equal to the original
 |      floating point number, and with a positive denominator.
 |      Raise `OverflowError` on infinities and a `ValueError` on NaNs.
 |
 |      >>> np.double(10.0).as_integer_ratio()
 |      (10, 1)
 |      >>> np.double(0.0).as_integer_ratio()
 |      (0, 1)
 |      >>> np.double(-.25).as_integer_ratio()
 |      (-1, 4)
 |
 |  is_integer(...)
 |      double.is_integer() -> bool
 |
 |      Return ``True`` if the floating point number is finite with integral
 |      value, and ``False`` otherwise.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> np.double(-2.0).is_integer()
 |      True
 |      >>> np.double(3.2).is_integer()
 |      False
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from floating:
 |
 |  __round__(...)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from builtins.float:
 |
 |  __ceil__(self, /)
 |      Return the ceiling as an Integral.
 |
 |  __floor__(self, /)
 |      Return the floor as an Integral.
 |
 |  __getnewargs__(self, /)
 |
 |  __trunc__(self, /)
 |      Return the Integral closest to x between 0 and x.
 |
 |  hex(self, /)
 |      Return a hexadecimal representation of a floating-point number.
 |
 |      >>> (-0.1).hex()
 |      '-0x1.999999999999ap-4'
 |      >>> 3.14159.hex()
 |      '0x1.921f9f01b866ep+1'
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from builtins.float:
 |
 |  __getformat__(typestr, /)
 |      You probably don't want to use this function.
 |
 |        typestr
 |          Must be 'double' or 'float'.
 |
 |      It exists mainly to be used in Python's test suite.
 |
 |      This function returns whichever of 'unknown', 'IEEE, big-endian' or 'IEEE,
 |      little-endian' best describes the format of floating-point numbers used by the
 |      C type named by typestr.
 |
 |  fromhex(string, /)
 |      Create a floating-point number from a hexadecimal string.
 |
 |      >>> float.fromhex('0x1.ffffp10')
 |      2047.984375
 |      >>> float.fromhex('-0x1p-1074')
 |      -5e-324

Python Library Documentation: function float_power in module autograd.tracer

float_power(*args, called_by_autograd_dispatcher=False, **kwargs)
    float_power(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    First array elements raised to powers from second array, element-wise.

    Raise each base in `x1` to the positionally-corresponding power in `x2`.
    `x1` and `x2` must be broadcastable to the same shape. This differs from
    the power function in that integers, float16, and float32  are promoted to
    floats with a minimum precision of float64 so that the result is always
    inexact.  The intent is that the function will return a usable result for
    negative powers and seldom overflow for positive powers.

    Negative values raised to a non-integral value will return ``nan``.
    To get complex results, cast the input to complex, or specify the
    ``dtype`` to be ``complex`` (see the example below).

    .. versionadded:: 1.12.0

    Parameters
    ----------
    x1 : array_like
        The bases.
    x2 : array_like
        The exponents.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The bases in `x1` raised to the exponents in `x2`.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    power : power function that preserves type

    Examples
    --------
    >>> import numpy as np

    Cube each element in a list.

    >>> x1 = range(6)
    >>> x1
    [0, 1, 2, 3, 4, 5]
    >>> np.float_power(x1, 3)
    array([   0.,    1.,    8.,   27.,   64.,  125.])

    Raise the bases to different exponents.

    >>> x2 = [1.0, 2.0, 3.0, 3.0, 2.0, 1.0]
    >>> np.float_power(x1, x2)
    array([  0.,   1.,   8.,  27.,  16.,   5.])

    The effect of broadcasting.

    >>> x2 = np.array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]])
    >>> x2
    array([[1, 2, 3, 3, 2, 1],
           [1, 2, 3, 3, 2, 1]])
    >>> np.float_power(x1, x2)
    array([[  0.,   1.,   8.,  27.,  16.,   5.],
           [  0.,   1.,   8.,  27.,  16.,   5.]])

    Negative values raised to a non-integral value will result in ``nan``
    (and a warning will be generated).

    >>> x3 = np.array([-1, -4])
    >>> with np.errstate(invalid='ignore'):
    ...     p = np.float_power(x3, 1.5)
    ...
    >>> p
    array([nan, nan])

    To get complex results, give the argument ``dtype=complex``.

    >>> np.float_power(x3, 1.5, dtype=complex)
    array([-1.83697020e-16-1.j, -1.46957616e-15-8.j])

Python Library Documentation: class floating in module numpy

class floating(inexact)
 |  Abstract base class of all floating-point scalar types.
 |
 |  Method resolution order:
 |      floating
 |      inexact
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __round__(...)
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from number:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes inherited from generic:
 |
 |  __hash__ = None

Python Library Documentation: function floor in module autograd.tracer

floor(*args, called_by_autograd_dispatcher=False, **kwargs)
    floor(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the floor of the input, element-wise.

    The floor of the scalar `x` is the largest integer `i`, such that
    `i <= x`.  It is often denoted as :math:`\lfloor x \rfloor`.

    Parameters
    ----------
    x : array_like
        Input data.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray or scalar
        The floor of each element in `x`.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    ceil, trunc, rint, fix

    Notes
    -----
    Some spreadsheet programs calculate the "floor-towards-zero", where
    ``floor(-2.5) == -2``.  NumPy instead uses the definition of
    `floor` where `floor(-2.5) == -3`. The "floor-towards-zero"
    function is called ``fix`` in NumPy.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
    >>> np.floor(a)
    array([-2., -2., -1.,  0.,  1.,  1.,  2.])

Python Library Documentation: function floor_divide in module autograd.tracer

floor_divide(*args, called_by_autograd_dispatcher=False, **kwargs)
    floor_divide(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the largest integer smaller or equal to the division of the inputs.
    It is equivalent to the Python ``//`` operator and pairs with the
    Python ``%`` (`remainder`), function so that ``a = a % b + b * (a // b)``
    up to roundoff.

    Parameters
    ----------
    x1 : array_like
        Numerator.
    x2 : array_like
        Denominator.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        y = floor(`x1`/`x2`)
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    remainder : Remainder complementary to floor_divide.
    divmod : Simultaneous floor division and remainder.
    divide : Standard division.
    floor : Round a number to the nearest integer toward minus infinity.
    ceil : Round a number to the nearest integer toward infinity.

    Examples
    --------
    >>> import numpy as np
    >>> np.floor_divide(7,3)
    2
    >>> np.floor_divide([1., 2., 3., 4.], 2.5)
    array([ 0.,  0.,  1.,  1.])

    The ``//`` operator can be used as a shorthand for ``np.floor_divide``
    on ndarrays.

    >>> x1 = np.array([1., 2., 3., 4.])
    >>> x1 // 2.5
    array([0., 0., 1., 1.])

Python Library Documentation: function fmax in module autograd.tracer

fmax(*args, called_by_autograd_dispatcher=False, **kwargs)
    fmax(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Element-wise maximum of array elements.

    Compare two arrays and return a new array containing the element-wise
    maxima. If one of the elements being compared is a NaN, then the
    non-nan element is returned. If both elements are NaNs then the first
    is returned.  The latter distinction is important for complex NaNs,
    which are defined as at least one of the real or imaginary parts being
    a NaN. The net effect is that NaNs are ignored when possible.

    Parameters
    ----------
    x1, x2 : array_like
        The arrays holding the elements to be compared.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray or scalar
        The maximum of `x1` and `x2`, element-wise.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    fmin :
        Element-wise minimum of two arrays, ignores NaNs.
    maximum :
        Element-wise maximum of two arrays, propagates NaNs.
    amax :
        The maximum value of an array along a given axis, propagates NaNs.
    nanmax :
        The maximum value of an array along a given axis, ignores NaNs.

    minimum, amin, nanmin

    Notes
    -----
    .. versionadded:: 1.3.0

    The fmax is equivalent to ``np.where(x1 >= x2, x1, x2)`` when neither
    x1 nor x2 are NaNs, but it is faster and does proper broadcasting.

    Examples
    --------
    >>> import numpy as np
    >>> np.fmax([2, 3, 4], [1, 5, 2])
    array([ 2.,  5.,  4.])

    >>> np.fmax(np.eye(2), [0.5, 2])
    array([[ 1. ,  2. ],
           [ 0.5,  2. ]])

    >>> np.fmax([np.nan, 0, np.nan],[0, np.nan, np.nan])
    array([ 0.,  0., nan])

Python Library Documentation: function fmin in module autograd.tracer

fmin(*args, called_by_autograd_dispatcher=False, **kwargs)
    fmin(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Element-wise minimum of array elements.

    Compare two arrays and return a new array containing the element-wise
    minima. If one of the elements being compared is a NaN, then the
    non-nan element is returned. If both elements are NaNs then the first
    is returned.  The latter distinction is important for complex NaNs,
    which are defined as at least one of the real or imaginary parts being
    a NaN. The net effect is that NaNs are ignored when possible.

    Parameters
    ----------
    x1, x2 : array_like
        The arrays holding the elements to be compared.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray or scalar
        The minimum of `x1` and `x2`, element-wise.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    fmax :
        Element-wise maximum of two arrays, ignores NaNs.
    minimum :
        Element-wise minimum of two arrays, propagates NaNs.
    amin :
        The minimum value of an array along a given axis, propagates NaNs.
    nanmin :
        The minimum value of an array along a given axis, ignores NaNs.

    maximum, amax, nanmax

    Notes
    -----
    .. versionadded:: 1.3.0

    The fmin is equivalent to ``np.where(x1 <= x2, x1, x2)`` when neither
    x1 nor x2 are NaNs, but it is faster and does proper broadcasting.

    Examples
    --------
    >>> import numpy as np
    >>> np.fmin([2, 3, 4], [1, 5, 2])
    array([1, 3, 2])

    >>> np.fmin(np.eye(2), [0.5, 2])
    array([[ 0.5,  0. ],
           [ 0. ,  1. ]])

    >>> np.fmin([np.nan, 0, np.nan],[0, np.nan, np.nan])
    array([ 0.,  0., nan])

Python Library Documentation: function fmod in module autograd.tracer

fmod(*args, called_by_autograd_dispatcher=False, **kwargs)
    fmod(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Returns the element-wise remainder of division.

    This is the NumPy implementation of the C library function fmod, the
    remainder has the same sign as the dividend `x1`. It is equivalent to
    the Matlab(TM) ``rem`` function and should not be confused with the
    Python modulus operator ``x1 % x2``.

    Parameters
    ----------
    x1 : array_like
        Dividend.
    x2 : array_like
        Divisor.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : array_like
        The remainder of the division of `x1` by `x2`.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    remainder : Equivalent to the Python ``%`` operator.
    divide

    Notes
    -----
    The result of the modulo operation for negative dividend and divisors
    is bound by conventions. For `fmod`, the sign of result is the sign of
    the dividend, while for `remainder` the sign of the result is the sign
    of the divisor. The `fmod` function is equivalent to the Matlab(TM)
    ``rem`` function.

    Examples
    --------
    >>> import numpy as np
    >>> np.fmod([-3, -2, -1, 1, 2, 3], 2)
    array([-1,  0, -1,  1,  0,  1])
    >>> np.remainder([-3, -2, -1, 1, 2, 3], 2)
    array([1, 0, 1, 1, 0, 1])

    >>> np.fmod([5, 3], [2, 2.])
    array([ 1.,  1.])
    >>> a = np.arange(-3, 3).reshape(3, 2)
    >>> a
    array([[-3, -2],
           [-1,  0],
           [ 1,  2]])
    >>> np.fmod(a, [2,2])
    array([[-1,  0],
           [-1,  0],
           [ 1,  0]])

Python Library Documentation: function format_float_positional in module autograd.tracer

format_float_positional(*args, called_by_autograd_dispatcher=False, **kwargs)
    Format a floating-point scalar as a decimal string in positional notation.

    Provides control over rounding, trimming and padding. Uses and assumes
    IEEE unbiased rounding. Uses the "Dragon4" algorithm.

    Parameters
    ----------
    x : python float or numpy floating scalar
        Value to format.
    precision : non-negative integer or None, optional
        Maximum number of digits to print. May be None if `unique` is
        `True`, but must be an integer if unique is `False`.
    unique : boolean, optional
        If `True`, use a digit-generation strategy which gives the shortest
        representation which uniquely identifies the floating-point number from
        other values of the same type, by judicious rounding. If `precision`
        is given fewer digits than necessary can be printed, or if `min_digits`
        is given more can be printed, in which cases the last digit is rounded
        with unbiased rounding.
        If `False`, digits are generated as if printing an infinite-precision
        value and stopping after `precision` digits, rounding the remaining
        value with unbiased rounding
    fractional : boolean, optional
        If `True`, the cutoffs of `precision` and `min_digits` refer to the
        total number of digits after the decimal point, including leading
        zeros.
        If `False`, `precision` and `min_digits` refer to the total number of
        significant digits, before or after the decimal point, ignoring leading
        zeros.
    trim : one of 'k', '.', '0', '-', optional
        Controls post-processing trimming of trailing digits, as follows:

        * 'k' : keep trailing zeros, keep decimal point (no trimming)
        * '.' : trim all trailing zeros, leave decimal point
        * '0' : trim all but the zero before the decimal point. Insert the
          zero if it is missing.
        * '-' : trim trailing zeros and any trailing decimal point
    sign : boolean, optional
        Whether to show the sign for positive values.
    pad_left : non-negative integer, optional
        Pad the left side of the string with whitespace until at least that
        many characters are to the left of the decimal point.
    pad_right : non-negative integer, optional
        Pad the right side of the string with whitespace until at least that
        many characters are to the right of the decimal point.
    min_digits : non-negative integer or None, optional
        Minimum number of digits to print. Only has an effect if `unique=True`
        in which case additional digits past those necessary to uniquely
        identify the value may be printed, rounding the last additional digit.

        .. versionadded:: 1.21.0

    Returns
    -------
    rep : string
        The string representation of the floating point value

    See Also
    --------
    format_float_scientific

    Examples
    --------
    >>> import numpy as np
    >>> np.format_float_positional(np.float32(np.pi))
    '3.1415927'
    >>> np.format_float_positional(np.float16(np.pi))
    '3.14'
    >>> np.format_float_positional(np.float16(0.3))
    '0.3'
    >>> np.format_float_positional(np.float16(0.3), unique=False, precision=10)
    '0.3000488281'

Python Library Documentation: function format_float_scientific in module autograd.tracer

format_float_scientific(*args, called_by_autograd_dispatcher=False, **kwargs)
    Format a floating-point scalar as a decimal string in scientific notation.

    Provides control over rounding, trimming and padding. Uses and assumes
    IEEE unbiased rounding. Uses the "Dragon4" algorithm.

    Parameters
    ----------
    x : python float or numpy floating scalar
        Value to format.
    precision : non-negative integer or None, optional
        Maximum number of digits to print. May be None if `unique` is
        `True`, but must be an integer if unique is `False`.
    unique : boolean, optional
        If `True`, use a digit-generation strategy which gives the shortest
        representation which uniquely identifies the floating-point number from
        other values of the same type, by judicious rounding. If `precision`
        is given fewer digits than necessary can be printed. If `min_digits`
        is given more can be printed, in which cases the last digit is rounded
        with unbiased rounding.
        If `False`, digits are generated as if printing an infinite-precision
        value and stopping after `precision` digits, rounding the remaining
        value with unbiased rounding
    trim : one of 'k', '.', '0', '-', optional
        Controls post-processing trimming of trailing digits, as follows:

        * 'k' : keep trailing zeros, keep decimal point (no trimming)
        * '.' : trim all trailing zeros, leave decimal point
        * '0' : trim all but the zero before the decimal point. Insert the
          zero if it is missing.
        * '-' : trim trailing zeros and any trailing decimal point
    sign : boolean, optional
        Whether to show the sign for positive values.
    pad_left : non-negative integer, optional
        Pad the left side of the string with whitespace until at least that
        many characters are to the left of the decimal point.
    exp_digits : non-negative integer, optional
        Pad the exponent with zeros until it contains at least this
        many digits. If omitted, the exponent will be at least 2 digits.
    min_digits : non-negative integer or None, optional
        Minimum number of digits to print. This only has an effect for
        `unique=True`. In that case more digits than necessary to uniquely
        identify the value may be printed and rounded unbiased.

        .. versionadded:: 1.21.0

    Returns
    -------
    rep : string
        The string representation of the floating point value

    See Also
    --------
    format_float_positional

    Examples
    --------
    >>> import numpy as np
    >>> np.format_float_scientific(np.float32(np.pi))
    '3.1415927e+00'
    >>> s = np.float32(1.23e24)
    >>> np.format_float_scientific(s, unique=False, precision=15)
    '1.230000071797338e+24'
    >>> np.format_float_scientific(s, exp_digits=4)
    '1.23e+0024'

Python Library Documentation: function frexp in module autograd.tracer

frexp(*args, called_by_autograd_dispatcher=False, **kwargs)
    frexp(x[, out1, out2], / [, out=(None, None)], *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Decompose the elements of x into mantissa and twos exponent.

    Returns (`mantissa`, `exponent`), where ``x = mantissa * 2**exponent``.
    The mantissa lies in the open interval(-1, 1), while the twos
    exponent is a signed integer.

    Parameters
    ----------
    x : array_like
        Array of numbers to be decomposed.
    out1 : ndarray, optional
        Output array for the mantissa. Must have the same shape as `x`.
    out2 : ndarray, optional
        Output array for the exponent. Must have the same shape as `x`.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    mantissa : ndarray
        Floating values between -1 and 1.
        This is a scalar if `x` is a scalar.
    exponent : ndarray
        Integer exponents of 2.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    ldexp : Compute ``y = x1 * 2**x2``, the inverse of `frexp`.

    Notes
    -----
    Complex dtypes are not supported, they will raise a TypeError.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.arange(9)
    >>> y1, y2 = np.frexp(x)
    >>> y1
    array([ 0.   ,  0.5  ,  0.5  ,  0.75 ,  0.5  ,  0.625,  0.75 ,  0.875,
            0.5  ])
    >>> y2
    array([0, 1, 2, 2, 3, 3, 3, 3, 4])
    >>> y1 * 2**y2
    array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.])

Python Library Documentation: function from_dlpack in module autograd.tracer

from_dlpack(*args, called_by_autograd_dispatcher=False, **kwargs)
    from_dlpack(x, /, *, device=None, copy=None)

    Create a NumPy array from an object implementing the ``__dlpack__``
    protocol. Generally, the returned NumPy array is a read-only view
    of the input object. See [1]_ and [2]_ for more details.

    Parameters
    ----------
    x : object
        A Python object that implements the ``__dlpack__`` and
        ``__dlpack_device__`` methods.
    device : device, optional
        Device on which to place the created array. Default: ``None``.
        Must be ``"cpu"`` if passed which may allow importing an array
        that is not already CPU available.
    copy : bool, optional
        Boolean indicating whether or not to copy the input. If ``True``,
        the copy will be made. If ``False``, the function will never copy,
        and will raise ``BufferError`` in case a copy is deemed necessary.
        Passing it requests a copy from the exporter who may or may not
        implement the capability.
        If ``None``, the function will reuse the existing memory buffer if
        possible and copy otherwise. Default: ``None``.


    Returns
    -------
    out : ndarray

    References
    ----------
    .. [1] Array API documentation,
       https://data-apis.org/array-api/latest/design_topics/data_interchange.html#syntax-for-data-interchange-with-dlpack

    .. [2] Python specification for DLPack,
       https://dmlc.github.io/dlpack/latest/python_spec.html

    Examples
    --------
    >>> import torch  # doctest: +SKIP
    >>> x = torch.arange(10)  # doctest: +SKIP
    >>> # create a view of the torch tensor "x" in NumPy
    >>> y = np.from_dlpack(x)  # doctest: +SKIP

Python Library Documentation: function frombuffer in module autograd.tracer

frombuffer(*args, called_by_autograd_dispatcher=False, **kwargs)
    frombuffer(buffer, dtype=float, count=-1, offset=0, *, like=None)

    Interpret a buffer as a 1-dimensional array.

    Parameters
    ----------
    buffer : buffer_like
        An object that exposes the buffer interface.
    dtype : data-type, optional
        Data-type of the returned array; default: float.
    count : int, optional
        Number of items to read. ``-1`` means all data in the buffer.
    offset : int, optional
        Start reading the buffer from this offset (in bytes); default: 0.
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    out : ndarray

    See also
    --------
    ndarray.tobytes
        Inverse of this operation, construct Python bytes from the raw data
        bytes in the array.

    Notes
    -----
    If the buffer has data that is not in machine byte-order, this should
    be specified as part of the data-type, e.g.::

      >>> dt = np.dtype(int)
      >>> dt = dt.newbyteorder('>')
      >>> np.frombuffer(buf, dtype=dt) # doctest: +SKIP

    The data of the resulting array will not be byteswapped, but will be
    interpreted correctly.

    This function creates a view into the original object.  This should be safe
    in general, but it may make sense to copy the result when the original
    object is mutable or untrusted.

    Examples
    --------
    >>> import numpy as np
    >>> s = b'hello world'
    >>> np.frombuffer(s, dtype='S1', count=5, offset=6)
    array([b'w', b'o', b'r', b'l', b'd'], dtype='|S1')

    >>> np.frombuffer(b'\x01\x02', dtype=np.uint8)
    array([1, 2], dtype=uint8)
    >>> np.frombuffer(b'\x01\x02\x03\x04\x05', dtype=np.uint8, count=3)
    array([1, 2, 3], dtype=uint8)

Python Library Documentation: function fromfile in module autograd.tracer

fromfile(*args, called_by_autograd_dispatcher=False, **kwargs)
    fromfile(file, dtype=float, count=-1, sep='', offset=0, *, like=None)

    Construct an array from data in a text or binary file.

    A highly efficient way of reading binary data with a known data-type,
    as well as parsing simply formatted text files.  Data written using the
    `tofile` method can be read using this function.

    Parameters
    ----------
    file : file or str or Path
        Open file object or filename.

        .. versionchanged:: 1.17.0
            `pathlib.Path` objects are now accepted.

    dtype : data-type
        Data type of the returned array.
        For binary files, it is used to determine the size and byte-order
        of the items in the file.
        Most builtin numeric types are supported and extension types may be supported.

        .. versionadded:: 1.18.0
            Complex dtypes.

    count : int
        Number of items to read. ``-1`` means all items (i.e., the complete
        file).
    sep : str
        Separator between items if file is a text file.
        Empty ("") separator means the file should be treated as binary.
        Spaces (" ") in the separator match zero or more whitespace characters.
        A separator consisting only of spaces must match at least one
        whitespace.
    offset : int
        The offset (in bytes) from the file's current position. Defaults to 0.
        Only permitted for binary files.

        .. versionadded:: 1.17.0
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    See also
    --------
    load, save
    ndarray.tofile
    loadtxt : More flexible way of loading data from a text file.

    Notes
    -----
    Do not rely on the combination of `tofile` and `fromfile` for
    data storage, as the binary files generated are not platform
    independent.  In particular, no byte-order or data-type information is
    saved.  Data can be stored in the platform independent ``.npy`` format
    using `save` and `load` instead.

    Examples
    --------
    Construct an ndarray:

    >>> import numpy as np
    >>> dt = np.dtype([('time', [('min', np.int64), ('sec', np.int64)]),
    ...                ('temp', float)])
    >>> x = np.zeros((1,), dtype=dt)
    >>> x['time']['min'] = 10; x['temp'] = 98.25
    >>> x
    array([((10, 0), 98.25)],
          dtype=[('time', [('min', '<i8'), ('sec', '<i8')]), ('temp', '<f8')])

    Save the raw data to disk:

    >>> import tempfile
    >>> fname = tempfile.mkstemp()[1]
    >>> x.tofile(fname)

    Read the raw data from disk:

    >>> np.fromfile(fname, dtype=dt)
    array([((10, 0), 98.25)],
          dtype=[('time', [('min', '<i8'), ('sec', '<i8')]), ('temp', '<f8')])

    The recommended way to store and load data:

    >>> np.save(fname, x)
    >>> np.load(fname + '.npy')
    array([((10, 0), 98.25)],
          dtype=[('time', [('min', '<i8'), ('sec', '<i8')]), ('temp', '<f8')])

Python Library Documentation: function fromfunction in module autograd.tracer

fromfunction(*args, called_by_autograd_dispatcher=False, **kwargs)
    Construct an array by executing a function over each coordinate.

    The resulting array therefore has a value ``fn(x, y, z)`` at
    coordinate ``(x, y, z)``.

    Parameters
    ----------
    function : callable
        The function is called with N parameters, where N is the rank of
        `shape`.  Each parameter represents the coordinates of the array
        varying along a specific axis.  For example, if `shape`
        were ``(2, 2)``, then the parameters would be
        ``array([[0, 0], [1, 1]])`` and ``array([[0, 1], [0, 1]])``
    shape : (N,) tuple of ints
        Shape of the output array, which also determines the shape of
        the coordinate arrays passed to `function`.
    dtype : data-type, optional
        Data-type of the coordinate arrays passed to `function`.
        By default, `dtype` is float.
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    fromfunction : any
        The result of the call to `function` is passed back directly.
        Therefore the shape of `fromfunction` is completely determined by
        `function`.  If `function` returns a scalar value, the shape of
        `fromfunction` would not match the `shape` parameter.

    See Also
    --------
    indices, meshgrid

    Notes
    -----
    Keywords other than `dtype` and `like` are passed to `function`.

    Examples
    --------
    >>> import numpy as np
    >>> np.fromfunction(lambda i, j: i, (2, 2), dtype=float)
    array([[0., 0.],
           [1., 1.]])

    >>> np.fromfunction(lambda i, j: j, (2, 2), dtype=float)
    array([[0., 1.],
           [0., 1.]])

    >>> np.fromfunction(lambda i, j: i == j, (3, 3), dtype=int)
    array([[ True, False, False],
           [False,  True, False],
           [False, False,  True]])

    >>> np.fromfunction(lambda i, j: i + j, (3, 3), dtype=int)
    array([[0, 1, 2],
           [1, 2, 3],
           [2, 3, 4]])

Python Library Documentation: function fromiter in module autograd.tracer

fromiter(*args, called_by_autograd_dispatcher=False, **kwargs)
    fromiter(iter, dtype, count=-1, *, like=None)

    Create a new 1-dimensional array from an iterable object.

    Parameters
    ----------
    iter : iterable object
        An iterable object providing data for the array.
    dtype : data-type
        The data-type of the returned array.

        .. versionchanged:: 1.23
            Object and subarray dtypes are now supported (note that the final
            result is not 1-D for a subarray dtype).

    count : int, optional
        The number of items to read from *iterable*.  The default is -1,
        which means all data is read.
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    out : ndarray
        The output array.

    Notes
    -----
    Specify `count` to improve performance.  It allows ``fromiter`` to
    pre-allocate the output array, instead of resizing it on demand.

    Examples
    --------
    >>> import numpy as np
    >>> iterable = (x*x for x in range(5))
    >>> np.fromiter(iterable, float)
    array([  0.,   1.,   4.,   9.,  16.])

    A carefully constructed subarray dtype will lead to higher dimensional
    results:

    >>> iterable = ((x+1, x+2) for x in range(5))
    >>> np.fromiter(iterable, dtype=np.dtype((int, 2)))
    array([[1, 2],
           [2, 3],
           [3, 4],
           [4, 5],
           [5, 6]])

Python Library Documentation: function frompyfunc in module autograd.tracer

frompyfunc(*args, called_by_autograd_dispatcher=False, **kwargs)
    frompyfunc(func, /, nin, nout, *[, identity])

    Takes an arbitrary Python function and returns a NumPy ufunc.

    Can be used, for example, to add broadcasting to a built-in Python
    function (see Examples section).

    Parameters
    ----------
    func : Python function object
        An arbitrary Python function.
    nin : int
        The number of input arguments.
    nout : int
        The number of objects returned by `func`.
    identity : object, optional
        The value to use for the `~numpy.ufunc.identity` attribute of the resulting
        object. If specified, this is equivalent to setting the underlying
        C ``identity`` field to ``PyUFunc_IdentityValue``.
        If omitted, the identity is set to ``PyUFunc_None``. Note that this is
        _not_ equivalent to setting the identity to ``None``, which implies the
        operation is reorderable.

    Returns
    -------
    out : ufunc
        Returns a NumPy universal function (``ufunc``) object.

    See Also
    --------
    vectorize : Evaluates pyfunc over input arrays using broadcasting rules of numpy.

    Notes
    -----
    The returned ufunc always returns PyObject arrays.

    Examples
    --------
    Use frompyfunc to add broadcasting to the Python function ``oct``:

    >>> import numpy as np
    >>> oct_array = np.frompyfunc(oct, 1, 1)
    >>> oct_array(np.array((10, 30, 100)))
    array(['0o12', '0o36', '0o144'], dtype=object)
    >>> np.array((oct(10), oct(30), oct(100))) # for comparison
    array(['0o12', '0o36', '0o144'], dtype='<U5')

Python Library Documentation: function fromregex in module autograd.tracer

fromregex(*args, called_by_autograd_dispatcher=False, **kwargs)
    Construct an array from a text file, using regular expression parsing.

    The returned array is always a structured array, and is constructed from
    all matches of the regular expression in the file. Groups in the regular
    expression are converted to fields of the structured array.

    Parameters
    ----------
    file : file, str, or pathlib.Path
        Filename or file object to read.

        .. versionchanged:: 1.22.0
            Now accepts `os.PathLike` implementations.
    regexp : str or regexp
        Regular expression used to parse the file.
        Groups in the regular expression correspond to fields in the dtype.
    dtype : dtype or list of dtypes
        Dtype for the structured array; must be a structured datatype.
    encoding : str, optional
        Encoding used to decode the inputfile. Does not apply to input streams.

        .. versionadded:: 1.14.0

    Returns
    -------
    output : ndarray
        The output array, containing the part of the content of `file` that
        was matched by `regexp`. `output` is always a structured array.

    Raises
    ------
    TypeError
        When `dtype` is not a valid dtype for a structured array.

    See Also
    --------
    fromstring, loadtxt

    Notes
    -----
    Dtypes for structured arrays can be specified in several forms, but all
    forms specify at least the data type and field name. For details see
    `basics.rec`.

    Examples
    --------
    >>> import numpy as np
    >>> from io import StringIO
    >>> text = StringIO("1312 foo\n1534  bar\n444   qux")

    >>> regexp = r"(\d+)\s+(...)"  # match [digits, whitespace, anything]
    >>> output = np.fromregex(text, regexp,
    ...                       [('num', np.int64), ('key', 'S3')])
    >>> output
    array([(1312, b'foo'), (1534, b'bar'), ( 444, b'qux')],
          dtype=[('num', '<i8'), ('key', 'S3')])
    >>> output['num']
    array([1312, 1534,  444])

Python Library Documentation: function fromstring in module autograd.tracer

fromstring(*args, called_by_autograd_dispatcher=False, **kwargs)
    fromstring(string, dtype=float, count=-1, *, sep, like=None)

    A new 1-D array initialized from text data in a string.

    Parameters
    ----------
    string : str
        A string containing the data.
    dtype : data-type, optional
        The data type of the array; default: float.  For binary input data,
        the data must be in exactly this format. Most builtin numeric types are
        supported and extension types may be supported.

        .. versionadded:: 1.18.0
            Complex dtypes.

    count : int, optional
        Read this number of `dtype` elements from the data.  If this is
        negative (the default), the count will be determined from the
        length of the data.
    sep : str, optional
        The string separating numbers in the data; extra whitespace between
        elements is also ignored.

        .. deprecated:: 1.14
            Passing ``sep=''``, the default, is deprecated since it will
            trigger the deprecated binary mode of this function. This mode
            interprets `string` as binary bytes, rather than ASCII text with
            decimal numbers, an operation which is better spelt
            ``frombuffer(string, dtype, count)``. If `string` contains unicode
            text, the binary mode of `fromstring` will first encode it into
            bytes using utf-8, which will not produce sane results.

    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    arr : ndarray
        The constructed array.

    Raises
    ------
    ValueError
        If the string is not the correct size to satisfy the requested
        `dtype` and `count`.

    See Also
    --------
    frombuffer, fromfile, fromiter

    Examples
    --------
    >>> import numpy as np
    >>> np.fromstring('1 2', dtype=int, sep=' ')
    array([1, 2])
    >>> np.fromstring('1, 2', dtype=int, sep=',')
    array([1, 2])

Python Library Documentation: function full in module autograd.tracer

full(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return a new array of given shape and type, filled with `fill_value`.

    Parameters
    ----------
    shape : int or sequence of ints
        Shape of the new array, e.g., ``(2, 3)`` or ``2``.
    fill_value : scalar or array_like
        Fill value.
    dtype : data-type, optional
        The desired data-type for the array  The default, None, means
         ``np.array(fill_value).dtype``.
    order : {'C', 'F'}, optional
        Whether to store multidimensional data in C- or Fortran-contiguous
        (row- or column-wise) order in memory.
    device : str, optional
        The device on which to place the created array. Default: None.
        For Array-API interoperability only, so must be ``"cpu"`` if passed.

        .. versionadded:: 2.0.0
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    out : ndarray
        Array of `fill_value` with the given shape, dtype, and order.

    See Also
    --------
    full_like : Return a new array with shape of input filled with value.
    empty : Return a new uninitialized array.
    ones : Return a new array setting values to one.
    zeros : Return a new array setting values to zero.

    Examples
    --------
    >>> import numpy as np
    >>> np.full((2, 2), np.inf)
    array([[inf, inf],
           [inf, inf]])
    >>> np.full((2, 2), 10)
    array([[10, 10],
           [10, 10]])

    >>> np.full((2, 2), [1, 2])
    array([[1, 2],
           [1, 2]])

Python Library Documentation: function full_like in module autograd.tracer

full_like(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return a full array with the same shape and type as a given array.

    Parameters
    ----------
    a : array_like
        The shape and data-type of `a` define these same attributes of
        the returned array.
    fill_value : array_like
        Fill value.
    dtype : data-type, optional
        Overrides the data type of the result.
    order : {'C', 'F', 'A', or 'K'}, optional
        Overrides the memory layout of the result. 'C' means C-order,
        'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
        'C' otherwise. 'K' means match the layout of `a` as closely
        as possible.
    subok : bool, optional.
        If True, then the newly created array will use the sub-class
        type of `a`, otherwise it will be a base-class array. Defaults
        to True.
    shape : int or sequence of ints, optional.
        Overrides the shape of the result. If order='K' and the number of
        dimensions is unchanged, will try to keep order, otherwise,
        order='C' is implied.

        .. versionadded:: 1.17.0
    device : str, optional
        The device on which to place the created array. Default: None.
        For Array-API interoperability only, so must be ``"cpu"`` if passed.

        .. versionadded:: 2.0.0

    Returns
    -------
    out : ndarray
        Array of `fill_value` with the same shape and type as `a`.

    See Also
    --------
    empty_like : Return an empty array with shape and type of input.
    ones_like : Return an array of ones with shape and type of input.
    zeros_like : Return an array of zeros with shape and type of input.
    full : Return a new array of given shape filled with value.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.arange(6, dtype=int)
    >>> np.full_like(x, 1)
    array([1, 1, 1, 1, 1, 1])
    >>> np.full_like(x, 0.1)
    array([0, 0, 0, 0, 0, 0])
    >>> np.full_like(x, 0.1, dtype=np.double)
    array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1])
    >>> np.full_like(x, np.nan, dtype=np.double)
    array([nan, nan, nan, nan, nan, nan])

    >>> y = np.arange(6, dtype=np.double)
    >>> np.full_like(y, 0.1)
    array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1])

    >>> y = np.zeros([2, 2, 3], dtype=int)
    >>> np.full_like(y, [0, 0, 255])
    array([[[  0,   0, 255],
            [  0,   0, 255]],
           [[  0,   0, 255],
            [  0,   0, 255]]])

Python Library Documentation: function gcd in module autograd.tracer

gcd(*args, called_by_autograd_dispatcher=False, **kwargs)
    gcd(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Returns the greatest common divisor of ``|x1|`` and ``|x2|``

    Parameters
    ----------
    x1, x2 : array_like, int
        Arrays of values.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).

    Returns
    -------
    y : ndarray or scalar
        The greatest common divisor of the absolute value of the inputs
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    lcm : The lowest common multiple

    Examples
    --------
    >>> import numpy as np
    >>> np.gcd(12, 20)
    4
    >>> np.gcd.reduce([15, 25, 35])
    5
    >>> np.gcd(np.arange(6), 20)
    array([20,  1,  2,  1,  4,  5])

Python Library Documentation: class generic in module numpy

class generic(builtins.object)
 |  Base class for numpy scalar types.
 |
 |  Class from which most (all?) numpy scalar types are derived.  For
 |  consistency, exposes the same API as `ndarray`, despite many
 |  consequent attributes being either "get-only," or completely irrelevant.
 |  This is the class from which it is strongly suggested users should derive
 |  custom scalar types.
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes defined here:
 |
 |  __hash__ = None

Python Library Documentation: function genfromtxt in module autograd.tracer

genfromtxt(*args, called_by_autograd_dispatcher=False, **kwargs)
    Load data from a text file, with missing values handled as specified.

    Each line past the first `skip_header` lines is split at the `delimiter`
    character, and characters following the `comments` character are discarded.

    Parameters
    ----------
    fname : file, str, pathlib.Path, list of str, generator
        File, filename, list, or generator to read.  If the filename
        extension is ``.gz`` or ``.bz2``, the file is first decompressed. Note
        that generators must return bytes or strings. The strings
        in a list or produced by a generator are treated as lines.
    dtype : dtype, optional
        Data type of the resulting array.
        If None, the dtypes will be determined by the contents of each
        column, individually.
    comments : str, optional
        The character used to indicate the start of a comment.
        All the characters occurring on a line after a comment are discarded.
    delimiter : str, int, or sequence, optional
        The string used to separate values.  By default, any consecutive
        whitespaces act as delimiter.  An integer or sequence of integers
        can also be provided as width(s) of each field.
    skiprows : int, optional
        `skiprows` was removed in numpy 1.10. Please use `skip_header` instead.
    skip_header : int, optional
        The number of lines to skip at the beginning of the file.
    skip_footer : int, optional
        The number of lines to skip at the end of the file.
    converters : variable, optional
        The set of functions that convert the data of a column to a value.
        The converters can also be used to provide a default value
        for missing data: ``converters = {3: lambda s: float(s or 0)}``.
    missing : variable, optional
        `missing` was removed in numpy 1.10. Please use `missing_values`
        instead.
    missing_values : variable, optional
        The set of strings corresponding to missing data.
    filling_values : variable, optional
        The set of values to be used as default when the data are missing.
    usecols : sequence, optional
        Which columns to read, with 0 being the first.  For example,
        ``usecols = (1, 4, 5)`` will extract the 2nd, 5th and 6th columns.
    names : {None, True, str, sequence}, optional
        If `names` is True, the field names are read from the first line after
        the first `skip_header` lines. This line can optionally be preceded
        by a comment delimiter. Any content before the comment delimiter is
        discarded. If `names` is a sequence or a single-string of
        comma-separated names, the names will be used to define the field
        names in a structured dtype. If `names` is None, the names of the
        dtype fields will be used, if any.
    excludelist : sequence, optional
        A list of names to exclude. This list is appended to the default list
        ['return','file','print']. Excluded names are appended with an
        underscore: for example, `file` would become `file_`.
    deletechars : str, optional
        A string combining invalid characters that must be deleted from the
        names.
    defaultfmt : str, optional
        A format used to define default field names, such as "f%i" or "f_%02i".
    autostrip : bool, optional
        Whether to automatically strip white spaces from the variables.
    replace_space : char, optional
        Character(s) used in replacement of white spaces in the variable
        names. By default, use a '_'.
    case_sensitive : {True, False, 'upper', 'lower'}, optional
        If True, field names are case sensitive.
        If False or 'upper', field names are converted to upper case.
        If 'lower', field names are converted to lower case.
    unpack : bool, optional
        If True, the returned array is transposed, so that arguments may be
        unpacked using ``x, y, z = genfromtxt(...)``.  When used with a
        structured data-type, arrays are returned for each field.
        Default is False.
    usemask : bool, optional
        If True, return a masked array.
        If False, return a regular array.
    loose : bool, optional
        If True, do not raise errors for invalid values.
    invalid_raise : bool, optional
        If True, an exception is raised if an inconsistency is detected in the
        number of columns.
        If False, a warning is emitted and the offending lines are skipped.
    max_rows : int,  optional
        The maximum number of rows to read. Must not be used with skip_footer
        at the same time.  If given, the value must be at least 1. Default is
        to read the entire file.

        .. versionadded:: 1.10.0
    encoding : str, optional
        Encoding used to decode the inputfile. Does not apply when `fname`
        is a file object. The special value 'bytes' enables backward
        compatibility workarounds that ensure that you receive byte arrays
        when possible and passes latin1 encoded strings to converters.
        Override this value to receive unicode arrays and pass strings
        as input to converters.  If set to None the system default is used.
        The default value is 'bytes'.

        .. versionadded:: 1.14.0
        .. versionchanged:: 2.0
            Before NumPy 2, the default was ``'bytes'`` for Python 2
            compatibility. The default is now ``None``.

    ndmin : int, optional
        Same parameter as `loadtxt`

        .. versionadded:: 1.23.0
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    out : ndarray
        Data read from the text file. If `usemask` is True, this is a
        masked array.

    See Also
    --------
    numpy.loadtxt : equivalent function when no data is missing.

    Notes
    -----
    * When spaces are used as delimiters, or when no delimiter has been given
      as input, there should not be any missing data between two fields.
    * When variables are named (either by a flexible dtype or with a `names`
      sequence), there must not be any header in the file (else a ValueError
      exception is raised).
    * Individual values are not stripped of spaces by default.
      When using a custom converter, make sure the function does remove spaces.
    * Custom converters may receive unexpected values due to dtype
      discovery.

    References
    ----------
    .. [1] NumPy User Guide, section `I/O with NumPy
           <https://docs.scipy.org/doc/numpy/user/basics.io.genfromtxt.html>`_.

    Examples
    --------
    >>> from io import StringIO
    >>> import numpy as np

    Comma delimited file with mixed dtype

    >>> s = StringIO("1,1.3,abcde")
    >>> data = np.genfromtxt(s, dtype=[('myint','i8'),('myfloat','f8'),
    ... ('mystring','S5')], delimiter=",")
    >>> data
    array((1, 1.3, b'abcde'),
          dtype=[('myint', '<i8'), ('myfloat', '<f8'), ('mystring', 'S5')])

    Using dtype = None

    >>> _ = s.seek(0) # needed for StringIO example only
    >>> data = np.genfromtxt(s, dtype=None,
    ... names = ['myint','myfloat','mystring'], delimiter=",")
    >>> data
    array((1, 1.3, 'abcde'),
          dtype=[('myint', '<i8'), ('myfloat', '<f8'), ('mystring', '<U5')])

    Specifying dtype and names

    >>> _ = s.seek(0)
    >>> data = np.genfromtxt(s, dtype="i8,f8,S5",
    ... names=['myint','myfloat','mystring'], delimiter=",")
    >>> data
    array((1, 1.3, b'abcde'),
          dtype=[('myint', '<i8'), ('myfloat', '<f8'), ('mystring', 'S5')])

    An example with fixed-width columns

    >>> s = StringIO("11.3abcde")
    >>> data = np.genfromtxt(s, dtype=None, names=['intvar','fltvar','strvar'],
    ...     delimiter=[1,3,5])
    >>> data
    array((1, 1.3, 'abcde'),
          dtype=[('intvar', '<i8'), ('fltvar', '<f8'), ('strvar', '<U5')])

    An example to show comments

    >>> f = StringIO('''
    ... text,# of chars
    ... hello world,11
    ... numpy,5''')
    >>> np.genfromtxt(f, dtype='S12,S12', delimiter=',')
    array([(b'text', b''), (b'hello world', b'11'), (b'numpy', b'5')],
      dtype=[('f0', 'S12'), ('f1', 'S12')])

Python Library Documentation: function geomspace in module autograd.tracer

geomspace(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return numbers spaced evenly on a log scale (a geometric progression).

    This is similar to `logspace`, but with endpoints specified directly.
    Each output sample is a constant multiple of the previous.

    .. versionchanged:: 1.16.0
        Non-scalar `start` and `stop` are now supported.

    Parameters
    ----------
    start : array_like
        The starting value of the sequence.
    stop : array_like
        The final value of the sequence, unless `endpoint` is False.
        In that case, ``num + 1`` values are spaced over the
        interval in log-space, of which all but the last (a sequence of
        length `num`) are returned.
    num : integer, optional
        Number of samples to generate.  Default is 50.
    endpoint : boolean, optional
        If true, `stop` is the last sample. Otherwise, it is not included.
        Default is True.
    dtype : dtype
        The type of the output array.  If `dtype` is not given, the data type
        is inferred from `start` and `stop`. The inferred dtype will never be
        an integer; `float` is chosen even if the arguments would produce an
        array of integers.
    axis : int, optional
        The axis in the result to store the samples.  Relevant only if start
        or stop are array-like.  By default (0), the samples will be along a
        new axis inserted at the beginning. Use -1 to get an axis at the end.

        .. versionadded:: 1.16.0

    Returns
    -------
    samples : ndarray
        `num` samples, equally spaced on a log scale.

    See Also
    --------
    logspace : Similar to geomspace, but with endpoints specified using log
               and base.
    linspace : Similar to geomspace, but with arithmetic instead of geometric
               progression.
    arange : Similar to linspace, with the step size specified instead of the
             number of samples.
    :ref:`how-to-partition`

    Notes
    -----
    If the inputs or dtype are complex, the output will follow a logarithmic
    spiral in the complex plane.  (There are an infinite number of spirals
    passing through two points; the output will follow the shortest such path.)

    Examples
    --------
    >>> import numpy as np
    >>> np.geomspace(1, 1000, num=4)
    array([    1.,    10.,   100.,  1000.])
    >>> np.geomspace(1, 1000, num=3, endpoint=False)
    array([   1.,   10.,  100.])
    >>> np.geomspace(1, 1000, num=4, endpoint=False)
    array([   1.        ,    5.62341325,   31.6227766 ,  177.827941  ])
    >>> np.geomspace(1, 256, num=9)
    array([   1.,    2.,    4.,    8.,   16.,   32.,   64.,  128.,  256.])

    Note that the above may not produce exact integers:

    >>> np.geomspace(1, 256, num=9, dtype=int)
    array([  1,   2,   4,   7,  16,  32,  63, 127, 256])
    >>> np.around(np.geomspace(1, 256, num=9)).astype(int)
    array([  1,   2,   4,   8,  16,  32,  64, 128, 256])

    Negative, decreasing, and complex inputs are allowed:

    >>> np.geomspace(1000, 1, num=4)
    array([1000.,  100.,   10.,    1.])
    >>> np.geomspace(-1000, -1, num=4)
    array([-1000.,  -100.,   -10.,    -1.])
    >>> np.geomspace(1j, 1000j, num=4)  # Straight line
    array([0.   +1.j, 0.  +10.j, 0. +100.j, 0.+1000.j])
    >>> np.geomspace(-1+0j, 1+0j, num=5)  # Circle
    array([-1.00000000e+00+1.22464680e-16j, -7.07106781e-01+7.07106781e-01j,
            6.12323400e-17+1.00000000e+00j,  7.07106781e-01+7.07106781e-01j,
            1.00000000e+00+0.00000000e+00j])

    Graphical illustration of `endpoint` parameter:

    >>> import matplotlib.pyplot as plt
    >>> N = 10
    >>> y = np.zeros(N)
    >>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=True), y + 1, 'o')
    [<matplotlib.lines.Line2D object at 0x...>]
    >>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=False), y + 2, 'o')
    [<matplotlib.lines.Line2D object at 0x...>]
    >>> plt.axis([0.5, 2000, 0, 3])
    [0.5, 2000, 0, 3]
    >>> plt.grid(True, color='0.7', linestyle='-', which='both', axis='both')
    >>> plt.show()

Python Library Documentation: function get_include in module autograd.tracer

get_include(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the directory that contains the NumPy \*.h header files.

    Extension modules that need to compile against NumPy may need to use this
    function to locate the appropriate include directory.

    Notes
    -----
    When using ``setuptools``, for example in ``setup.py``::

        import numpy as np
        ...
        Extension('extension_name', ...
                  include_dirs=[np.get_include()])
        ...

    Note that a CLI tool ``numpy-config`` was introduced in NumPy 2.0, using
    that is likely preferred for build systems other than ``setuptools``::

        $ numpy-config --cflags
        -I/path/to/site-packages/numpy/_core/include

        # Or rely on pkg-config:
        $ export PKG_CONFIG_PATH=$(numpy-config --pkgconfigdir)
        $ pkg-config --cflags
        -I/path/to/site-packages/numpy/_core/include

    Examples
    --------
    >>> np.get_include()
    '.../site-packages/numpy/core/include'  # may vary

Python Library Documentation: function get_printoptions in module autograd.tracer

get_printoptions(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the current print options.

    Returns
    -------
    print_opts : dict
        Dictionary of current print options with keys

        - precision : int
        - threshold : int
        - edgeitems : int
        - linewidth : int
        - suppress : bool
        - nanstr : str
        - infstr : str
        - sign : str
        - formatter : dict of callables
        - floatmode : str
        - legacy : str or False

        For a full description of these options, see `set_printoptions`.

    See Also
    --------
    set_printoptions, printoptions

    Examples
    --------
    >>> import numpy as np

    >>> np.get_printoptions()
    {'edgeitems': 3, 'threshold': 1000, ..., 'override_repr': None}

    >>> np.get_printoptions()['linewidth']
    75
    >>> np.set_printoptions(linewidth=100)
    >>> np.get_printoptions()['linewidth']
    100

Python Library Documentation: function getbufsize in module autograd.tracer

getbufsize(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the size of the buffer used in ufuncs.

    Returns
    -------
    getbufsize : int
        Size of ufunc buffer in bytes.

    Examples
    --------
    >>> import numpy as np
    >>> np.getbufsize()
    8192

Python Library Documentation: function geterr in module autograd.tracer

geterr(*args, called_by_autograd_dispatcher=False, **kwargs)
    Get the current way of handling floating-point errors.

    Returns
    -------
    res : dict
        A dictionary with keys "divide", "over", "under", and "invalid",
        whose values are from the strings "ignore", "print", "log", "warn",
        "raise", and "call". The keys represent possible floating-point
        exceptions, and the values define how these exceptions are handled.

    See Also
    --------
    geterrcall, seterr, seterrcall

    Notes
    -----
    For complete documentation of the types of floating-point exceptions and
    treatment options, see `seterr`.

    Examples
    --------
    >>> import numpy as np
    >>> np.geterr()
    {'divide': 'warn', 'over': 'warn', 'under': 'ignore', 'invalid': 'warn'}
    >>> np.arange(3.) / np.arange(3.)  # doctest: +SKIP
    array([nan,  1.,  1.])
    RuntimeWarning: invalid value encountered in divide

    >>> oldsettings = np.seterr(all='warn', invalid='raise')
    >>> np.geterr()
    {'divide': 'warn', 'over': 'warn', 'under': 'warn', 'invalid': 'raise'}
    >>> np.arange(3.) / np.arange(3.)
    Traceback (most recent call last):
      ...
    FloatingPointError: invalid value encountered in divide
    >>> oldsettings = np.seterr(**oldsettings)  # restore original

Python Library Documentation: function geterrcall in module autograd.tracer

geterrcall(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the current callback function used on floating-point errors.

    When the error handling for a floating-point error (one of "divide",
    "over", "under", or "invalid") is set to 'call' or 'log', the function
    that is called or the log instance that is written to is returned by
    `geterrcall`. This function or log instance has been set with
    `seterrcall`.

    Returns
    -------
    errobj : callable, log instance or None
        The current error handler. If no handler was set through `seterrcall`,
        ``None`` is returned.

    See Also
    --------
    seterrcall, seterr, geterr

    Notes
    -----
    For complete documentation of the types of floating-point exceptions and
    treatment options, see `seterr`.

    Examples
    --------
    >>> import numpy as np
    >>> np.geterrcall()  # we did not yet set a handler, returns None

    >>> orig_settings = np.seterr(all='call')
    >>> def err_handler(type, flag):
    ...     print("Floating point error (%s), with flag %s" % (type, flag))
    >>> old_handler = np.seterrcall(err_handler)
    >>> np.array([1, 2, 3]) / 0.0
    Floating point error (divide by zero), with flag 1
    array([inf, inf, inf])

    >>> cur_handler = np.geterrcall()
    >>> cur_handler is err_handler
    True
    >>> old_settings = np.seterr(**orig_settings)  # restore original
    >>> old_handler = np.seterrcall(None)  # restore original

Python Library Documentation: function gradient in module autograd.tracer

gradient(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the gradient of an N-dimensional array.

    The gradient is computed using second order accurate central differences
    in the interior points and either first or second order accurate one-sides
    (forward or backwards) differences at the boundaries.
    The returned gradient hence has the same shape as the input array.

    Parameters
    ----------
    f : array_like
        An N-dimensional array containing samples of a scalar function.
    varargs : list of scalar or array, optional
        Spacing between f values. Default unitary spacing for all dimensions.
        Spacing can be specified using:

        1. single scalar to specify a sample distance for all dimensions.
        2. N scalars to specify a constant sample distance for each dimension.
           i.e. `dx`, `dy`, `dz`, ...
        3. N arrays to specify the coordinates of the values along each
           dimension of F. The length of the array must match the size of
           the corresponding dimension
        4. Any combination of N scalars/arrays with the meaning of 2. and 3.

        If `axis` is given, the number of varargs must equal the number of axes.
        Default: 1. (see Examples below).

    edge_order : {1, 2}, optional
        Gradient is calculated using N-th order accurate differences
        at the boundaries. Default: 1.

        .. versionadded:: 1.9.1

    axis : None or int or tuple of ints, optional
        Gradient is calculated only along the given axis or axes
        The default (axis = None) is to calculate the gradient for all the axes
        of the input array. axis may be negative, in which case it counts from
        the last to the first axis.

        .. versionadded:: 1.11.0

    Returns
    -------
    gradient : ndarray or tuple of ndarray
        A tuple of ndarrays (or a single ndarray if there is only one
        dimension) corresponding to the derivatives of f with respect
        to each dimension. Each derivative has the same shape as f.

    Examples
    --------
    >>> import numpy as np
    >>> f = np.array([1, 2, 4, 7, 11, 16])
    >>> np.gradient(f)
    array([1. , 1.5, 2.5, 3.5, 4.5, 5. ])
    >>> np.gradient(f, 2)
    array([0.5 ,  0.75,  1.25,  1.75,  2.25,  2.5 ])

    Spacing can be also specified with an array that represents the coordinates
    of the values F along the dimensions.
    For instance a uniform spacing:

    >>> x = np.arange(f.size)
    >>> np.gradient(f, x)
    array([1. ,  1.5,  2.5,  3.5,  4.5,  5. ])

    Or a non uniform one:

    >>> x = np.array([0., 1., 1.5, 3.5, 4., 6.])
    >>> np.gradient(f, x)
    array([1. ,  3. ,  3.5,  6.7,  6.9,  2.5])

    For two dimensional arrays, the return will be two arrays ordered by
    axis. In this example the first array stands for the gradient in
    rows and the second one in columns direction:

    >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]]))
    (array([[ 2.,  2., -1.],
            [ 2.,  2., -1.]]),
     array([[1. , 2.5, 4. ],
            [1. , 1. , 1. ]]))

    In this example the spacing is also specified:
    uniform for axis=0 and non uniform for axis=1

    >>> dx = 2.
    >>> y = [1., 1.5, 3.5]
    >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]]), dx, y)
    (array([[ 1. ,  1. , -0.5],
            [ 1. ,  1. , -0.5]]),
     array([[2. , 2. , 2. ],
            [2. , 1.7, 0.5]]))

    It is possible to specify how boundaries are treated using `edge_order`

    >>> x = np.array([0, 1, 2, 3, 4])
    >>> f = x**2
    >>> np.gradient(f, edge_order=1)
    array([1.,  2.,  4.,  6.,  7.])
    >>> np.gradient(f, edge_order=2)
    array([0., 2., 4., 6., 8.])

    The `axis` keyword can be used to specify a subset of axes of which the
    gradient is calculated

    >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]]), axis=0)
    array([[ 2.,  2., -1.],
           [ 2.,  2., -1.]])

    The `varargs` argument defines the spacing between sample points in the
    input array. It can take two forms:

    1. An array, specifying coordinates, which may be unevenly spaced:

    >>> x = np.array([0., 2., 3., 6., 8.])
    >>> y = x ** 2
    >>> np.gradient(y, x, edge_order=2)
    array([ 0.,  4.,  6., 12., 16.])

    2. A scalar, representing the fixed sample distance:

    >>> dx = 2
    >>> x = np.array([0., 2., 4., 6., 8.])
    >>> y = x ** 2
    >>> np.gradient(y, dx, edge_order=2)
    array([ 0.,  4.,  8., 12., 16.])

    It's possible to provide different data for spacing along each dimension.
    The number of arguments must match the number of dimensions in the input
    data.

    >>> dx = 2
    >>> dy = 3
    >>> x = np.arange(0, 6, dx)
    >>> y = np.arange(0, 9, dy)
    >>> xs, ys = np.meshgrid(x, y)
    >>> zs = xs + 2 * ys
    >>> np.gradient(zs, dy, dx)  # Passing two scalars
    (array([[2., 2., 2.],
            [2., 2., 2.],
            [2., 2., 2.]]),
     array([[1., 1., 1.],
            [1., 1., 1.],
            [1., 1., 1.]]))

    Mixing scalars and arrays is also allowed:

    >>> np.gradient(zs, y, dx)  # Passing one array and one scalar
    (array([[2., 2., 2.],
            [2., 2., 2.],
            [2., 2., 2.]]),
     array([[1., 1., 1.],
            [1., 1., 1.],
            [1., 1., 1.]]))

    Notes
    -----
    Assuming that :math:`f\in C^{3}` (i.e., :math:`f` has at least 3 continuous
    derivatives) and let :math:`h_{*}` be a non-homogeneous stepsize, we
    minimize the "consistency error" :math:`\eta_{i}` between the true gradient
    and its estimate from a linear combination of the neighboring grid-points:

    .. math::

        \eta_{i} = f_{i}^{\left(1\right)} -
                    \left[ \alpha f\left(x_{i}\right) +
                            \beta f\left(x_{i} + h_{d}\right) +
                            \gamma f\left(x_{i}-h_{s}\right)
                    \right]

    By substituting :math:`f(x_{i} + h_{d})` and :math:`f(x_{i} - h_{s})`
    with their Taylor series expansion, this translates into solving
    the following the linear system:

    .. math::

        \left\{
            \begin{array}{r}
                \alpha+\beta+\gamma=0 \\
                \beta h_{d}-\gamma h_{s}=1 \\
                \beta h_{d}^{2}+\gamma h_{s}^{2}=0
            \end{array}
        \right.

    The resulting approximation of :math:`f_{i}^{(1)}` is the following:

    .. math::

        \hat f_{i}^{(1)} =
            \frac{
                h_{s}^{2}f\left(x_{i} + h_{d}\right)
                + \left(h_{d}^{2} - h_{s}^{2}\right)f\left(x_{i}\right)
                - h_{d}^{2}f\left(x_{i}-h_{s}\right)}
                { h_{s}h_{d}\left(h_{d} + h_{s}\right)}
            + \mathcal{O}\left(\frac{h_{d}h_{s}^{2}
                                + h_{s}h_{d}^{2}}{h_{d}
                                + h_{s}}\right)

    It is worth noting that if :math:`h_{s}=h_{d}`
    (i.e., data are evenly spaced)
    we find the standard second order approximation:

    .. math::

        \hat f_{i}^{(1)}=
            \frac{f\left(x_{i+1}\right) - f\left(x_{i-1}\right)}{2h}
            + \mathcal{O}\left(h^{2}\right)

    With a similar procedure the forward/backward approximations used for
    boundaries can be derived.

    References
    ----------
    .. [1]  Quarteroni A., Sacco R., Saleri F. (2007) Numerical Mathematics
            (Texts in Applied Mathematics). New York: Springer.
    .. [2]  Durran D. R. (1999) Numerical Methods for Wave Equations
            in Geophysical Fluid Dynamics. New York: Springer.
    .. [3]  Fornberg B. (1988) Generation of Finite Difference Formulas on
            Arbitrarily Spaced Grids,
            Mathematics of Computation 51, no. 184 : 699-706.
            `PDF <https://www.ams.org/journals/mcom/1988-51-184/
            S0025-5718-1988-0935077-0/S0025-5718-1988-0935077-0.pdf>`_.

Python Library Documentation: function greater in module autograd.tracer

greater(*args, called_by_autograd_dispatcher=False, **kwargs)
    greater(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the truth value of (x1 > x2) element-wise.

    Parameters
    ----------
    x1, x2 : array_like
        Input arrays.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Output array, element-wise comparison of `x1` and `x2`.
        Typically of type bool, unless ``dtype=object`` is passed.
        This is a scalar if both `x1` and `x2` are scalars.


    See Also
    --------
    greater_equal, less, less_equal, equal, not_equal

    Examples
    --------
    >>> import numpy as np
    >>> np.greater([4,2],[2,2])
    array([ True, False])

    The ``>`` operator can be used as a shorthand for ``np.greater`` on
    ndarrays.

    >>> a = np.array([4, 2])
    >>> b = np.array([2, 2])
    >>> a > b
    array([ True, False])

Python Library Documentation: function greater_equal in module autograd.tracer

greater_equal(*args, called_by_autograd_dispatcher=False, **kwargs)
    greater_equal(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the truth value of (x1 >= x2) element-wise.

    Parameters
    ----------
    x1, x2 : array_like
        Input arrays.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : bool or ndarray of bool
        Output array, element-wise comparison of `x1` and `x2`.
        Typically of type bool, unless ``dtype=object`` is passed.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    greater, less, less_equal, equal, not_equal

    Examples
    --------
    >>> import numpy as np
    >>> np.greater_equal([4, 2, 1], [2, 2, 2])
    array([ True, True, False])

    The ``>=`` operator can be used as a shorthand for ``np.greater_equal``
    on ndarrays.

    >>> a = np.array([4, 2, 1])
    >>> b = np.array([2, 2, 2])
    >>> a >= b
    array([ True,  True, False])

Python Library Documentation: class float16 in module numpy

class float16(floating)
 |  Half-precision floating-point number type.
 |
 |  :Character code: ``'e'``
 |  :Canonical name: `numpy.half`
 |  :Alias on this platform (win32 AMD64): `numpy.float16`: 16-bit-precision floating-point number type: sign bit, 5 bits exponent, 10 bits mantissa.
 |
 |  Method resolution order:
 |      float16
 |      floating
 |      inexact
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  as_integer_ratio(...)
 |      half.as_integer_ratio() -> (int, int)
 |
 |      Return a pair of integers, whose ratio is exactly equal to the original
 |      floating point number, and with a positive denominator.
 |      Raise `OverflowError` on infinities and a `ValueError` on NaNs.
 |
 |      >>> np.half(10.0).as_integer_ratio()
 |      (10, 1)
 |      >>> np.half(0.0).as_integer_ratio()
 |      (0, 1)
 |      >>> np.half(-.25).as_integer_ratio()
 |      (-1, 4)
 |
 |  is_integer(...)
 |      half.is_integer() -> bool
 |
 |      Return ``True`` if the floating point number is finite with integral
 |      value, and ``False`` otherwise.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> np.half(-2.0).is_integer()
 |      True
 |      >>> np.half(3.2).is_integer()
 |      False
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from floating:
 |
 |  __round__(...)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: function hamming in module autograd.tracer

hamming(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the Hamming window.

    The Hamming window is a taper formed by using a weighted cosine.

    Parameters
    ----------
    M : int
        Number of points in the output window. If zero or less, an
        empty array is returned.

    Returns
    -------
    out : ndarray
        The window, with the maximum value normalized to one (the value
        one appears only if the number of samples is odd).

    See Also
    --------
    bartlett, blackman, hanning, kaiser

    Notes
    -----
    The Hamming window is defined as

    .. math::  w(n) = 0.54 - 0.46\cos\left(\frac{2\pi{n}}{M-1}\right)
               \qquad 0 \leq n \leq M-1

    The Hamming was named for R. W. Hamming, an associate of J. W. Tukey
    and is described in Blackman and Tukey. It was recommended for
    smoothing the truncated autocovariance function in the time domain.
    Most references to the Hamming window come from the signal processing
    literature, where it is used as one of many windowing functions for
    smoothing values.  It is also known as an apodization (which means
    "removing the foot", i.e. smoothing discontinuities at the beginning
    and end of the sampled signal) or tapering function.

    References
    ----------
    .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power
           spectra, Dover Publications, New York.
    .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The
           University of Alberta Press, 1975, pp. 109-110.
    .. [3] Wikipedia, "Window function",
           https://en.wikipedia.org/wiki/Window_function
    .. [4] W.H. Press,  B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
           "Numerical Recipes", Cambridge University Press, 1986, page 425.

    Examples
    --------
    >>> import numpy as np
    >>> np.hamming(12)
    array([ 0.08      ,  0.15302337,  0.34890909,  0.60546483,  0.84123594, # may vary
            0.98136677,  0.98136677,  0.84123594,  0.60546483,  0.34890909,
            0.15302337,  0.08      ])

    Plot the window and the frequency response.

    .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from numpy.fft import fft, fftshift
        window = np.hamming(51)
        plt.plot(window)
        plt.title("Hamming window")
        plt.ylabel("Amplitude")
        plt.xlabel("Sample")
        plt.show()

        plt.figure()
        A = fft(window, 2048) / 25.5
        mag = np.abs(fftshift(A))
        freq = np.linspace(-0.5, 0.5, len(A))
        response = 20 * np.log10(mag)
        response = np.clip(response, -100, 100)
        plt.plot(freq, response)
        plt.title("Frequency response of Hamming window")
        plt.ylabel("Magnitude [dB]")
        plt.xlabel("Normalized frequency [cycles per sample]")
        plt.axis('tight')
        plt.show()

Python Library Documentation: function hanning in module autograd.tracer

hanning(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the Hanning window.

    The Hanning window is a taper formed by using a weighted cosine.

    Parameters
    ----------
    M : int
        Number of points in the output window. If zero or less, an
        empty array is returned.

    Returns
    -------
    out : ndarray, shape(M,)
        The window, with the maximum value normalized to one (the value
        one appears only if `M` is odd).

    See Also
    --------
    bartlett, blackman, hamming, kaiser

    Notes
    -----
    The Hanning window is defined as

    .. math::  w(n) = 0.5 - 0.5\cos\left(\frac{2\pi{n}}{M-1}\right)
               \qquad 0 \leq n \leq M-1

    The Hanning was named for Julius von Hann, an Austrian meteorologist.
    It is also known as the Cosine Bell. Some authors prefer that it be
    called a Hann window, to help avoid confusion with the very similar
    Hamming window.

    Most references to the Hanning window come from the signal processing
    literature, where it is used as one of many windowing functions for
    smoothing values.  It is also known as an apodization (which means
    "removing the foot", i.e. smoothing discontinuities at the beginning
    and end of the sampled signal) or tapering function.

    References
    ----------
    .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power
           spectra, Dover Publications, New York.
    .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics",
           The University of Alberta Press, 1975, pp. 106-108.
    .. [3] Wikipedia, "Window function",
           https://en.wikipedia.org/wiki/Window_function
    .. [4] W.H. Press,  B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
           "Numerical Recipes", Cambridge University Press, 1986, page 425.

    Examples
    --------
    >>> import numpy as np
    >>> np.hanning(12)
    array([0.        , 0.07937323, 0.29229249, 0.57115742, 0.82743037,
           0.97974649, 0.97974649, 0.82743037, 0.57115742, 0.29229249,
           0.07937323, 0.        ])

    Plot the window and its frequency response.

    .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from numpy.fft import fft, fftshift
        window = np.hanning(51)
        plt.plot(window)
        plt.title("Hann window")
        plt.ylabel("Amplitude")
        plt.xlabel("Sample")
        plt.show()

        plt.figure()
        A = fft(window, 2048) / 25.5
        mag = np.abs(fftshift(A))
        freq = np.linspace(-0.5, 0.5, len(A))
        with np.errstate(divide='ignore', invalid='ignore'):
            response = 20 * np.log10(mag)
        response = np.clip(response, -100, 100)
        plt.plot(freq, response)
        plt.title("Frequency response of the Hann window")
        plt.ylabel("Magnitude [dB]")
        plt.xlabel("Normalized frequency [cycles per sample]")
        plt.axis('tight')
        plt.show()

Python Library Documentation: function heaviside in module autograd.tracer

heaviside(*args, called_by_autograd_dispatcher=False, **kwargs)
    heaviside(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Compute the Heaviside step function.

    The Heaviside step function [1]_ is defined as::

                              0   if x1 < 0
        heaviside(x1, x2) =  x2   if x1 == 0
                              1   if x1 > 0

    where `x2` is often taken to be 0.5, but 0 and 1 are also sometimes used.

    Parameters
    ----------
    x1 : array_like
        Input values.
    x2 : array_like
        The value of the function when x1 is 0.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        The output array, element-wise Heaviside step function of `x1`.
        This is a scalar if both `x1` and `x2` are scalars.

    Notes
    -----
    .. versionadded:: 1.13.0

    References
    ----------
    .. [1] Wikipedia, "Heaviside step function",
           https://en.wikipedia.org/wiki/Heaviside_step_function

    Examples
    --------
    >>> import numpy as np
    >>> np.heaviside([-1.5, 0, 2.0], 0.5)
    array([ 0. ,  0.5,  1. ])
    >>> np.heaviside([-1.5, 0, 2.0], 1)
    array([ 0.,  1.,  1.])

Python Library Documentation: function histogram in module autograd.tracer

histogram(*args, called_by_autograd_dispatcher=False, **kwargs)
    Compute the histogram of a dataset.

    Parameters
    ----------
    a : array_like
        Input data. The histogram is computed over the flattened array.
    bins : int or sequence of scalars or str, optional
        If `bins` is an int, it defines the number of equal-width
        bins in the given range (10, by default). If `bins` is a
        sequence, it defines a monotonically increasing array of bin edges,
        including the rightmost edge, allowing for non-uniform bin widths.

        .. versionadded:: 1.11.0

        If `bins` is a string, it defines the method used to calculate the
        optimal bin width, as defined by `histogram_bin_edges`.

    range : (float, float), optional
        The lower and upper range of the bins.  If not provided, range
        is simply ``(a.min(), a.max())``.  Values outside the range are
        ignored. The first element of the range must be less than or
        equal to the second. `range` affects the automatic bin
        computation as well. While bin width is computed to be optimal
        based on the actual data within `range`, the bin count will fill
        the entire range including portions containing no data.
    weights : array_like, optional
        An array of weights, of the same shape as `a`.  Each value in
        `a` only contributes its associated weight towards the bin count
        (instead of 1). If `density` is True, the weights are
        normalized, so that the integral of the density over the range
        remains 1.
        Please note that the ``dtype`` of `weights` will also become the
        ``dtype`` of the returned accumulator (`hist`), so it must be
        large enough to hold accumulated values as well.
    density : bool, optional
        If ``False``, the result will contain the number of samples in
        each bin. If ``True``, the result is the value of the
        probability *density* function at the bin, normalized such that
        the *integral* over the range is 1. Note that the sum of the
        histogram values will not be equal to 1 unless bins of unity
        width are chosen; it is not a probability *mass* function.

    Returns
    -------
    hist : array
        The values of the histogram. See `density` and `weights` for a
        description of the possible semantics.  If `weights` are given,
        ``hist.dtype`` will be taken from `weights`.
    bin_edges : array of dtype float
        Return the bin edges ``(length(hist)+1)``.


    See Also
    --------
    histogramdd, bincount, searchsorted, digitize, histogram_bin_edges

    Notes
    -----
    All but the last (righthand-most) bin is half-open.  In other words,
    if `bins` is::

      [1, 2, 3, 4]

    then the first bin is ``[1, 2)`` (including 1, but excluding 2) and
    the second ``[2, 3)``.  The last bin, however, is ``[3, 4]``, which
    *includes* 4.


    Examples
    --------
    >>> import numpy as np
    >>> np.histogram([1, 2, 1], bins=[0, 1, 2, 3])
    (array([0, 2, 1]), array([0, 1, 2, 3]))
    >>> np.histogram(np.arange(4), bins=np.arange(5), density=True)
    (array([0.25, 0.25, 0.25, 0.25]), array([0, 1, 2, 3, 4]))
    >>> np.histogram([[1, 2, 1], [1, 0, 1]], bins=[0,1,2,3])
    (array([1, 4, 1]), array([0, 1, 2, 3]))

    >>> a = np.arange(5)
    >>> hist, bin_edges = np.histogram(a, density=True)
    >>> hist
    array([0.5, 0. , 0.5, 0. , 0. , 0.5, 0. , 0.5, 0. , 0.5])
    >>> hist.sum()
    2.4999999999999996
    >>> np.sum(hist * np.diff(bin_edges))
    1.0

    .. versionadded:: 1.11.0

    Automated Bin Selection Methods example, using 2 peak random data
    with 2000 points.

    .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        import numpy as np

        rng = np.random.RandomState(10)  # deterministic random data
        a = np.hstack((rng.normal(size=1000),
                       rng.normal(loc=5, scale=2, size=1000)))
        plt.hist(a, bins='auto')  # arguments are passed to np.histogram
        plt.title("Histogram with 'auto' bins")
        plt.show()

Python Library Documentation: function histogram2d in module autograd.tracer

histogram2d(*args, called_by_autograd_dispatcher=False, **kwargs)
    Compute the bi-dimensional histogram of two data samples.

    Parameters
    ----------
    x : array_like, shape (N,)
        An array containing the x coordinates of the points to be
        histogrammed.
    y : array_like, shape (N,)
        An array containing the y coordinates of the points to be
        histogrammed.
    bins : int or array_like or [int, int] or [array, array], optional
        The bin specification:

        * If int, the number of bins for the two dimensions (nx=ny=bins).
        * If array_like, the bin edges for the two dimensions
          (x_edges=y_edges=bins).
        * If [int, int], the number of bins in each dimension
          (nx, ny = bins).
        * If [array, array], the bin edges in each dimension
          (x_edges, y_edges = bins).
        * A combination [int, array] or [array, int], where int
          is the number of bins and array is the bin edges.

    range : array_like, shape(2,2), optional
        The leftmost and rightmost edges of the bins along each dimension
        (if not specified explicitly in the `bins` parameters):
        ``[[xmin, xmax], [ymin, ymax]]``. All values outside of this range
        will be considered outliers and not tallied in the histogram.
    density : bool, optional
        If False, the default, returns the number of samples in each bin.
        If True, returns the probability *density* function at the bin,
        ``bin_count / sample_count / bin_area``.
    weights : array_like, shape(N,), optional
        An array of values ``w_i`` weighing each sample ``(x_i, y_i)``.
        Weights are normalized to 1 if `density` is True. If `density` is
        False, the values of the returned histogram are equal to the sum of
        the weights belonging to the samples falling into each bin.

    Returns
    -------
    H : ndarray, shape(nx, ny)
        The bi-dimensional histogram of samples `x` and `y`. Values in `x`
        are histogrammed along the first dimension and values in `y` are
        histogrammed along the second dimension.
    xedges : ndarray, shape(nx+1,)
        The bin edges along the first dimension.
    yedges : ndarray, shape(ny+1,)
        The bin edges along the second dimension.

    See Also
    --------
    histogram : 1D histogram
    histogramdd : Multidimensional histogram

    Notes
    -----
    When `density` is True, then the returned histogram is the sample
    density, defined such that the sum over bins of the product
    ``bin_value * bin_area`` is 1.

    Please note that the histogram does not follow the Cartesian convention
    where `x` values are on the abscissa and `y` values on the ordinate
    axis.  Rather, `x` is histogrammed along the first dimension of the
    array (vertical), and `y` along the second dimension of the array
    (horizontal).  This ensures compatibility with `histogramdd`.

    Examples
    --------
    >>> import numpy as np
    >>> from matplotlib.image import NonUniformImage
    >>> import matplotlib.pyplot as plt

    Construct a 2-D histogram with variable bin width. First define the bin
    edges:

    >>> xedges = [0, 1, 3, 5]
    >>> yedges = [0, 2, 3, 4, 6]

    Next we create a histogram H with random bin content:

    >>> x = np.random.normal(2, 1, 100)
    >>> y = np.random.normal(1, 1, 100)
    >>> H, xedges, yedges = np.histogram2d(x, y, bins=(xedges, yedges))
    >>> # Histogram does not follow Cartesian convention (see Notes),
    >>> # therefore transpose H for visualization purposes.
    >>> H = H.T

    :func:`imshow <matplotlib.pyplot.imshow>` can only display square bins:

    >>> fig = plt.figure(figsize=(7, 3))
    >>> ax = fig.add_subplot(131, title='imshow: square bins')
    >>> plt.imshow(H, interpolation='nearest', origin='lower',
    ...         extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]])
    <matplotlib.image.AxesImage object at 0x...>

    :func:`pcolormesh <matplotlib.pyplot.pcolormesh>` can display actual edges:

    >>> ax = fig.add_subplot(132, title='pcolormesh: actual edges',
    ...         aspect='equal')
    >>> X, Y = np.meshgrid(xedges, yedges)
    >>> ax.pcolormesh(X, Y, H)
    <matplotlib.collections.QuadMesh object at 0x...>

    :class:`NonUniformImage <matplotlib.image.NonUniformImage>` can be used to
    display actual bin edges with interpolation:

    >>> ax = fig.add_subplot(133, title='NonUniformImage: interpolated',
    ...         aspect='equal', xlim=xedges[[0, -1]], ylim=yedges[[0, -1]])
    >>> im = NonUniformImage(ax, interpolation='bilinear')
    >>> xcenters = (xedges[:-1] + xedges[1:]) / 2
    >>> ycenters = (yedges[:-1] + yedges[1:]) / 2
    >>> im.set_data(xcenters, ycenters, H)
    >>> ax.add_image(im)
    >>> plt.show()

    It is also possible to construct a 2-D histogram without specifying bin
    edges:

    >>> # Generate non-symmetric test data
    >>> n = 10000
    >>> x = np.linspace(1, 100, n)
    >>> y = 2*np.log(x) + np.random.rand(n) - 0.5
    >>> # Compute 2d histogram. Note the order of x/y and xedges/yedges
    >>> H, yedges, xedges = np.histogram2d(y, x, bins=20)

    Now we can plot the histogram using
    :func:`pcolormesh <matplotlib.pyplot.pcolormesh>`, and a
    :func:`hexbin <matplotlib.pyplot.hexbin>` for comparison.

    >>> # Plot histogram using pcolormesh
    >>> fig, (ax1, ax2) = plt.subplots(ncols=2, sharey=True)
    >>> ax1.pcolormesh(xedges, yedges, H, cmap='rainbow')
    >>> ax1.plot(x, 2*np.log(x), 'k-')
    >>> ax1.set_xlim(x.min(), x.max())
    >>> ax1.set_ylim(y.min(), y.max())
    >>> ax1.set_xlabel('x')
    >>> ax1.set_ylabel('y')
    >>> ax1.set_title('histogram2d')
    >>> ax1.grid()

    >>> # Create hexbin plot for comparison
    >>> ax2.hexbin(x, y, gridsize=20, cmap='rainbow')
    >>> ax2.plot(x, 2*np.log(x), 'k-')
    >>> ax2.set_title('hexbin')
    >>> ax2.set_xlim(x.min(), x.max())
    >>> ax2.set_xlabel('x')
    >>> ax2.grid()

    >>> plt.show()

Python Library Documentation: function histogram_bin_edges in module autograd.tracer

histogram_bin_edges(*args, called_by_autograd_dispatcher=False, **kwargs)
    Function to calculate only the edges of the bins used by the `histogram`
    function.

    Parameters
    ----------
    a : array_like
        Input data. The histogram is computed over the flattened array.
    bins : int or sequence of scalars or str, optional
        If `bins` is an int, it defines the number of equal-width
        bins in the given range (10, by default). If `bins` is a
        sequence, it defines the bin edges, including the rightmost
        edge, allowing for non-uniform bin widths.

        If `bins` is a string from the list below, `histogram_bin_edges` will
        use the method chosen to calculate the optimal bin width and
        consequently the number of bins (see the Notes section for more detail
        on the estimators) from the data that falls within the requested range.
        While the bin width will be optimal for the actual data
        in the range, the number of bins will be computed to fill the
        entire range, including the empty portions. For visualisation,
        using the 'auto' option is suggested. Weighted data is not
        supported for automated bin size selection.

        'auto'
            Minimum bin width between the 'sturges' and 'fd' estimators.
            Provides good all-around performance.

        'fd' (Freedman Diaconis Estimator)
            Robust (resilient to outliers) estimator that takes into
            account data variability and data size.

        'doane'
            An improved version of Sturges' estimator that works better
            with non-normal datasets.

        'scott'
            Less robust estimator that takes into account data variability
            and data size.

        'stone'
            Estimator based on leave-one-out cross-validation estimate of
            the integrated squared error. Can be regarded as a generalization
            of Scott's rule.

        'rice'
            Estimator does not take variability into account, only data
            size. Commonly overestimates number of bins required.

        'sturges'
            R's default method, only accounts for data size. Only
            optimal for gaussian data and underestimates number of bins
            for large non-gaussian datasets.

        'sqrt'
            Square root (of data size) estimator, used by Excel and
            other programs for its speed and simplicity.

    range : (float, float), optional
        The lower and upper range of the bins.  If not provided, range
        is simply ``(a.min(), a.max())``.  Values outside the range are
        ignored. The first element of the range must be less than or
        equal to the second. `range` affects the automatic bin
        computation as well. While bin width is computed to be optimal
        based on the actual data within `range`, the bin count will fill
        the entire range including portions containing no data.

    weights : array_like, optional
        An array of weights, of the same shape as `a`.  Each value in
        `a` only contributes its associated weight towards the bin count
        (instead of 1). This is currently not used by any of the bin estimators,
        but may be in the future.

    Returns
    -------
    bin_edges : array of dtype float
        The edges to pass into `histogram`

    See Also
    --------
    histogram

    Notes
    -----
    The methods to estimate the optimal number of bins are well founded
    in literature, and are inspired by the choices R provides for
    histogram visualisation. Note that having the number of bins
    proportional to :math:`n^{1/3}` is asymptotically optimal, which is
    why it appears in most estimators. These are simply plug-in methods
    that give good starting points for number of bins. In the equations
    below, :math:`h` is the binwidth and :math:`n_h` is the number of
    bins. All estimators that compute bin counts are recast to bin width
    using the `ptp` of the data. The final bin count is obtained from
    ``np.round(np.ceil(range / h))``. The final bin width is often less
    than what is returned by the estimators below.

    'auto' (minimum bin width of the 'sturges' and 'fd' estimators)
        A compromise to get a good value. For small datasets the Sturges
        value will usually be chosen, while larger datasets will usually
        default to FD.  Avoids the overly conservative behaviour of FD
        and Sturges for small and large datasets respectively.
        Switchover point is usually :math:`a.size \approx 1000`.

    'fd' (Freedman Diaconis Estimator)
        .. math:: h = 2 \frac{IQR}{n^{1/3}}

        The binwidth is proportional to the interquartile range (IQR)
        and inversely proportional to cube root of a.size. Can be too
        conservative for small datasets, but is quite good for large
        datasets. The IQR is very robust to outliers.

    'scott'
        .. math:: h = \sigma \sqrt[3]{\frac{24 \sqrt{\pi}}{n}}

        The binwidth is proportional to the standard deviation of the
        data and inversely proportional to cube root of ``x.size``. Can
        be too conservative for small datasets, but is quite good for
        large datasets. The standard deviation is not very robust to
        outliers. Values are very similar to the Freedman-Diaconis
        estimator in the absence of outliers.

    'rice'
        .. math:: n_h = 2n^{1/3}

        The number of bins is only proportional to cube root of
        ``a.size``. It tends to overestimate the number of bins and it
        does not take into account data variability.

    'sturges'
        .. math:: n_h = \log _{2}(n) + 1

        The number of bins is the base 2 log of ``a.size``.  This
        estimator assumes normality of data and is too conservative for
        larger, non-normal datasets. This is the default method in R's
        ``hist`` method.

    'doane'
        .. math:: n_h = 1 + \log_{2}(n) +
                        \log_{2}\left(1 + \frac{|g_1|}{\sigma_{g_1}}\right)

            g_1 = mean\left[\left(\frac{x - \mu}{\sigma}\right)^3\right]

            \sigma_{g_1} = \sqrt{\frac{6(n - 2)}{(n + 1)(n + 3)}}

        An improved version of Sturges' formula that produces better
        estimates for non-normal datasets. This estimator attempts to
        account for the skew of the data.

    'sqrt'
        .. math:: n_h = \sqrt n

        The simplest and fastest estimator. Only takes into account the
        data size.

    Additionally, if the data is of integer dtype, then the binwidth will never
    be less than 1.

    Examples
    --------
    >>> import numpy as np
    >>> arr = np.array([0, 0, 0, 1, 2, 3, 3, 4, 5])
    >>> np.histogram_bin_edges(arr, bins='auto', range=(0, 1))
    array([0.  , 0.25, 0.5 , 0.75, 1.  ])
    >>> np.histogram_bin_edges(arr, bins=2)
    array([0. , 2.5, 5. ])

    For consistency with histogram, an array of pre-computed bins is
    passed through unmodified:

    >>> np.histogram_bin_edges(arr, [1, 2])
    array([1, 2])

    This function allows one set of bins to be computed, and reused across
    multiple histograms:

    >>> shared_bins = np.histogram_bin_edges(arr, bins='auto')
    >>> shared_bins
    array([0., 1., 2., 3., 4., 5.])

    >>> group_id = np.array([0, 1, 1, 0, 1, 1, 0, 1, 1])
    >>> hist_0, _ = np.histogram(arr[group_id == 0], bins=shared_bins)
    >>> hist_1, _ = np.histogram(arr[group_id == 1], bins=shared_bins)

    >>> hist_0; hist_1
    array([1, 1, 0, 1, 0])
    array([2, 0, 1, 1, 2])

    Which gives more easily comparable results than using separate bins for
    each histogram:

    >>> hist_0, bins_0 = np.histogram(arr[group_id == 0], bins='auto')
    >>> hist_1, bins_1 = np.histogram(arr[group_id == 1], bins='auto')
    >>> hist_0; hist_1
    array([1, 1, 1])
    array([2, 1, 1, 2])
    >>> bins_0; bins_1
    array([0., 1., 2., 3.])
    array([0.  , 1.25, 2.5 , 3.75, 5.  ])

Python Library Documentation: function histogramdd in module autograd.tracer

histogramdd(*args, called_by_autograd_dispatcher=False, **kwargs)
    Compute the multidimensional histogram of some data.

    Parameters
    ----------
    sample : (N, D) array, or (N, D) array_like
        The data to be histogrammed.

        Note the unusual interpretation of sample when an array_like:

        * When an array, each row is a coordinate in a D-dimensional space -
          such as ``histogramdd(np.array([p1, p2, p3]))``.
        * When an array_like, each element is the list of values for single
          coordinate - such as ``histogramdd((X, Y, Z))``.

        The first form should be preferred.

    bins : sequence or int, optional
        The bin specification:

        * A sequence of arrays describing the monotonically increasing bin
          edges along each dimension.
        * The number of bins for each dimension (nx, ny, ... =bins)
        * The number of bins for all dimensions (nx=ny=...=bins).

    range : sequence, optional
        A sequence of length D, each an optional (lower, upper) tuple giving
        the outer bin edges to be used if the edges are not given explicitly in
        `bins`.
        An entry of None in the sequence results in the minimum and maximum
        values being used for the corresponding dimension.
        The default, None, is equivalent to passing a tuple of D None values.
    density : bool, optional
        If False, the default, returns the number of samples in each bin.
        If True, returns the probability *density* function at the bin,
        ``bin_count / sample_count / bin_volume``.
    weights : (N,) array_like, optional
        An array of values `w_i` weighing each sample `(x_i, y_i, z_i, ...)`.
        Weights are normalized to 1 if density is True. If density is False,
        the values of the returned histogram are equal to the sum of the
        weights belonging to the samples falling into each bin.

    Returns
    -------
    H : ndarray
        The multidimensional histogram of sample x. See density and weights
        for the different possible semantics.
    edges : tuple of ndarrays
        A tuple of D arrays describing the bin edges for each dimension.

    See Also
    --------
    histogram: 1-D histogram
    histogram2d: 2-D histogram

    Examples
    --------
    >>> import numpy as np
    >>> rng = np.random.default_rng()
    >>> r = rng.normal(size=(100,3))
    >>> H, edges = np.histogramdd(r, bins = (5, 8, 4))
    >>> H.shape, edges[0].size, edges[1].size, edges[2].size
    ((5, 8, 4), 6, 9, 5)

Python Library Documentation: function hsplit in module autograd.tracer

hsplit(*args, called_by_autograd_dispatcher=False, **kwargs)
    Split an array into multiple sub-arrays horizontally (column-wise).

    Please refer to the `split` documentation.  `hsplit` is equivalent
    to `split` with ``axis=1``, the array is always split along the second
    axis except for 1-D arrays, where it is split at ``axis=0``.

    See Also
    --------
    split : Split an array into multiple sub-arrays of equal size.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.arange(16.0).reshape(4, 4)
    >>> x
    array([[ 0.,   1.,   2.,   3.],
           [ 4.,   5.,   6.,   7.],
           [ 8.,   9.,  10.,  11.],
           [12.,  13.,  14.,  15.]])
    >>> np.hsplit(x, 2)
    [array([[  0.,   1.],
           [  4.,   5.],
           [  8.,   9.],
           [12.,  13.]]),
     array([[  2.,   3.],
           [  6.,   7.],
           [10.,  11.],
           [14.,  15.]])]
    >>> np.hsplit(x, np.array([3, 6]))
    [array([[ 0.,   1.,   2.],
           [ 4.,   5.,   6.],
           [ 8.,   9.,  10.],
           [12.,  13.,  14.]]),
     array([[ 3.],
           [ 7.],
           [11.],
           [15.]]),
     array([], shape=(4, 0), dtype=float64)]

    With a higher dimensional array the split is still along the second axis.

    >>> x = np.arange(8.0).reshape(2, 2, 2)
    >>> x
    array([[[0.,  1.],
            [2.,  3.]],
           [[4.,  5.],
            [6.,  7.]]])
    >>> np.hsplit(x, 2)
    [array([[[0.,  1.]],
           [[4.,  5.]]]),
     array([[[2.,  3.]],
           [[6.,  7.]]])]

    With a 1-D array, the split is along axis 0.

    >>> x = np.array([0, 1, 2, 3, 4, 5])
    >>> np.hsplit(x, 2)
    [array([0, 1, 2]), array([3, 4, 5])]

Python Library Documentation: function hstack in module autograd.numpy.numpy_wrapper

hstack(tup)

Python Library Documentation: function hypot in module autograd.tracer

hypot(*args, called_by_autograd_dispatcher=False, **kwargs)
    hypot(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Given the "legs" of a right triangle, return its hypotenuse.

    Equivalent to ``sqrt(x1**2 + x2**2)``, element-wise.  If `x1` or
    `x2` is scalar_like (i.e., unambiguously cast-able to a scalar type),
    it is broadcast for use with each element of the other argument.
    (See Examples)

    Parameters
    ----------
    x1, x2 : array_like
        Leg of the triangle(s).
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    z : ndarray
        The hypotenuse of the triangle(s).
        This is a scalar if both `x1` and `x2` are scalars.

    Examples
    --------
    >>> import numpy as np
    >>> np.hypot(3*np.ones((3, 3)), 4*np.ones((3, 3)))
    array([[ 5.,  5.,  5.],
           [ 5.,  5.,  5.],
           [ 5.,  5.,  5.]])

    Example showing broadcast of scalar_like argument:

    >>> np.hypot(3*np.ones((3, 3)), [4])
    array([[ 5.,  5.,  5.],
           [ 5.,  5.,  5.],
           [ 5.,  5.,  5.]])

Python Library Documentation: function i0 in module autograd.tracer

i0(*args, called_by_autograd_dispatcher=False, **kwargs)
    Modified Bessel function of the first kind, order 0.

    Usually denoted :math:`I_0`.

    Parameters
    ----------
    x : array_like of float
        Argument of the Bessel function.

    Returns
    -------
    out : ndarray, shape = x.shape, dtype = float
        The modified Bessel function evaluated at each of the elements of `x`.

    See Also
    --------
    scipy.special.i0, scipy.special.iv, scipy.special.ive

    Notes
    -----
    The scipy implementation is recommended over this function: it is a
    proper ufunc written in C, and more than an order of magnitude faster.

    We use the algorithm published by Clenshaw [1]_ and referenced by
    Abramowitz and Stegun [2]_, for which the function domain is
    partitioned into the two intervals [0,8] and (8,inf), and Chebyshev
    polynomial expansions are employed in each interval. Relative error on
    the domain [0,30] using IEEE arithmetic is documented [3]_ as having a
    peak of 5.8e-16 with an rms of 1.4e-16 (n = 30000).

    References
    ----------
    .. [1] C. W. Clenshaw, "Chebyshev series for mathematical functions", in
           *National Physical Laboratory Mathematical Tables*, vol. 5, London:
           Her Majesty's Stationery Office, 1962.
    .. [2] M. Abramowitz and I. A. Stegun, *Handbook of Mathematical
           Functions*, 10th printing, New York: Dover, 1964, pp. 379.
           https://personal.math.ubc.ca/~cbm/aands/page_379.htm
    .. [3] https://metacpan.org/pod/distribution/Math-Cephes/lib/Math/Cephes.pod#i0:-Modified-Bessel-function-of-order-zero

    Examples
    --------
    >>> import numpy as np
    >>> np.i0(0.)
    array(1.0)
    >>> np.i0([0, 1, 2, 3])
    array([1.        , 1.26606588, 2.2795853 , 4.88079259])

Python Library Documentation: function identity in module autograd.tracer

identity(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the identity array.

    The identity array is a square array with ones on
    the main diagonal.

    Parameters
    ----------
    n : int
        Number of rows (and columns) in `n` x `n` output.
    dtype : data-type, optional
        Data-type of the output.  Defaults to ``float``.
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    out : ndarray
        `n` x `n` array with its main diagonal set to one,
        and all other elements 0.

    Examples
    --------
    >>> import numpy as np
    >>> np.identity(3)
    array([[1.,  0.,  0.],
           [0.,  1.,  0.],
           [0.,  0.,  1.]])

Python Library Documentation: class iinfo in module numpy

class iinfo(builtins.object)
 |  iinfo(int_type)
 |
 |  iinfo(type)
 |
 |  Machine limits for integer types.
 |
 |  Attributes
 |  ----------
 |  bits : int
 |      The number of bits occupied by the type.
 |  dtype : dtype
 |      Returns the dtype for which `iinfo` returns information.
 |  min : int
 |      The smallest integer expressible by the type.
 |  max : int
 |      The largest integer expressible by the type.
 |
 |  Parameters
 |  ----------
 |  int_type : integer type, dtype, or instance
 |      The kind of integer data type to get information about.
 |
 |  See Also
 |  --------
 |  finfo : The equivalent for floating point data types.
 |
 |  Examples
 |  --------
 |  With types:
 |
 |  >>> import numpy as np
 |  >>> ii16 = np.iinfo(np.int16)
 |  >>> ii16.min
 |  -32768
 |  >>> ii16.max
 |  32767
 |  >>> ii32 = np.iinfo(np.int32)
 |  >>> ii32.min
 |  -2147483648
 |  >>> ii32.max
 |  2147483647
 |
 |  With instances:
 |
 |  >>> ii32 = np.iinfo(np.int32(10))
 |  >>> ii32.min
 |  -2147483648
 |  >>> ii32.max
 |  2147483647
 |
 |  Methods defined here:
 |
 |  __init__(self, int_type) from numpy._core.getlimits.iinfo
 |      Initialize self.  See help(type(self)) for accurate signature.
 |
 |  __repr__(self) from numpy._core.getlimits.iinfo
 |      Return repr(self).
 |
 |  __str__(self) from numpy._core.getlimits.iinfo
 |      String representation.
 |
 |  ----------------------------------------------------------------------
 |  Readonly properties defined here:
 |
 |  max
 |      Maximum value of given dtype.
 |
 |  min
 |      Minimum value of given dtype.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object

Python Library Documentation: function imag in module autograd.tracer

imag(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the imaginary part of the complex argument.

    Parameters
    ----------
    val : array_like
        Input array.

    Returns
    -------
    out : ndarray or scalar
        The imaginary component of the complex argument. If `val` is real,
        the type of `val` is used for the output.  If `val` has complex
        elements, the returned type is float.

    See Also
    --------
    real, angle, real_if_close

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([1+2j, 3+4j, 5+6j])
    >>> a.imag
    array([2.,  4.,  6.])
    >>> a.imag = np.array([8, 10, 12])
    >>> a
    array([1. +8.j,  3.+10.j,  5.+12.j])
    >>> np.imag(1 + 1j)
    1.0

Python Library Documentation: function in1d in module autograd.tracer

in1d(*args, called_by_autograd_dispatcher=False, **kwargs)
    Test whether each element of a 1-D array is also present in a second array.

    .. deprecated:: 2.0
        Use :func:`isin` instead of `in1d` for new code.

    Returns a boolean array the same length as `ar1` that is True
    where an element of `ar1` is in `ar2` and False otherwise.

    Parameters
    ----------
    ar1 : (M,) array_like
        Input array.
    ar2 : array_like
        The values against which to test each value of `ar1`.
    assume_unique : bool, optional
        If True, the input arrays are both assumed to be unique, which
        can speed up the calculation.  Default is False.
    invert : bool, optional
        If True, the values in the returned array are inverted (that is,
        False where an element of `ar1` is in `ar2` and True otherwise).
        Default is False. ``np.in1d(a, b, invert=True)`` is equivalent
        to (but is faster than) ``np.invert(in1d(a, b))``.
    kind : {None, 'sort', 'table'}, optional
        The algorithm to use. This will not affect the final result,
        but will affect the speed and memory use. The default, None,
        will select automatically based on memory considerations.

        * If 'sort', will use a mergesort-based approach. This will have
          a memory usage of roughly 6 times the sum of the sizes of
          `ar1` and `ar2`, not accounting for size of dtypes.
        * If 'table', will use a lookup table approach similar
          to a counting sort. This is only available for boolean and
          integer arrays. This will have a memory usage of the
          size of `ar1` plus the max-min value of `ar2`. `assume_unique`
          has no effect when the 'table' option is used.
        * If None, will automatically choose 'table' if
          the required memory allocation is less than or equal to
          6 times the sum of the sizes of `ar1` and `ar2`,
          otherwise will use 'sort'. This is done to not use
          a large amount of memory by default, even though
          'table' may be faster in most cases. If 'table' is chosen,
          `assume_unique` will have no effect.

        .. versionadded:: 1.8.0

    Returns
    -------
    in1d : (M,) ndarray, bool
        The values `ar1[in1d]` are in `ar2`.

    See Also
    --------
    isin                  : Version of this function that preserves the
                            shape of ar1.

    Notes
    -----
    `in1d` can be considered as an element-wise function version of the
    python keyword `in`, for 1-D sequences. ``in1d(a, b)`` is roughly
    equivalent to ``np.array([item in b for item in a])``.
    However, this idea fails if `ar2` is a set, or similar (non-sequence)
    container:  As ``ar2`` is converted to an array, in those cases
    ``asarray(ar2)`` is an object array rather than the expected array of
    contained values.

    Using ``kind='table'`` tends to be faster than `kind='sort'` if the
    following relationship is true:
    ``log10(len(ar2)) > (log10(max(ar2)-min(ar2)) - 2.27) / 0.927``,
    but may use greater memory. The default value for `kind` will
    be automatically selected based only on memory usage, so one may
    manually set ``kind='table'`` if memory constraints can be relaxed.

    .. versionadded:: 1.4.0

    Examples
    --------
    >>> import numpy as np
    >>> test = np.array([0, 1, 2, 5, 0])
    >>> states = [0, 2]
    >>> mask = np.in1d(test, states)
    >>> mask
    array([ True, False,  True, False,  True])
    >>> test[mask]
    array([0, 2, 0])
    >>> mask = np.in1d(test, states, invert=True)
    >>> mask
    array([False,  True, False,  True, False])
    >>> test[mask]
    array([1, 5])

Python Library Documentation: function indices in module autograd.tracer

indices(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return an array representing the indices of a grid.

    Compute an array where the subarrays contain index values 0, 1, ...
    varying only along the corresponding axis.

    Parameters
    ----------
    dimensions : sequence of ints
        The shape of the grid.
    dtype : dtype, optional
        Data type of the result.
    sparse : boolean, optional
        Return a sparse representation of the grid instead of a dense
        representation. Default is False.

        .. versionadded:: 1.17

    Returns
    -------
    grid : one ndarray or tuple of ndarrays
        If sparse is False:
            Returns one array of grid indices,
            ``grid.shape = (len(dimensions),) + tuple(dimensions)``.
        If sparse is True:
            Returns a tuple of arrays, with
            ``grid[i].shape = (1, ..., 1, dimensions[i], 1, ..., 1)`` with
            dimensions[i] in the ith place

    See Also
    --------
    mgrid, ogrid, meshgrid

    Notes
    -----
    The output shape in the dense case is obtained by prepending the number
    of dimensions in front of the tuple of dimensions, i.e. if `dimensions`
    is a tuple ``(r0, ..., rN-1)`` of length ``N``, the output shape is
    ``(N, r0, ..., rN-1)``.

    The subarrays ``grid[k]`` contains the N-D array of indices along the
    ``k-th`` axis. Explicitly::

        grid[k, i0, i1, ..., iN-1] = ik

    Examples
    --------
    >>> import numpy as np
    >>> grid = np.indices((2, 3))
    >>> grid.shape
    (2, 2, 3)
    >>> grid[0]        # row indices
    array([[0, 0, 0],
           [1, 1, 1]])
    >>> grid[1]        # column indices
    array([[0, 1, 2],
           [0, 1, 2]])

    The indices can be used as an index into an array.

    >>> x = np.arange(20).reshape(5, 4)
    >>> row, col = np.indices((2, 3))
    >>> x[row, col]
    array([[0, 1, 2],
           [4, 5, 6]])

    Note that it would be more straightforward in the above example to
    extract the required elements directly with ``x[:2, :3]``.

    If sparse is set to true, the grid will be returned in a sparse
    representation.

    >>> i, j = np.indices((2, 3), sparse=True)
    >>> i.shape
    (2, 1)
    >>> j.shape
    (1, 3)
    >>> i        # row indices
    array([[0],
           [1]])
    >>> j        # column indices
    array([[0, 1, 2]])

Python Library Documentation: class inexact in module numpy

class inexact(number)
 |  Abstract base class of all numeric scalar types with a (potentially)
 |  inexact representation of the values in its range, such as
 |  floating-point numbers.
 |
 |  Method resolution order:
 |      inexact
 |      number
 |      generic
 |      builtins.object
 |
 |  Class methods inherited from number:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes inherited from generic:
 |
 |  __hash__ = None

Python Library Documentation: float object

class float(object)
 |  float(x=0, /)
 |
 |  Convert a string or number to a floating-point number, if possible.
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __ceil__(self, /)
 |      Return the ceiling as an Integral.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floor__(self, /)
 |      Return the floor as an Integral.
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(self, format_spec, /)
 |      Formats the float according to format_spec.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getnewargs__(self, /)
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __round__(self, ndigits=None, /)
 |      Return the Integral closest to x, rounding half toward even.
 |
 |      When an argument is passed, work like built-in round(x, ndigits).
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __trunc__(self, /)
 |      Return the Integral closest to x between 0 and x.
 |
 |  as_integer_ratio(self, /)
 |      Return a pair of integers, whose ratio is exactly equal to the original float.
 |
 |      The ratio is in lowest terms and has a positive denominator.  Raise
 |      OverflowError on infinities and a ValueError on NaNs.
 |
 |      >>> (10.0).as_integer_ratio()
 |      (10, 1)
 |      >>> (0.0).as_integer_ratio()
 |      (0, 1)
 |      >>> (-.25).as_integer_ratio()
 |      (-1, 4)
 |
 |  conjugate(self, /)
 |      Return self, the complex conjugate of any float.
 |
 |  hex(self, /)
 |      Return a hexadecimal representation of a floating-point number.
 |
 |      >>> (-0.1).hex()
 |      '-0x1.999999999999ap-4'
 |      >>> 3.14159.hex()
 |      '0x1.921f9f01b866ep+1'
 |
 |  is_integer(self, /)
 |      Return True if the float is an integer.
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __getformat__(typestr, /)
 |      You probably don't want to use this function.
 |
 |        typestr
 |          Must be 'double' or 'float'.
 |
 |      It exists mainly to be used in Python's test suite.
 |
 |      This function returns whichever of 'unknown', 'IEEE, big-endian' or 'IEEE,
 |      little-endian' best describes the format of floating-point numbers used by the
 |      C type named by typestr.
 |
 |  fromhex(string, /)
 |      Create a floating-point number from a hexadecimal string.
 |
 |      >>> float.fromhex('0x1.ffffp10')
 |      2047.984375
 |      >>> float.fromhex('-0x1p-1074')
 |      -5e-324
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  imag
 |      the imaginary part of a complex number
 |
 |  real
 |      the real part of a complex number

Python Library Documentation: function info in module autograd.tracer

info(*args, called_by_autograd_dispatcher=False, **kwargs)
    Get help information for an array, function, class, or module.

    Parameters
    ----------
    object : object or str, optional
        Input object or name to get information about. If `object` is
        an `ndarray` instance, information about the array is printed.
        If `object` is a numpy object, its docstring is given. If it is
        a string, available modules are searched for matching objects.
        If None, information about `info` itself is returned.
    maxwidth : int, optional
        Printing width.
    output : file like object, optional
        File like object that the output is written to, default is
        ``None``, in which case ``sys.stdout`` will be used.
        The object has to be opened in 'w' or 'a' mode.
    toplevel : str, optional
        Start search at this level.

    Notes
    -----
    When used interactively with an object, ``np.info(obj)`` is equivalent
    to ``help(obj)`` on the Python prompt or ``obj?`` on the IPython
    prompt.

    Examples
    --------
    >>> np.info(np.polyval) # doctest: +SKIP
       polyval(p, x)
         Evaluate the polynomial p at x.
         ...

    When using a string for `object` it is possible to get multiple results.

    >>> np.info('fft') # doctest: +SKIP
         *** Found in numpy ***
    Core FFT routines
    ...
         *** Found in numpy.fft ***
     fft(a, n=None, axis=-1)
    ...
         *** Repeat reference found in numpy.fft.fftpack ***
         *** Total of 3 references found. ***

    When the argument is an array, information about the array is printed.

    >>> a = np.array([[1 + 2j, 3, -4], [-5j, 6, 0]], dtype=np.complex64)
    >>> np.info(a)
    class:  ndarray
    shape:  (2, 3)
    strides:  (24, 8)
    itemsize:  8
    aligned:  True
    contiguous:  True
    fortran:  False
    data pointer: 0x562b6e0d2860  # may vary
    byteorder:  little
    byteswap:  False
    type: complex64

Python Library Documentation: function inner in module autograd.tracer

inner(*args, called_by_autograd_dispatcher=False, **kwargs)
    inner(a, b, /)

    Inner product of two arrays.

    Ordinary inner product of vectors for 1-D arrays (without complex
    conjugation), in higher dimensions a sum product over the last axes.

    Parameters
    ----------
    a, b : array_like
        If `a` and `b` are nonscalar, their last dimensions must match.

    Returns
    -------
    out : ndarray
        If `a` and `b` are both
        scalars or both 1-D arrays then a scalar is returned; otherwise
        an array is returned.
        ``out.shape = (*a.shape[:-1], *b.shape[:-1])``

    Raises
    ------
    ValueError
        If both `a` and `b` are nonscalar and their last dimensions have
        different sizes.

    See Also
    --------
    tensordot : Sum products over arbitrary axes.
    dot : Generalised matrix product, using second last dimension of `b`.
    einsum : Einstein summation convention.

    Notes
    -----
    For vectors (1-D arrays) it computes the ordinary inner-product::

        np.inner(a, b) = sum(a[:]*b[:])

    More generally, if ``ndim(a) = r > 0`` and ``ndim(b) = s > 0``::

        np.inner(a, b) = np.tensordot(a, b, axes=(-1,-1))

    or explicitly::

        np.inner(a, b)[i0,...,ir-2,j0,...,js-2]
             = sum(a[i0,...,ir-2,:]*b[j0,...,js-2,:])

    In addition `a` or `b` may be scalars, in which case::

       np.inner(a,b) = a*b

    Examples
    --------
    Ordinary inner product for vectors:

    >>> import numpy as np
    >>> a = np.array([1,2,3])
    >>> b = np.array([0,1,0])
    >>> np.inner(a, b)
    2

    Some multidimensional examples:

    >>> a = np.arange(24).reshape((2,3,4))
    >>> b = np.arange(4)
    >>> c = np.inner(a, b)
    >>> c.shape
    (2, 3)
    >>> c
    array([[ 14,  38,  62],
           [ 86, 110, 134]])

    >>> a = np.arange(2).reshape((1,1,2))
    >>> b = np.arange(6).reshape((3,2))
    >>> c = np.inner(a, b)
    >>> c.shape
    (1, 1, 3)
    >>> c
    array([[[1, 3, 5]]])

    An example where `b` is a scalar:

    >>> np.inner(np.eye(2), 7)
    array([[7., 0.],
           [0., 7.]])

Python Library Documentation: function insert in module autograd.tracer

insert(*args, called_by_autograd_dispatcher=False, **kwargs)
    Insert values along the given axis before the given indices.

    Parameters
    ----------
    arr : array_like
        Input array.
    obj : int, slice or sequence of ints
        Object that defines the index or indices before which `values` is
        inserted.

        .. versionadded:: 1.8.0

        Support for multiple insertions when `obj` is a single scalar or a
        sequence with one element (similar to calling insert multiple
        times).
    values : array_like
        Values to insert into `arr`. If the type of `values` is different
        from that of `arr`, `values` is converted to the type of `arr`.
        `values` should be shaped so that ``arr[...,obj,...] = values``
        is legal.
    axis : int, optional
        Axis along which to insert `values`.  If `axis` is None then `arr`
        is flattened first.

    Returns
    -------
    out : ndarray
        A copy of `arr` with `values` inserted.  Note that `insert`
        does not occur in-place: a new array is returned. If
        `axis` is None, `out` is a flattened array.

    See Also
    --------
    append : Append elements at the end of an array.
    concatenate : Join a sequence of arrays along an existing axis.
    delete : Delete elements from an array.

    Notes
    -----
    Note that for higher dimensional inserts ``obj=0`` behaves very different
    from ``obj=[0]`` just like ``arr[:,0,:] = values`` is different from
    ``arr[:,[0],:] = values``. This is because of the difference between basic
    and advanced :ref:`indexing <basics.indexing>`.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.arange(6).reshape(3, 2)
    >>> a
    array([[0, 1],
           [2, 3],
           [4, 5]])
    >>> np.insert(a, 1, 6)
    array([0, 6, 1, 2, 3, 4, 5])
    >>> np.insert(a, 1, 6, axis=1)
    array([[0, 6, 1],
           [2, 6, 3],
           [4, 6, 5]])

    Difference between sequence and scalars,
    showing how ``obj=[1]`` behaves different from ``obj=1``:

    >>> np.insert(a, [1], [[7],[8],[9]], axis=1)
    array([[0, 7, 1],
           [2, 8, 3],
           [4, 9, 5]])
    >>> np.insert(a, 1, [[7],[8],[9]], axis=1)
    array([[0, 7, 8, 9, 1],
           [2, 7, 8, 9, 3],
           [4, 7, 8, 9, 5]])
    >>> np.array_equal(np.insert(a, 1, [7, 8, 9], axis=1),
    ...                np.insert(a, [1], [[7],[8],[9]], axis=1))
    True

    >>> b = a.flatten()
    >>> b
    array([0, 1, 2, 3, 4, 5])
    >>> np.insert(b, [2, 2], [6, 7])
    array([0, 1, 6, 7, 2, 3, 4, 5])

    >>> np.insert(b, slice(2, 4), [7, 8])
    array([0, 1, 7, 2, 8, 3, 4, 5])

    >>> np.insert(b, [2, 2], [7.13, False]) # type casting
    array([0, 1, 7, 0, 2, 3, 4, 5])

    >>> x = np.arange(8).reshape(2, 4)
    >>> idx = (1, 3)
    >>> np.insert(x, idx, 999, axis=1)
    array([[  0, 999,   1,   2, 999,   3],
           [  4, 999,   5,   6, 999,   7]])

Python Library Documentation: class IntdtypeSubclass in module autograd.numpy.numpy_wrapper

class IntdtypeSubclass(numpy.int16)
 |  IntdtypeSubclass(*args, **kwargs)
 |
 |  Method resolution order:
 |      IntdtypeSubclass
 |      numpy.int16
 |      numpy.signedinteger
 |      numpy.integer
 |      numpy.number
 |      numpy.generic
 |      builtins.object
 |
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs) from autograd.tracer.notrace_primitive.<locals>
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.int16:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      int16.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.int16(127).bit_count()
 |      7
 |      >>> np.int16(-127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from numpy.int16:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class IntdtypeSubclass in module autograd.numpy.numpy_wrapper

class IntdtypeSubclass(numpy.int32)
 |  IntdtypeSubclass(*args, **kwargs)
 |
 |  Method resolution order:
 |      IntdtypeSubclass
 |      numpy.int32
 |      numpy.signedinteger
 |      numpy.integer
 |      numpy.number
 |      numpy.generic
 |      builtins.object
 |
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs) from autograd.tracer.notrace_primitive.<locals>
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.int32:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      int32.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.int32(127).bit_count()
 |      7
 |      >>> np.int32(-127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from numpy.int32:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class IntdtypeSubclass in module autograd.numpy.numpy_wrapper

class IntdtypeSubclass(numpy.int64)
 |  IntdtypeSubclass(*args, **kwargs)
 |
 |  Method resolution order:
 |      IntdtypeSubclass
 |      numpy.int64
 |      numpy.signedinteger
 |      numpy.integer
 |      numpy.number
 |      numpy.generic
 |      builtins.object
 |
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs) from autograd.tracer.notrace_primitive.<locals>
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.int64:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      int64.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.int64(127).bit_count()
 |      7
 |      >>> np.int64(-127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from numpy.int64:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class IntdtypeSubclass in module autograd.numpy.numpy_wrapper

class IntdtypeSubclass(numpy.int8)
 |  IntdtypeSubclass(*args, **kwargs)
 |
 |  Method resolution order:
 |      IntdtypeSubclass
 |      numpy.int8
 |      numpy.signedinteger
 |      numpy.integer
 |      numpy.number
 |      numpy.generic
 |      builtins.object
 |
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs) from autograd.tracer.notrace_primitive.<locals>
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.int8:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      int8.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.int8(127).bit_count()
 |      7
 |      >>> np.int8(-127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from numpy.int8:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class IntdtypeSubclass in module autograd.numpy.numpy_wrapper

class IntdtypeSubclass(numpy.int64)
 |  IntdtypeSubclass(*args, **kwargs)
 |
 |  Method resolution order:
 |      IntdtypeSubclass
 |      numpy.int64
 |      numpy.signedinteger
 |      numpy.integer
 |      numpy.number
 |      numpy.generic
 |      builtins.object
 |
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs) from autograd.tracer.notrace_primitive.<locals>
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.int64:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      int64.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.int64(127).bit_count()
 |      7
 |      >>> np.int64(-127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from numpy.int64:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class intc in module numpy

class intc(signedinteger)
 |  Signed integer type, compatible with C ``int``.
 |
 |  :Character code: ``'i'``
 |
 |  Method resolution order:
 |      intc
 |      signedinteger
 |      integer
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class IntdtypeSubclass in module autograd.numpy.numpy_wrapper

class IntdtypeSubclass(numpy.integer)
 |  IntdtypeSubclass(*args, **kwargs)
 |
 |  Method resolution order:
 |      IntdtypeSubclass
 |      numpy.integer
 |      numpy.number
 |      numpy.generic
 |      builtins.object
 |
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs) from autograd.tracer.notrace_primitive.<locals>
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from numpy.number:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes inherited from numpy.generic:
 |
 |  __hash__ = None

Python Library Documentation: function interp in module autograd.tracer

interp(*args, called_by_autograd_dispatcher=False, **kwargs)
    One-dimensional linear interpolation for monotonically increasing sample points.

    Returns the one-dimensional piecewise linear interpolant to a function
    with given discrete data points (`xp`, `fp`), evaluated at `x`.

    Parameters
    ----------
    x : array_like
        The x-coordinates at which to evaluate the interpolated values.

    xp : 1-D sequence of floats
        The x-coordinates of the data points, must be increasing if argument
        `period` is not specified. Otherwise, `xp` is internally sorted after
        normalizing the periodic boundaries with ``xp = xp % period``.

    fp : 1-D sequence of float or complex
        The y-coordinates of the data points, same length as `xp`.

    left : optional float or complex corresponding to fp
        Value to return for `x < xp[0]`, default is `fp[0]`.

    right : optional float or complex corresponding to fp
        Value to return for `x > xp[-1]`, default is `fp[-1]`.

    period : None or float, optional
        A period for the x-coordinates. This parameter allows the proper
        interpolation of angular x-coordinates. Parameters `left` and `right`
        are ignored if `period` is specified.

        .. versionadded:: 1.10.0

    Returns
    -------
    y : float or complex (corresponding to fp) or ndarray
        The interpolated values, same shape as `x`.

    Raises
    ------
    ValueError
        If `xp` and `fp` have different length
        If `xp` or `fp` are not 1-D sequences
        If `period == 0`

    See Also
    --------
    scipy.interpolate

    Warnings
    --------
    The x-coordinate sequence is expected to be increasing, but this is not
    explicitly enforced.  However, if the sequence `xp` is non-increasing,
    interpolation results are meaningless.

    Note that, since NaN is unsortable, `xp` also cannot contain NaNs.

    A simple check for `xp` being strictly increasing is::

        np.all(np.diff(xp) > 0)

    Examples
    --------
    >>> import numpy as np
    >>> xp = [1, 2, 3]
    >>> fp = [3, 2, 0]
    >>> np.interp(2.5, xp, fp)
    1.0
    >>> np.interp([0, 1, 1.5, 2.72, 3.14], xp, fp)
    array([3.  , 3.  , 2.5 , 0.56, 0.  ])
    >>> UNDEF = -99.0
    >>> np.interp(3.14, xp, fp, right=UNDEF)
    -99.0

    Plot an interpolant to the sine function:

    >>> x = np.linspace(0, 2*np.pi, 10)
    >>> y = np.sin(x)
    >>> xvals = np.linspace(0, 2*np.pi, 50)
    >>> yinterp = np.interp(xvals, x, y)
    >>> import matplotlib.pyplot as plt
    >>> plt.plot(x, y, 'o')
    [<matplotlib.lines.Line2D object at 0x...>]
    >>> plt.plot(xvals, yinterp, '-x')
    [<matplotlib.lines.Line2D object at 0x...>]
    >>> plt.show()

    Interpolation with periodic x-coordinates:

    >>> x = [-180, -170, -185, 185, -10, -5, 0, 365]
    >>> xp = [190, -190, 350, -350]
    >>> fp = [5, 10, 3, 4]
    >>> np.interp(x, xp, fp, period=360)
    array([7.5 , 5.  , 8.75, 6.25, 3.  , 3.25, 3.5 , 3.75])

    Complex interpolation:

    >>> x = [1.5, 4.0]
    >>> xp = [2,3,5]
    >>> fp = [1.0j, 0, 2+3j]
    >>> np.interp(x, xp, fp)
    array([0.+1.j , 1.+1.5j])

Python Library Documentation: function intersect1d in module autograd.tracer

intersect1d(*args, called_by_autograd_dispatcher=False, **kwargs)
    Find the intersection of two arrays.

    Return the sorted, unique values that are in both of the input arrays.

    Parameters
    ----------
    ar1, ar2 : array_like
        Input arrays. Will be flattened if not already 1D.
    assume_unique : bool
        If True, the input arrays are both assumed to be unique, which
        can speed up the calculation.  If True but ``ar1`` or ``ar2`` are not
        unique, incorrect results and out-of-bounds indices could result.
        Default is False.
    return_indices : bool
        If True, the indices which correspond to the intersection of the two
        arrays are returned. The first instance of a value is used if there are
        multiple. Default is False.

        .. versionadded:: 1.15.0

    Returns
    -------
    intersect1d : ndarray
        Sorted 1D array of common and unique elements.
    comm1 : ndarray
        The indices of the first occurrences of the common values in `ar1`.
        Only provided if `return_indices` is True.
    comm2 : ndarray
        The indices of the first occurrences of the common values in `ar2`.
        Only provided if `return_indices` is True.

    Examples
    --------
    >>> import numpy as np
    >>> np.intersect1d([1, 3, 4, 3], [3, 1, 2, 1])
    array([1, 3])

    To intersect more than two arrays, use functools.reduce:

    >>> from functools import reduce
    >>> reduce(np.intersect1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2]))
    array([3])

    To return the indices of the values common to the input arrays
    along with the intersected values:

    >>> x = np.array([1, 1, 2, 3, 4])
    >>> y = np.array([2, 1, 4, 6])
    >>> xy, x_ind, y_ind = np.intersect1d(x, y, return_indices=True)
    >>> x_ind, y_ind
    (array([0, 2, 4]), array([1, 0, 2]))
    >>> xy, x[x_ind], y[y_ind]
    (array([1, 2, 4]), array([1, 2, 4]), array([1, 2, 4]))

Python Library Documentation: class IntdtypeSubclass in module autograd.numpy.numpy_wrapper

class IntdtypeSubclass(numpy.int64)
 |  IntdtypeSubclass(*args, **kwargs)
 |
 |  Method resolution order:
 |      IntdtypeSubclass
 |      numpy.int64
 |      numpy.signedinteger
 |      numpy.integer
 |      numpy.number
 |      numpy.generic
 |      builtins.object
 |
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs) from autograd.tracer.notrace_primitive.<locals>
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.int64:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      int64.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.int64(127).bit_count()
 |      7
 |      >>> np.int64(-127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from numpy.int64:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: function invert in module autograd.tracer

invert(*args, called_by_autograd_dispatcher=False, **kwargs)
    invert(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Compute bit-wise inversion, or bit-wise NOT, element-wise.

    Computes the bit-wise NOT of the underlying binary representation of
    the integers in the input arrays. This ufunc implements the C/Python
    operator ``~``.

    For signed integer inputs, the bit-wise NOT of the absolute value is
    returned. In a two's-complement system, this operation effectively flips
    all the bits, resulting in a representation that corresponds to the
    negative of the input plus one. This is the most common method of
    representing signed integers on computers [1]_. A N-bit two's-complement
    system can represent every integer in the range :math:`-2^{N-1}` to
    :math:`+2^{N-1}-1`.

    Parameters
    ----------
    x : array_like
        Only integer and boolean types are handled.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Result.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    bitwise_and, bitwise_or, bitwise_xor
    logical_not
    binary_repr :
        Return the binary representation of the input number as a string.

    Notes
    -----
    ``numpy.bitwise_not`` is an alias for `invert`:

    >>> np.bitwise_not is np.invert
    True

    References
    ----------
    .. [1] Wikipedia, "Two's complement",
        https://en.wikipedia.org/wiki/Two's_complement

    Examples
    --------
    >>> import numpy as np

    We've seen that 13 is represented by ``00001101``.
    The invert or bit-wise NOT of 13 is then:

    >>> x = np.invert(np.array(13, dtype=np.uint8))
    >>> x
    242
    >>> np.binary_repr(x, width=8)
    '11110010'

    The result depends on the bit-width:

    >>> x = np.invert(np.array(13, dtype=np.uint16))
    >>> x
    65522
    >>> np.binary_repr(x, width=16)
    '1111111111110010'

    When using signed integer types, the result is the bit-wise NOT of
    the unsigned type, interpreted as a signed integer:

    >>> np.invert(np.array([13], dtype=np.int8))
    array([-14], dtype=int8)
    >>> np.binary_repr(-14, width=8)
    '11110010'

    Booleans are accepted as well:

    >>> np.invert(np.array([True, False]))
    array([False,  True])

    The ``~`` operator can be used as a shorthand for ``np.invert`` on
    ndarrays.

    >>> x1 = np.array([True, False])
    >>> ~x1
    array([False,  True])

Python Library Documentation: function is_busday in module autograd.tracer

is_busday(*args, called_by_autograd_dispatcher=False, **kwargs)
    is_busday(
        dates,
        weekmask='1111100',
        holidays=None,
        busdaycal=None,
        out=None
    )

    Calculates which of the given dates are valid days, and which are not.

    .. versionadded:: 1.7.0

    Parameters
    ----------
    dates : array_like of datetime64[D]
        The array of dates to process.
    weekmask : str or array_like of bool, optional
        A seven-element array indicating which of Monday through Sunday are
        valid days. May be specified as a length-seven list or array, like
        [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string
        like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for
        weekdays, optionally separated by white space. Valid abbreviations
        are: Mon Tue Wed Thu Fri Sat Sun
    holidays : array_like of datetime64[D], optional
        An array of dates to consider as invalid dates.  They may be
        specified in any order, and NaT (not-a-time) dates are ignored.
        This list is saved in a normalized form that is suited for
        fast calculations of valid days.
    busdaycal : busdaycalendar, optional
        A `busdaycalendar` object which specifies the valid days. If this
        parameter is provided, neither weekmask nor holidays may be
        provided.
    out : array of bool, optional
        If provided, this array is filled with the result.

    Returns
    -------
    out : array of bool
        An array with the same shape as ``dates``, containing True for
        each valid day, and False for each invalid day.

    See Also
    --------
    busdaycalendar : An object that specifies a custom set of valid days.
    busday_offset : Applies an offset counted in valid days.
    busday_count : Counts how many valid days are in a half-open date range.

    Examples
    --------
    >>> import numpy as np
    >>> # The weekdays are Friday, Saturday, and Monday
    ... np.is_busday(['2011-07-01', '2011-07-02', '2011-07-18'],
    ...                 holidays=['2011-07-01', '2011-07-04', '2011-07-17'])
    array([False, False,  True])

Python Library Documentation: function isclose in module autograd.tracer

isclose(*args, called_by_autograd_dispatcher=False, **kwargs)
    Returns a boolean array where two arrays are element-wise equal within a
    tolerance.

    The tolerance values are positive, typically very small numbers.  The
    relative difference (`rtol` * abs(`b`)) and the absolute difference
    `atol` are added together to compare against the absolute difference
    between `a` and `b`.

    .. warning:: The default `atol` is not appropriate for comparing numbers
                 with magnitudes much smaller than one (see Notes).

    Parameters
    ----------
    a, b : array_like
        Input arrays to compare.
    rtol : array_like
        The relative tolerance parameter (see Notes).
    atol : array_like
        The absolute tolerance parameter (see Notes).
    equal_nan : bool
        Whether to compare NaN's as equal.  If True, NaN's in `a` will be
        considered equal to NaN's in `b` in the output array.

    Returns
    -------
    y : array_like
        Returns a boolean array of where `a` and `b` are equal within the
        given tolerance. If both `a` and `b` are scalars, returns a single
        boolean value.

    See Also
    --------
    allclose
    math.isclose

    Notes
    -----
    .. versionadded:: 1.7.0

    For finite values, isclose uses the following equation to test whether
    two floating point values are equivalent.::

     absolute(a - b) <= (atol + rtol * absolute(b))

    Unlike the built-in `math.isclose`, the above equation is not symmetric
    in `a` and `b` -- it assumes `b` is the reference value -- so that
    `isclose(a, b)` might be different from `isclose(b, a)`.

    The default value of `atol` is not appropriate when the reference value
    `b` has magnitude smaller than one. For example, it is unlikely that
    ``a = 1e-9`` and ``b = 2e-9`` should be considered "close", yet
    ``isclose(1e-9, 2e-9)`` is ``True`` with default settings. Be sure
    to select `atol` for the use case at hand, especially for defining the
    threshold below which a non-zero value in `a` will be considered "close"
    to a very small or zero value in `b`.

    `isclose` is not defined for non-numeric data types.
    :class:`bool` is considered a numeric data-type for this purpose.

    Examples
    --------
    >>> import numpy as np
    >>> np.isclose([1e10,1e-7], [1.00001e10,1e-8])
    array([ True, False])

    >>> np.isclose([1e10,1e-8], [1.00001e10,1e-9])
    array([ True, True])

    >>> np.isclose([1e10,1e-8], [1.0001e10,1e-9])
    array([False,  True])

    >>> np.isclose([1.0, np.nan], [1.0, np.nan])
    array([ True, False])

    >>> np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)
    array([ True, True])

    >>> np.isclose([1e-8, 1e-7], [0.0, 0.0])
    array([ True, False])

    >>> np.isclose([1e-100, 1e-7], [0.0, 0.0], atol=0.0)
    array([False, False])

    >>> np.isclose([1e-10, 1e-10], [1e-20, 0.0])
    array([ True,  True])

    >>> np.isclose([1e-10, 1e-10], [1e-20, 0.999999e-10], atol=0.0)
    array([False,  True])

Python Library Documentation: function iscomplex in module autograd.tracer

iscomplex(*args, called_by_autograd_dispatcher=False, **kwargs)
    Returns a bool array, where True if input element is complex.

    What is tested is whether the input has a non-zero imaginary part, not if
    the input type is complex.

    Parameters
    ----------
    x : array_like
        Input array.

    Returns
    -------
    out : ndarray of bools
        Output array.

    See Also
    --------
    isreal
    iscomplexobj : Return True if x is a complex type or an array of complex
                   numbers.

    Examples
    --------
    >>> import numpy as np
    >>> np.iscomplex([1+1j, 1+0j, 4.5, 3, 2, 2j])
    array([ True, False, False, False, False,  True])

Python Library Documentation: function iscomplexobj in module autograd.tracer

iscomplexobj(*args, **kwargs)
    Check for a complex type or an array of complex numbers.

    The type of the input is checked, not the value. Even if the input
    has an imaginary part equal to zero, `iscomplexobj` evaluates to True.

    Parameters
    ----------
    x : any
        The input can be of any type and shape.

    Returns
    -------
    iscomplexobj : bool
        The return value, True if `x` is of a complex type or has at least
        one complex element.

    See Also
    --------
    isrealobj, iscomplex

    Examples
    --------
    >>> import numpy as np
    >>> np.iscomplexobj(1)
    False
    >>> np.iscomplexobj(1+0j)
    True
    >>> np.iscomplexobj([3, 1+0j, True])
    True

Python Library Documentation: function isdtype in module autograd.tracer

isdtype(*args, called_by_autograd_dispatcher=False, **kwargs)
    Determine if a provided dtype is of a specified data type ``kind``.

    This function only supports built-in NumPy's data types.
    Third-party dtypes are not yet supported.

    Parameters
    ----------
    dtype : dtype
        The input dtype.
    kind : dtype or str or tuple of dtypes/strs.
        dtype or dtype kind. Allowed dtype kinds are:
        * ``'bool'`` : boolean kind
        * ``'signed integer'`` : signed integer data types
        * ``'unsigned integer'`` : unsigned integer data types
        * ``'integral'`` : integer data types
        * ``'real floating'`` : real-valued floating-point data types
        * ``'complex floating'`` : complex floating-point data types
        * ``'numeric'`` : numeric data types

    Returns
    -------
    out : bool

    See Also
    --------
    issubdtype

    Examples
    --------
    >>> import numpy as np
    >>> np.isdtype(np.float32, np.float64)
    False
    >>> np.isdtype(np.float32, "real floating")
    True
    >>> np.isdtype(np.complex128, ("real floating", "complex floating"))
    True

Python Library Documentation: function isfinite in module autograd.tracer

isfinite(*args, called_by_autograd_dispatcher=False, **kwargs)
    isfinite(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Test element-wise for finiteness (not infinity and not Not a Number).

    The result is returned as a boolean array.

    Parameters
    ----------
    x : array_like
        Input values.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray, bool
        True where ``x`` is not positive infinity, negative infinity,
        or NaN; false otherwise.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    isinf, isneginf, isposinf, isnan

    Notes
    -----
    Not a Number, positive infinity and negative infinity are considered
    to be non-finite.

    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754). This means that Not a Number is not equivalent to infinity.
    Also that positive infinity is not equivalent to negative infinity. But
    infinity is equivalent to positive infinity.  Errors result if the
    second argument is also supplied when `x` is a scalar input, or if
    first and second arguments have different shapes.

    Examples
    --------
    >>> import numpy as np
    >>> np.isfinite(1)
    True
    >>> np.isfinite(0)
    True
    >>> np.isfinite(np.nan)
    False
    >>> np.isfinite(np.inf)
    False
    >>> np.isfinite(-np.inf)
    False
    >>> np.isfinite([np.log(-1.),1.,np.log(0)])
    array([False,  True, False])

    >>> x = np.array([-np.inf, 0., np.inf])
    >>> y = np.array([2, 2, 2])
    >>> np.isfinite(x, y)
    array([0, 1, 0])
    >>> y
    array([0, 1, 0])

Python Library Documentation: function isfortran in module autograd.tracer

isfortran(*args, called_by_autograd_dispatcher=False, **kwargs)
    Check if the array is Fortran contiguous but *not* C contiguous.

    This function is obsolete. If you only want to check if an array is Fortran
    contiguous use ``a.flags.f_contiguous`` instead.

    Parameters
    ----------
    a : ndarray
        Input array.

    Returns
    -------
    isfortran : bool
        Returns True if the array is Fortran contiguous but *not* C contiguous.


    Examples
    --------

    np.array allows to specify whether the array is written in C-contiguous
    order (last index varies the fastest), or FORTRAN-contiguous order in
    memory (first index varies the fastest).

    >>> import numpy as np
    >>> a = np.array([[1, 2, 3], [4, 5, 6]], order='C')
    >>> a
    array([[1, 2, 3],
           [4, 5, 6]])
    >>> np.isfortran(a)
    False

    >>> b = np.array([[1, 2, 3], [4, 5, 6]], order='F')
    >>> b
    array([[1, 2, 3],
           [4, 5, 6]])
    >>> np.isfortran(b)
    True


    The transpose of a C-ordered array is a FORTRAN-ordered array.

    >>> a = np.array([[1, 2, 3], [4, 5, 6]], order='C')
    >>> a
    array([[1, 2, 3],
           [4, 5, 6]])
    >>> np.isfortran(a)
    False
    >>> b = a.T
    >>> b
    array([[1, 4],
           [2, 5],
           [3, 6]])
    >>> np.isfortran(b)
    True

    C-ordered arrays evaluate as False even if they are also FORTRAN-ordered.

    >>> np.isfortran(np.array([1, 2], order='F'))
    False

Python Library Documentation: function isin in module autograd.tracer

isin(*args, called_by_autograd_dispatcher=False, **kwargs)
    Calculates ``element in test_elements``, broadcasting over `element` only.
    Returns a boolean array of the same shape as `element` that is True
    where an element of `element` is in `test_elements` and False otherwise.

    Parameters
    ----------
    element : array_like
        Input array.
    test_elements : array_like
        The values against which to test each value of `element`.
        This argument is flattened if it is an array or array_like.
        See notes for behavior with non-array-like parameters.
    assume_unique : bool, optional
        If True, the input arrays are both assumed to be unique, which
        can speed up the calculation.  Default is False.
    invert : bool, optional
        If True, the values in the returned array are inverted, as if
        calculating `element not in test_elements`. Default is False.
        ``np.isin(a, b, invert=True)`` is equivalent to (but faster
        than) ``np.invert(np.isin(a, b))``.
    kind : {None, 'sort', 'table'}, optional
        The algorithm to use. This will not affect the final result,
        but will affect the speed and memory use. The default, None,
        will select automatically based on memory considerations.

        * If 'sort', will use a mergesort-based approach. This will have
          a memory usage of roughly 6 times the sum of the sizes of
          `element` and `test_elements`, not accounting for size of dtypes.
        * If 'table', will use a lookup table approach similar
          to a counting sort. This is only available for boolean and
          integer arrays. This will have a memory usage of the
          size of `element` plus the max-min value of `test_elements`.
          `assume_unique` has no effect when the 'table' option is used.
        * If None, will automatically choose 'table' if
          the required memory allocation is less than or equal to
          6 times the sum of the sizes of `element` and `test_elements`,
          otherwise will use 'sort'. This is done to not use
          a large amount of memory by default, even though
          'table' may be faster in most cases. If 'table' is chosen,
          `assume_unique` will have no effect.


    Returns
    -------
    isin : ndarray, bool
        Has the same shape as `element`. The values `element[isin]`
        are in `test_elements`.

    Notes
    -----

    `isin` is an element-wise function version of the python keyword `in`.
    ``isin(a, b)`` is roughly equivalent to
    ``np.array([item in b for item in a])`` if `a` and `b` are 1-D sequences.

    `element` and `test_elements` are converted to arrays if they are not
    already. If `test_elements` is a set (or other non-sequence collection)
    it will be converted to an object array with one element, rather than an
    array of the values contained in `test_elements`. This is a consequence
    of the `array` constructor's way of handling non-sequence collections.
    Converting the set to a list usually gives the desired behavior.

    Using ``kind='table'`` tends to be faster than `kind='sort'` if the
    following relationship is true:
    ``log10(len(test_elements)) >
    (log10(max(test_elements)-min(test_elements)) - 2.27) / 0.927``,
    but may use greater memory. The default value for `kind` will
    be automatically selected based only on memory usage, so one may
    manually set ``kind='table'`` if memory constraints can be relaxed.

    .. versionadded:: 1.13.0

    Examples
    --------
    >>> import numpy as np
    >>> element = 2*np.arange(4).reshape((2, 2))
    >>> element
    array([[0, 2],
           [4, 6]])
    >>> test_elements = [1, 2, 4, 8]
    >>> mask = np.isin(element, test_elements)
    >>> mask
    array([[False,  True],
           [ True, False]])
    >>> element[mask]
    array([2, 4])

    The indices of the matched values can be obtained with `nonzero`:

    >>> np.nonzero(mask)
    (array([0, 1]), array([1, 0]))

    The test can also be inverted:

    >>> mask = np.isin(element, test_elements, invert=True)
    >>> mask
    array([[ True, False],
           [False,  True]])
    >>> element[mask]
    array([0, 6])

    Because of how `array` handles sets, the following does not
    work as expected:

    >>> test_set = {1, 2, 4, 8}
    >>> np.isin(element, test_set)
    array([[False, False],
           [False, False]])

    Casting the set to a list gives the expected result:

    >>> np.isin(element, list(test_set))
    array([[False,  True],
           [ True, False]])

Python Library Documentation: function isinf in module autograd.tracer

isinf(*args, called_by_autograd_dispatcher=False, **kwargs)
    isinf(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Test element-wise for positive or negative infinity.

    Returns a boolean array of the same shape as `x`, True where ``x ==
    +/-inf``, otherwise False.

    Parameters
    ----------
    x : array_like
        Input values
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : bool (scalar) or boolean ndarray
        True where ``x`` is positive or negative infinity, false otherwise.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    isneginf, isposinf, isnan, isfinite

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754).

    Errors result if the second argument is supplied when the first
    argument is a scalar, or if the first and second arguments have
    different shapes.

    Examples
    --------
    >>> import numpy as np
    >>> np.isinf(np.inf)
    True
    >>> np.isinf(np.nan)
    False
    >>> np.isinf(-np.inf)
    True
    >>> np.isinf([np.inf, -np.inf, 1.0, np.nan])
    array([ True,  True, False, False])

    >>> x = np.array([-np.inf, 0., np.inf])
    >>> y = np.array([2, 2, 2])
    >>> np.isinf(x, y)
    array([1, 0, 1])
    >>> y
    array([1, 0, 1])

Python Library Documentation: function isnan in module autograd.tracer

isnan(*args, called_by_autograd_dispatcher=False, **kwargs)
    isnan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Test element-wise for NaN and return result as a boolean array.

    Parameters
    ----------
    x : array_like
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray or bool
        True where ``x`` is NaN, false otherwise.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    isinf, isneginf, isposinf, isfinite, isnat

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754). This means that Not a Number is not equivalent to infinity.

    Examples
    --------
    >>> import numpy as np
    >>> np.isnan(np.nan)
    True
    >>> np.isnan(np.inf)
    False
    >>> np.isnan([np.log(-1.),1.,np.log(0)])
    array([ True, False, False])

Python Library Documentation: function isnat in module autograd.tracer

isnat(*args, called_by_autograd_dispatcher=False, **kwargs)
    isnat(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Test element-wise for NaT (not a time) and return result as a boolean array.

    .. versionadded:: 1.13.0

    Parameters
    ----------
    x : array_like
        Input array with datetime or timedelta data type.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray or bool
        True where ``x`` is NaT, false otherwise.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    isnan, isinf, isneginf, isposinf, isfinite

    Examples
    --------
    >>> import numpy as np
    >>> np.isnat(np.datetime64("NaT"))
    True
    >>> np.isnat(np.datetime64("2016-01-01"))
    False
    >>> np.isnat(np.array(["NaT", "2016-01-01"], dtype="datetime64[ns]"))
    array([ True, False])

Python Library Documentation: function isneginf in module autograd.tracer

isneginf(*args, called_by_autograd_dispatcher=False, **kwargs)
    Test element-wise for negative infinity, return result as bool array.

    Parameters
    ----------
    x : array_like
        The input array.
    out : array_like, optional
        A location into which the result is stored. If provided, it must have a
        shape that the input broadcasts to. If not provided or None, a
        freshly-allocated boolean array is returned.

    Returns
    -------
    out : ndarray
        A boolean array with the same dimensions as the input.
        If second argument is not supplied then a numpy boolean array is
        returned with values True where the corresponding element of the
        input is negative infinity and values False where the element of
        the input is not negative infinity.

        If a second argument is supplied the result is stored there. If the
        type of that array is a numeric type the result is represented as
        zeros and ones, if the type is boolean then as False and True. The
        return value `out` is then a reference to that array.

    See Also
    --------
    isinf, isposinf, isnan, isfinite

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754).

    Errors result if the second argument is also supplied when x is a scalar
    input, if first and second arguments have different shapes, or if the
    first argument has complex values.

    Examples
    --------
    >>> import numpy as np
    >>> np.isneginf(-np.inf)
    True
    >>> np.isneginf(np.inf)
    False
    >>> np.isneginf([-np.inf, 0., np.inf])
    array([ True, False, False])

    >>> x = np.array([-np.inf, 0., np.inf])
    >>> y = np.array([2, 2, 2])
    >>> np.isneginf(x, y)
    array([1, 0, 0])
    >>> y
    array([1, 0, 0])

Python Library Documentation: function isposinf in module autograd.tracer

isposinf(*args, called_by_autograd_dispatcher=False, **kwargs)
    Test element-wise for positive infinity, return result as bool array.

    Parameters
    ----------
    x : array_like
        The input array.
    out : array_like, optional
        A location into which the result is stored. If provided, it must have a
        shape that the input broadcasts to. If not provided or None, a
        freshly-allocated boolean array is returned.

    Returns
    -------
    out : ndarray
        A boolean array with the same dimensions as the input.
        If second argument is not supplied then a boolean array is returned
        with values True where the corresponding element of the input is
        positive infinity and values False where the element of the input is
        not positive infinity.

        If a second argument is supplied the result is stored there. If the
        type of that array is a numeric type the result is represented as zeros
        and ones, if the type is boolean then as False and True.
        The return value `out` is then a reference to that array.

    See Also
    --------
    isinf, isneginf, isfinite, isnan

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754).

    Errors result if the second argument is also supplied when x is a scalar
    input, if first and second arguments have different shapes, or if the
    first argument has complex values

    Examples
    --------
    >>> import numpy as np
    >>> np.isposinf(np.inf)
    True
    >>> np.isposinf(-np.inf)
    False
    >>> np.isposinf([-np.inf, 0., np.inf])
    array([False, False,  True])

    >>> x = np.array([-np.inf, 0., np.inf])
    >>> y = np.array([2, 2, 2])
    >>> np.isposinf(x, y)
    array([0, 0, 1])
    >>> y
    array([0, 0, 1])

Python Library Documentation: function isreal in module autograd.tracer

isreal(*args, called_by_autograd_dispatcher=False, **kwargs)
    Returns a bool array, where True if input element is real.

    If element has complex type with zero imaginary part, the return value
    for that element is True.

    Parameters
    ----------
    x : array_like
        Input array.

    Returns
    -------
    out : ndarray, bool
        Boolean array of same shape as `x`.

    Notes
    -----
    `isreal` may behave unexpectedly for string or object arrays (see examples)

    See Also
    --------
    iscomplex
    isrealobj : Return True if x is not a complex type.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([1+1j, 1+0j, 4.5, 3, 2, 2j], dtype=complex)
    >>> np.isreal(a)
    array([False,  True,  True,  True,  True, False])

    The function does not work on string arrays.

    >>> a = np.array([2j, "a"], dtype="U")
    >>> np.isreal(a)  # Warns about non-elementwise comparison
    False

    Returns True for all elements in input array of ``dtype=object`` even if
    any of the elements is complex.

    >>> a = np.array([1, "2", 3+4j], dtype=object)
    >>> np.isreal(a)
    array([ True,  True,  True])

    isreal should not be used with object arrays

    >>> a = np.array([1+2j, 2+1j], dtype=object)
    >>> np.isreal(a)
    array([ True,  True])

Python Library Documentation: function isrealobj in module autograd.tracer

isrealobj(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return True if x is a not complex type or an array of complex numbers.

    The type of the input is checked, not the value. So even if the input
    has an imaginary part equal to zero, `isrealobj` evaluates to False
    if the data type is complex.

    Parameters
    ----------
    x : any
        The input can be of any type and shape.

    Returns
    -------
    y : bool
        The return value, False if `x` is of a complex type.

    See Also
    --------
    iscomplexobj, isreal

    Notes
    -----
    The function is only meant for arrays with numerical values but it
    accepts all other objects. Since it assumes array input, the return
    value of other objects may be True.

    >>> np.isrealobj('A string')
    True
    >>> np.isrealobj(False)
    True
    >>> np.isrealobj(None)
    True

    Examples
    --------
    >>> import numpy as np
    >>> np.isrealobj(1)
    True
    >>> np.isrealobj(1+0j)
    False
    >>> np.isrealobj([3, 1+0j, True])
    False

Python Library Documentation: function isscalar in module autograd.tracer

isscalar(*args, called_by_autograd_dispatcher=False, **kwargs)
    Returns True if the type of `element` is a scalar type.

    Parameters
    ----------
    element : any
        Input argument, can be of any type and shape.

    Returns
    -------
    val : bool
        True if `element` is a scalar type, False if it is not.

    See Also
    --------
    ndim : Get the number of dimensions of an array

    Notes
    -----
    If you need a stricter way to identify a *numerical* scalar, use
    ``isinstance(x, numbers.Number)``, as that returns ``False`` for most
    non-numerical elements such as strings.

    In most cases ``np.ndim(x) == 0`` should be used instead of this function,
    as that will also return true for 0d arrays. This is how numpy overloads
    functions in the style of the ``dx`` arguments to `gradient` and
    the ``bins`` argument to `histogram`. Some key differences:

    +------------------------------------+---------------+-------------------+
    | x                                  |``isscalar(x)``|``np.ndim(x) == 0``|
    +====================================+===============+===================+
    | PEP 3141 numeric objects           | ``True``      | ``True``          |
    | (including builtins)               |               |                   |
    +------------------------------------+---------------+-------------------+
    | builtin string and buffer objects  | ``True``      | ``True``          |
    +------------------------------------+---------------+-------------------+
    | other builtin objects, like        | ``False``     | ``True``          |
    | `pathlib.Path`, `Exception`,       |               |                   |
    | the result of `re.compile`         |               |                   |
    +------------------------------------+---------------+-------------------+
    | third-party objects like           | ``False``     | ``True``          |
    | `matplotlib.figure.Figure`         |               |                   |
    +------------------------------------+---------------+-------------------+
    | zero-dimensional numpy arrays      | ``False``     | ``True``          |
    +------------------------------------+---------------+-------------------+
    | other numpy arrays                 | ``False``     | ``False``         |
    +------------------------------------+---------------+-------------------+
    | `list`, `tuple`, and other         | ``False``     | ``False``         |
    | sequence objects                   |               |                   |
    +------------------------------------+---------------+-------------------+

    Examples
    --------
    >>> import numpy as np

    >>> np.isscalar(3.1)
    True

    >>> np.isscalar(np.array(3.1))
    False

    >>> np.isscalar([3.1])
    False

    >>> np.isscalar(False)
    True

    >>> np.isscalar('numpy')
    True

    NumPy supports PEP 3141 numbers:

    >>> from fractions import Fraction
    >>> np.isscalar(Fraction(5, 17))
    True
    >>> from numbers import Number
    >>> np.isscalar(Number())
    True

Python Library Documentation: function issubdtype in module autograd.tracer

issubdtype(*args, called_by_autograd_dispatcher=False, **kwargs)
    Returns True if first argument is a typecode lower/equal in type hierarchy.

    This is like the builtin :func:`issubclass`, but for `dtype`\ s.

    Parameters
    ----------
    arg1, arg2 : dtype_like
        `dtype` or object coercible to one

    Returns
    -------
    out : bool

    See Also
    --------
    :ref:`arrays.scalars` : Overview of the numpy type hierarchy.

    Examples
    --------
    `issubdtype` can be used to check the type of arrays:

    >>> ints = np.array([1, 2, 3], dtype=np.int32)
    >>> np.issubdtype(ints.dtype, np.integer)
    True
    >>> np.issubdtype(ints.dtype, np.floating)
    False

    >>> floats = np.array([1, 2, 3], dtype=np.float32)
    >>> np.issubdtype(floats.dtype, np.integer)
    False
    >>> np.issubdtype(floats.dtype, np.floating)
    True

    Similar types of different sizes are not subdtypes of each other:

    >>> np.issubdtype(np.float64, np.float32)
    False
    >>> np.issubdtype(np.float32, np.float64)
    False

    but both are subtypes of `floating`:

    >>> np.issubdtype(np.float64, np.floating)
    True
    >>> np.issubdtype(np.float32, np.floating)
    True

    For convenience, dtype-like objects are allowed too:

    >>> np.issubdtype('S1', np.bytes_)
    True
    >>> np.issubdtype('i4', np.signedinteger)
    True

Python Library Documentation: function iterable in module autograd.tracer

iterable(*args, called_by_autograd_dispatcher=False, **kwargs)
    Check whether or not an object can be iterated over.

    Parameters
    ----------
    y : object
      Input object.

    Returns
    -------
    b : bool
      Return ``True`` if the object has an iterator method or is a
      sequence and ``False`` otherwise.


    Examples
    --------
    >>> import numpy as np
    >>> np.iterable([1, 2, 3])
    True
    >>> np.iterable(2)
    False

    Notes
    -----
    In most cases, the results of ``np.iterable(obj)`` are consistent with
    ``isinstance(obj, collections.abc.Iterable)``. One notable exception is
    the treatment of 0-dimensional arrays::

        >>> from collections.abc import Iterable
        >>> a = np.array(1.0)  # 0-dimensional numpy array
        >>> isinstance(a, Iterable)
        True
        >>> np.iterable(a)
        False

Python Library Documentation: function ix_ in module autograd.tracer

ix_(*args, called_by_autograd_dispatcher=False, **kwargs)
    Construct an open mesh from multiple sequences.

    This function takes N 1-D sequences and returns N outputs with N
    dimensions each, such that the shape is 1 in all but one dimension
    and the dimension with the non-unit shape value cycles through all
    N dimensions.

    Using `ix_` one can quickly construct index arrays that will index
    the cross product. ``a[np.ix_([1,3],[2,5])]`` returns the array
    ``[[a[1,2] a[1,5]], [a[3,2] a[3,5]]]``.

    Parameters
    ----------
    args : 1-D sequences
        Each sequence should be of integer or boolean type.
        Boolean sequences will be interpreted as boolean masks for the
        corresponding dimension (equivalent to passing in
        ``np.nonzero(boolean_sequence)``).

    Returns
    -------
    out : tuple of ndarrays
        N arrays with N dimensions each, with N the number of input
        sequences. Together these arrays form an open mesh.

    See Also
    --------
    ogrid, mgrid, meshgrid

    Examples
    --------
    >>> import numpy as np
    >>> a = np.arange(10).reshape(2, 5)
    >>> a
    array([[0, 1, 2, 3, 4],
           [5, 6, 7, 8, 9]])
    >>> ixgrid = np.ix_([0, 1], [2, 4])
    >>> ixgrid
    (array([[0],
           [1]]), array([[2, 4]]))
    >>> ixgrid[0].shape, ixgrid[1].shape
    ((2, 1), (1, 2))
    >>> a[ixgrid]
    array([[2, 4],
           [7, 9]])

    >>> ixgrid = np.ix_([True, True], [2, 4])
    >>> a[ixgrid]
    array([[2, 4],
           [7, 9]])
    >>> ixgrid = np.ix_([True, True], [False, False, True, False, True])
    >>> a[ixgrid]
    array([[2, 4],
           [7, 9]])

Python Library Documentation: function kaiser in module autograd.tracer

kaiser(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the Kaiser window.

    The Kaiser window is a taper formed by using a Bessel function.

    Parameters
    ----------
    M : int
        Number of points in the output window. If zero or less, an
        empty array is returned.
    beta : float
        Shape parameter for window.

    Returns
    -------
    out : array
        The window, with the maximum value normalized to one (the value
        one appears only if the number of samples is odd).

    See Also
    --------
    bartlett, blackman, hamming, hanning

    Notes
    -----
    The Kaiser window is defined as

    .. math::  w(n) = I_0\left( \beta \sqrt{1-\frac{4n^2}{(M-1)^2}}
               \right)/I_0(\beta)

    with

    .. math:: \quad -\frac{M-1}{2} \leq n \leq \frac{M-1}{2},

    where :math:`I_0` is the modified zeroth-order Bessel function.

    The Kaiser was named for Jim Kaiser, who discovered a simple
    approximation to the DPSS window based on Bessel functions.  The Kaiser
    window is a very good approximation to the Digital Prolate Spheroidal
    Sequence, or Slepian window, which is the transform which maximizes the
    energy in the main lobe of the window relative to total energy.

    The Kaiser can approximate many other windows by varying the beta
    parameter.

    ====  =======================
    beta  Window shape
    ====  =======================
    0     Rectangular
    5     Similar to a Hamming
    6     Similar to a Hanning
    8.6   Similar to a Blackman
    ====  =======================

    A beta value of 14 is probably a good starting point. Note that as beta
    gets large, the window narrows, and so the number of samples needs to be
    large enough to sample the increasingly narrow spike, otherwise NaNs will
    get returned.

    Most references to the Kaiser window come from the signal processing
    literature, where it is used as one of many windowing functions for
    smoothing values.  It is also known as an apodization (which means
    "removing the foot", i.e. smoothing discontinuities at the beginning
    and end of the sampled signal) or tapering function.

    References
    ----------
    .. [1] J. F. Kaiser, "Digital Filters" - Ch 7 in "Systems analysis by
           digital computer", Editors: F.F. Kuo and J.F. Kaiser, p 218-285.
           John Wiley and Sons, New York, (1966).
    .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The
           University of Alberta Press, 1975, pp. 177-178.
    .. [3] Wikipedia, "Window function",
           https://en.wikipedia.org/wiki/Window_function

    Examples
    --------
    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> np.kaiser(12, 14)
     array([7.72686684e-06, 3.46009194e-03, 4.65200189e-02, # may vary
            2.29737120e-01, 5.99885316e-01, 9.45674898e-01,
            9.45674898e-01, 5.99885316e-01, 2.29737120e-01,
            4.65200189e-02, 3.46009194e-03, 7.72686684e-06])


    Plot the window and the frequency response.

    .. plot::
        :include-source:

        import matplotlib.pyplot as plt
        from numpy.fft import fft, fftshift
        window = np.kaiser(51, 14)
        plt.plot(window)
        plt.title("Kaiser window")
        plt.ylabel("Amplitude")
        plt.xlabel("Sample")
        plt.show()

        plt.figure()
        A = fft(window, 2048) / 25.5
        mag = np.abs(fftshift(A))
        freq = np.linspace(-0.5, 0.5, len(A))
        response = 20 * np.log10(mag)
        response = np.clip(response, -100, 100)
        plt.plot(freq, response)
        plt.title("Frequency response of Kaiser window")
        plt.ylabel("Magnitude [dB]")
        plt.xlabel("Normalized frequency [cycles per sample]")
        plt.axis('tight')
        plt.show()

Python Library Documentation: function kron in module autograd.tracer

kron(*args, called_by_autograd_dispatcher=False, **kwargs)
    Kronecker product of two arrays.

    Computes the Kronecker product, a composite array made of blocks of the
    second array scaled by the first.

    Parameters
    ----------
    a, b : array_like

    Returns
    -------
    out : ndarray

    See Also
    --------
    outer : The outer product

    Notes
    -----
    The function assumes that the number of dimensions of `a` and `b`
    are the same, if necessary prepending the smallest with ones.
    If ``a.shape = (r0,r1,..,rN)`` and ``b.shape = (s0,s1,...,sN)``,
    the Kronecker product has shape ``(r0*s0, r1*s1, ..., rN*SN)``.
    The elements are products of elements from `a` and `b`, organized
    explicitly by::

        kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN]

    where::

        kt = it * st + jt,  t = 0,...,N

    In the common 2-D case (N=1), the block structure can be visualized::

        [[ a[0,0]*b,   a[0,1]*b,  ... , a[0,-1]*b  ],
         [  ...                              ...   ],
         [ a[-1,0]*b,  a[-1,1]*b, ... , a[-1,-1]*b ]]


    Examples
    --------
    >>> import numpy as np
    >>> np.kron([1,10,100], [5,6,7])
    array([  5,   6,   7, ..., 500, 600, 700])
    >>> np.kron([5,6,7], [1,10,100])
    array([  5,  50, 500, ...,   7,  70, 700])

    >>> np.kron(np.eye(2), np.ones((2,2)))
    array([[1.,  1.,  0.,  0.],
           [1.,  1.,  0.,  0.],
           [0.,  0.,  1.,  1.],
           [0.,  0.,  1.,  1.]])

    >>> a = np.arange(100).reshape((2,5,2,5))
    >>> b = np.arange(24).reshape((2,3,4))
    >>> c = np.kron(a,b)
    >>> c.shape
    (2, 10, 6, 20)
    >>> I = (1,3,0,2)
    >>> J = (0,2,1)
    >>> J1 = (0,) + J             # extend to ndim=4
    >>> S1 = (1,) + b.shape
    >>> K = tuple(np.array(I) * np.array(S1) + np.array(J1))
    >>> c[K] == a[I]*b[J]
    True

Python Library Documentation: function lcm in module autograd.tracer

lcm(*args, called_by_autograd_dispatcher=False, **kwargs)
    lcm(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Returns the lowest common multiple of ``|x1|`` and ``|x2|``

    Parameters
    ----------
    x1, x2 : array_like, int
        Arrays of values.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).

    Returns
    -------
    y : ndarray or scalar
        The lowest common multiple of the absolute value of the inputs
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    gcd : The greatest common divisor

    Examples
    --------
    >>> import numpy as np
    >>> np.lcm(12, 20)
    60
    >>> np.lcm.reduce([3, 12, 20])
    60
    >>> np.lcm.reduce([40, 12, 20])
    120
    >>> np.lcm(np.arange(6), 20)
    array([ 0, 20, 20, 60, 20, 20])

Python Library Documentation: function ldexp in module autograd.tracer

ldexp(*args, called_by_autograd_dispatcher=False, **kwargs)
    ldexp(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Returns x1 * 2**x2, element-wise.

    The mantissas `x1` and twos exponents `x2` are used to construct
    floating point numbers ``x1 * 2**x2``.

    Parameters
    ----------
    x1 : array_like
        Array of multipliers.
    x2 : array_like, int
        Array of twos exponents.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray or scalar
        The result of ``x1 * 2**x2``.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    frexp : Return (y1, y2) from ``x = y1 * 2**y2``, inverse to `ldexp`.

    Notes
    -----
    Complex dtypes are not supported, they will raise a TypeError.

    `ldexp` is useful as the inverse of `frexp`, if used by itself it is
    more clear to simply use the expression ``x1 * 2**x2``.

    Examples
    --------
    >>> import numpy as np
    >>> np.ldexp(5, np.arange(4))
    array([ 5., 10., 20., 40.], dtype=float16)

    >>> x = np.arange(6)
    >>> np.ldexp(*np.frexp(x))
    array([ 0.,  1.,  2.,  3.,  4.,  5.])

Python Library Documentation: function left_shift in module autograd.tracer

left_shift(*args, called_by_autograd_dispatcher=False, **kwargs)
    left_shift(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Shift the bits of an integer to the left.

    Bits are shifted to the left by appending `x2` 0s at the right of `x1`.
    Since the internal representation of numbers is in binary format, this
    operation is equivalent to multiplying `x1` by ``2**x2``.

    Parameters
    ----------
    x1 : array_like of integer type
        Input values.
    x2 : array_like of integer type
        Number of zeros to append to `x1`. Has to be non-negative.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : array of integer type
        Return `x1` with bits shifted `x2` times to the left.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    right_shift : Shift the bits of an integer to the right.
    binary_repr : Return the binary representation of the input number
        as a string.

    Examples
    --------
    >>> import numpy as np
    >>> np.binary_repr(5)
    '101'
    >>> np.left_shift(5, 2)
    20
    >>> np.binary_repr(20)
    '10100'

    >>> np.left_shift(5, [1,2,3])
    array([10, 20, 40])

    Note that the dtype of the second argument may change the dtype of the
    result and can lead to unexpected results in some cases (see
    :ref:`Casting Rules <ufuncs.casting>`):

    >>> a = np.left_shift(np.uint8(255), np.int64(1))  # Expect 254
    >>> print(a, type(a)) # Unexpected result due to upcasting
    510 <class 'numpy.int64'>
    >>> b = np.left_shift(np.uint8(255), np.uint8(1))
    >>> print(b, type(b))
    254 <class 'numpy.uint8'>

    The ``<<`` operator can be used as a shorthand for ``np.left_shift`` on
    ndarrays.

    >>> x1 = 5
    >>> x2 = np.array([1, 2, 3])
    >>> x1 << x2
    array([10, 20, 40])

Python Library Documentation: function less in module autograd.tracer

less(*args, called_by_autograd_dispatcher=False, **kwargs)
    less(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the truth value of (x1 < x2) element-wise.

    Parameters
    ----------
    x1, x2 : array_like
        Input arrays.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Output array, element-wise comparison of `x1` and `x2`.
        Typically of type bool, unless ``dtype=object`` is passed.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    greater, less_equal, greater_equal, equal, not_equal

    Examples
    --------
    >>> import numpy as np
    >>> np.less([1, 2], [2, 2])
    array([ True, False])

    The ``<`` operator can be used as a shorthand for ``np.less`` on ndarrays.

    >>> a = np.array([1, 2])
    >>> b = np.array([2, 2])
    >>> a < b
    array([ True, False])

Python Library Documentation: function less_equal in module autograd.tracer

less_equal(*args, called_by_autograd_dispatcher=False, **kwargs)
    less_equal(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the truth value of (x1 <= x2) element-wise.

    Parameters
    ----------
    x1, x2 : array_like
        Input arrays.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Output array, element-wise comparison of `x1` and `x2`.
        Typically of type bool, unless ``dtype=object`` is passed.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    greater, less, greater_equal, equal, not_equal

    Examples
    --------
    >>> import numpy as np
    >>> np.less_equal([4, 2, 1], [2, 2, 2])
    array([False,  True,  True])

    The ``<=`` operator can be used as a shorthand for ``np.less_equal`` on
    ndarrays.

    >>> a = np.array([4, 2, 1])
    >>> b = np.array([2, 2, 2])
    >>> a <= b
    array([False,  True,  True])

Python Library Documentation: function lexsort in module autograd.tracer

lexsort(*args, called_by_autograd_dispatcher=False, **kwargs)
    lexsort(keys, axis=-1)

    Perform an indirect stable sort using a sequence of keys.

    Given multiple sorting keys, lexsort returns an array of integer indices
    that describes the sort order by multiple keys. The last key in the
    sequence is used for the primary sort order, ties are broken by the
    second-to-last key, and so on.

    Parameters
    ----------
    keys : (k, m, n, ...) array-like
        The `k` keys to be sorted. The *last* key (e.g, the last
        row if `keys` is a 2D array) is the primary sort key.
        Each element of `keys` along the zeroth axis must be
        an array-like object of the same shape.
    axis : int, optional
        Axis to be indirectly sorted. By default, sort over the last axis
        of each sequence. Separate slices along `axis` sorted over
        independently; see last example.

    Returns
    -------
    indices : (m, n, ...) ndarray of ints
        Array of indices that sort the keys along the specified axis.

    See Also
    --------
    argsort : Indirect sort.
    ndarray.sort : In-place sort.
    sort : Return a sorted copy of an array.

    Examples
    --------
    Sort names: first by surname, then by name.

    >>> import numpy as np
    >>> surnames =    ('Hertz',    'Galilei', 'Hertz')
    >>> first_names = ('Heinrich', 'Galileo', 'Gustav')
    >>> ind = np.lexsort((first_names, surnames))
    >>> ind
    array([1, 2, 0])

    >>> [surnames[i] + ", " + first_names[i] for i in ind]
    ['Galilei, Galileo', 'Hertz, Gustav', 'Hertz, Heinrich']

    Sort according to two numerical keys, first by elements
    of ``a``, then breaking ties according to elements of ``b``:

    >>> a = [1, 5, 1, 4, 3, 4, 4]  # First sequence
    >>> b = [9, 4, 0, 4, 0, 2, 1]  # Second sequence
    >>> ind = np.lexsort((b, a))  # Sort by `a`, then by `b`
    >>> ind
    array([2, 0, 4, 6, 5, 3, 1])
    >>> [(a[i], b[i]) for i in ind]
    [(1, 0), (1, 9), (3, 0), (4, 1), (4, 2), (4, 4), (5, 4)]

    Compare against `argsort`, which would sort each key independently.

    >>> np.argsort((b, a), kind='stable')
    array([[2, 4, 6, 5, 1, 3, 0],
           [0, 2, 4, 3, 5, 6, 1]])

    To sort lexicographically with `argsort`, we would need to provide a
    structured array.

    >>> x = np.array([(ai, bi) for ai, bi in zip(a, b)],
    ...              dtype = np.dtype([('x', int), ('y', int)]))
    >>> np.argsort(x)  # or np.argsort(x, order=('x', 'y'))
    array([2, 0, 4, 6, 5, 3, 1])

    The zeroth axis of `keys` always corresponds with the sequence of keys,
    so 2D arrays are treated just like other sequences of keys.

    >>> arr = np.asarray([b, a])
    >>> ind2 = np.lexsort(arr)
    >>> np.testing.assert_equal(ind2, ind)

    Accordingly, the `axis` parameter refers to an axis of *each* key, not of
    the `keys` argument itself. For instance, the array ``arr`` is treated as
    a sequence of two 1-D keys, so specifying ``axis=0`` is equivalent to
    using the default axis, ``axis=-1``.

    >>> np.testing.assert_equal(np.lexsort(arr, axis=0),
    ...                         np.lexsort(arr, axis=-1))

    For higher-dimensional arrays, the axis parameter begins to matter. The
    resulting array has the same shape as each key, and the values are what
    we would expect if `lexsort` were performed on corresponding slices
    of the keys independently. For instance,

    >>> x = [[1, 2, 3, 4],
    ...      [4, 3, 2, 1],
    ...      [2, 1, 4, 3]]
    >>> y = [[2, 2, 1, 1],
    ...      [1, 2, 1, 2],
    ...      [1, 1, 2, 1]]
    >>> np.lexsort((x, y), axis=1)
    array([[2, 3, 0, 1],
           [2, 0, 3, 1],
           [1, 0, 3, 2]])

    Each row of the result is what we would expect if we were to perform
    `lexsort` on the corresponding row of the keys:

    >>> for i in range(3):
    ...     print(np.lexsort((x[i], y[i])))
    [2 3 0 1]
    [2 0 3 1]
    [1 0 3 2]

Python Library Documentation: function linspace in module autograd.tracer

linspace(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return evenly spaced numbers over a specified interval.

    Returns `num` evenly spaced samples, calculated over the
    interval [`start`, `stop`].

    The endpoint of the interval can optionally be excluded.

    .. versionchanged:: 1.16.0
        Non-scalar `start` and `stop` are now supported.

    .. versionchanged:: 1.20.0
        Values are rounded towards ``-inf`` instead of ``0`` when an
        integer ``dtype`` is specified. The old behavior can
        still be obtained with ``np.linspace(start, stop, num).astype(int)``

    Parameters
    ----------
    start : array_like
        The starting value of the sequence.
    stop : array_like
        The end value of the sequence, unless `endpoint` is set to False.
        In that case, the sequence consists of all but the last of ``num + 1``
        evenly spaced samples, so that `stop` is excluded.  Note that the step
        size changes when `endpoint` is False.
    num : int, optional
        Number of samples to generate. Default is 50. Must be non-negative.
    endpoint : bool, optional
        If True, `stop` is the last sample. Otherwise, it is not included.
        Default is True.
    retstep : bool, optional
        If True, return (`samples`, `step`), where `step` is the spacing
        between samples.
    dtype : dtype, optional
        The type of the output array.  If `dtype` is not given, the data type
        is inferred from `start` and `stop`. The inferred dtype will never be
        an integer; `float` is chosen even if the arguments would produce an
        array of integers.

        .. versionadded:: 1.9.0
    axis : int, optional
        The axis in the result to store the samples.  Relevant only if start
        or stop are array-like.  By default (0), the samples will be along a
        new axis inserted at the beginning. Use -1 to get an axis at the end.

        .. versionadded:: 1.16.0
    device : str, optional
        The device on which to place the created array. Default: None.
        For Array-API interoperability only, so must be ``"cpu"`` if passed.

        .. versionadded:: 2.0.0

    Returns
    -------
    samples : ndarray
        There are `num` equally spaced samples in the closed interval
        ``[start, stop]`` or the half-open interval ``[start, stop)``
        (depending on whether `endpoint` is True or False).
    step : float, optional
        Only returned if `retstep` is True

        Size of spacing between samples.


    See Also
    --------
    arange : Similar to `linspace`, but uses a step size (instead of the
             number of samples).
    geomspace : Similar to `linspace`, but with numbers spaced evenly on a log
                scale (a geometric progression).
    logspace : Similar to `geomspace`, but with the end points specified as
               logarithms.
    :ref:`how-to-partition`

    Examples
    --------
    >>> import numpy as np
    >>> np.linspace(2.0, 3.0, num=5)
    array([2.  , 2.25, 2.5 , 2.75, 3.  ])
    >>> np.linspace(2.0, 3.0, num=5, endpoint=False)
    array([2. ,  2.2,  2.4,  2.6,  2.8])
    >>> np.linspace(2.0, 3.0, num=5, retstep=True)
    (array([2.  ,  2.25,  2.5 ,  2.75,  3.  ]), 0.25)

    Graphical illustration:

    >>> import matplotlib.pyplot as plt
    >>> N = 8
    >>> y = np.zeros(N)
    >>> x1 = np.linspace(0, 10, N, endpoint=True)
    >>> x2 = np.linspace(0, 10, N, endpoint=False)
    >>> plt.plot(x1, y, 'o')
    [<matplotlib.lines.Line2D object at 0x...>]
    >>> plt.plot(x2, y + 0.5, 'o')
    [<matplotlib.lines.Line2D object at 0x...>]
    >>> plt.ylim([-0.5, 1])
    (-0.5, 1)
    >>> plt.show()

Python Library Documentation: function load in module autograd.tracer

load(*args, called_by_autograd_dispatcher=False, **kwargs)
    Load arrays or pickled objects from ``.npy``, ``.npz`` or pickled files.

    .. warning:: Loading files that contain object arrays uses the ``pickle``
                 module, which is not secure against erroneous or maliciously
                 constructed data. Consider passing ``allow_pickle=False`` to
                 load data that is known not to contain object arrays for the
                 safer handling of untrusted sources.

    Parameters
    ----------
    file : file-like object, string, or pathlib.Path
        The file to read. File-like objects must support the
        ``seek()`` and ``read()`` methods and must always
        be opened in binary mode.  Pickled files require that the
        file-like object support the ``readline()`` method as well.
    mmap_mode : {None, 'r+', 'r', 'w+', 'c'}, optional
        If not None, then memory-map the file, using the given mode (see
        `numpy.memmap` for a detailed description of the modes).  A
        memory-mapped array is kept on disk. However, it can be accessed
        and sliced like any ndarray.  Memory mapping is especially useful
        for accessing small fragments of large files without reading the
        entire file into memory.
    allow_pickle : bool, optional
        Allow loading pickled object arrays stored in npy files. Reasons for
        disallowing pickles include security, as loading pickled data can
        execute arbitrary code. If pickles are disallowed, loading object
        arrays will fail. Default: False

        .. versionchanged:: 1.16.3
            Made default False in response to CVE-2019-6446.

    fix_imports : bool, optional
        Only useful when loading Python 2 generated pickled files on Python 3,
        which includes npy/npz files containing object arrays. If `fix_imports`
        is True, pickle will try to map the old Python 2 names to the new names
        used in Python 3.
    encoding : str, optional
        What encoding to use when reading Python 2 strings. Only useful when
        loading Python 2 generated pickled files in Python 3, which includes
        npy/npz files containing object arrays. Values other than 'latin1',
        'ASCII', and 'bytes' are not allowed, as they can corrupt numerical
        data. Default: 'ASCII'
    max_header_size : int, optional
        Maximum allowed size of the header.  Large headers may not be safe
        to load securely and thus require explicitly passing a larger value.
        See :py:func:`ast.literal_eval()` for details.
        This option is ignored when `allow_pickle` is passed.  In that case
        the file is by definition trusted and the limit is unnecessary.

    Returns
    -------
    result : array, tuple, dict, etc.
        Data stored in the file. For ``.npz`` files, the returned instance
        of NpzFile class must be closed to avoid leaking file descriptors.

    Raises
    ------
    OSError
        If the input file does not exist or cannot be read.
    UnpicklingError
        If ``allow_pickle=True``, but the file cannot be loaded as a pickle.
    ValueError
        The file contains an object array, but ``allow_pickle=False`` given.
    EOFError
        When calling ``np.load`` multiple times on the same file handle,
        if all data has already been read

    See Also
    --------
    save, savez, savez_compressed, loadtxt
    memmap : Create a memory-map to an array stored in a file on disk.
    lib.format.open_memmap : Create or load a memory-mapped ``.npy`` file.

    Notes
    -----
    - If the file contains pickle data, then whatever object is stored
      in the pickle is returned.
    - If the file is a ``.npy`` file, then a single array is returned.
    - If the file is a ``.npz`` file, then a dictionary-like object is
      returned, containing ``{filename: array}`` key-value pairs, one for
      each file in the archive.
    - If the file is a ``.npz`` file, the returned value supports the
      context manager protocol in a similar fashion to the open function::

        with load('foo.npz') as data:
            a = data['a']

      The underlying file descriptor is closed when exiting the 'with'
      block.

    Examples
    --------
    >>> import numpy as np

    Store data to disk, and load it again:

    >>> np.save('/tmp/123', np.array([[1, 2, 3], [4, 5, 6]]))
    >>> np.load('/tmp/123.npy')
    array([[1, 2, 3],
           [4, 5, 6]])

    Store compressed data to disk, and load it again:

    >>> a=np.array([[1, 2, 3], [4, 5, 6]])
    >>> b=np.array([1, 2])
    >>> np.savez('/tmp/123.npz', a=a, b=b)
    >>> data = np.load('/tmp/123.npz')
    >>> data['a']
    array([[1, 2, 3],
           [4, 5, 6]])
    >>> data['b']
    array([1, 2])
    >>> data.close()

    Mem-map the stored array, and then access the second row
    directly from disk:

    >>> X = np.load('/tmp/123.npy', mmap_mode='r')
    >>> X[1, :]
    memmap([4, 5, 6])

Python Library Documentation: function loadtxt in module autograd.tracer

loadtxt(*args, called_by_autograd_dispatcher=False, **kwargs)
    Load data from a text file.

    Parameters
    ----------
    fname : file, str, pathlib.Path, list of str, generator
        File, filename, list, or generator to read.  If the filename
        extension is ``.gz`` or ``.bz2``, the file is first decompressed. Note
        that generators must return bytes or strings. The strings
        in a list or produced by a generator are treated as lines.
    dtype : data-type, optional
        Data-type of the resulting array; default: float.  If this is a
        structured data-type, the resulting array will be 1-dimensional, and
        each row will be interpreted as an element of the array.  In this
        case, the number of columns used must match the number of fields in
        the data-type.
    comments : str or sequence of str or None, optional
        The characters or list of characters used to indicate the start of a
        comment. None implies no comments. For backwards compatibility, byte
        strings will be decoded as 'latin1'. The default is '#'.
    delimiter : str, optional
        The character used to separate the values. For backwards compatibility,
        byte strings will be decoded as 'latin1'. The default is whitespace.

        .. versionchanged:: 1.23.0
           Only single character delimiters are supported. Newline characters
           cannot be used as the delimiter.

    converters : dict or callable, optional
        Converter functions to customize value parsing. If `converters` is
        callable, the function is applied to all columns, else it must be a
        dict that maps column number to a parser function.
        See examples for further details.
        Default: None.

        .. versionchanged:: 1.23.0
           The ability to pass a single callable to be applied to all columns
           was added.

    skiprows : int, optional
        Skip the first `skiprows` lines, including comments; default: 0.
    usecols : int or sequence, optional
        Which columns to read, with 0 being the first. For example,
        ``usecols = (1,4,5)`` will extract the 2nd, 5th and 6th columns.
        The default, None, results in all columns being read.

        .. versionchanged:: 1.11.0
            When a single column has to be read it is possible to use
            an integer instead of a tuple. E.g ``usecols = 3`` reads the
            fourth column the same way as ``usecols = (3,)`` would.
    unpack : bool, optional
        If True, the returned array is transposed, so that arguments may be
        unpacked using ``x, y, z = loadtxt(...)``.  When used with a
        structured data-type, arrays are returned for each field.
        Default is False.
    ndmin : int, optional
        The returned array will have at least `ndmin` dimensions.
        Otherwise mono-dimensional axes will be squeezed.
        Legal values: 0 (default), 1 or 2.

        .. versionadded:: 1.6.0
    encoding : str, optional
        Encoding used to decode the inputfile. Does not apply to input streams.
        The special value 'bytes' enables backward compatibility workarounds
        that ensures you receive byte arrays as results if possible and passes
        'latin1' encoded strings to converters. Override this value to receive
        unicode arrays and pass strings as input to converters.  If set to None
        the system default is used. The default value is 'bytes'.

        .. versionadded:: 1.14.0
        .. versionchanged:: 2.0
            Before NumPy 2, the default was ``'bytes'`` for Python 2
            compatibility. The default is now ``None``.

    max_rows : int, optional
        Read `max_rows` rows of content after `skiprows` lines. The default is
        to read all the rows. Note that empty rows containing no data such as
        empty lines and comment lines are not counted towards `max_rows`,
        while such lines are counted in `skiprows`.

        .. versionadded:: 1.16.0

        .. versionchanged:: 1.23.0
            Lines containing no data, including comment lines (e.g., lines
            starting with '#' or as specified via `comments`) are not counted
            towards `max_rows`.
    quotechar : unicode character or None, optional
        The character used to denote the start and end of a quoted item.
        Occurrences of the delimiter or comment characters are ignored within
        a quoted item. The default value is ``quotechar=None``, which means
        quoting support is disabled.

        If two consecutive instances of `quotechar` are found within a quoted
        field, the first is treated as an escape character. See examples.

        .. versionadded:: 1.23.0
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    out : ndarray
        Data read from the text file.

    See Also
    --------
    load, fromstring, fromregex
    genfromtxt : Load data with missing values handled as specified.
    scipy.io.loadmat : reads MATLAB data files

    Notes
    -----
    This function aims to be a fast reader for simply formatted files.  The
    `genfromtxt` function provides more sophisticated handling of, e.g.,
    lines with missing values.

    Each row in the input text file must have the same number of values to be
    able to read all values. If all rows do not have same number of values, a
    subset of up to n columns (where n is the least number of values present
    in all rows) can be read by specifying the columns via `usecols`.

    .. versionadded:: 1.10.0

    The strings produced by the Python float.hex method can be used as
    input for floats.

    Examples
    --------
    >>> import numpy as np
    >>> from io import StringIO   # StringIO behaves like a file object
    >>> c = StringIO("0 1\n2 3")
    >>> np.loadtxt(c)
    array([[0., 1.],
           [2., 3.]])

    >>> d = StringIO("M 21 72\nF 35 58")
    >>> np.loadtxt(d, dtype={'names': ('gender', 'age', 'weight'),
    ...                      'formats': ('S1', 'i4', 'f4')})
    array([(b'M', 21, 72.), (b'F', 35, 58.)],
          dtype=[('gender', 'S1'), ('age', '<i4'), ('weight', '<f4')])

    >>> c = StringIO("1,0,2\n3,0,4")
    >>> x, y = np.loadtxt(c, delimiter=',', usecols=(0, 2), unpack=True)
    >>> x
    array([1., 3.])
    >>> y
    array([2., 4.])

    The `converters` argument is used to specify functions to preprocess the
    text prior to parsing. `converters` can be a dictionary that maps
    preprocessing functions to each column:

    >>> s = StringIO("1.618, 2.296\n3.141, 4.669\n")
    >>> conv = {
    ...     0: lambda x: np.floor(float(x)),  # conversion fn for column 0
    ...     1: lambda x: np.ceil(float(x)),  # conversion fn for column 1
    ... }
    >>> np.loadtxt(s, delimiter=",", converters=conv)
    array([[1., 3.],
           [3., 5.]])

    `converters` can be a callable instead of a dictionary, in which case it
    is applied to all columns:

    >>> s = StringIO("0xDE 0xAD\n0xC0 0xDE")
    >>> import functools
    >>> conv = functools.partial(int, base=16)
    >>> np.loadtxt(s, converters=conv)
    array([[222., 173.],
           [192., 222.]])

    This example shows how `converters` can be used to convert a field
    with a trailing minus sign into a negative number.

    >>> s = StringIO("10.01 31.25-\n19.22 64.31\n17.57- 63.94")
    >>> def conv(fld):
    ...     return -float(fld[:-1]) if fld.endswith("-") else float(fld)
    ...
    >>> np.loadtxt(s, converters=conv)
    array([[ 10.01, -31.25],
           [ 19.22,  64.31],
           [-17.57,  63.94]])

    Using a callable as the converter can be particularly useful for handling
    values with different formatting, e.g. floats with underscores:

    >>> s = StringIO("1 2.7 100_000")
    >>> np.loadtxt(s, converters=float)
    array([1.e+00, 2.7e+00, 1.e+05])

    This idea can be extended to automatically handle values specified in
    many different formats, such as hex values:

    >>> def conv(val):
    ...     try:
    ...         return float(val)
    ...     except ValueError:
    ...         return float.fromhex(val)
    >>> s = StringIO("1, 2.5, 3_000, 0b4, 0x1.4000000000000p+2")
    >>> np.loadtxt(s, delimiter=",", converters=conv)
    array([1.0e+00, 2.5e+00, 3.0e+03, 1.8e+02, 5.0e+00])

    Or a format where the ``-`` sign comes after the number:

    >>> s = StringIO("10.01 31.25-\n19.22 64.31\n17.57- 63.94")
    >>> conv = lambda x: -float(x[:-1]) if x.endswith("-") else float(x)
    >>> np.loadtxt(s, converters=conv)
    array([[ 10.01, -31.25],
           [ 19.22,  64.31],
           [-17.57,  63.94]])

    Support for quoted fields is enabled with the `quotechar` parameter.
    Comment and delimiter characters are ignored when they appear within a
    quoted item delineated by `quotechar`:

    >>> s = StringIO('"alpha, #42", 10.0\n"beta, #64", 2.0\n')
    >>> dtype = np.dtype([("label", "U12"), ("value", float)])
    >>> np.loadtxt(s, dtype=dtype, delimiter=",", quotechar='"')
    array([('alpha, #42', 10.), ('beta, #64',  2.)],
          dtype=[('label', '<U12'), ('value', '<f8')])

    Quoted fields can be separated by multiple whitespace characters:

    >>> s = StringIO('"alpha, #42"       10.0\n"beta, #64" 2.0\n')
    >>> dtype = np.dtype([("label", "U12"), ("value", float)])
    >>> np.loadtxt(s, dtype=dtype, delimiter=None, quotechar='"')
    array([('alpha, #42', 10.), ('beta, #64',  2.)],
          dtype=[('label', '<U12'), ('value', '<f8')])

    Two consecutive quote characters within a quoted field are treated as a
    single escaped character:

    >>> s = StringIO('"Hello, my name is ""Monty""!"')
    >>> np.loadtxt(s, dtype="U", delimiter=",", quotechar='"')
    array('Hello, my name is "Monty"!', dtype='<U26')

    Read subset of columns when all rows do not contain equal number of values:

    >>> d = StringIO("1 2\n2 4\n3 9 12\n4 16 20")
    >>> np.loadtxt(d, usecols=(0, 1))
    array([[ 1.,  2.],
           [ 2.,  4.],
           [ 3.,  9.],
           [ 4., 16.]])

Python Library Documentation: function log in module autograd.tracer

log(*args, called_by_autograd_dispatcher=False, **kwargs)
    log(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Natural logarithm, element-wise.

    The natural logarithm `log` is the inverse of the exponential function,
    so that `log(exp(x)) = x`. The natural logarithm is logarithm in base
    `e`.

    Parameters
    ----------
    x : array_like
        Input value.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The natural logarithm of `x`, element-wise.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    log10, log2, log1p, emath.log

    Notes
    -----
    Logarithm is a multivalued function: for each `x` there is an infinite
    number of `z` such that `exp(z) = x`. The convention is to return the
    `z` whose imaginary part lies in `(-pi, pi]`.

    For real-valued input data types, `log` always returns real output. For
    each value that cannot be expressed as a real number or infinity, it
    yields ``nan`` and sets the `invalid` floating point error flag.

    For complex-valued input, `log` is a complex analytical function that
    has a branch cut `[-inf, 0]` and is continuous from above on it. `log`
    handles the floating-point negative zero as an infinitesimal negative
    number, conforming to the C99 standard.

    In the cases where the input has a negative real part and a very small
    negative complex part (approaching 0), the result is so close to `-pi`
    that it evaluates to exactly `-pi`.

    References
    ----------
    .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions",
           10th printing, 1964, pp. 67.
           https://personal.math.ubc.ca/~cbm/aands/page_67.htm
    .. [2] Wikipedia, "Logarithm". https://en.wikipedia.org/wiki/Logarithm

    Examples
    --------
    >>> import numpy as np
    >>> np.log([1, np.e, np.e**2, 0])
    array([  0.,   1.,   2., -inf])

Python Library Documentation: function log10 in module autograd.tracer

log10(*args, called_by_autograd_dispatcher=False, **kwargs)
    log10(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the base 10 logarithm of the input array, element-wise.

    Parameters
    ----------
    x : array_like
        Input values.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The logarithm to the base 10 of `x`, element-wise. NaNs are
        returned where x is negative.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    emath.log10

    Notes
    -----
    Logarithm is a multivalued function: for each `x` there is an infinite
    number of `z` such that `10**z = x`. The convention is to return the
    `z` whose imaginary part lies in `(-pi, pi]`.

    For real-valued input data types, `log10` always returns real output.
    For each value that cannot be expressed as a real number or infinity,
    it yields ``nan`` and sets the `invalid` floating point error flag.

    For complex-valued input, `log10` is a complex analytical function that
    has a branch cut `[-inf, 0]` and is continuous from above on it.
    `log10` handles the floating-point negative zero as an infinitesimal
    negative number, conforming to the C99 standard.

    In the cases where the input has a negative real part and a very small
    negative complex part (approaching 0), the result is so close to `-pi`
    that it evaluates to exactly `-pi`.

    References
    ----------
    .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions",
           10th printing, 1964, pp. 67.
           https://personal.math.ubc.ca/~cbm/aands/page_67.htm
    .. [2] Wikipedia, "Logarithm". https://en.wikipedia.org/wiki/Logarithm

    Examples
    --------
    >>> import numpy as np
    >>> np.log10([1e-15, -3.])
    array([-15.,  nan])

Python Library Documentation: function log1p in module autograd.tracer

log1p(*args, called_by_autograd_dispatcher=False, **kwargs)
    log1p(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the natural logarithm of one plus the input array, element-wise.

    Calculates ``log(1 + x)``.

    Parameters
    ----------
    x : array_like
        Input values.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        Natural logarithm of `1 + x`, element-wise.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    expm1 : ``exp(x) - 1``, the inverse of `log1p`.

    Notes
    -----
    For real-valued input, `log1p` is accurate also for `x` so small
    that `1 + x == 1` in floating-point accuracy.

    Logarithm is a multivalued function: for each `x` there is an infinite
    number of `z` such that `exp(z) = 1 + x`. The convention is to return
    the `z` whose imaginary part lies in `[-pi, pi]`.

    For real-valued input data types, `log1p` always returns real output.
    For each value that cannot be expressed as a real number or infinity,
    it yields ``nan`` and sets the `invalid` floating point error flag.

    For complex-valued input, `log1p` is a complex analytical function that
    has a branch cut `[-inf, -1]` and is continuous from above on it.
    `log1p` handles the floating-point negative zero as an infinitesimal
    negative number, conforming to the C99 standard.

    References
    ----------
    .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions",
           10th printing, 1964, pp. 67.
           https://personal.math.ubc.ca/~cbm/aands/page_67.htm
    .. [2] Wikipedia, "Logarithm". https://en.wikipedia.org/wiki/Logarithm

    Examples
    --------
    >>> import numpy as np
    >>> np.log1p(1e-99)
    1e-99
    >>> np.log(1 + 1e-99)
    0.0

Python Library Documentation: function log2 in module autograd.tracer

log2(*args, called_by_autograd_dispatcher=False, **kwargs)
    log2(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Base-2 logarithm of `x`.

    Parameters
    ----------
    x : array_like
        Input values.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        Base-2 logarithm of `x`.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    log, log10, log1p, emath.log2

    Notes
    -----
    .. versionadded:: 1.3.0

    Logarithm is a multivalued function: for each `x` there is an infinite
    number of `z` such that `2**z = x`. The convention is to return the `z`
    whose imaginary part lies in `(-pi, pi]`.

    For real-valued input data types, `log2` always returns real output.
    For each value that cannot be expressed as a real number or infinity,
    it yields ``nan`` and sets the `invalid` floating point error flag.

    For complex-valued input, `log2` is a complex analytical function that
    has a branch cut `[-inf, 0]` and is continuous from above on it. `log2`
    handles the floating-point negative zero as an infinitesimal negative
    number, conforming to the C99 standard.

    In the cases where the input has a negative real part and a very small
    negative complex part (approaching 0), the result is so close to `-pi`
    that it evaluates to exactly `-pi`.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([0, 1, 2, 2**4])
    >>> np.log2(x)
    array([-inf,   0.,   1.,   4.])

    >>> xi = np.array([0+1.j, 1, 2+0.j, 4.j])
    >>> np.log2(xi)
    array([ 0.+2.26618007j,  0.+0.j        ,  1.+0.j        ,  2.+2.26618007j])

Python Library Documentation: function logaddexp in module autograd.tracer

logaddexp(*args, called_by_autograd_dispatcher=False, **kwargs)
    logaddexp(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Logarithm of the sum of exponentiations of the inputs.

    Calculates ``log(exp(x1) + exp(x2))``. This function is useful in
    statistics where the calculated probabilities of events may be so small
    as to exceed the range of normal floating point numbers.  In such cases
    the logarithm of the calculated probability is stored. This function
    allows adding probabilities stored in such a fashion.

    Parameters
    ----------
    x1, x2 : array_like
        Input values.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    result : ndarray
        Logarithm of ``exp(x1) + exp(x2)``.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    logaddexp2: Logarithm of the sum of exponentiations of inputs in base 2.

    Notes
    -----
    .. versionadded:: 1.3.0

    Examples
    --------
    >>> import numpy as np
    >>> prob1 = np.log(1e-50)
    >>> prob2 = np.log(2.5e-50)
    >>> prob12 = np.logaddexp(prob1, prob2)
    >>> prob12
    -113.87649168120691
    >>> np.exp(prob12)
    3.5000000000000057e-50

Python Library Documentation: function logaddexp2 in module autograd.tracer

logaddexp2(*args, called_by_autograd_dispatcher=False, **kwargs)
    logaddexp2(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Logarithm of the sum of exponentiations of the inputs in base-2.

    Calculates ``log2(2**x1 + 2**x2)``. This function is useful in machine
    learning when the calculated probabilities of events may be so small as
    to exceed the range of normal floating point numbers.  In such cases
    the base-2 logarithm of the calculated probability can be used instead.
    This function allows adding probabilities stored in such a fashion.

    Parameters
    ----------
    x1, x2 : array_like
        Input values.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    result : ndarray
        Base-2 logarithm of ``2**x1 + 2**x2``.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    logaddexp: Logarithm of the sum of exponentiations of the inputs.

    Notes
    -----
    .. versionadded:: 1.3.0

    Examples
    --------
    >>> import numpy as np
    >>> prob1 = np.log2(1e-50)
    >>> prob2 = np.log2(2.5e-50)
    >>> prob12 = np.logaddexp2(prob1, prob2)
    >>> prob1, prob2, prob12
    (-166.09640474436813, -164.77447664948076, -164.28904982231052)
    >>> 2**prob12
    3.4999999999999914e-50

Python Library Documentation: function logical_and in module autograd.tracer

logical_and(*args, called_by_autograd_dispatcher=False, **kwargs)
    logical_and(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Compute the truth value of x1 AND x2 element-wise.

    Parameters
    ----------
    x1, x2 : array_like
        Input arrays.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray or bool
        Boolean result of the logical AND operation applied to the elements
        of `x1` and `x2`; the shape is determined by broadcasting.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    logical_or, logical_not, logical_xor
    bitwise_and

    Examples
    --------
    >>> import numpy as np
    >>> np.logical_and(True, False)
    False
    >>> np.logical_and([True, False], [False, False])
    array([False, False])

    >>> x = np.arange(5)
    >>> np.logical_and(x>1, x<4)
    array([False, False,  True,  True, False])


    The ``&`` operator can be used as a shorthand for ``np.logical_and`` on
    boolean ndarrays.

    >>> a = np.array([True, False])
    >>> b = np.array([False, False])
    >>> a & b
    array([False, False])

Python Library Documentation: function logical_not in module autograd.tracer

logical_not(*args, called_by_autograd_dispatcher=False, **kwargs)
    logical_not(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Compute the truth value of NOT x element-wise.

    Parameters
    ----------
    x : array_like
        Logical NOT is applied to the elements of `x`.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : bool or ndarray of bool
        Boolean result with the same shape as `x` of the NOT operation
        on elements of `x`.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    logical_and, logical_or, logical_xor

    Examples
    --------
    >>> import numpy as np
    >>> np.logical_not(3)
    False
    >>> np.logical_not([True, False, 0, 1])
    array([False,  True,  True, False])

    >>> x = np.arange(5)
    >>> np.logical_not(x<3)
    array([False, False, False,  True,  True])

Python Library Documentation: function logical_or in module autograd.tracer

logical_or(*args, called_by_autograd_dispatcher=False, **kwargs)
    logical_or(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Compute the truth value of x1 OR x2 element-wise.

    Parameters
    ----------
    x1, x2 : array_like
        Logical OR is applied to the elements of `x1` and `x2`.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray or bool
        Boolean result of the logical OR operation applied to the elements
        of `x1` and `x2`; the shape is determined by broadcasting.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    logical_and, logical_not, logical_xor
    bitwise_or

    Examples
    --------
    >>> import numpy as np
    >>> np.logical_or(True, False)
    True
    >>> np.logical_or([True, False], [False, False])
    array([ True, False])

    >>> x = np.arange(5)
    >>> np.logical_or(x < 1, x > 3)
    array([ True, False, False, False,  True])

    The ``|`` operator can be used as a shorthand for ``np.logical_or`` on
    boolean ndarrays.

    >>> a = np.array([True, False])
    >>> b = np.array([False, False])
    >>> a | b
    array([ True, False])

Python Library Documentation: function logical_xor in module autograd.tracer

logical_xor(*args, called_by_autograd_dispatcher=False, **kwargs)
    logical_xor(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Compute the truth value of x1 XOR x2, element-wise.

    Parameters
    ----------
    x1, x2 : array_like
        Logical XOR is applied to the elements of `x1` and `x2`.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : bool or ndarray of bool
        Boolean result of the logical XOR operation applied to the elements
        of `x1` and `x2`; the shape is determined by broadcasting.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    logical_and, logical_or, logical_not, bitwise_xor

    Examples
    --------
    >>> import numpy as np
    >>> np.logical_xor(True, False)
    True
    >>> np.logical_xor([True, True, False, False], [True, False, True, False])
    array([False,  True,  True, False])

    >>> x = np.arange(5)
    >>> np.logical_xor(x < 1, x > 3)
    array([ True, False, False, False,  True])

    Simple example showing support of broadcasting

    >>> np.logical_xor(0, np.eye(2))
    array([[ True, False],
           [False,  True]])

Python Library Documentation: function logspace in module autograd.tracer

logspace(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return numbers spaced evenly on a log scale.

    In linear space, the sequence starts at ``base ** start``
    (`base` to the power of `start`) and ends with ``base ** stop``
    (see `endpoint` below).

    .. versionchanged:: 1.16.0
        Non-scalar `start` and `stop` are now supported.

    .. versionchanged:: 1.25.0
        Non-scalar 'base` is now supported

    Parameters
    ----------
    start : array_like
        ``base ** start`` is the starting value of the sequence.
    stop : array_like
        ``base ** stop`` is the final value of the sequence, unless `endpoint`
        is False.  In that case, ``num + 1`` values are spaced over the
        interval in log-space, of which all but the last (a sequence of
        length `num`) are returned.
    num : integer, optional
        Number of samples to generate.  Default is 50.
    endpoint : boolean, optional
        If true, `stop` is the last sample. Otherwise, it is not included.
        Default is True.
    base : array_like, optional
        The base of the log space. The step size between the elements in
        ``ln(samples) / ln(base)`` (or ``log_base(samples)``) is uniform.
        Default is 10.0.
    dtype : dtype
        The type of the output array.  If `dtype` is not given, the data type
        is inferred from `start` and `stop`. The inferred type will never be
        an integer; `float` is chosen even if the arguments would produce an
        array of integers.
    axis : int, optional
        The axis in the result to store the samples.  Relevant only if start,
        stop, or base are array-like.  By default (0), the samples will be
        along a new axis inserted at the beginning. Use -1 to get an axis at
        the end.

        .. versionadded:: 1.16.0


    Returns
    -------
    samples : ndarray
        `num` samples, equally spaced on a log scale.

    See Also
    --------
    arange : Similar to linspace, with the step size specified instead of the
             number of samples. Note that, when used with a float endpoint, the
             endpoint may or may not be included.
    linspace : Similar to logspace, but with the samples uniformly distributed
               in linear space, instead of log space.
    geomspace : Similar to logspace, but with endpoints specified directly.
    :ref:`how-to-partition`

    Notes
    -----
    If base is a scalar, logspace is equivalent to the code

    >>> y = np.linspace(start, stop, num=num, endpoint=endpoint)
    ... # doctest: +SKIP
    >>> power(base, y).astype(dtype)
    ... # doctest: +SKIP

    Examples
    --------
    >>> import numpy as np
    >>> np.logspace(2.0, 3.0, num=4)
    array([ 100.        ,  215.443469  ,  464.15888336, 1000.        ])
    >>> np.logspace(2.0, 3.0, num=4, endpoint=False)
    array([100.        ,  177.827941  ,  316.22776602,  562.34132519])
    >>> np.logspace(2.0, 3.0, num=4, base=2.0)
    array([4.        ,  5.0396842 ,  6.34960421,  8.        ])
    >>> np.logspace(2.0, 3.0, num=4, base=[2.0, 3.0], axis=-1)
    array([[ 4.        ,  5.0396842 ,  6.34960421,  8.        ],
           [ 9.        , 12.98024613, 18.72075441, 27.        ]])

    Graphical illustration:

    >>> import matplotlib.pyplot as plt
    >>> N = 10
    >>> x1 = np.logspace(0.1, 1, N, endpoint=True)
    >>> x2 = np.logspace(0.1, 1, N, endpoint=False)
    >>> y = np.zeros(N)
    >>> plt.plot(x1, y, 'o')
    [<matplotlib.lines.Line2D object at 0x...>]
    >>> plt.plot(x2, y + 0.5, 'o')
    [<matplotlib.lines.Line2D object at 0x...>]
    >>> plt.ylim([-0.5, 1])
    (-0.5, 1)
    >>> plt.show()

Python Library Documentation: class IntdtypeSubclass in module autograd.numpy.numpy_wrapper

class IntdtypeSubclass(numpy.int32)
 |  IntdtypeSubclass(*args, **kwargs)
 |
 |  Method resolution order:
 |      IntdtypeSubclass
 |      numpy.int32
 |      numpy.signedinteger
 |      numpy.integer
 |      numpy.number
 |      numpy.generic
 |      builtins.object
 |
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs) from autograd.tracer.notrace_primitive.<locals>
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.int32:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      int32.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.int32(127).bit_count()
 |      7
 |      >>> np.int32(-127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from numpy.int32:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class longdouble in module numpy

class longdouble(floating)
 |  Extended-precision floating-point number type, compatible with C
 |  ``long double`` but not necessarily with IEEE 754 quadruple-precision.
 |
 |  :Character code: ``'g'``
 |
 |  Method resolution order:
 |      longdouble
 |      floating
 |      inexact
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  as_integer_ratio(...)
 |      longdouble.as_integer_ratio() -> (int, int)
 |
 |      Return a pair of integers, whose ratio is exactly equal to the original
 |      floating point number, and with a positive denominator.
 |      Raise `OverflowError` on infinities and a `ValueError` on NaNs.
 |
 |      >>> np.longdouble(10.0).as_integer_ratio()
 |      (10, 1)
 |      >>> np.longdouble(0.0).as_integer_ratio()
 |      (0, 1)
 |      >>> np.longdouble(-.25).as_integer_ratio()
 |      (-1, 4)
 |
 |  is_integer(...)
 |      longdouble.is_integer() -> bool
 |
 |      Return ``True`` if the floating point number is finite with integral
 |      value, and ``False`` otherwise.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> np.longdouble(-2.0).is_integer()
 |      True
 |      >>> np.longdouble(3.2).is_integer()
 |      False
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from floating:
 |
 |  __round__(...)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class IntdtypeSubclass in module autograd.numpy.numpy_wrapper

class IntdtypeSubclass(numpy.int64)
 |  IntdtypeSubclass(*args, **kwargs)
 |
 |  Method resolution order:
 |      IntdtypeSubclass
 |      numpy.int64
 |      numpy.signedinteger
 |      numpy.integer
 |      numpy.number
 |      numpy.generic
 |      builtins.object
 |
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs) from autograd.tracer.notrace_primitive.<locals>
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.int64:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      int64.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.int64(127).bit_count()
 |      7
 |      >>> np.int64(-127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from numpy.int64:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: function make_diagonal in module autograd.tracer

make_diagonal(*args, called_by_autograd_dispatcher=False, **kwargs)
    None

Python Library Documentation: function mask_indices in module autograd.tracer

mask_indices(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the indices to access (n, n) arrays, given a masking function.

    Assume `mask_func` is a function that, for a square array a of size
    ``(n, n)`` with a possible offset argument `k`, when called as
    ``mask_func(a, k)`` returns a new array with zeros in certain locations
    (functions like `triu` or `tril` do precisely this). Then this function
    returns the indices where the non-zero values would be located.

    Parameters
    ----------
    n : int
        The returned indices will be valid to access arrays of shape (n, n).
    mask_func : callable
        A function whose call signature is similar to that of `triu`, `tril`.
        That is, ``mask_func(x, k)`` returns a boolean array, shaped like `x`.
        `k` is an optional argument to the function.
    k : scalar
        An optional argument which is passed through to `mask_func`. Functions
        like `triu`, `tril` take a second argument that is interpreted as an
        offset.

    Returns
    -------
    indices : tuple of arrays.
        The `n` arrays of indices corresponding to the locations where
        ``mask_func(np.ones((n, n)), k)`` is True.

    See Also
    --------
    triu, tril, triu_indices, tril_indices

    Notes
    -----
    .. versionadded:: 1.4.0

    Examples
    --------
    >>> import numpy as np

    These are the indices that would allow you to access the upper triangular
    part of any 3x3 array:

    >>> iu = np.mask_indices(3, np.triu)

    For example, if `a` is a 3x3 array:

    >>> a = np.arange(9).reshape(3, 3)
    >>> a
    array([[0, 1, 2],
           [3, 4, 5],
           [6, 7, 8]])
    >>> a[iu]
    array([0, 1, 2, 4, 5, 8])

    An offset can be passed also to the masking function.  This gets us the
    indices starting on the first diagonal right of the main one:

    >>> iu1 = np.mask_indices(3, np.triu, 1)

    with which we now extract only three elements:

    >>> a[iu1]
    array([1, 2, 5])

Python Library Documentation: function matmul in module autograd.tracer

matmul(*args, called_by_autograd_dispatcher=False, **kwargs)
    matmul(x1, x2, /, out=None, *, casting='same_kind', order='K', dtype=None, subok=True[, signature, axes, axis])

    Matrix product of two arrays.

    Parameters
    ----------
    x1, x2 : array_like
        Input arrays, scalars not allowed.
    out : ndarray, optional
        A location into which the result is stored. If provided, it must have
        a shape that matches the signature `(n,k),(k,m)->(n,m)`. If not
        provided or None, a freshly-allocated array is returned.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

        .. versionadded:: 1.16
           Now handles ufunc kwargs

    Returns
    -------
    y : ndarray
        The matrix product of the inputs.
        This is a scalar only when both x1, x2 are 1-d vectors.

    Raises
    ------
    ValueError
        If the last dimension of `x1` is not the same size as
        the second-to-last dimension of `x2`.

        If a scalar value is passed in.

    See Also
    --------
    vdot : Complex-conjugating dot product.
    tensordot : Sum products over arbitrary axes.
    einsum : Einstein summation convention.
    dot : alternative matrix product with different broadcasting rules.

    Notes
    -----

    The behavior depends on the arguments in the following way.

    - If both arguments are 2-D they are multiplied like conventional
      matrices.
    - If either argument is N-D, N > 2, it is treated as a stack of
      matrices residing in the last two indexes and broadcast accordingly.
    - If the first argument is 1-D, it is promoted to a matrix by
      prepending a 1 to its dimensions. After matrix multiplication
      the prepended 1 is removed.
    - If the second argument is 1-D, it is promoted to a matrix by
      appending a 1 to its dimensions. After matrix multiplication
      the appended 1 is removed.

    ``matmul`` differs from ``dot`` in two important ways:

    - Multiplication by scalars is not allowed, use ``*`` instead.
    - Stacks of matrices are broadcast together as if the matrices
      were elements, respecting the signature ``(n,k),(k,m)->(n,m)``:

      >>> a = np.ones([9, 5, 7, 4])
      >>> c = np.ones([9, 5, 4, 3])
      >>> np.dot(a, c).shape
      (9, 5, 7, 9, 5, 3)
      >>> np.matmul(a, c).shape
      (9, 5, 7, 3)
      >>> # n is 7, k is 4, m is 3

    The matmul function implements the semantics of the ``@`` operator
    introduced in Python 3.5 following :pep:`465`.

    It uses an optimized BLAS library when possible (see `numpy.linalg`).

    Examples
    --------
    For 2-D arrays it is the matrix product:

    >>> import numpy as np

    >>> a = np.array([[1, 0],
    ...               [0, 1]])
    >>> b = np.array([[4, 1],
    ...               [2, 2]])
    >>> np.matmul(a, b)
    array([[4, 1],
           [2, 2]])

    For 2-D mixed with 1-D, the result is the usual.

    >>> a = np.array([[1, 0],
    ...               [0, 1]])
    >>> b = np.array([1, 2])
    >>> np.matmul(a, b)
    array([1, 2])
    >>> np.matmul(b, a)
    array([1, 2])


    Broadcasting is conventional for stacks of arrays

    >>> a = np.arange(2 * 2 * 4).reshape((2, 2, 4))
    >>> b = np.arange(2 * 2 * 4).reshape((2, 4, 2))
    >>> np.matmul(a,b).shape
    (2, 2, 2)
    >>> np.matmul(a, b)[0, 1, 1]
    98
    >>> sum(a[0, 1, :] * b[0 , :, 1])
    98

    Vector, vector returns the scalar inner product, but neither argument
    is complex-conjugated:

    >>> np.matmul([2j, 3j], [2j, 3j])
    (-13+0j)

    Scalar multiplication raises an error.

    >>> np.matmul([1,2], 3)
    Traceback (most recent call last):
    ...
    ValueError: matmul: Input operand 1 does not have enough dimensions ...

    The ``@`` operator can be used as a shorthand for ``np.matmul`` on
    ndarrays.

    >>> x1 = np.array([2j, 3j])
    >>> x2 = np.array([2j, 3j])
    >>> x1 @ x2
    (-13+0j)

    .. versionadded:: 1.10.0

Python Library Documentation: class matrix in module numpy

class matrix(ndarray)
 |  matrix(data, dtype=None, copy=True)
 |
 |  matrix(data, dtype=None, copy=True)
 |
 |  Returns a matrix from an array-like object, or from a string of data.
 |
 |  A matrix is a specialized 2-D array that retains its 2-D nature
 |  through operations.  It has certain special operators, such as ``*``
 |  (matrix multiplication) and ``**`` (matrix power).
 |
 |  .. note:: It is no longer recommended to use this class, even for linear
 |            algebra. Instead use regular arrays. The class may be removed
 |            in the future.
 |
 |  Parameters
 |  ----------
 |  data : array_like or string
 |     If `data` is a string, it is interpreted as a matrix with commas
 |     or spaces separating columns, and semicolons separating rows.
 |  dtype : data-type
 |     Data-type of the output matrix.
 |  copy : bool
 |     If `data` is already an `ndarray`, then this flag determines
 |     whether the data is copied (the default), or whether a view is
 |     constructed.
 |
 |  See Also
 |  --------
 |  array
 |
 |  Examples
 |  --------
 |  >>> import numpy as np
 |  >>> a = np.matrix('1 2; 3 4')
 |  >>> a
 |  matrix([[1, 2],
 |          [3, 4]])
 |
 |  >>> np.matrix([[1, 2], [3, 4]])
 |  matrix([[1, 2],
 |          [3, 4]])
 |
 |  Method resolution order:
 |      matrix
 |      ndarray
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __array_finalize__(self, obj) from numpy.matrixlib.defmatrix.matrix
 |      a.__array_finalize__(obj, /)
 |
 |      Present so subclasses can call super. Does nothing.
 |
 |  __getitem__(self, index) from numpy.matrixlib.defmatrix.matrix
 |      Return self[key].
 |
 |  __imul__(self, other) from numpy.matrixlib.defmatrix.matrix
 |      Return self*=value.
 |
 |  __ipow__(self, other) from numpy.matrixlib.defmatrix.matrix
 |      Return self**=value.
 |
 |  __mul__(self, other) from numpy.matrixlib.defmatrix.matrix
 |      Return self*value.
 |
 |  __pow__(self, other) from numpy.matrixlib.defmatrix.matrix
 |      Return pow(self, value, mod).
 |
 |  __rmul__(self, other) from numpy.matrixlib.defmatrix.matrix
 |      Return value*self.
 |
 |  __rpow__(self, other) from numpy.matrixlib.defmatrix.matrix
 |      Return pow(value, self, mod).
 |
 |  all(self, axis=None, out=None) from numpy.matrixlib.defmatrix.matrix
 |      Test whether all matrix elements along a given axis evaluate to True.
 |
 |      Parameters
 |      ----------
 |      See `numpy.all` for complete descriptions
 |
 |      See Also
 |      --------
 |      numpy.all
 |
 |      Notes
 |      -----
 |      This is the same as `ndarray.all`, but it returns a `matrix` object.
 |
 |      Examples
 |      --------
 |      >>> x = np.matrix(np.arange(12).reshape((3,4))); x
 |      matrix([[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]])
 |      >>> y = x[0]; y
 |      matrix([[0, 1, 2, 3]])
 |      >>> (x == y)
 |      matrix([[ True,  True,  True,  True],
 |              [False, False, False, False],
 |              [False, False, False, False]])
 |      >>> (x == y).all()
 |      False
 |      >>> (x == y).all(0)
 |      matrix([[False, False, False, False]])
 |      >>> (x == y).all(1)
 |      matrix([[ True],
 |              [False],
 |              [False]])
 |
 |  any(self, axis=None, out=None) from numpy.matrixlib.defmatrix.matrix
 |      Test whether any array element along a given axis evaluates to True.
 |
 |      Refer to `numpy.any` for full documentation.
 |
 |      Parameters
 |      ----------
 |      axis : int, optional
 |          Axis along which logical OR is performed
 |      out : ndarray, optional
 |          Output to existing array instead of creating new one, must have
 |          same shape as expected output
 |
 |      Returns
 |      -------
 |          any : bool, ndarray
 |              Returns a single bool if `axis` is ``None``; otherwise,
 |              returns `ndarray`
 |
 |  argmax(self, axis=None, out=None) from numpy.matrixlib.defmatrix.matrix
 |      Indexes of the maximum values along an axis.
 |
 |      Return the indexes of the first occurrences of the maximum values
 |      along the specified axis.  If axis is None, the index is for the
 |      flattened matrix.
 |
 |      Parameters
 |      ----------
 |      See `numpy.argmax` for complete descriptions
 |
 |      See Also
 |      --------
 |      numpy.argmax
 |
 |      Notes
 |      -----
 |      This is the same as `ndarray.argmax`, but returns a `matrix` object
 |      where `ndarray.argmax` would return an `ndarray`.
 |
 |      Examples
 |      --------
 |      >>> x = np.matrix(np.arange(12).reshape((3,4))); x
 |      matrix([[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]])
 |      >>> x.argmax()
 |      11
 |      >>> x.argmax(0)
 |      matrix([[2, 2, 2, 2]])
 |      >>> x.argmax(1)
 |      matrix([[3],
 |              [3],
 |              [3]])
 |
 |  argmin(self, axis=None, out=None) from numpy.matrixlib.defmatrix.matrix
 |      Indexes of the minimum values along an axis.
 |
 |      Return the indexes of the first occurrences of the minimum values
 |      along the specified axis.  If axis is None, the index is for the
 |      flattened matrix.
 |
 |      Parameters
 |      ----------
 |      See `numpy.argmin` for complete descriptions.
 |
 |      See Also
 |      --------
 |      numpy.argmin
 |
 |      Notes
 |      -----
 |      This is the same as `ndarray.argmin`, but returns a `matrix` object
 |      where `ndarray.argmin` would return an `ndarray`.
 |
 |      Examples
 |      --------
 |      >>> x = -np.matrix(np.arange(12).reshape((3,4))); x
 |      matrix([[  0,  -1,  -2,  -3],
 |              [ -4,  -5,  -6,  -7],
 |              [ -8,  -9, -10, -11]])
 |      >>> x.argmin()
 |      11
 |      >>> x.argmin(0)
 |      matrix([[2, 2, 2, 2]])
 |      >>> x.argmin(1)
 |      matrix([[3],
 |              [3],
 |              [3]])
 |
 |  flatten(self, order='C') from numpy.matrixlib.defmatrix.matrix
 |      Return a flattened copy of the matrix.
 |
 |      All `N` elements of the matrix are placed into a single row.
 |
 |      Parameters
 |      ----------
 |      order : {'C', 'F', 'A', 'K'}, optional
 |          'C' means to flatten in row-major (C-style) order. 'F' means to
 |          flatten in column-major (Fortran-style) order. 'A' means to
 |          flatten in column-major order if `m` is Fortran *contiguous* in
 |          memory, row-major order otherwise. 'K' means to flatten `m` in
 |          the order the elements occur in memory. The default is 'C'.
 |
 |      Returns
 |      -------
 |      y : matrix
 |          A copy of the matrix, flattened to a `(1, N)` matrix where `N`
 |          is the number of elements in the original matrix.
 |
 |      See Also
 |      --------
 |      ravel : Return a flattened array.
 |      flat : A 1-D flat iterator over the matrix.
 |
 |      Examples
 |      --------
 |      >>> m = np.matrix([[1,2], [3,4]])
 |      >>> m.flatten()
 |      matrix([[1, 2, 3, 4]])
 |      >>> m.flatten('F')
 |      matrix([[1, 3, 2, 4]])
 |
 |  getA = A(self) from numpy.matrixlib.defmatrix.matrix
 |      Return `self` as an `ndarray` object.
 |
 |      Equivalent to ``np.asarray(self)``.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      ret : ndarray
 |          `self` as an `ndarray`
 |
 |      Examples
 |      --------
 |      >>> x = np.matrix(np.arange(12).reshape((3,4))); x
 |      matrix([[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]])
 |      >>> x.getA()
 |      array([[ 0,  1,  2,  3],
 |             [ 4,  5,  6,  7],
 |             [ 8,  9, 10, 11]])
 |
 |  getA1 = A1(self) from numpy.matrixlib.defmatrix.matrix
 |      Return `self` as a flattened `ndarray`.
 |
 |      Equivalent to ``np.asarray(x).ravel()``
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      ret : ndarray
 |          `self`, 1-D, as an `ndarray`
 |
 |      Examples
 |      --------
 |      >>> x = np.matrix(np.arange(12).reshape((3,4))); x
 |      matrix([[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]])
 |      >>> x.getA1()
 |      array([ 0,  1,  2, ...,  9, 10, 11])
 |
 |  getH = H(self) from numpy.matrixlib.defmatrix.matrix
 |      Returns the (complex) conjugate transpose of `self`.
 |
 |      Equivalent to ``np.transpose(self)`` if `self` is real-valued.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      ret : matrix object
 |          complex conjugate transpose of `self`
 |
 |      Examples
 |      --------
 |      >>> x = np.matrix(np.arange(12).reshape((3,4)))
 |      >>> z = x - 1j*x; z
 |      matrix([[  0. +0.j,   1. -1.j,   2. -2.j,   3. -3.j],
 |              [  4. -4.j,   5. -5.j,   6. -6.j,   7. -7.j],
 |              [  8. -8.j,   9. -9.j,  10.-10.j,  11.-11.j]])
 |      >>> z.getH()
 |      matrix([[ 0. -0.j,  4. +4.j,  8. +8.j],
 |              [ 1. +1.j,  5. +5.j,  9. +9.j],
 |              [ 2. +2.j,  6. +6.j, 10.+10.j],
 |              [ 3. +3.j,  7. +7.j, 11.+11.j]])
 |
 |  getI = I(self) from numpy.matrixlib.defmatrix.matrix
 |      Returns the (multiplicative) inverse of invertible `self`.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      ret : matrix object
 |          If `self` is non-singular, `ret` is such that ``ret * self`` ==
 |          ``self * ret`` == ``np.matrix(np.eye(self[0,:].size))`` all return
 |          ``True``.
 |
 |      Raises
 |      ------
 |      numpy.linalg.LinAlgError: Singular matrix
 |          If `self` is singular.
 |
 |      See Also
 |      --------
 |      linalg.inv
 |
 |      Examples
 |      --------
 |      >>> m = np.matrix('[1, 2; 3, 4]'); m
 |      matrix([[1, 2],
 |              [3, 4]])
 |      >>> m.getI()
 |      matrix([[-2. ,  1. ],
 |              [ 1.5, -0.5]])
 |      >>> m.getI() * m
 |      matrix([[ 1.,  0.], # may vary
 |              [ 0.,  1.]])
 |
 |  getT = T(self) from numpy.matrixlib.defmatrix.matrix
 |      Returns the transpose of the matrix.
 |
 |      Does *not* conjugate!  For the complex conjugate transpose, use ``.H``.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      ret : matrix object
 |          The (non-conjugated) transpose of the matrix.
 |
 |      See Also
 |      --------
 |      transpose, getH
 |
 |      Examples
 |      --------
 |      >>> m = np.matrix('[1, 2; 3, 4]')
 |      >>> m
 |      matrix([[1, 2],
 |              [3, 4]])
 |      >>> m.getT()
 |      matrix([[1, 3],
 |              [2, 4]])
 |
 |  max(self, axis=None, out=None) from numpy.matrixlib.defmatrix.matrix
 |      Return the maximum value along an axis.
 |
 |      Parameters
 |      ----------
 |      See `amax` for complete descriptions
 |
 |      See Also
 |      --------
 |      amax, ndarray.max
 |
 |      Notes
 |      -----
 |      This is the same as `ndarray.max`, but returns a `matrix` object
 |      where `ndarray.max` would return an ndarray.
 |
 |      Examples
 |      --------
 |      >>> x = np.matrix(np.arange(12).reshape((3,4))); x
 |      matrix([[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]])
 |      >>> x.max()
 |      11
 |      >>> x.max(0)
 |      matrix([[ 8,  9, 10, 11]])
 |      >>> x.max(1)
 |      matrix([[ 3],
 |              [ 7],
 |              [11]])
 |
 |  mean(self, axis=None, dtype=None, out=None) from numpy.matrixlib.defmatrix.matrix
 |      Returns the average of the matrix elements along the given axis.
 |
 |      Refer to `numpy.mean` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.mean
 |
 |      Notes
 |      -----
 |      Same as `ndarray.mean` except that, where that returns an `ndarray`,
 |      this returns a `matrix` object.
 |
 |      Examples
 |      --------
 |      >>> x = np.matrix(np.arange(12).reshape((3, 4)))
 |      >>> x
 |      matrix([[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]])
 |      >>> x.mean()
 |      5.5
 |      >>> x.mean(0)
 |      matrix([[4., 5., 6., 7.]])
 |      >>> x.mean(1)
 |      matrix([[ 1.5],
 |              [ 5.5],
 |              [ 9.5]])
 |
 |  min(self, axis=None, out=None) from numpy.matrixlib.defmatrix.matrix
 |      Return the minimum value along an axis.
 |
 |      Parameters
 |      ----------
 |      See `amin` for complete descriptions.
 |
 |      See Also
 |      --------
 |      amin, ndarray.min
 |
 |      Notes
 |      -----
 |      This is the same as `ndarray.min`, but returns a `matrix` object
 |      where `ndarray.min` would return an ndarray.
 |
 |      Examples
 |      --------
 |      >>> x = -np.matrix(np.arange(12).reshape((3,4))); x
 |      matrix([[  0,  -1,  -2,  -3],
 |              [ -4,  -5,  -6,  -7],
 |              [ -8,  -9, -10, -11]])
 |      >>> x.min()
 |      -11
 |      >>> x.min(0)
 |      matrix([[ -8,  -9, -10, -11]])
 |      >>> x.min(1)
 |      matrix([[ -3],
 |              [ -7],
 |              [-11]])
 |
 |  prod(self, axis=None, dtype=None, out=None) from numpy.matrixlib.defmatrix.matrix
 |      Return the product of the array elements over the given axis.
 |
 |      Refer to `prod` for full documentation.
 |
 |      See Also
 |      --------
 |      prod, ndarray.prod
 |
 |      Notes
 |      -----
 |      Same as `ndarray.prod`, except, where that returns an `ndarray`, this
 |      returns a `matrix` object instead.
 |
 |      Examples
 |      --------
 |      >>> x = np.matrix(np.arange(12).reshape((3,4))); x
 |      matrix([[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]])
 |      >>> x.prod()
 |      0
 |      >>> x.prod(0)
 |      matrix([[  0,  45, 120, 231]])
 |      >>> x.prod(1)
 |      matrix([[   0],
 |              [ 840],
 |              [7920]])
 |
 |  ptp(self, axis=None, out=None) from numpy.matrixlib.defmatrix.matrix
 |      Peak-to-peak (maximum - minimum) value along the given axis.
 |
 |      Refer to `numpy.ptp` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.ptp
 |
 |      Notes
 |      -----
 |      Same as `ndarray.ptp`, except, where that would return an `ndarray` object,
 |      this returns a `matrix` object.
 |
 |      Examples
 |      --------
 |      >>> x = np.matrix(np.arange(12).reshape((3,4))); x
 |      matrix([[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]])
 |      >>> x.ptp()
 |      11
 |      >>> x.ptp(0)
 |      matrix([[8, 8, 8, 8]])
 |      >>> x.ptp(1)
 |      matrix([[3],
 |              [3],
 |              [3]])
 |
 |  ravel(self, order='C') from numpy.matrixlib.defmatrix.matrix
 |      Return a flattened matrix.
 |
 |      Refer to `numpy.ravel` for more documentation.
 |
 |      Parameters
 |      ----------
 |      order : {'C', 'F', 'A', 'K'}, optional
 |          The elements of `m` are read using this index order. 'C' means to
 |          index the elements in C-like order, with the last axis index
 |          changing fastest, back to the first axis index changing slowest.
 |          'F' means to index the elements in Fortran-like index order, with
 |          the first index changing fastest, and the last index changing
 |          slowest. Note that the 'C' and 'F' options take no account of the
 |          memory layout of the underlying array, and only refer to the order
 |          of axis indexing.  'A' means to read the elements in Fortran-like
 |          index order if `m` is Fortran *contiguous* in memory, C-like order
 |          otherwise.  'K' means to read the elements in the order they occur
 |          in memory, except for reversing the data when strides are negative.
 |          By default, 'C' index order is used.
 |
 |      Returns
 |      -------
 |      ret : matrix
 |          Return the matrix flattened to shape `(1, N)` where `N`
 |          is the number of elements in the original matrix.
 |          A copy is made only if necessary.
 |
 |      See Also
 |      --------
 |      matrix.flatten : returns a similar output matrix but always a copy
 |      matrix.flat : a flat iterator on the array.
 |      numpy.ravel : related function which returns an ndarray
 |
 |  squeeze(self, axis=None) from numpy.matrixlib.defmatrix.matrix
 |      Return a possibly reshaped matrix.
 |
 |      Refer to `numpy.squeeze` for more documentation.
 |
 |      Parameters
 |      ----------
 |      axis : None or int or tuple of ints, optional
 |          Selects a subset of the axes of length one in the shape.
 |          If an axis is selected with shape entry greater than one,
 |          an error is raised.
 |
 |      Returns
 |      -------
 |      squeezed : matrix
 |          The matrix, but as a (1, N) matrix if it had shape (N, 1).
 |
 |      See Also
 |      --------
 |      numpy.squeeze : related function
 |
 |      Notes
 |      -----
 |      If `m` has a single column then that column is returned
 |      as the single row of a matrix.  Otherwise `m` is returned.
 |      The returned matrix is always either `m` itself or a view into `m`.
 |      Supplying an axis keyword argument will not affect the returned matrix
 |      but it may cause an error to be raised.
 |
 |      Examples
 |      --------
 |      >>> c = np.matrix([[1], [2]])
 |      >>> c
 |      matrix([[1],
 |              [2]])
 |      >>> c.squeeze()
 |      matrix([[1, 2]])
 |      >>> r = c.T
 |      >>> r
 |      matrix([[1, 2]])
 |      >>> r.squeeze()
 |      matrix([[1, 2]])
 |      >>> m = np.matrix([[1, 2], [3, 4]])
 |      >>> m.squeeze()
 |      matrix([[1, 2],
 |              [3, 4]])
 |
 |  std(self, axis=None, dtype=None, out=None, ddof=0) from numpy.matrixlib.defmatrix.matrix
 |      Return the standard deviation of the array elements along the given axis.
 |
 |      Refer to `numpy.std` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.std
 |
 |      Notes
 |      -----
 |      This is the same as `ndarray.std`, except that where an `ndarray` would
 |      be returned, a `matrix` object is returned instead.
 |
 |      Examples
 |      --------
 |      >>> x = np.matrix(np.arange(12).reshape((3, 4)))
 |      >>> x
 |      matrix([[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]])
 |      >>> x.std()
 |      3.4520525295346629 # may vary
 |      >>> x.std(0)
 |      matrix([[ 3.26598632,  3.26598632,  3.26598632,  3.26598632]]) # may vary
 |      >>> x.std(1)
 |      matrix([[ 1.11803399],
 |              [ 1.11803399],
 |              [ 1.11803399]])
 |
 |  sum(self, axis=None, dtype=None, out=None) from numpy.matrixlib.defmatrix.matrix
 |      Returns the sum of the matrix elements, along the given axis.
 |
 |      Refer to `numpy.sum` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.sum
 |
 |      Notes
 |      -----
 |      This is the same as `ndarray.sum`, except that where an `ndarray` would
 |      be returned, a `matrix` object is returned instead.
 |
 |      Examples
 |      --------
 |      >>> x = np.matrix([[1, 2], [4, 3]])
 |      >>> x.sum()
 |      10
 |      >>> x.sum(axis=1)
 |      matrix([[3],
 |              [7]])
 |      >>> x.sum(axis=1, dtype='float')
 |      matrix([[3.],
 |              [7.]])
 |      >>> out = np.zeros((2, 1), dtype='float')
 |      >>> x.sum(axis=1, dtype='float', out=np.asmatrix(out))
 |      matrix([[3.],
 |              [7.]])
 |
 |  tolist(self) from numpy.matrixlib.defmatrix.matrix
 |      Return the matrix as a (possibly nested) list.
 |
 |      See `ndarray.tolist` for full documentation.
 |
 |      See Also
 |      --------
 |      ndarray.tolist
 |
 |      Examples
 |      --------
 |      >>> x = np.matrix(np.arange(12).reshape((3,4))); x
 |      matrix([[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]])
 |      >>> x.tolist()
 |      [[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]]
 |
 |  var(self, axis=None, dtype=None, out=None, ddof=0) from numpy.matrixlib.defmatrix.matrix
 |      Returns the variance of the matrix elements, along the given axis.
 |
 |      Refer to `numpy.var` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.var
 |
 |      Notes
 |      -----
 |      This is the same as `ndarray.var`, except that where an `ndarray` would
 |      be returned, a `matrix` object is returned instead.
 |
 |      Examples
 |      --------
 |      >>> x = np.matrix(np.arange(12).reshape((3, 4)))
 |      >>> x
 |      matrix([[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]])
 |      >>> x.var()
 |      11.916666666666666
 |      >>> x.var(0)
 |      matrix([[ 10.66666667,  10.66666667,  10.66666667,  10.66666667]]) # may vary
 |      >>> x.var(1)
 |      matrix([[1.25],
 |              [1.25],
 |              [1.25]])
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(subtype, data, dtype=None, copy=True) from numpy.matrixlib.defmatrix.matrix
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Readonly properties defined here:
 |
 |  A
 |      Return `self` as an `ndarray` object.
 |
 |      Equivalent to ``np.asarray(self)``.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      ret : ndarray
 |          `self` as an `ndarray`
 |
 |      Examples
 |      --------
 |      >>> x = np.matrix(np.arange(12).reshape((3,4))); x
 |      matrix([[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]])
 |      >>> x.getA()
 |      array([[ 0,  1,  2,  3],
 |             [ 4,  5,  6,  7],
 |             [ 8,  9, 10, 11]])
 |
 |  A1
 |      Return `self` as a flattened `ndarray`.
 |
 |      Equivalent to ``np.asarray(x).ravel()``
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      ret : ndarray
 |          `self`, 1-D, as an `ndarray`
 |
 |      Examples
 |      --------
 |      >>> x = np.matrix(np.arange(12).reshape((3,4))); x
 |      matrix([[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]])
 |      >>> x.getA1()
 |      array([ 0,  1,  2, ...,  9, 10, 11])
 |
 |  H
 |      Returns the (complex) conjugate transpose of `self`.
 |
 |      Equivalent to ``np.transpose(self)`` if `self` is real-valued.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      ret : matrix object
 |          complex conjugate transpose of `self`
 |
 |      Examples
 |      --------
 |      >>> x = np.matrix(np.arange(12).reshape((3,4)))
 |      >>> z = x - 1j*x; z
 |      matrix([[  0. +0.j,   1. -1.j,   2. -2.j,   3. -3.j],
 |              [  4. -4.j,   5. -5.j,   6. -6.j,   7. -7.j],
 |              [  8. -8.j,   9. -9.j,  10.-10.j,  11.-11.j]])
 |      >>> z.getH()
 |      matrix([[ 0. -0.j,  4. +4.j,  8. +8.j],
 |              [ 1. +1.j,  5. +5.j,  9. +9.j],
 |              [ 2. +2.j,  6. +6.j, 10.+10.j],
 |              [ 3. +3.j,  7. +7.j, 11.+11.j]])
 |
 |  I
 |      Returns the (multiplicative) inverse of invertible `self`.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      ret : matrix object
 |          If `self` is non-singular, `ret` is such that ``ret * self`` ==
 |          ``self * ret`` == ``np.matrix(np.eye(self[0,:].size))`` all return
 |          ``True``.
 |
 |      Raises
 |      ------
 |      numpy.linalg.LinAlgError: Singular matrix
 |          If `self` is singular.
 |
 |      See Also
 |      --------
 |      linalg.inv
 |
 |      Examples
 |      --------
 |      >>> m = np.matrix('[1, 2; 3, 4]'); m
 |      matrix([[1, 2],
 |              [3, 4]])
 |      >>> m.getI()
 |      matrix([[-2. ,  1. ],
 |              [ 1.5, -0.5]])
 |      >>> m.getI() * m
 |      matrix([[ 1.,  0.], # may vary
 |              [ 0.,  1.]])
 |
 |  T
 |      Returns the transpose of the matrix.
 |
 |      Does *not* conjugate!  For the complex conjugate transpose, use ``.H``.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      ret : matrix object
 |          The (non-conjugated) transpose of the matrix.
 |
 |      See Also
 |      --------
 |      transpose, getH
 |
 |      Examples
 |      --------
 |      >>> m = np.matrix('[1, 2; 3, 4]')
 |      >>> m
 |      matrix([[1, 2],
 |              [3, 4]])
 |      >>> m.getT()
 |      matrix([[1, 3],
 |              [2, 4]])
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes defined here:
 |
 |  __annotations__ = {}
 |
 |  __array_priority__ = 10.0
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from ndarray:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      a.__array__([dtype], *, copy=None)
 |
 |      For ``dtype`` parameter it returns a new reference to self if
 |      ``dtype`` is not given or it matches array's data type.
 |      A new array of provided data type is returned if ``dtype``
 |      is different from the current data type of the array.
 |      For ``copy`` parameter it returns a new reference to self if
 |      ``copy=False`` or ``copy=None`` and copying isn't enforced by ``dtype``
 |      parameter. The method returns a new array for ``copy=True``, regardless of
 |      ``dtype`` parameter.
 |
 |      A more detailed explanation of the ``__array__`` interface
 |      can be found in :ref:`dunder_array.interface`.
 |
 |  __array_function__(...)
 |
 |  __array_namespace__(...)
 |
 |  __array_ufunc__(...)
 |
 |  __array_wrap__(...)
 |      a.__array_wrap__(array[, context], /)
 |
 |      Returns a view of `array` with the same type as self.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __complex__(...)
 |
 |  __contains__(self, key, /)
 |      Return bool(key in self).
 |
 |  __copy__(...)
 |      a.__copy__()
 |
 |      Used if :func:`copy.copy` is called on an array. Returns a copy of the array.
 |
 |      Equivalent to ``a.copy(order='K')``.
 |
 |  __deepcopy__(...)
 |      a.__deepcopy__(memo, /)
 |
 |      Used if :func:`copy.deepcopy` is called on an array.
 |
 |  __delitem__(self, key, /)
 |      Delete self[key].
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __dlpack__(...)
 |      a.__dlpack__(*, stream=None, max_version=None, dl_device=None, copy=None)
 |
 |      DLPack Protocol: Part of the Array API.
 |
 |  __dlpack_device__(...)
 |      a.__dlpack_device__()
 |
 |      DLPack Protocol: Part of the Array API.
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      Default object formatter.
 |
 |      Return str(self) if format_spec is empty. Raise TypeError otherwise.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __iadd__(self, value, /)
 |      Return self+=value.
 |
 |  __iand__(self, value, /)
 |      Return self&=value.
 |
 |  __ifloordiv__(self, value, /)
 |      Return self//=value.
 |
 |  __ilshift__(self, value, /)
 |      Return self<<=value.
 |
 |  __imatmul__(self, value, /)
 |      Return self@=value.
 |
 |  __imod__(self, value, /)
 |      Return self%=value.
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __ior__(self, value, /)
 |      Return self|=value.
 |
 |  __irshift__(self, value, /)
 |      Return self>>=value.
 |
 |  __isub__(self, value, /)
 |      Return self-=value.
 |
 |  __iter__(self, /)
 |      Implement iter(self).
 |
 |  __itruediv__(self, value, /)
 |      Return self/=value.
 |
 |  __ixor__(self, value, /)
 |      Return self^=value.
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __matmul__(self, value, /)
 |      Return self@value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      a.__reduce__()
 |
 |      For pickling.
 |
 |  __reduce_ex__(...)
 |      Helper for pickle.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmatmul__(self, value, /)
 |      Return value@self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setitem__(self, key, value, /)
 |      Set self[key] to value.
 |
 |  __setstate__(...)
 |      a.__setstate__(state, /)
 |
 |      For unpickling.
 |
 |      The `state` argument must be a sequence that contains the following
 |      elements:
 |
 |      Parameters
 |      ----------
 |      version : int
 |          optional pickle version. If omitted defaults to 0.
 |      shape : tuple
 |      dtype : data-type
 |      isFortran : bool
 |      rawdata : string or list
 |          a binary string with the data (or a list if 'a' is an object array)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  argpartition(...)
 |      a.argpartition(kth, axis=-1, kind='introselect', order=None)
 |
 |      Returns the indices that would partition this array.
 |
 |      Refer to `numpy.argpartition` for full documentation.
 |
 |      .. versionadded:: 1.8.0
 |
 |      See Also
 |      --------
 |      numpy.argpartition : equivalent function
 |
 |  argsort(...)
 |      a.argsort(axis=-1, kind=None, order=None)
 |
 |      Returns the indices that would sort this array.
 |
 |      Refer to `numpy.argsort` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.argsort : equivalent function
 |
 |  astype(...)
 |      a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True)
 |
 |      Copy of the array, cast to a specified type.
 |
 |      Parameters
 |      ----------
 |      dtype : str or dtype
 |          Typecode or data-type to which the array is cast.
 |      order : {'C', 'F', 'A', 'K'}, optional
 |          Controls the memory layout order of the result.
 |          'C' means C order, 'F' means Fortran order, 'A'
 |          means 'F' order if all the arrays are Fortran contiguous,
 |          'C' order otherwise, and 'K' means as close to the
 |          order the array elements appear in memory as possible.
 |          Default is 'K'.
 |      casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
 |          Controls what kind of data casting may occur. Defaults to 'unsafe'
 |          for backwards compatibility.
 |
 |          * 'no' means the data types should not be cast at all.
 |          * 'equiv' means only byte-order changes are allowed.
 |          * 'safe' means only casts which can preserve values are allowed.
 |          * 'same_kind' means only safe casts or casts within a kind,
 |            like float64 to float32, are allowed.
 |          * 'unsafe' means any data conversions may be done.
 |      subok : bool, optional
 |          If True, then sub-classes will be passed-through (default), otherwise
 |          the returned array will be forced to be a base-class array.
 |      copy : bool, optional
 |          By default, astype always returns a newly allocated array. If this
 |          is set to false, and the `dtype`, `order`, and `subok`
 |          requirements are satisfied, the input array is returned instead
 |          of a copy.
 |
 |      Returns
 |      -------
 |      arr_t : ndarray
 |          Unless `copy` is False and the other conditions for returning the input
 |          array are satisfied (see description for `copy` input parameter), `arr_t`
 |          is a new array of the same shape as the input array, with dtype, order
 |          given by `dtype`, `order`.
 |
 |      Notes
 |      -----
 |      .. versionchanged:: 1.17.0
 |         Casting between a simple data type and a structured one is possible only
 |         for "unsafe" casting.  Casting to multiple fields is allowed, but
 |         casting from multiple fields is not.
 |
 |      .. versionchanged:: 1.9.0
 |         Casting from numeric to string types in 'safe' casting mode requires
 |         that the string dtype length is long enough to store the max
 |         integer/float value converted.
 |
 |      Raises
 |      ------
 |      ComplexWarning
 |          When casting from complex to float or int. To avoid this,
 |          one should use ``a.real.astype(t)``.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 2.5])
 |      >>> x
 |      array([1. ,  2. ,  2.5])
 |
 |      >>> x.astype(int)
 |      array([1, 2, 2])
 |
 |  byteswap(...)
 |      a.byteswap(inplace=False)
 |
 |      Swap the bytes of the array elements
 |
 |      Toggle between low-endian and big-endian data representation by
 |      returning a byteswapped array, optionally swapped in-place.
 |      Arrays of byte-strings are not swapped. The real and imaginary
 |      parts of a complex number are swapped individually.
 |
 |      Parameters
 |      ----------
 |      inplace : bool, optional
 |          If ``True``, swap bytes in-place, default is ``False``.
 |
 |      Returns
 |      -------
 |      out : ndarray
 |          The byteswapped array. If `inplace` is ``True``, this is
 |          a view to self.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> A = np.array([1, 256, 8755], dtype=np.int16)
 |      >>> list(map(hex, A))
 |      ['0x1', '0x100', '0x2233']
 |      >>> A.byteswap(inplace=True)
 |      array([  256,     1, 13090], dtype=int16)
 |      >>> list(map(hex, A))
 |      ['0x100', '0x1', '0x3322']
 |
 |      Arrays of byte-strings are not swapped
 |
 |      >>> A = np.array([b'ceg', b'fac'])
 |      >>> A.byteswap()
 |      array([b'ceg', b'fac'], dtype='|S3')
 |
 |      ``A.view(A.dtype.newbyteorder()).byteswap()`` produces an array with
 |      the same values but different representation in memory
 |
 |      >>> A = np.array([1, 2, 3])
 |      >>> A.view(np.uint8)
 |      array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,
 |             0, 0], dtype=uint8)
 |      >>> A.view(A.dtype.newbyteorder()).byteswap(inplace=True)
 |      array([1, 2, 3])
 |      >>> A.view(np.uint8)
 |      array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0,
 |             0, 3], dtype=uint8)
 |
 |  choose(...)
 |      a.choose(choices, out=None, mode='raise')
 |
 |      Use an index array to construct a new array from a set of choices.
 |
 |      Refer to `numpy.choose` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.choose : equivalent function
 |
 |  clip(...)
 |      a.clip(min=None, max=None, out=None, **kwargs)
 |
 |      Return an array whose values are limited to ``[min, max]``.
 |      One of max or min must be given.
 |
 |      Refer to `numpy.clip` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.clip : equivalent function
 |
 |  compress(...)
 |      a.compress(condition, axis=None, out=None)
 |
 |      Return selected slices of this array along given axis.
 |
 |      Refer to `numpy.compress` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.compress : equivalent function
 |
 |  conj(...)
 |      a.conj()
 |
 |      Complex-conjugate all elements.
 |
 |      Refer to `numpy.conjugate` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.conjugate : equivalent function
 |
 |  conjugate(...)
 |      a.conjugate()
 |
 |      Return the complex conjugate, element-wise.
 |
 |      Refer to `numpy.conjugate` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.conjugate : equivalent function
 |
 |  copy(...)
 |      a.copy(order='C')
 |
 |      Return a copy of the array.
 |
 |      Parameters
 |      ----------
 |      order : {'C', 'F', 'A', 'K'}, optional
 |          Controls the memory layout of the copy. 'C' means C-order,
 |          'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
 |          'C' otherwise. 'K' means match the layout of `a` as closely
 |          as possible. (Note that this function and :func:`numpy.copy` are very
 |          similar but have different default values for their order=
 |          arguments, and this function always passes sub-classes through.)
 |
 |      See also
 |      --------
 |      numpy.copy : Similar function with different default behavior
 |      numpy.copyto
 |
 |      Notes
 |      -----
 |      This function is the preferred method for creating an array copy.  The
 |      function :func:`numpy.copy` is similar, but it defaults to using order 'K',
 |      and will not pass sub-classes through by default.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([[1,2,3],[4,5,6]], order='F')
 |
 |      >>> y = x.copy()
 |
 |      >>> x.fill(0)
 |
 |      >>> x
 |      array([[0, 0, 0],
 |             [0, 0, 0]])
 |
 |      >>> y
 |      array([[1, 2, 3],
 |             [4, 5, 6]])
 |
 |      >>> y.flags['C_CONTIGUOUS']
 |      True
 |
 |      For arrays containing Python objects (e.g. dtype=object),
 |      the copy is a shallow one. The new array will contain the
 |      same object which may lead to surprises if that object can
 |      be modified (is mutable):
 |
 |      >>> a = np.array([1, 'm', [2, 3, 4]], dtype=object)
 |      >>> b = a.copy()
 |      >>> b[2][0] = 10
 |      >>> a
 |      array([1, 'm', list([10, 3, 4])], dtype=object)
 |
 |      To ensure all elements within an ``object`` array are copied,
 |      use `copy.deepcopy`:
 |
 |      >>> import copy
 |      >>> a = np.array([1, 'm', [2, 3, 4]], dtype=object)
 |      >>> c = copy.deepcopy(a)
 |      >>> c[2][0] = 10
 |      >>> c
 |      array([1, 'm', list([10, 3, 4])], dtype=object)
 |      >>> a
 |      array([1, 'm', list([2, 3, 4])], dtype=object)
 |
 |  cumprod(...)
 |      a.cumprod(axis=None, dtype=None, out=None)
 |
 |      Return the cumulative product of the elements along the given axis.
 |
 |      Refer to `numpy.cumprod` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.cumprod : equivalent function
 |
 |  cumsum(...)
 |      a.cumsum(axis=None, dtype=None, out=None)
 |
 |      Return the cumulative sum of the elements along the given axis.
 |
 |      Refer to `numpy.cumsum` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.cumsum : equivalent function
 |
 |  diagonal(...)
 |      a.diagonal(offset=0, axis1=0, axis2=1)
 |
 |      Return specified diagonals. In NumPy 1.9 the returned array is a
 |      read-only view instead of a copy as in previous NumPy versions.  In
 |      a future version the read-only restriction will be removed.
 |
 |      Refer to :func:`numpy.diagonal` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.diagonal : equivalent function
 |
 |  dot(...)
 |
 |  dump(...)
 |      a.dump(file)
 |
 |      Dump a pickle of the array to the specified file.
 |      The array can be read back with pickle.load or numpy.load.
 |
 |      Parameters
 |      ----------
 |      file : str or Path
 |          A string naming the dump file.
 |
 |          .. versionchanged:: 1.17.0
 |              `pathlib.Path` objects are now accepted.
 |
 |  dumps(...)
 |      a.dumps()
 |
 |      Returns the pickle of the array as a string.
 |      pickle.loads will convert the string back to an array.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |  fill(...)
 |      a.fill(value)
 |
 |      Fill the array with a scalar value.
 |
 |      Parameters
 |      ----------
 |      value : scalar
 |          All elements of `a` will be assigned this value.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([1, 2])
 |      >>> a.fill(0)
 |      >>> a
 |      array([0, 0])
 |      >>> a = np.empty(2)
 |      >>> a.fill(1)
 |      >>> a
 |      array([1.,  1.])
 |
 |      Fill expects a scalar value and always behaves the same as assigning
 |      to a single array element.  The following is a rare example where this
 |      distinction is important:
 |
 |      >>> a = np.array([None, None], dtype=object)
 |      >>> a[0] = np.array(3)
 |      >>> a
 |      array([array(3), None], dtype=object)
 |      >>> a.fill(np.array(3))
 |      >>> a
 |      array([array(3), array(3)], dtype=object)
 |
 |      Where other forms of assignments will unpack the array being assigned:
 |
 |      >>> a[...] = np.array(3)
 |      >>> a
 |      array([3, 3], dtype=object)
 |
 |  getfield(...)
 |      a.getfield(dtype, offset=0)
 |
 |      Returns a field of the given array as a certain type.
 |
 |      A field is a view of the array data with a given data-type. The values in
 |      the view are determined by the given type and the offset into the current
 |      array in bytes. The offset needs to be such that the view dtype fits in the
 |      array dtype; for example an array of dtype complex128 has 16-byte elements.
 |      If taking a view with a 32-bit integer (4 bytes), the offset needs to be
 |      between 0 and 12 bytes.
 |
 |      Parameters
 |      ----------
 |      dtype : str or dtype
 |          The data type of the view. The dtype size of the view can not be larger
 |          than that of the array itself.
 |      offset : int
 |          Number of bytes to skip before beginning the element view.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.diag([1.+1.j]*2)
 |      >>> x[1, 1] = 2 + 4.j
 |      >>> x
 |      array([[1.+1.j,  0.+0.j],
 |             [0.+0.j,  2.+4.j]])
 |      >>> x.getfield(np.float64)
 |      array([[1.,  0.],
 |             [0.,  2.]])
 |
 |      By choosing an offset of 8 bytes we can select the complex part of the
 |      array for our view:
 |
 |      >>> x.getfield(np.float64, offset=8)
 |      array([[1.,  0.],
 |             [0.,  4.]])
 |
 |  item(...)
 |      a.item(*args)
 |
 |      Copy an element of an array to a standard Python scalar and return it.
 |
 |      Parameters
 |      ----------
 |      \*args : Arguments (variable number and type)
 |
 |          * none: in this case, the method only works for arrays
 |            with one element (`a.size == 1`), which element is
 |            copied into a standard Python scalar object and returned.
 |
 |          * int_type: this argument is interpreted as a flat index into
 |            the array, specifying which element to copy and return.
 |
 |          * tuple of int_types: functions as does a single int_type argument,
 |            except that the argument is interpreted as an nd-index into the
 |            array.
 |
 |      Returns
 |      -------
 |      z : Standard Python scalar object
 |          A copy of the specified element of the array as a suitable
 |          Python scalar
 |
 |      Notes
 |      -----
 |      When the data type of `a` is longdouble or clongdouble, item() returns
 |      a scalar array object because there is no available Python scalar that
 |      would not lose information. Void arrays return a buffer object for item(),
 |      unless fields are defined, in which case a tuple is returned.
 |
 |      `item` is very similar to a[args], except, instead of an array scalar,
 |      a standard Python scalar is returned. This can be useful for speeding up
 |      access to elements of the array and doing arithmetic on elements of the
 |      array using Python's optimized math.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.random.seed(123)
 |      >>> x = np.random.randint(9, size=(3, 3))
 |      >>> x
 |      array([[2, 2, 6],
 |             [1, 3, 6],
 |             [1, 0, 1]])
 |      >>> x.item(3)
 |      1
 |      >>> x.item(7)
 |      0
 |      >>> x.item((0, 1))
 |      2
 |      >>> x.item((2, 2))
 |      1
 |
 |      For an array with object dtype, elements are returned as-is.
 |
 |      >>> a = np.array([np.int64(1)], dtype=object)
 |      >>> a.item() #return np.int64
 |      np.int64(1)
 |
 |  nonzero(...)
 |      a.nonzero()
 |
 |      Return the indices of the elements that are non-zero.
 |
 |      Refer to `numpy.nonzero` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.nonzero : equivalent function
 |
 |  partition(...)
 |      a.partition(kth, axis=-1, kind='introselect', order=None)
 |
 |      Partially sorts the elements in the array in such a way that the value of
 |      the element in k-th position is in the position it would be in a sorted
 |      array. In the output array, all elements smaller than the k-th element
 |      are located to the left of this element and all equal or greater are
 |      located to its right. The ordering of the elements in the two partitions
 |      on the either side of the k-th element in the output array is undefined.
 |
 |      .. versionadded:: 1.8.0
 |
 |      Parameters
 |      ----------
 |      kth : int or sequence of ints
 |          Element index to partition by. The kth element value will be in its
 |          final sorted position and all smaller elements will be moved before it
 |          and all equal or greater elements behind it.
 |          The order of all elements in the partitions is undefined.
 |          If provided with a sequence of kth it will partition all elements
 |          indexed by kth of them into their sorted position at once.
 |
 |          .. deprecated:: 1.22.0
 |              Passing booleans as index is deprecated.
 |      axis : int, optional
 |          Axis along which to sort. Default is -1, which means sort along the
 |          last axis.
 |      kind : {'introselect'}, optional
 |          Selection algorithm. Default is 'introselect'.
 |      order : str or list of str, optional
 |          When `a` is an array with fields defined, this argument specifies
 |          which fields to compare first, second, etc. A single field can
 |          be specified as a string, and not all fields need to be specified,
 |          but unspecified fields will still be used, in the order in which
 |          they come up in the dtype, to break ties.
 |
 |      See Also
 |      --------
 |      numpy.partition : Return a partitioned copy of an array.
 |      argpartition : Indirect partition.
 |      sort : Full sort.
 |
 |      Notes
 |      -----
 |      See ``np.partition`` for notes on the different algorithms.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([3, 4, 2, 1])
 |      >>> a.partition(3)
 |      >>> a
 |      array([2, 1, 3, 4]) # may vary
 |
 |      >>> a.partition((1, 3))
 |      >>> a
 |      array([1, 2, 3, 4])
 |
 |  put(...)
 |      a.put(indices, values, mode='raise')
 |
 |      Set ``a.flat[n] = values[n]`` for all `n` in indices.
 |
 |      Refer to `numpy.put` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.put : equivalent function
 |
 |  repeat(...)
 |      a.repeat(repeats, axis=None)
 |
 |      Repeat elements of an array.
 |
 |      Refer to `numpy.repeat` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.repeat : equivalent function
 |
 |  reshape(...)
 |      a.reshape(shape, /, *, order='C', copy=None)
 |
 |      Returns an array containing the same data with a new shape.
 |
 |      Refer to `numpy.reshape` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.reshape : equivalent function
 |
 |      Notes
 |      -----
 |      Unlike the free function `numpy.reshape`, this method on `ndarray` allows
 |      the elements of the shape parameter to be passed in as separate arguments.
 |      For example, ``a.reshape(10, 11)`` is equivalent to
 |      ``a.reshape((10, 11))``.
 |
 |  resize(...)
 |      a.resize(new_shape, refcheck=True)
 |
 |      Change shape and size of array in-place.
 |
 |      Parameters
 |      ----------
 |      new_shape : tuple of ints, or `n` ints
 |          Shape of resized array.
 |      refcheck : bool, optional
 |          If False, reference count will not be checked. Default is True.
 |
 |      Returns
 |      -------
 |      None
 |
 |      Raises
 |      ------
 |      ValueError
 |          If `a` does not own its own data or references or views to it exist,
 |          and the data memory must be changed.
 |          PyPy only: will always raise if the data memory must be changed, since
 |          there is no reliable way to determine if references or views to it
 |          exist.
 |
 |      SystemError
 |          If the `order` keyword argument is specified. This behaviour is a
 |          bug in NumPy.
 |
 |      See Also
 |      --------
 |      resize : Return a new array with the specified shape.
 |
 |      Notes
 |      -----
 |      This reallocates space for the data area if necessary.
 |
 |      Only contiguous arrays (data elements consecutive in memory) can be
 |      resized.
 |
 |      The purpose of the reference count check is to make sure you
 |      do not use this array as a buffer for another Python object and then
 |      reallocate the memory. However, reference counts can increase in
 |      other ways so if you are sure that you have not shared the memory
 |      for this array with another Python object, then you may safely set
 |      `refcheck` to False.
 |
 |      Examples
 |      --------
 |      Shrinking an array: array is flattened (in the order that the data are
 |      stored in memory), resized, and reshaped:
 |
 |      >>> import numpy as np
 |
 |      >>> a = np.array([[0, 1], [2, 3]], order='C')
 |      >>> a.resize((2, 1))
 |      >>> a
 |      array([[0],
 |             [1]])
 |
 |      >>> a = np.array([[0, 1], [2, 3]], order='F')
 |      >>> a.resize((2, 1))
 |      >>> a
 |      array([[0],
 |             [2]])
 |
 |      Enlarging an array: as above, but missing entries are filled with zeros:
 |
 |      >>> b = np.array([[0, 1], [2, 3]])
 |      >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple
 |      >>> b
 |      array([[0, 1, 2],
 |             [3, 0, 0]])
 |
 |      Referencing an array prevents resizing...
 |
 |      >>> c = a
 |      >>> a.resize((1, 1))
 |      Traceback (most recent call last):
 |      ...
 |      ValueError: cannot resize an array that references or is referenced ...
 |
 |      Unless `refcheck` is False:
 |
 |      >>> a.resize((1, 1), refcheck=False)
 |      >>> a
 |      array([[0]])
 |      >>> c
 |      array([[0]])
 |
 |  round(...)
 |      a.round(decimals=0, out=None)
 |
 |      Return `a` with each element rounded to the given number of decimals.
 |
 |      Refer to `numpy.around` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.around : equivalent function
 |
 |  searchsorted(...)
 |      a.searchsorted(v, side='left', sorter=None)
 |
 |      Find indices where elements of v should be inserted in a to maintain order.
 |
 |      For full documentation, see `numpy.searchsorted`
 |
 |      See Also
 |      --------
 |      numpy.searchsorted : equivalent function
 |
 |  setfield(...)
 |      a.setfield(val, dtype, offset=0)
 |
 |      Put a value into a specified place in a field defined by a data-type.
 |
 |      Place `val` into `a`'s field defined by `dtype` and beginning `offset`
 |      bytes into the field.
 |
 |      Parameters
 |      ----------
 |      val : object
 |          Value to be placed in field.
 |      dtype : dtype object
 |          Data-type of the field in which to place `val`.
 |      offset : int, optional
 |          The number of bytes into the field at which to place `val`.
 |
 |      Returns
 |      -------
 |      None
 |
 |      See Also
 |      --------
 |      getfield
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.eye(3)
 |      >>> x.getfield(np.float64)
 |      array([[1.,  0.,  0.],
 |             [0.,  1.,  0.],
 |             [0.,  0.,  1.]])
 |      >>> x.setfield(3, np.int32)
 |      >>> x.getfield(np.int32)
 |      array([[3, 3, 3],
 |             [3, 3, 3],
 |             [3, 3, 3]], dtype=int32)
 |      >>> x
 |      array([[1.0e+000, 1.5e-323, 1.5e-323],
 |             [1.5e-323, 1.0e+000, 1.5e-323],
 |             [1.5e-323, 1.5e-323, 1.0e+000]])
 |      >>> x.setfield(np.eye(3), np.int32)
 |      >>> x
 |      array([[1.,  0.,  0.],
 |             [0.,  1.,  0.],
 |             [0.,  0.,  1.]])
 |
 |  setflags(...)
 |      a.setflags(write=None, align=None, uic=None)
 |
 |      Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY,
 |      respectively.
 |
 |      These Boolean-valued flags affect how numpy interprets the memory
 |      area used by `a` (see Notes below). The ALIGNED flag can only
 |      be set to True if the data is actually aligned according to the type.
 |      The WRITEBACKIFCOPY flag can never be set
 |      to True. The flag WRITEABLE can only be set to True if the array owns its
 |      own memory, or the ultimate owner of the memory exposes a writeable buffer
 |      interface, or is a string. (The exception for string is made so that
 |      unpickling can be done without copying memory.)
 |
 |      Parameters
 |      ----------
 |      write : bool, optional
 |          Describes whether or not `a` can be written to.
 |      align : bool, optional
 |          Describes whether or not `a` is aligned properly for its type.
 |      uic : bool, optional
 |          Describes whether or not `a` is a copy of another "base" array.
 |
 |      Notes
 |      -----
 |      Array flags provide information about how the memory area used
 |      for the array is to be interpreted. There are 7 Boolean flags
 |      in use, only three of which can be changed by the user:
 |      WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.
 |
 |      WRITEABLE (W) the data area can be written to;
 |
 |      ALIGNED (A) the data and strides are aligned appropriately for the hardware
 |      (as determined by the compiler);
 |
 |      WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced
 |      by .base). When the C-API function PyArray_ResolveWritebackIfCopy is
 |      called, the base array will be updated with the contents of this array.
 |
 |      All flags can be accessed using the single (upper case) letter as well
 |      as the full name.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> y = np.array([[3, 1, 7],
 |      ...               [2, 0, 0],
 |      ...               [8, 5, 9]])
 |      >>> y
 |      array([[3, 1, 7],
 |             [2, 0, 0],
 |             [8, 5, 9]])
 |      >>> y.flags
 |        C_CONTIGUOUS : True
 |        F_CONTIGUOUS : False
 |        OWNDATA : True
 |        WRITEABLE : True
 |        ALIGNED : True
 |        WRITEBACKIFCOPY : False
 |      >>> y.setflags(write=0, align=0)
 |      >>> y.flags
 |        C_CONTIGUOUS : True
 |        F_CONTIGUOUS : False
 |        OWNDATA : True
 |        WRITEABLE : False
 |        ALIGNED : False
 |        WRITEBACKIFCOPY : False
 |      >>> y.setflags(uic=1)
 |      Traceback (most recent call last):
 |        File "<stdin>", line 1, in <module>
 |      ValueError: cannot set WRITEBACKIFCOPY flag to True
 |
 |  sort(...)
 |      a.sort(axis=-1, kind=None, order=None)
 |
 |      Sort an array in-place. Refer to `numpy.sort` for full documentation.
 |
 |      Parameters
 |      ----------
 |      axis : int, optional
 |          Axis along which to sort. Default is -1, which means sort along the
 |          last axis.
 |      kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
 |          Sorting algorithm. The default is 'quicksort'. Note that both 'stable'
 |          and 'mergesort' use timsort under the covers and, in general, the
 |          actual implementation will vary with datatype. The 'mergesort' option
 |          is retained for backwards compatibility.
 |
 |          .. versionchanged:: 1.15.0
 |             The 'stable' option was added.
 |
 |      order : str or list of str, optional
 |          When `a` is an array with fields defined, this argument specifies
 |          which fields to compare first, second, etc.  A single field can
 |          be specified as a string, and not all fields need be specified,
 |          but unspecified fields will still be used, in the order in which
 |          they come up in the dtype, to break ties.
 |
 |      See Also
 |      --------
 |      numpy.sort : Return a sorted copy of an array.
 |      numpy.argsort : Indirect sort.
 |      numpy.lexsort : Indirect stable sort on multiple keys.
 |      numpy.searchsorted : Find elements in sorted array.
 |      numpy.partition: Partial sort.
 |
 |      Notes
 |      -----
 |      See `numpy.sort` for notes on the different sorting algorithms.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1,4], [3,1]])
 |      >>> a.sort(axis=1)
 |      >>> a
 |      array([[1, 4],
 |             [1, 3]])
 |      >>> a.sort(axis=0)
 |      >>> a
 |      array([[1, 3],
 |             [1, 4]])
 |
 |      Use the `order` keyword to specify a field to use when sorting a
 |      structured array:
 |
 |      >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])
 |      >>> a.sort(order='y')
 |      >>> a
 |      array([(b'c', 1), (b'a', 2)],
 |            dtype=[('x', 'S1'), ('y', '<i8')])
 |
 |  swapaxes(...)
 |      a.swapaxes(axis1, axis2)
 |
 |      Return a view of the array with `axis1` and `axis2` interchanged.
 |
 |      Refer to `numpy.swapaxes` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.swapaxes : equivalent function
 |
 |  take(...)
 |      a.take(indices, axis=None, out=None, mode='raise')
 |
 |      Return an array formed from the elements of `a` at the given indices.
 |
 |      Refer to `numpy.take` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.take : equivalent function
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |      a.tobytes(order='C')
 |
 |      Construct Python bytes containing the raw data bytes in the array.
 |
 |      Constructs Python bytes showing a copy of the raw contents of
 |      data memory. The bytes object is produced in C-order by default.
 |      This behavior is controlled by the ``order`` parameter.
 |
 |      .. versionadded:: 1.9.0
 |
 |      Parameters
 |      ----------
 |      order : {'C', 'F', 'A'}, optional
 |          Controls the memory layout of the bytes object. 'C' means C-order,
 |          'F' means F-order, 'A' (short for *Any*) means 'F' if `a` is
 |          Fortran contiguous, 'C' otherwise. Default is 'C'.
 |
 |      Returns
 |      -------
 |      s : bytes
 |          Python bytes exhibiting a copy of `a`'s raw data.
 |
 |      See also
 |      --------
 |      frombuffer
 |          Inverse of this operation, construct a 1-dimensional array from Python
 |          bytes.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([[0, 1], [2, 3]], dtype='<u2')
 |      >>> x.tobytes()
 |      b'\x00\x00\x01\x00\x02\x00\x03\x00'
 |      >>> x.tobytes('C') == x.tobytes()
 |      True
 |      >>> x.tobytes('F')
 |      b'\x00\x00\x02\x00\x01\x00\x03\x00'
 |
 |  tofile(...)
 |      a.tofile(fid, sep="", format="%s")
 |
 |      Write array to a file as text or binary (default).
 |
 |      Data is always written in 'C' order, independent of the order of `a`.
 |      The data produced by this method can be recovered using the function
 |      fromfile().
 |
 |      Parameters
 |      ----------
 |      fid : file or str or Path
 |          An open file object, or a string containing a filename.
 |
 |          .. versionchanged:: 1.17.0
 |              `pathlib.Path` objects are now accepted.
 |
 |      sep : str
 |          Separator between array items for text output.
 |          If "" (empty), a binary file is written, equivalent to
 |          ``file.write(a.tobytes())``.
 |      format : str
 |          Format string for text file output.
 |          Each entry in the array is formatted to text by first converting
 |          it to the closest Python type, and then using "format" % item.
 |
 |      Notes
 |      -----
 |      This is a convenience function for quick storage of array data.
 |      Information on endianness and precision is lost, so this method is not a
 |      good choice for files intended to archive data or transport data between
 |      machines with different endianness. Some of these problems can be overcome
 |      by outputting the data as text files, at the expense of speed and file
 |      size.
 |
 |      When fid is a file object, array contents are directly written to the
 |      file, bypassing the file object's ``write`` method. As a result, tofile
 |      cannot be used with files objects supporting compression (e.g., GzipFile)
 |      or file-like objects that do not support ``fileno()`` (e.g., BytesIO).
 |
 |  tostring(...)
 |      a.tostring(order='C')
 |
 |      A compatibility alias for `~ndarray.tobytes`, with exactly the same
 |      behavior.
 |
 |      Despite its name, it returns :class:`bytes` not :class:`str`\ s.
 |
 |      .. deprecated:: 1.19.0
 |
 |  trace(...)
 |      a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)
 |
 |      Return the sum along diagonals of the array.
 |
 |      Refer to `numpy.trace` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.trace : equivalent function
 |
 |  transpose(...)
 |      a.transpose(*axes)
 |
 |      Returns a view of the array with axes transposed.
 |
 |      Refer to `numpy.transpose` for full documentation.
 |
 |      Parameters
 |      ----------
 |      axes : None, tuple of ints, or `n` ints
 |
 |       * None or no argument: reverses the order of the axes.
 |
 |       * tuple of ints: `i` in the `j`-th place in the tuple means that the
 |         array's `i`-th axis becomes the transposed array's `j`-th axis.
 |
 |       * `n` ints: same as an n-tuple of the same ints (this form is
 |         intended simply as a "convenience" alternative to the tuple form).
 |
 |      Returns
 |      -------
 |      p : ndarray
 |          View of the array with its axes suitably permuted.
 |
 |      See Also
 |      --------
 |      transpose : Equivalent function.
 |      ndarray.T : Array property returning the array transposed.
 |      ndarray.reshape : Give a new shape to an array without changing its data.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1, 2], [3, 4]])
 |      >>> a
 |      array([[1, 2],
 |             [3, 4]])
 |      >>> a.transpose()
 |      array([[1, 3],
 |             [2, 4]])
 |      >>> a.transpose((1, 0))
 |      array([[1, 3],
 |             [2, 4]])
 |      >>> a.transpose(1, 0)
 |      array([[1, 3],
 |             [2, 4]])
 |
 |      >>> a = np.array([1, 2, 3, 4])
 |      >>> a
 |      array([1, 2, 3, 4])
 |      >>> a.transpose()
 |      array([1, 2, 3, 4])
 |
 |  view(...)
 |      a.view([dtype][, type])
 |
 |      New view of array with the same data.
 |
 |      .. note::
 |          Passing None for ``dtype`` is different from omitting the parameter,
 |          since the former invokes ``dtype(None)`` which is an alias for
 |          ``dtype('float64')``.
 |
 |      Parameters
 |      ----------
 |      dtype : data-type or ndarray sub-class, optional
 |          Data-type descriptor of the returned view, e.g., float32 or int16.
 |          Omitting it results in the view having the same data-type as `a`.
 |          This argument can also be specified as an ndarray sub-class, which
 |          then specifies the type of the returned object (this is equivalent to
 |          setting the ``type`` parameter).
 |      type : Python type, optional
 |          Type of the returned view, e.g., ndarray or matrix.  Again, omission
 |          of the parameter results in type preservation.
 |
 |      Notes
 |      -----
 |      ``a.view()`` is used two different ways:
 |
 |      ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view
 |      of the array's memory with a different data-type.  This can cause a
 |      reinterpretation of the bytes of memory.
 |
 |      ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just
 |      returns an instance of `ndarray_subclass` that looks at the same array
 |      (same shape, dtype, etc.)  This does not cause a reinterpretation of the
 |      memory.
 |
 |      For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of
 |      bytes per entry than the previous dtype (for example, converting a regular
 |      array to a structured array), then the last axis of ``a`` must be
 |      contiguous. This axis will be resized in the result.
 |
 |      .. versionchanged:: 1.23.0
 |         Only the last axis needs to be contiguous. Previously, the entire array
 |         had to be C-contiguous.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([(-1, 2)], dtype=[('a', np.int8), ('b', np.int8)])
 |
 |      Viewing array data using a different type and dtype:
 |
 |      >>> nonneg = np.dtype([("a", np.uint8), ("b", np.uint8)])
 |      >>> y = x.view(dtype=nonneg, type=np.recarray)
 |      >>> x["a"]
 |      array([-1], dtype=int8)
 |      >>> y.a
 |      array([255], dtype=uint8)
 |
 |      Creating a view on a structured array so it can be used in calculations
 |
 |      >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])
 |      >>> xv = x.view(dtype=np.int8).reshape(-1,2)
 |      >>> xv
 |      array([[1, 2],
 |             [3, 4]], dtype=int8)
 |      >>> xv.mean(0)
 |      array([2.,  3.])
 |
 |      Making changes to the view changes the underlying array
 |
 |      >>> xv[0,1] = 20
 |      >>> x
 |      array([(1, 20), (3,  4)], dtype=[('a', 'i1'), ('b', 'i1')])
 |
 |      Using a view to convert an array to a recarray:
 |
 |      >>> z = x.view(np.recarray)
 |      >>> z.a
 |      array([1, 3], dtype=int8)
 |
 |      Views share data:
 |
 |      >>> x[0] = (9, 10)
 |      >>> z[0]
 |      np.record((9, 10), dtype=[('a', 'i1'), ('b', 'i1')])
 |
 |      Views that change the dtype size (bytes per entry) should normally be
 |      avoided on arrays defined by slices, transposes, fortran-ordering, etc.:
 |
 |      >>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16)
 |      >>> y = x[:, ::2]
 |      >>> y
 |      array([[1, 3],
 |             [4, 6]], dtype=int16)
 |      >>> y.view(dtype=[('width', np.int16), ('length', np.int16)])
 |      Traceback (most recent call last):
 |          ...
 |      ValueError: To change to a dtype of a different size, the last axis must be contiguous
 |      >>> z = y.copy()
 |      >>> z.view(dtype=[('width', np.int16), ('length', np.int16)])
 |      array([[(1, 3)],
 |             [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])
 |
 |      However, views that change dtype are totally fine for arrays with a
 |      contiguous last axis, even if the rest of the axes are not C-contiguous:
 |
 |      >>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4)
 |      >>> x.transpose(1, 0, 2).view(np.int16)
 |      array([[[ 256,  770],
 |              [3340, 3854]],
 |      <BLANKLINE>
 |             [[1284, 1798],
 |              [4368, 4882]],
 |      <BLANKLINE>
 |             [[2312, 2826],
 |              [5396, 5910]]], dtype=int16)
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from ndarray:
 |
 |  __class_getitem__(...)
 |      a.__class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.ndarray` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.ndarray` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.ndarray[Any, np.dtype[Any]]
 |      numpy.ndarray[typing.Any, numpy.dtype[typing.Any]]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |      numpy.typing.NDArray : An ndarray alias :term:`generic <generic type>`
 |                          w.r.t. its `dtype.type <numpy.dtype.type>`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from ndarray:
 |
 |  __array_interface__
 |      Array protocol: Python side.
 |
 |  __array_struct__
 |      Array protocol: C-struct side.
 |
 |  base
 |      Base object if memory is from some other object.
 |
 |      Examples
 |      --------
 |      The base of an array that owns its memory is None:
 |
 |      >>> import numpy as np
 |      >>> x = np.array([1,2,3,4])
 |      >>> x.base is None
 |      True
 |
 |      Slicing creates a view, whose memory is shared with x:
 |
 |      >>> y = x[2:]
 |      >>> y.base is x
 |      True
 |
 |  ctypes
 |      An object to simplify the interaction of the array with the ctypes
 |      module.
 |
 |      This attribute creates an object that makes it easier to use arrays
 |      when calling shared libraries with the ctypes module. The returned
 |      object has, among others, data, shape, and strides attributes (see
 |      Notes below) which themselves return ctypes objects that can be used
 |      as arguments to a shared library.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      c : Python object
 |          Possessing attributes data, shape, strides, etc.
 |
 |      See Also
 |      --------
 |      numpy.ctypeslib
 |
 |      Notes
 |      -----
 |      Below are the public attributes of this object which were documented
 |      in "Guide to NumPy" (we have omitted undocumented public attributes,
 |      as well as documented private attributes):
 |
 |      .. autoattribute:: numpy._core._internal._ctypes.data
 |          :noindex:
 |
 |      .. autoattribute:: numpy._core._internal._ctypes.shape
 |          :noindex:
 |
 |      .. autoattribute:: numpy._core._internal._ctypes.strides
 |          :noindex:
 |
 |      .. automethod:: numpy._core._internal._ctypes.data_as
 |          :noindex:
 |
 |      .. automethod:: numpy._core._internal._ctypes.shape_as
 |          :noindex:
 |
 |      .. automethod:: numpy._core._internal._ctypes.strides_as
 |          :noindex:
 |
 |      If the ctypes module is not available, then the ctypes attribute
 |      of array objects still returns something useful, but ctypes objects
 |      are not returned and errors may be raised instead. In particular,
 |      the object will still have the ``as_parameter`` attribute which will
 |      return an integer equal to the data attribute.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> import ctypes
 |      >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)
 |      >>> x
 |      array([[0, 1],
 |             [2, 3]], dtype=int32)
 |      >>> x.ctypes.data
 |      31962608 # may vary
 |      >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))
 |      <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary
 |      >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents
 |      c_uint(0)
 |      >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents
 |      c_ulong(4294967296)
 |      >>> x.ctypes.shape
 |      <numpy._core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary
 |      >>> x.ctypes.strides
 |      <numpy._core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary
 |
 |  data
 |      Python buffer object pointing to the start of the array's data.
 |
 |  device
 |
 |  dtype
 |      Data-type of the array's elements.
 |
 |      .. warning::
 |
 |          Setting ``arr.dtype`` is discouraged and may be deprecated in the
 |          future.  Setting will replace the ``dtype`` without modifying the
 |          memory (see also `ndarray.view` and `ndarray.astype`).
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      d : numpy dtype object
 |
 |      See Also
 |      --------
 |      ndarray.astype : Cast the values contained in the array to a new data-type.
 |      ndarray.view : Create a view of the same data but a different data-type.
 |      numpy.dtype
 |
 |      Examples
 |      --------
 |      >>> x
 |      array([[0, 1],
 |             [2, 3]])
 |      >>> x.dtype
 |      dtype('int32')
 |      >>> type(x.dtype)
 |      <type 'numpy.dtype'>
 |
 |  flags
 |      Information about the memory layout of the array.
 |
 |      Attributes
 |      ----------
 |      C_CONTIGUOUS (C)
 |          The data is in a single, C-style contiguous segment.
 |      F_CONTIGUOUS (F)
 |          The data is in a single, Fortran-style contiguous segment.
 |      OWNDATA (O)
 |          The array owns the memory it uses or borrows it from another object.
 |      WRITEABLE (W)
 |          The data area can be written to.  Setting this to False locks
 |          the data, making it read-only.  A view (slice, etc.) inherits WRITEABLE
 |          from its base array at creation time, but a view of a writeable
 |          array may be subsequently locked while the base array remains writeable.
 |          (The opposite is not true, in that a view of a locked array may not
 |          be made writeable.  However, currently, locking a base object does not
 |          lock any views that already reference it, so under that circumstance it
 |          is possible to alter the contents of a locked array via a previously
 |          created writeable view onto it.)  Attempting to change a non-writeable
 |          array raises a RuntimeError exception.
 |      ALIGNED (A)
 |          The data and all elements are aligned appropriately for the hardware.
 |      WRITEBACKIFCOPY (X)
 |          This array is a copy of some other array. The C-API function
 |          PyArray_ResolveWritebackIfCopy must be called before deallocating
 |          to the base array will be updated with the contents of this array.
 |      FNC
 |          F_CONTIGUOUS and not C_CONTIGUOUS.
 |      FORC
 |          F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).
 |      BEHAVED (B)
 |          ALIGNED and WRITEABLE.
 |      CARRAY (CA)
 |          BEHAVED and C_CONTIGUOUS.
 |      FARRAY (FA)
 |          BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.
 |
 |      Notes
 |      -----
 |      The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``),
 |      or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag
 |      names are only supported in dictionary access.
 |
 |      Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be
 |      changed by the user, via direct assignment to the attribute or dictionary
 |      entry, or by calling `ndarray.setflags`.
 |
 |      The array flags cannot be set arbitrarily:
 |
 |      - WRITEBACKIFCOPY can only be set ``False``.
 |      - ALIGNED can only be set ``True`` if the data is truly aligned.
 |      - WRITEABLE can only be set ``True`` if the array owns its own memory
 |        or the ultimate owner of the memory exposes a writeable buffer
 |        interface or is a string.
 |
 |      Arrays can be both C-style and Fortran-style contiguous simultaneously.
 |      This is clear for 1-dimensional arrays, but can also be true for higher
 |      dimensional arrays.
 |
 |      Even for contiguous arrays a stride for a given dimension
 |      ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1``
 |      or the array has no elements.
 |      It does *not* generally hold that ``self.strides[-1] == self.itemsize``
 |      for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for
 |      Fortran-style contiguous arrays is true.
 |
 |  flat
 |      A 1-D iterator over the array.
 |
 |      This is a `numpy.flatiter` instance, which acts similarly to, but is not
 |      a subclass of, Python's built-in iterator object.
 |
 |      See Also
 |      --------
 |      flatten : Return a copy of the array collapsed into one dimension.
 |
 |      flatiter
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.arange(1, 7).reshape(2, 3)
 |      >>> x
 |      array([[1, 2, 3],
 |             [4, 5, 6]])
 |      >>> x.flat[3]
 |      4
 |      >>> x.T
 |      array([[1, 4],
 |             [2, 5],
 |             [3, 6]])
 |      >>> x.T.flat[3]
 |      5
 |      >>> type(x.flat)
 |      <class 'numpy.flatiter'>
 |
 |      An assignment example:
 |
 |      >>> x.flat = 3; x
 |      array([[3, 3, 3],
 |             [3, 3, 3]])
 |      >>> x.flat[[1,4]] = 1; x
 |      array([[3, 1, 3],
 |             [3, 1, 3]])
 |
 |  imag
 |      The imaginary part of the array.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.sqrt([1+0j, 0+1j])
 |      >>> x.imag
 |      array([ 0.        ,  0.70710678])
 |      >>> x.imag.dtype
 |      dtype('float64')
 |
 |  itemset
 |
 |  itemsize
 |      Length of one array element in bytes.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1,2,3], dtype=np.float64)
 |      >>> x.itemsize
 |      8
 |      >>> x = np.array([1,2,3], dtype=np.complex128)
 |      >>> x.itemsize
 |      16
 |
 |  mT
 |      View of the matrix transposed array.
 |
 |      The matrix transpose is the transpose of the last two dimensions, even
 |      if the array is of higher dimension.
 |
 |      .. versionadded:: 2.0
 |
 |      Raises
 |      ------
 |      ValueError
 |          If the array is of dimension less than 2.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1, 2], [3, 4]])
 |      >>> a
 |      array([[1, 2],
 |             [3, 4]])
 |      >>> a.mT
 |      array([[1, 3],
 |             [2, 4]])
 |
 |      >>> a = np.arange(8).reshape((2, 2, 2))
 |      >>> a
 |      array([[[0, 1],
 |              [2, 3]],
 |      <BLANKLINE>
 |             [[4, 5],
 |              [6, 7]]])
 |      >>> a.mT
 |      array([[[0, 2],
 |              [1, 3]],
 |      <BLANKLINE>
 |             [[4, 6],
 |              [5, 7]]])
 |
 |  nbytes
 |      Total bytes consumed by the elements of the array.
 |
 |      Notes
 |      -----
 |      Does not include memory consumed by non-element attributes of the
 |      array object.
 |
 |      See Also
 |      --------
 |      sys.getsizeof
 |          Memory consumed by the object itself without parents in case view.
 |          This does include memory consumed by non-element attributes.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.zeros((3,5,2), dtype=np.complex128)
 |      >>> x.nbytes
 |      480
 |      >>> np.prod(x.shape) * x.itemsize
 |      480
 |
 |  ndim
 |      Number of array dimensions.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 3])
 |      >>> x.ndim
 |      1
 |      >>> y = np.zeros((2, 3, 4))
 |      >>> y.ndim
 |      3
 |
 |  newbyteorder
 |
 |  real
 |      The real part of the array.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.sqrt([1+0j, 0+1j])
 |      >>> x.real
 |      array([ 1.        ,  0.70710678])
 |      >>> x.real.dtype
 |      dtype('float64')
 |
 |      See Also
 |      --------
 |      numpy.real : equivalent function
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |      The shape property is usually used to get the current shape of an array,
 |      but may also be used to reshape the array in-place by assigning a tuple of
 |      array dimensions to it.  As with `numpy.reshape`, one of the new shape
 |      dimensions can be -1, in which case its value is inferred from the size of
 |      the array and the remaining dimensions. Reshaping an array in-place will
 |      fail if a copy is required.
 |
 |      .. warning::
 |
 |          Setting ``arr.shape`` is discouraged and may be deprecated in the
 |          future.  Using `ndarray.reshape` is the preferred approach.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 3, 4])
 |      >>> x.shape
 |      (4,)
 |      >>> y = np.zeros((2, 3, 4))
 |      >>> y.shape
 |      (2, 3, 4)
 |      >>> y.shape = (3, 8)
 |      >>> y
 |      array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
 |             [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
 |             [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])
 |      >>> y.shape = (3, 6)
 |      Traceback (most recent call last):
 |        File "<stdin>", line 1, in <module>
 |      ValueError: total size of new array must be unchanged
 |      >>> np.zeros((4,2))[::2].shape = (-1,)
 |      Traceback (most recent call last):
 |        File "<stdin>", line 1, in <module>
 |      AttributeError: Incompatible shape for in-place modification. Use
 |      `.reshape()` to make a copy with the desired shape.
 |
 |      See Also
 |      --------
 |      numpy.shape : Equivalent getter function.
 |      numpy.reshape : Function similar to setting ``shape``.
 |      ndarray.reshape : Method similar to setting ``shape``.
 |
 |  size
 |      Number of elements in the array.
 |
 |      Equal to ``np.prod(a.shape)``, i.e., the product of the array's
 |      dimensions.
 |
 |      Notes
 |      -----
 |      `a.size` returns a standard arbitrary precision Python integer. This
 |      may not be the case with other methods of obtaining the same value
 |      (like the suggested ``np.prod(a.shape)``, which returns an instance
 |      of ``np.int_``), and may be relevant if the value is used further in
 |      calculations that may overflow a fixed size integer type.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.zeros((3, 5, 2), dtype=np.complex128)
 |      >>> x.size
 |      30
 |      >>> np.prod(x.shape)
 |      30
 |
 |  strides
 |      Tuple of bytes to step in each dimension when traversing an array.
 |
 |      The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a`
 |      is::
 |
 |          offset = sum(np.array(i) * a.strides)
 |
 |      A more detailed explanation of strides can be found in
 |      :ref:`arrays.ndarray`.
 |
 |      .. warning::
 |
 |          Setting ``arr.strides`` is discouraged and may be deprecated in the
 |          future.  `numpy.lib.stride_tricks.as_strided` should be preferred
 |          to create a new view of the same data in a safer way.
 |
 |      Notes
 |      -----
 |      Imagine an array of 32-bit integers (each 4 bytes)::
 |
 |        x = np.array([[0, 1, 2, 3, 4],
 |                      [5, 6, 7, 8, 9]], dtype=np.int32)
 |
 |      This array is stored in memory as 40 bytes, one after the other
 |      (known as a contiguous block of memory).  The strides of an array tell
 |      us how many bytes we have to skip in memory to move to the next position
 |      along a certain axis.  For example, we have to skip 4 bytes (1 value) to
 |      move to the next column, but 20 bytes (5 values) to get to the same
 |      position in the next row.  As such, the strides for the array `x` will be
 |      ``(20, 4)``.
 |
 |      See Also
 |      --------
 |      numpy.lib.stride_tricks.as_strided
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> y = np.reshape(np.arange(2*3*4), (2,3,4))
 |      >>> y
 |      array([[[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]],
 |             [[12, 13, 14, 15],
 |              [16, 17, 18, 19],
 |              [20, 21, 22, 23]]])
 |      >>> y.strides
 |      (48, 16, 4)
 |      >>> y[1,1,1]
 |      17
 |      >>> offset=sum(y.strides * np.array((1,1,1)))
 |      >>> offset/y.itemsize
 |      17
 |
 |      >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)
 |      >>> x.strides
 |      (32, 4, 224, 1344)
 |      >>> i = np.array([3,5,2,2])
 |      >>> offset = sum(i * x.strides)
 |      >>> x[3,5,2,2]
 |      813
 |      >>> offset / x.itemsize
 |      813
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes inherited from ndarray:
 |
 |  __hash__ = None

Python Library Documentation: function matrix_transpose in module autograd.tracer

matrix_transpose(*args, called_by_autograd_dispatcher=False, **kwargs)
    Transposes a matrix (or a stack of matrices) ``x``.

    This function is Array API compatible.

    Parameters
    ----------
    x : array_like
        Input array having shape (..., M, N) and whose two innermost
        dimensions form ``MxN`` matrices.

    Returns
    -------
    out : ndarray
        An array containing the transpose for each matrix and having shape
        (..., N, M).

    See Also
    --------
    transpose : Generic transpose method.

    Examples
    --------
    >>> import numpy as np
    >>> np.matrix_transpose([[1, 2], [3, 4]])
    array([[1, 3],
           [2, 4]])

    >>> np.matrix_transpose([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
    array([[[1, 3],
            [2, 4]],
           [[5, 7],
            [6, 8]]])

Python Library Documentation: function max in module autograd.tracer

max(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the maximum of an array or maximum along an axis.

    Parameters
    ----------
    a : array_like
        Input data.
    axis : None or int or tuple of ints, optional
        Axis or axes along which to operate.  By default, flattened input is
        used.

        .. versionadded:: 1.7.0

        If this is a tuple of ints, the maximum is selected over multiple axes,
        instead of a single axis or all the axes as before.
    out : ndarray, optional
        Alternative output array in which to place the result.  Must
        be of the same shape and buffer length as the expected output.
        See :ref:`ufuncs-output-type` for more details.

    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the input array.

        If the default value is passed, then `keepdims` will not be
        passed through to the ``max`` method of sub-classes of
        `ndarray`, however any non-default value will be.  If the
        sub-class' method does not implement `keepdims` any
        exceptions will be raised.

    initial : scalar, optional
        The minimum value of an output element. Must be present to allow
        computation on empty slice. See `~numpy.ufunc.reduce` for details.

        .. versionadded:: 1.15.0

    where : array_like of bool, optional
        Elements to compare for the maximum. See `~numpy.ufunc.reduce`
        for details.

        .. versionadded:: 1.17.0

    Returns
    -------
    max : ndarray or scalar
        Maximum of `a`. If `axis` is None, the result is a scalar value.
        If `axis` is an int, the result is an array of dimension
        ``a.ndim - 1``. If `axis` is a tuple, the result is an array of
        dimension ``a.ndim - len(axis)``.

    See Also
    --------
    amin :
        The minimum value of an array along a given axis, propagating any NaNs.
    nanmax :
        The maximum value of an array along a given axis, ignoring any NaNs.
    maximum :
        Element-wise maximum of two arrays, propagating any NaNs.
    fmax :
        Element-wise maximum of two arrays, ignoring any NaNs.
    argmax :
        Return the indices of the maximum values.

    nanmin, minimum, fmin

    Notes
    -----
    NaN values are propagated, that is if at least one item is NaN, the
    corresponding max value will be NaN as well. To ignore NaN values
    (MATLAB behavior), please use nanmax.

    Don't use `~numpy.max` for element-wise comparison of 2 arrays; when
    ``a.shape[0]`` is 2, ``maximum(a[0], a[1])`` is faster than
    ``max(a, axis=0)``.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.arange(4).reshape((2,2))
    >>> a
    array([[0, 1],
           [2, 3]])
    >>> np.max(a)           # Maximum of the flattened array
    3
    >>> np.max(a, axis=0)   # Maxima along the first axis
    array([2, 3])
    >>> np.max(a, axis=1)   # Maxima along the second axis
    array([1, 3])
    >>> np.max(a, where=[False, True], initial=-1, axis=0)
    array([-1,  3])
    >>> b = np.arange(5, dtype=float)
    >>> b[2] = np.nan
    >>> np.max(b)
    np.float64(nan)
    >>> np.max(b, where=~np.isnan(b), initial=-1)
    4.0
    >>> np.nanmax(b)
    4.0

    You can use an initial value to compute the maximum of an empty slice, or
    to initialize it to a different value:

    >>> np.max([[-50], [10]], axis=-1, initial=0)
    array([ 0, 10])

    Notice that the initial value is used as one of the elements for which the
    maximum is determined, unlike for the default argument Python's max
    function, which is only used for empty iterables.

    >>> np.max([5], initial=6)
    6
    >>> max([5], default=6)
    5

Python Library Documentation: function maximum in module autograd.tracer

maximum(*args, called_by_autograd_dispatcher=False, **kwargs)
    maximum(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Element-wise maximum of array elements.

    Compare two arrays and return a new array containing the element-wise
    maxima. If one of the elements being compared is a NaN, then that
    element is returned. If both elements are NaNs then the first is
    returned. The latter distinction is important for complex NaNs, which
    are defined as at least one of the real or imaginary parts being a NaN.
    The net effect is that NaNs are propagated.

    Parameters
    ----------
    x1, x2 : array_like
        The arrays holding the elements to be compared.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray or scalar
        The maximum of `x1` and `x2`, element-wise.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    minimum :
        Element-wise minimum of two arrays, propagates NaNs.
    fmax :
        Element-wise maximum of two arrays, ignores NaNs.
    amax :
        The maximum value of an array along a given axis, propagates NaNs.
    nanmax :
        The maximum value of an array along a given axis, ignores NaNs.

    fmin, amin, nanmin

    Notes
    -----
    The maximum is equivalent to ``np.where(x1 >= x2, x1, x2)`` when
    neither x1 nor x2 are nans, but it is faster and does proper
    broadcasting.

    Examples
    --------
    >>> import numpy as np
    >>> np.maximum([2, 3, 4], [1, 5, 2])
    array([2, 5, 4])

    >>> np.maximum(np.eye(2), [0.5, 2]) # broadcasting
    array([[ 1. ,  2. ],
           [ 0.5,  2. ]])

    >>> np.maximum([np.nan, 0, np.nan], [0, np.nan, np.nan])
    array([nan, nan, nan])
    >>> np.maximum(np.inf, 1)
    inf

Python Library Documentation: function may_share_memory in module autograd.tracer

may_share_memory(*args, called_by_autograd_dispatcher=False, **kwargs)
    may_share_memory(a, b, /, max_work=None)

    Determine if two arrays might share memory

    A return of True does not necessarily mean that the two arrays
    share any element.  It just means that they *might*.

    Only the memory bounds of a and b are checked by default.

    Parameters
    ----------
    a, b : ndarray
        Input arrays
    max_work : int, optional
        Effort to spend on solving the overlap problem.  See
        `shares_memory` for details.  Default for ``may_share_memory``
        is to do a bounds check.

    Returns
    -------
    out : bool

    See Also
    --------
    shares_memory

    Examples
    --------
    >>> import numpy as np
    >>> np.may_share_memory(np.array([1,2]), np.array([5,8,9]))
    False
    >>> x = np.zeros([3, 4])
    >>> np.may_share_memory(x[:,0], x[:,1])
    True

Python Library Documentation: function mean in module autograd.numpy.numpy_wrapper

mean(a, *args, **kwargs)
    Wrapper that converts list/tuple to array before computing mean.

    This is needed because numpy's internal mean implementation calls
    float() on the result, which fails for ArrayBox objects.

Python Library Documentation: function median in module autograd.tracer

median(*args, called_by_autograd_dispatcher=False, **kwargs)
    Compute the median along the specified axis.

    Returns the median of the array elements.

    Parameters
    ----------
    a : array_like
        Input array or object that can be converted to an array.
    axis : {int, sequence of int, None}, optional
        Axis or axes along which the medians are computed. The default,
        axis=None, will compute the median along a flattened version of
        the array.

        .. versionadded:: 1.9.0

        If a sequence of axes, the array is first flattened along the
        given axes, then the median is computed along the resulting
        flattened axis.
    out : ndarray, optional
        Alternative output array in which to place the result. It must
        have the same shape and buffer length as the expected output,
        but the type (of the output) will be cast if necessary.
    overwrite_input : bool, optional
       If True, then allow use of memory of input array `a` for
       calculations. The input array will be modified by the call to
       `median`. This will save memory when you do not need to preserve
       the contents of the input array. Treat the input as undefined,
       but it will probably be fully or partially sorted. Default is
       False. If `overwrite_input` is ``True`` and `a` is not already an
       `ndarray`, an error will be raised.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the original `arr`.

        .. versionadded:: 1.9.0

    Returns
    -------
    median : ndarray
        A new array holding the result. If the input contains integers
        or floats smaller than ``float64``, then the output data-type is
        ``np.float64``.  Otherwise, the data-type of the output is the
        same as that of the input. If `out` is specified, that array is
        returned instead.

    See Also
    --------
    mean, percentile

    Notes
    -----
    Given a vector ``V`` of length ``N``, the median of ``V`` is the
    middle value of a sorted copy of ``V``, ``V_sorted`` - i
    e., ``V_sorted[(N-1)/2]``, when ``N`` is odd, and the average of the
    two middle values of ``V_sorted`` when ``N`` is even.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[10, 7, 4], [3, 2, 1]])
    >>> a
    array([[10,  7,  4],
           [ 3,  2,  1]])
    >>> np.median(a)
    np.float64(3.5)
    >>> np.median(a, axis=0)
    array([6.5, 4.5, 2.5])
    >>> np.median(a, axis=1)
    array([7.,  2.])
    >>> np.median(a, axis=(0, 1))
    np.float64(3.5)
    >>> m = np.median(a, axis=0)
    >>> out = np.zeros_like(m)
    >>> np.median(a, axis=0, out=m)
    array([6.5,  4.5,  2.5])
    >>> m
    array([6.5,  4.5,  2.5])
    >>> b = a.copy()
    >>> np.median(b, axis=1, overwrite_input=True)
    array([7.,  2.])
    >>> assert not np.all(a==b)
    >>> b = a.copy()
    >>> np.median(b, axis=None, overwrite_input=True)
    np.float64(3.5)
    >>> assert not np.all(a==b)

Python Library Documentation: class memmap in module numpy

class memmap(ndarray)
 |  memmap(filename, dtype=<class 'numpy.uint8'>, mode='r+', offset=0, shape=None, order='C')
 |
 |  Create a memory-map to an array stored in a *binary* file on disk.
 |
 |  Memory-mapped files are used for accessing small segments of large files
 |  on disk, without reading the entire file into memory.  NumPy's
 |  memmap's are array-like objects.  This differs from Python's ``mmap``
 |  module, which uses file-like objects.
 |
 |  This subclass of ndarray has some unpleasant interactions with
 |  some operations, because it doesn't quite fit properly as a subclass.
 |  An alternative to using this subclass is to create the ``mmap``
 |  object yourself, then create an ndarray with ndarray.__new__ directly,
 |  passing the object created in its 'buffer=' parameter.
 |
 |  This class may at some point be turned into a factory function
 |  which returns a view into an mmap buffer.
 |
 |  Flush the memmap instance to write the changes to the file. Currently there
 |  is no API to close the underlying ``mmap``. It is tricky to ensure the
 |  resource is actually closed, since it may be shared between different
 |  memmap instances.
 |
 |
 |  Parameters
 |  ----------
 |  filename : str, file-like object, or pathlib.Path instance
 |      The file name or file object to be used as the array data buffer.
 |  dtype : data-type, optional
 |      The data-type used to interpret the file contents.
 |      Default is `uint8`.
 |  mode : {'r+', 'r', 'w+', 'c'}, optional
 |      The file is opened in this mode:
 |
 |      +------+-------------------------------------------------------------+
 |      | 'r'  | Open existing file for reading only.                        |
 |      +------+-------------------------------------------------------------+
 |      | 'r+' | Open existing file for reading and writing.                 |
 |      +------+-------------------------------------------------------------+
 |      | 'w+' | Create or overwrite existing file for reading and writing.  |
 |      |      | If ``mode == 'w+'`` then `shape` must also be specified.    |
 |      +------+-------------------------------------------------------------+
 |      | 'c'  | Copy-on-write: assignments affect data in memory, but       |
 |      |      | changes are not saved to disk.  The file on disk is         |
 |      |      | read-only.                                                  |
 |      +------+-------------------------------------------------------------+
 |
 |      Default is 'r+'.
 |  offset : int, optional
 |      In the file, array data starts at this offset. Since `offset` is
 |      measured in bytes, it should normally be a multiple of the byte-size
 |      of `dtype`. When ``mode != 'r'``, even positive offsets beyond end of
 |      file are valid; The file will be extended to accommodate the
 |      additional data. By default, ``memmap`` will start at the beginning of
 |      the file, even if ``filename`` is a file pointer ``fp`` and
 |      ``fp.tell() != 0``.
 |  shape : int or sequence of ints, optional
 |      The desired shape of the array. If ``mode == 'r'`` and the number
 |      of remaining bytes after `offset` is not a multiple of the byte-size
 |      of `dtype`, you must specify `shape`. By default, the returned array
 |      will be 1-D with the number of elements determined by file size
 |      and data-type.
 |
 |      .. versionchanged:: 2.0
 |       The shape parameter can now be any integer sequence type, previously
 |       types were limited to tuple and int.
 |
 |  order : {'C', 'F'}, optional
 |      Specify the order of the ndarray memory layout:
 |      :term:`row-major`, C-style or :term:`column-major`,
 |      Fortran-style.  This only has an effect if the shape is
 |      greater than 1-D.  The default order is 'C'.
 |
 |  Attributes
 |  ----------
 |  filename : str or pathlib.Path instance
 |      Path to the mapped file.
 |  offset : int
 |      Offset position in the file.
 |  mode : str
 |      File mode.
 |
 |  Methods
 |  -------
 |  flush
 |      Flush any changes in memory to file on disk.
 |      When you delete a memmap object, flush is called first to write
 |      changes to disk.
 |
 |
 |  See also
 |  --------
 |  lib.format.open_memmap : Create or load a memory-mapped ``.npy`` file.
 |
 |  Notes
 |  -----
 |  The memmap object can be used anywhere an ndarray is accepted.
 |  Given a memmap ``fp``, ``isinstance(fp, numpy.ndarray)`` returns
 |  ``True``.
 |
 |  Memory-mapped files cannot be larger than 2GB on 32-bit systems.
 |
 |  When a memmap causes a file to be created or extended beyond its
 |  current size in the filesystem, the contents of the new part are
 |  unspecified. On systems with POSIX filesystem semantics, the extended
 |  part will be filled with zero bytes.
 |
 |  Examples
 |  --------
 |  >>> import numpy as np
 |  >>> data = np.arange(12, dtype='float32')
 |  >>> data.resize((3,4))
 |
 |  This example uses a temporary file so that doctest doesn't write
 |  files to your directory. You would use a 'normal' filename.
 |
 |  >>> from tempfile import mkdtemp
 |  >>> import os.path as path
 |  >>> filename = path.join(mkdtemp(), 'newfile.dat')
 |
 |  Create a memmap with dtype and shape that matches our data:
 |
 |  >>> fp = np.memmap(filename, dtype='float32', mode='w+', shape=(3,4))
 |  >>> fp
 |  memmap([[0., 0., 0., 0.],
 |          [0., 0., 0., 0.],
 |          [0., 0., 0., 0.]], dtype=float32)
 |
 |  Write data to memmap array:
 |
 |  >>> fp[:] = data[:]
 |  >>> fp
 |  memmap([[  0.,   1.,   2.,   3.],
 |          [  4.,   5.,   6.,   7.],
 |          [  8.,   9.,  10.,  11.]], dtype=float32)
 |
 |  >>> fp.filename == path.abspath(filename)
 |  True
 |
 |  Flushes memory changes to disk in order to read them back
 |
 |  >>> fp.flush()
 |
 |  Load the memmap and verify data was stored:
 |
 |  >>> newfp = np.memmap(filename, dtype='float32', mode='r', shape=(3,4))
 |  >>> newfp
 |  memmap([[  0.,   1.,   2.,   3.],
 |          [  4.,   5.,   6.,   7.],
 |          [  8.,   9.,  10.,  11.]], dtype=float32)
 |
 |  Read-only memmap:
 |
 |  >>> fpr = np.memmap(filename, dtype='float32', mode='r', shape=(3,4))
 |  >>> fpr.flags.writeable
 |  False
 |
 |  Copy-on-write memmap:
 |
 |  >>> fpc = np.memmap(filename, dtype='float32', mode='c', shape=(3,4))
 |  >>> fpc.flags.writeable
 |  True
 |
 |  It's possible to assign to copy-on-write array, but values are only
 |  written into the memory copy of the array, and not written to disk:
 |
 |  >>> fpc
 |  memmap([[  0.,   1.,   2.,   3.],
 |          [  4.,   5.,   6.,   7.],
 |          [  8.,   9.,  10.,  11.]], dtype=float32)
 |  >>> fpc[0,:] = 0
 |  >>> fpc
 |  memmap([[  0.,   0.,   0.,   0.],
 |          [  4.,   5.,   6.,   7.],
 |          [  8.,   9.,  10.,  11.]], dtype=float32)
 |
 |  File on disk is unchanged:
 |
 |  >>> fpr
 |  memmap([[  0.,   1.,   2.,   3.],
 |          [  4.,   5.,   6.,   7.],
 |          [  8.,   9.,  10.,  11.]], dtype=float32)
 |
 |  Offset into a memmap:
 |
 |  >>> fpo = np.memmap(filename, dtype='float32', mode='r', offset=16)
 |  >>> fpo
 |  memmap([  4.,   5.,   6.,   7.,   8.,   9.,  10.,  11.], dtype=float32)
 |
 |  Method resolution order:
 |      memmap
 |      ndarray
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __array_finalize__(self, obj) from numpy._core.memmap.memmap
 |      a.__array_finalize__(obj, /)
 |
 |      Present so subclasses can call super. Does nothing.
 |
 |  __array_wrap__(self, arr, context=None, return_scalar=False) from numpy._core.memmap.memmap
 |      a.__array_wrap__(array[, context], /)
 |
 |      Returns a view of `array` with the same type as self.
 |
 |  __getitem__(self, index) from numpy._core.memmap.memmap
 |      Return self[key].
 |
 |  flush(self) from numpy._core.memmap.memmap
 |      Write any changes in the array to the file on disk.
 |
 |      For further information, see `memmap`.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      See Also
 |      --------
 |      memmap
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(subtype, filename, dtype=<class 'numpy.uint8'>, mode='r+', offset=0, shape=None, order='C') from numpy._core.memmap.memmap
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes defined here:
 |
 |  __array_priority__ = -100.0
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from ndarray:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      a.__array__([dtype], *, copy=None)
 |
 |      For ``dtype`` parameter it returns a new reference to self if
 |      ``dtype`` is not given or it matches array's data type.
 |      A new array of provided data type is returned if ``dtype``
 |      is different from the current data type of the array.
 |      For ``copy`` parameter it returns a new reference to self if
 |      ``copy=False`` or ``copy=None`` and copying isn't enforced by ``dtype``
 |      parameter. The method returns a new array for ``copy=True``, regardless of
 |      ``dtype`` parameter.
 |
 |      A more detailed explanation of the ``__array__`` interface
 |      can be found in :ref:`dunder_array.interface`.
 |
 |  __array_function__(...)
 |
 |  __array_namespace__(...)
 |
 |  __array_ufunc__(...)
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __complex__(...)
 |
 |  __contains__(self, key, /)
 |      Return bool(key in self).
 |
 |  __copy__(...)
 |      a.__copy__()
 |
 |      Used if :func:`copy.copy` is called on an array. Returns a copy of the array.
 |
 |      Equivalent to ``a.copy(order='K')``.
 |
 |  __deepcopy__(...)
 |      a.__deepcopy__(memo, /)
 |
 |      Used if :func:`copy.deepcopy` is called on an array.
 |
 |  __delitem__(self, key, /)
 |      Delete self[key].
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __dlpack__(...)
 |      a.__dlpack__(*, stream=None, max_version=None, dl_device=None, copy=None)
 |
 |      DLPack Protocol: Part of the Array API.
 |
 |  __dlpack_device__(...)
 |      a.__dlpack_device__()
 |
 |      DLPack Protocol: Part of the Array API.
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      Default object formatter.
 |
 |      Return str(self) if format_spec is empty. Raise TypeError otherwise.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __iadd__(self, value, /)
 |      Return self+=value.
 |
 |  __iand__(self, value, /)
 |      Return self&=value.
 |
 |  __ifloordiv__(self, value, /)
 |      Return self//=value.
 |
 |  __ilshift__(self, value, /)
 |      Return self<<=value.
 |
 |  __imatmul__(self, value, /)
 |      Return self@=value.
 |
 |  __imod__(self, value, /)
 |      Return self%=value.
 |
 |  __imul__(self, value, /)
 |      Return self*=value.
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __ior__(self, value, /)
 |      Return self|=value.
 |
 |  __ipow__(self, value, /)
 |      Return self**=value.
 |
 |  __irshift__(self, value, /)
 |      Return self>>=value.
 |
 |  __isub__(self, value, /)
 |      Return self-=value.
 |
 |  __iter__(self, /)
 |      Implement iter(self).
 |
 |  __itruediv__(self, value, /)
 |      Return self/=value.
 |
 |  __ixor__(self, value, /)
 |      Return self^=value.
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __matmul__(self, value, /)
 |      Return self@value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      a.__reduce__()
 |
 |      For pickling.
 |
 |  __reduce_ex__(...)
 |      Helper for pickle.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmatmul__(self, value, /)
 |      Return value@self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setitem__(self, key, value, /)
 |      Set self[key] to value.
 |
 |  __setstate__(...)
 |      a.__setstate__(state, /)
 |
 |      For unpickling.
 |
 |      The `state` argument must be a sequence that contains the following
 |      elements:
 |
 |      Parameters
 |      ----------
 |      version : int
 |          optional pickle version. If omitted defaults to 0.
 |      shape : tuple
 |      dtype : data-type
 |      isFortran : bool
 |      rawdata : string or list
 |          a binary string with the data (or a list if 'a' is an object array)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      a.all(axis=None, out=None, keepdims=False, *, where=True)
 |
 |      Returns True if all elements evaluate to True.
 |
 |      Refer to `numpy.all` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.all : equivalent function
 |
 |  any(...)
 |      a.any(axis=None, out=None, keepdims=False, *, where=True)
 |
 |      Returns True if any of the elements of `a` evaluate to True.
 |
 |      Refer to `numpy.any` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.any : equivalent function
 |
 |  argmax(...)
 |      a.argmax(axis=None, out=None, *, keepdims=False)
 |
 |      Return indices of the maximum values along the given axis.
 |
 |      Refer to `numpy.argmax` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.argmax : equivalent function
 |
 |  argmin(...)
 |      a.argmin(axis=None, out=None, *, keepdims=False)
 |
 |      Return indices of the minimum values along the given axis.
 |
 |      Refer to `numpy.argmin` for detailed documentation.
 |
 |      See Also
 |      --------
 |      numpy.argmin : equivalent function
 |
 |  argpartition(...)
 |      a.argpartition(kth, axis=-1, kind='introselect', order=None)
 |
 |      Returns the indices that would partition this array.
 |
 |      Refer to `numpy.argpartition` for full documentation.
 |
 |      .. versionadded:: 1.8.0
 |
 |      See Also
 |      --------
 |      numpy.argpartition : equivalent function
 |
 |  argsort(...)
 |      a.argsort(axis=-1, kind=None, order=None)
 |
 |      Returns the indices that would sort this array.
 |
 |      Refer to `numpy.argsort` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.argsort : equivalent function
 |
 |  astype(...)
 |      a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True)
 |
 |      Copy of the array, cast to a specified type.
 |
 |      Parameters
 |      ----------
 |      dtype : str or dtype
 |          Typecode or data-type to which the array is cast.
 |      order : {'C', 'F', 'A', 'K'}, optional
 |          Controls the memory layout order of the result.
 |          'C' means C order, 'F' means Fortran order, 'A'
 |          means 'F' order if all the arrays are Fortran contiguous,
 |          'C' order otherwise, and 'K' means as close to the
 |          order the array elements appear in memory as possible.
 |          Default is 'K'.
 |      casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
 |          Controls what kind of data casting may occur. Defaults to 'unsafe'
 |          for backwards compatibility.
 |
 |          * 'no' means the data types should not be cast at all.
 |          * 'equiv' means only byte-order changes are allowed.
 |          * 'safe' means only casts which can preserve values are allowed.
 |          * 'same_kind' means only safe casts or casts within a kind,
 |            like float64 to float32, are allowed.
 |          * 'unsafe' means any data conversions may be done.
 |      subok : bool, optional
 |          If True, then sub-classes will be passed-through (default), otherwise
 |          the returned array will be forced to be a base-class array.
 |      copy : bool, optional
 |          By default, astype always returns a newly allocated array. If this
 |          is set to false, and the `dtype`, `order`, and `subok`
 |          requirements are satisfied, the input array is returned instead
 |          of a copy.
 |
 |      Returns
 |      -------
 |      arr_t : ndarray
 |          Unless `copy` is False and the other conditions for returning the input
 |          array are satisfied (see description for `copy` input parameter), `arr_t`
 |          is a new array of the same shape as the input array, with dtype, order
 |          given by `dtype`, `order`.
 |
 |      Notes
 |      -----
 |      .. versionchanged:: 1.17.0
 |         Casting between a simple data type and a structured one is possible only
 |         for "unsafe" casting.  Casting to multiple fields is allowed, but
 |         casting from multiple fields is not.
 |
 |      .. versionchanged:: 1.9.0
 |         Casting from numeric to string types in 'safe' casting mode requires
 |         that the string dtype length is long enough to store the max
 |         integer/float value converted.
 |
 |      Raises
 |      ------
 |      ComplexWarning
 |          When casting from complex to float or int. To avoid this,
 |          one should use ``a.real.astype(t)``.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 2.5])
 |      >>> x
 |      array([1. ,  2. ,  2.5])
 |
 |      >>> x.astype(int)
 |      array([1, 2, 2])
 |
 |  byteswap(...)
 |      a.byteswap(inplace=False)
 |
 |      Swap the bytes of the array elements
 |
 |      Toggle between low-endian and big-endian data representation by
 |      returning a byteswapped array, optionally swapped in-place.
 |      Arrays of byte-strings are not swapped. The real and imaginary
 |      parts of a complex number are swapped individually.
 |
 |      Parameters
 |      ----------
 |      inplace : bool, optional
 |          If ``True``, swap bytes in-place, default is ``False``.
 |
 |      Returns
 |      -------
 |      out : ndarray
 |          The byteswapped array. If `inplace` is ``True``, this is
 |          a view to self.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> A = np.array([1, 256, 8755], dtype=np.int16)
 |      >>> list(map(hex, A))
 |      ['0x1', '0x100', '0x2233']
 |      >>> A.byteswap(inplace=True)
 |      array([  256,     1, 13090], dtype=int16)
 |      >>> list(map(hex, A))
 |      ['0x100', '0x1', '0x3322']
 |
 |      Arrays of byte-strings are not swapped
 |
 |      >>> A = np.array([b'ceg', b'fac'])
 |      >>> A.byteswap()
 |      array([b'ceg', b'fac'], dtype='|S3')
 |
 |      ``A.view(A.dtype.newbyteorder()).byteswap()`` produces an array with
 |      the same values but different representation in memory
 |
 |      >>> A = np.array([1, 2, 3])
 |      >>> A.view(np.uint8)
 |      array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,
 |             0, 0], dtype=uint8)
 |      >>> A.view(A.dtype.newbyteorder()).byteswap(inplace=True)
 |      array([1, 2, 3])
 |      >>> A.view(np.uint8)
 |      array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0,
 |             0, 3], dtype=uint8)
 |
 |  choose(...)
 |      a.choose(choices, out=None, mode='raise')
 |
 |      Use an index array to construct a new array from a set of choices.
 |
 |      Refer to `numpy.choose` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.choose : equivalent function
 |
 |  clip(...)
 |      a.clip(min=None, max=None, out=None, **kwargs)
 |
 |      Return an array whose values are limited to ``[min, max]``.
 |      One of max or min must be given.
 |
 |      Refer to `numpy.clip` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.clip : equivalent function
 |
 |  compress(...)
 |      a.compress(condition, axis=None, out=None)
 |
 |      Return selected slices of this array along given axis.
 |
 |      Refer to `numpy.compress` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.compress : equivalent function
 |
 |  conj(...)
 |      a.conj()
 |
 |      Complex-conjugate all elements.
 |
 |      Refer to `numpy.conjugate` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.conjugate : equivalent function
 |
 |  conjugate(...)
 |      a.conjugate()
 |
 |      Return the complex conjugate, element-wise.
 |
 |      Refer to `numpy.conjugate` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.conjugate : equivalent function
 |
 |  copy(...)
 |      a.copy(order='C')
 |
 |      Return a copy of the array.
 |
 |      Parameters
 |      ----------
 |      order : {'C', 'F', 'A', 'K'}, optional
 |          Controls the memory layout of the copy. 'C' means C-order,
 |          'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
 |          'C' otherwise. 'K' means match the layout of `a` as closely
 |          as possible. (Note that this function and :func:`numpy.copy` are very
 |          similar but have different default values for their order=
 |          arguments, and this function always passes sub-classes through.)
 |
 |      See also
 |      --------
 |      numpy.copy : Similar function with different default behavior
 |      numpy.copyto
 |
 |      Notes
 |      -----
 |      This function is the preferred method for creating an array copy.  The
 |      function :func:`numpy.copy` is similar, but it defaults to using order 'K',
 |      and will not pass sub-classes through by default.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([[1,2,3],[4,5,6]], order='F')
 |
 |      >>> y = x.copy()
 |
 |      >>> x.fill(0)
 |
 |      >>> x
 |      array([[0, 0, 0],
 |             [0, 0, 0]])
 |
 |      >>> y
 |      array([[1, 2, 3],
 |             [4, 5, 6]])
 |
 |      >>> y.flags['C_CONTIGUOUS']
 |      True
 |
 |      For arrays containing Python objects (e.g. dtype=object),
 |      the copy is a shallow one. The new array will contain the
 |      same object which may lead to surprises if that object can
 |      be modified (is mutable):
 |
 |      >>> a = np.array([1, 'm', [2, 3, 4]], dtype=object)
 |      >>> b = a.copy()
 |      >>> b[2][0] = 10
 |      >>> a
 |      array([1, 'm', list([10, 3, 4])], dtype=object)
 |
 |      To ensure all elements within an ``object`` array are copied,
 |      use `copy.deepcopy`:
 |
 |      >>> import copy
 |      >>> a = np.array([1, 'm', [2, 3, 4]], dtype=object)
 |      >>> c = copy.deepcopy(a)
 |      >>> c[2][0] = 10
 |      >>> c
 |      array([1, 'm', list([10, 3, 4])], dtype=object)
 |      >>> a
 |      array([1, 'm', list([2, 3, 4])], dtype=object)
 |
 |  cumprod(...)
 |      a.cumprod(axis=None, dtype=None, out=None)
 |
 |      Return the cumulative product of the elements along the given axis.
 |
 |      Refer to `numpy.cumprod` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.cumprod : equivalent function
 |
 |  cumsum(...)
 |      a.cumsum(axis=None, dtype=None, out=None)
 |
 |      Return the cumulative sum of the elements along the given axis.
 |
 |      Refer to `numpy.cumsum` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.cumsum : equivalent function
 |
 |  diagonal(...)
 |      a.diagonal(offset=0, axis1=0, axis2=1)
 |
 |      Return specified diagonals. In NumPy 1.9 the returned array is a
 |      read-only view instead of a copy as in previous NumPy versions.  In
 |      a future version the read-only restriction will be removed.
 |
 |      Refer to :func:`numpy.diagonal` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.diagonal : equivalent function
 |
 |  dot(...)
 |
 |  dump(...)
 |      a.dump(file)
 |
 |      Dump a pickle of the array to the specified file.
 |      The array can be read back with pickle.load or numpy.load.
 |
 |      Parameters
 |      ----------
 |      file : str or Path
 |          A string naming the dump file.
 |
 |          .. versionchanged:: 1.17.0
 |              `pathlib.Path` objects are now accepted.
 |
 |  dumps(...)
 |      a.dumps()
 |
 |      Returns the pickle of the array as a string.
 |      pickle.loads will convert the string back to an array.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |  fill(...)
 |      a.fill(value)
 |
 |      Fill the array with a scalar value.
 |
 |      Parameters
 |      ----------
 |      value : scalar
 |          All elements of `a` will be assigned this value.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([1, 2])
 |      >>> a.fill(0)
 |      >>> a
 |      array([0, 0])
 |      >>> a = np.empty(2)
 |      >>> a.fill(1)
 |      >>> a
 |      array([1.,  1.])
 |
 |      Fill expects a scalar value and always behaves the same as assigning
 |      to a single array element.  The following is a rare example where this
 |      distinction is important:
 |
 |      >>> a = np.array([None, None], dtype=object)
 |      >>> a[0] = np.array(3)
 |      >>> a
 |      array([array(3), None], dtype=object)
 |      >>> a.fill(np.array(3))
 |      >>> a
 |      array([array(3), array(3)], dtype=object)
 |
 |      Where other forms of assignments will unpack the array being assigned:
 |
 |      >>> a[...] = np.array(3)
 |      >>> a
 |      array([3, 3], dtype=object)
 |
 |  flatten(...)
 |      a.flatten(order='C')
 |
 |      Return a copy of the array collapsed into one dimension.
 |
 |      Parameters
 |      ----------
 |      order : {'C', 'F', 'A', 'K'}, optional
 |          'C' means to flatten in row-major (C-style) order.
 |          'F' means to flatten in column-major (Fortran-
 |          style) order. 'A' means to flatten in column-major
 |          order if `a` is Fortran *contiguous* in memory,
 |          row-major order otherwise. 'K' means to flatten
 |          `a` in the order the elements occur in memory.
 |          The default is 'C'.
 |
 |      Returns
 |      -------
 |      y : ndarray
 |          A copy of the input array, flattened to one dimension.
 |
 |      See Also
 |      --------
 |      ravel : Return a flattened array.
 |      flat : A 1-D flat iterator over the array.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1,2], [3,4]])
 |      >>> a.flatten()
 |      array([1, 2, 3, 4])
 |      >>> a.flatten('F')
 |      array([1, 3, 2, 4])
 |
 |  getfield(...)
 |      a.getfield(dtype, offset=0)
 |
 |      Returns a field of the given array as a certain type.
 |
 |      A field is a view of the array data with a given data-type. The values in
 |      the view are determined by the given type and the offset into the current
 |      array in bytes. The offset needs to be such that the view dtype fits in the
 |      array dtype; for example an array of dtype complex128 has 16-byte elements.
 |      If taking a view with a 32-bit integer (4 bytes), the offset needs to be
 |      between 0 and 12 bytes.
 |
 |      Parameters
 |      ----------
 |      dtype : str or dtype
 |          The data type of the view. The dtype size of the view can not be larger
 |          than that of the array itself.
 |      offset : int
 |          Number of bytes to skip before beginning the element view.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.diag([1.+1.j]*2)
 |      >>> x[1, 1] = 2 + 4.j
 |      >>> x
 |      array([[1.+1.j,  0.+0.j],
 |             [0.+0.j,  2.+4.j]])
 |      >>> x.getfield(np.float64)
 |      array([[1.,  0.],
 |             [0.,  2.]])
 |
 |      By choosing an offset of 8 bytes we can select the complex part of the
 |      array for our view:
 |
 |      >>> x.getfield(np.float64, offset=8)
 |      array([[1.,  0.],
 |             [0.,  4.]])
 |
 |  item(...)
 |      a.item(*args)
 |
 |      Copy an element of an array to a standard Python scalar and return it.
 |
 |      Parameters
 |      ----------
 |      \*args : Arguments (variable number and type)
 |
 |          * none: in this case, the method only works for arrays
 |            with one element (`a.size == 1`), which element is
 |            copied into a standard Python scalar object and returned.
 |
 |          * int_type: this argument is interpreted as a flat index into
 |            the array, specifying which element to copy and return.
 |
 |          * tuple of int_types: functions as does a single int_type argument,
 |            except that the argument is interpreted as an nd-index into the
 |            array.
 |
 |      Returns
 |      -------
 |      z : Standard Python scalar object
 |          A copy of the specified element of the array as a suitable
 |          Python scalar
 |
 |      Notes
 |      -----
 |      When the data type of `a` is longdouble or clongdouble, item() returns
 |      a scalar array object because there is no available Python scalar that
 |      would not lose information. Void arrays return a buffer object for item(),
 |      unless fields are defined, in which case a tuple is returned.
 |
 |      `item` is very similar to a[args], except, instead of an array scalar,
 |      a standard Python scalar is returned. This can be useful for speeding up
 |      access to elements of the array and doing arithmetic on elements of the
 |      array using Python's optimized math.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.random.seed(123)
 |      >>> x = np.random.randint(9, size=(3, 3))
 |      >>> x
 |      array([[2, 2, 6],
 |             [1, 3, 6],
 |             [1, 0, 1]])
 |      >>> x.item(3)
 |      1
 |      >>> x.item(7)
 |      0
 |      >>> x.item((0, 1))
 |      2
 |      >>> x.item((2, 2))
 |      1
 |
 |      For an array with object dtype, elements are returned as-is.
 |
 |      >>> a = np.array([np.int64(1)], dtype=object)
 |      >>> a.item() #return np.int64
 |      np.int64(1)
 |
 |  max(...)
 |      a.max(axis=None, out=None, keepdims=False, initial=<no value>, where=True)
 |
 |      Return the maximum along a given axis.
 |
 |      Refer to `numpy.amax` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.amax : equivalent function
 |
 |  mean(...)
 |      a.mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True)
 |
 |      Returns the average of the array elements along given axis.
 |
 |      Refer to `numpy.mean` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.mean : equivalent function
 |
 |  min(...)
 |      a.min(axis=None, out=None, keepdims=False, initial=<no value>, where=True)
 |
 |      Return the minimum along a given axis.
 |
 |      Refer to `numpy.amin` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.amin : equivalent function
 |
 |  nonzero(...)
 |      a.nonzero()
 |
 |      Return the indices of the elements that are non-zero.
 |
 |      Refer to `numpy.nonzero` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.nonzero : equivalent function
 |
 |  partition(...)
 |      a.partition(kth, axis=-1, kind='introselect', order=None)
 |
 |      Partially sorts the elements in the array in such a way that the value of
 |      the element in k-th position is in the position it would be in a sorted
 |      array. In the output array, all elements smaller than the k-th element
 |      are located to the left of this element and all equal or greater are
 |      located to its right. The ordering of the elements in the two partitions
 |      on the either side of the k-th element in the output array is undefined.
 |
 |      .. versionadded:: 1.8.0
 |
 |      Parameters
 |      ----------
 |      kth : int or sequence of ints
 |          Element index to partition by. The kth element value will be in its
 |          final sorted position and all smaller elements will be moved before it
 |          and all equal or greater elements behind it.
 |          The order of all elements in the partitions is undefined.
 |          If provided with a sequence of kth it will partition all elements
 |          indexed by kth of them into their sorted position at once.
 |
 |          .. deprecated:: 1.22.0
 |              Passing booleans as index is deprecated.
 |      axis : int, optional
 |          Axis along which to sort. Default is -1, which means sort along the
 |          last axis.
 |      kind : {'introselect'}, optional
 |          Selection algorithm. Default is 'introselect'.
 |      order : str or list of str, optional
 |          When `a` is an array with fields defined, this argument specifies
 |          which fields to compare first, second, etc. A single field can
 |          be specified as a string, and not all fields need to be specified,
 |          but unspecified fields will still be used, in the order in which
 |          they come up in the dtype, to break ties.
 |
 |      See Also
 |      --------
 |      numpy.partition : Return a partitioned copy of an array.
 |      argpartition : Indirect partition.
 |      sort : Full sort.
 |
 |      Notes
 |      -----
 |      See ``np.partition`` for notes on the different algorithms.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([3, 4, 2, 1])
 |      >>> a.partition(3)
 |      >>> a
 |      array([2, 1, 3, 4]) # may vary
 |
 |      >>> a.partition((1, 3))
 |      >>> a
 |      array([1, 2, 3, 4])
 |
 |  prod(...)
 |      a.prod(axis=None, dtype=None, out=None, keepdims=False,
 |          initial=1, where=True)
 |
 |      Return the product of the array elements over the given axis
 |
 |      Refer to `numpy.prod` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.prod : equivalent function
 |
 |  put(...)
 |      a.put(indices, values, mode='raise')
 |
 |      Set ``a.flat[n] = values[n]`` for all `n` in indices.
 |
 |      Refer to `numpy.put` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.put : equivalent function
 |
 |  ravel(...)
 |      a.ravel([order])
 |
 |      Return a flattened array.
 |
 |      Refer to `numpy.ravel` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.ravel : equivalent function
 |
 |      ndarray.flat : a flat iterator on the array.
 |
 |  repeat(...)
 |      a.repeat(repeats, axis=None)
 |
 |      Repeat elements of an array.
 |
 |      Refer to `numpy.repeat` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.repeat : equivalent function
 |
 |  reshape(...)
 |      a.reshape(shape, /, *, order='C', copy=None)
 |
 |      Returns an array containing the same data with a new shape.
 |
 |      Refer to `numpy.reshape` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.reshape : equivalent function
 |
 |      Notes
 |      -----
 |      Unlike the free function `numpy.reshape`, this method on `ndarray` allows
 |      the elements of the shape parameter to be passed in as separate arguments.
 |      For example, ``a.reshape(10, 11)`` is equivalent to
 |      ``a.reshape((10, 11))``.
 |
 |  resize(...)
 |      a.resize(new_shape, refcheck=True)
 |
 |      Change shape and size of array in-place.
 |
 |      Parameters
 |      ----------
 |      new_shape : tuple of ints, or `n` ints
 |          Shape of resized array.
 |      refcheck : bool, optional
 |          If False, reference count will not be checked. Default is True.
 |
 |      Returns
 |      -------
 |      None
 |
 |      Raises
 |      ------
 |      ValueError
 |          If `a` does not own its own data or references or views to it exist,
 |          and the data memory must be changed.
 |          PyPy only: will always raise if the data memory must be changed, since
 |          there is no reliable way to determine if references or views to it
 |          exist.
 |
 |      SystemError
 |          If the `order` keyword argument is specified. This behaviour is a
 |          bug in NumPy.
 |
 |      See Also
 |      --------
 |      resize : Return a new array with the specified shape.
 |
 |      Notes
 |      -----
 |      This reallocates space for the data area if necessary.
 |
 |      Only contiguous arrays (data elements consecutive in memory) can be
 |      resized.
 |
 |      The purpose of the reference count check is to make sure you
 |      do not use this array as a buffer for another Python object and then
 |      reallocate the memory. However, reference counts can increase in
 |      other ways so if you are sure that you have not shared the memory
 |      for this array with another Python object, then you may safely set
 |      `refcheck` to False.
 |
 |      Examples
 |      --------
 |      Shrinking an array: array is flattened (in the order that the data are
 |      stored in memory), resized, and reshaped:
 |
 |      >>> import numpy as np
 |
 |      >>> a = np.array([[0, 1], [2, 3]], order='C')
 |      >>> a.resize((2, 1))
 |      >>> a
 |      array([[0],
 |             [1]])
 |
 |      >>> a = np.array([[0, 1], [2, 3]], order='F')
 |      >>> a.resize((2, 1))
 |      >>> a
 |      array([[0],
 |             [2]])
 |
 |      Enlarging an array: as above, but missing entries are filled with zeros:
 |
 |      >>> b = np.array([[0, 1], [2, 3]])
 |      >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple
 |      >>> b
 |      array([[0, 1, 2],
 |             [3, 0, 0]])
 |
 |      Referencing an array prevents resizing...
 |
 |      >>> c = a
 |      >>> a.resize((1, 1))
 |      Traceback (most recent call last):
 |      ...
 |      ValueError: cannot resize an array that references or is referenced ...
 |
 |      Unless `refcheck` is False:
 |
 |      >>> a.resize((1, 1), refcheck=False)
 |      >>> a
 |      array([[0]])
 |      >>> c
 |      array([[0]])
 |
 |  round(...)
 |      a.round(decimals=0, out=None)
 |
 |      Return `a` with each element rounded to the given number of decimals.
 |
 |      Refer to `numpy.around` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.around : equivalent function
 |
 |  searchsorted(...)
 |      a.searchsorted(v, side='left', sorter=None)
 |
 |      Find indices where elements of v should be inserted in a to maintain order.
 |
 |      For full documentation, see `numpy.searchsorted`
 |
 |      See Also
 |      --------
 |      numpy.searchsorted : equivalent function
 |
 |  setfield(...)
 |      a.setfield(val, dtype, offset=0)
 |
 |      Put a value into a specified place in a field defined by a data-type.
 |
 |      Place `val` into `a`'s field defined by `dtype` and beginning `offset`
 |      bytes into the field.
 |
 |      Parameters
 |      ----------
 |      val : object
 |          Value to be placed in field.
 |      dtype : dtype object
 |          Data-type of the field in which to place `val`.
 |      offset : int, optional
 |          The number of bytes into the field at which to place `val`.
 |
 |      Returns
 |      -------
 |      None
 |
 |      See Also
 |      --------
 |      getfield
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.eye(3)
 |      >>> x.getfield(np.float64)
 |      array([[1.,  0.,  0.],
 |             [0.,  1.,  0.],
 |             [0.,  0.,  1.]])
 |      >>> x.setfield(3, np.int32)
 |      >>> x.getfield(np.int32)
 |      array([[3, 3, 3],
 |             [3, 3, 3],
 |             [3, 3, 3]], dtype=int32)
 |      >>> x
 |      array([[1.0e+000, 1.5e-323, 1.5e-323],
 |             [1.5e-323, 1.0e+000, 1.5e-323],
 |             [1.5e-323, 1.5e-323, 1.0e+000]])
 |      >>> x.setfield(np.eye(3), np.int32)
 |      >>> x
 |      array([[1.,  0.,  0.],
 |             [0.,  1.,  0.],
 |             [0.,  0.,  1.]])
 |
 |  setflags(...)
 |      a.setflags(write=None, align=None, uic=None)
 |
 |      Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY,
 |      respectively.
 |
 |      These Boolean-valued flags affect how numpy interprets the memory
 |      area used by `a` (see Notes below). The ALIGNED flag can only
 |      be set to True if the data is actually aligned according to the type.
 |      The WRITEBACKIFCOPY flag can never be set
 |      to True. The flag WRITEABLE can only be set to True if the array owns its
 |      own memory, or the ultimate owner of the memory exposes a writeable buffer
 |      interface, or is a string. (The exception for string is made so that
 |      unpickling can be done without copying memory.)
 |
 |      Parameters
 |      ----------
 |      write : bool, optional
 |          Describes whether or not `a` can be written to.
 |      align : bool, optional
 |          Describes whether or not `a` is aligned properly for its type.
 |      uic : bool, optional
 |          Describes whether or not `a` is a copy of another "base" array.
 |
 |      Notes
 |      -----
 |      Array flags provide information about how the memory area used
 |      for the array is to be interpreted. There are 7 Boolean flags
 |      in use, only three of which can be changed by the user:
 |      WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.
 |
 |      WRITEABLE (W) the data area can be written to;
 |
 |      ALIGNED (A) the data and strides are aligned appropriately for the hardware
 |      (as determined by the compiler);
 |
 |      WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced
 |      by .base). When the C-API function PyArray_ResolveWritebackIfCopy is
 |      called, the base array will be updated with the contents of this array.
 |
 |      All flags can be accessed using the single (upper case) letter as well
 |      as the full name.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> y = np.array([[3, 1, 7],
 |      ...               [2, 0, 0],
 |      ...               [8, 5, 9]])
 |      >>> y
 |      array([[3, 1, 7],
 |             [2, 0, 0],
 |             [8, 5, 9]])
 |      >>> y.flags
 |        C_CONTIGUOUS : True
 |        F_CONTIGUOUS : False
 |        OWNDATA : True
 |        WRITEABLE : True
 |        ALIGNED : True
 |        WRITEBACKIFCOPY : False
 |      >>> y.setflags(write=0, align=0)
 |      >>> y.flags
 |        C_CONTIGUOUS : True
 |        F_CONTIGUOUS : False
 |        OWNDATA : True
 |        WRITEABLE : False
 |        ALIGNED : False
 |        WRITEBACKIFCOPY : False
 |      >>> y.setflags(uic=1)
 |      Traceback (most recent call last):
 |        File "<stdin>", line 1, in <module>
 |      ValueError: cannot set WRITEBACKIFCOPY flag to True
 |
 |  sort(...)
 |      a.sort(axis=-1, kind=None, order=None)
 |
 |      Sort an array in-place. Refer to `numpy.sort` for full documentation.
 |
 |      Parameters
 |      ----------
 |      axis : int, optional
 |          Axis along which to sort. Default is -1, which means sort along the
 |          last axis.
 |      kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
 |          Sorting algorithm. The default is 'quicksort'. Note that both 'stable'
 |          and 'mergesort' use timsort under the covers and, in general, the
 |          actual implementation will vary with datatype. The 'mergesort' option
 |          is retained for backwards compatibility.
 |
 |          .. versionchanged:: 1.15.0
 |             The 'stable' option was added.
 |
 |      order : str or list of str, optional
 |          When `a` is an array with fields defined, this argument specifies
 |          which fields to compare first, second, etc.  A single field can
 |          be specified as a string, and not all fields need be specified,
 |          but unspecified fields will still be used, in the order in which
 |          they come up in the dtype, to break ties.
 |
 |      See Also
 |      --------
 |      numpy.sort : Return a sorted copy of an array.
 |      numpy.argsort : Indirect sort.
 |      numpy.lexsort : Indirect stable sort on multiple keys.
 |      numpy.searchsorted : Find elements in sorted array.
 |      numpy.partition: Partial sort.
 |
 |      Notes
 |      -----
 |      See `numpy.sort` for notes on the different sorting algorithms.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1,4], [3,1]])
 |      >>> a.sort(axis=1)
 |      >>> a
 |      array([[1, 4],
 |             [1, 3]])
 |      >>> a.sort(axis=0)
 |      >>> a
 |      array([[1, 3],
 |             [1, 4]])
 |
 |      Use the `order` keyword to specify a field to use when sorting a
 |      structured array:
 |
 |      >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])
 |      >>> a.sort(order='y')
 |      >>> a
 |      array([(b'c', 1), (b'a', 2)],
 |            dtype=[('x', 'S1'), ('y', '<i8')])
 |
 |  squeeze(...)
 |      a.squeeze(axis=None)
 |
 |      Remove axes of length one from `a`.
 |
 |      Refer to `numpy.squeeze` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.squeeze : equivalent function
 |
 |  std(...)
 |      a.std(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)
 |
 |      Returns the standard deviation of the array elements along given axis.
 |
 |      Refer to `numpy.std` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.std : equivalent function
 |
 |  sum(...)
 |      a.sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)
 |
 |      Return the sum of the array elements over the given axis.
 |
 |      Refer to `numpy.sum` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.sum : equivalent function
 |
 |  swapaxes(...)
 |      a.swapaxes(axis1, axis2)
 |
 |      Return a view of the array with `axis1` and `axis2` interchanged.
 |
 |      Refer to `numpy.swapaxes` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.swapaxes : equivalent function
 |
 |  take(...)
 |      a.take(indices, axis=None, out=None, mode='raise')
 |
 |      Return an array formed from the elements of `a` at the given indices.
 |
 |      Refer to `numpy.take` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.take : equivalent function
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |      a.tobytes(order='C')
 |
 |      Construct Python bytes containing the raw data bytes in the array.
 |
 |      Constructs Python bytes showing a copy of the raw contents of
 |      data memory. The bytes object is produced in C-order by default.
 |      This behavior is controlled by the ``order`` parameter.
 |
 |      .. versionadded:: 1.9.0
 |
 |      Parameters
 |      ----------
 |      order : {'C', 'F', 'A'}, optional
 |          Controls the memory layout of the bytes object. 'C' means C-order,
 |          'F' means F-order, 'A' (short for *Any*) means 'F' if `a` is
 |          Fortran contiguous, 'C' otherwise. Default is 'C'.
 |
 |      Returns
 |      -------
 |      s : bytes
 |          Python bytes exhibiting a copy of `a`'s raw data.
 |
 |      See also
 |      --------
 |      frombuffer
 |          Inverse of this operation, construct a 1-dimensional array from Python
 |          bytes.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([[0, 1], [2, 3]], dtype='<u2')
 |      >>> x.tobytes()
 |      b'\x00\x00\x01\x00\x02\x00\x03\x00'
 |      >>> x.tobytes('C') == x.tobytes()
 |      True
 |      >>> x.tobytes('F')
 |      b'\x00\x00\x02\x00\x01\x00\x03\x00'
 |
 |  tofile(...)
 |      a.tofile(fid, sep="", format="%s")
 |
 |      Write array to a file as text or binary (default).
 |
 |      Data is always written in 'C' order, independent of the order of `a`.
 |      The data produced by this method can be recovered using the function
 |      fromfile().
 |
 |      Parameters
 |      ----------
 |      fid : file or str or Path
 |          An open file object, or a string containing a filename.
 |
 |          .. versionchanged:: 1.17.0
 |              `pathlib.Path` objects are now accepted.
 |
 |      sep : str
 |          Separator between array items for text output.
 |          If "" (empty), a binary file is written, equivalent to
 |          ``file.write(a.tobytes())``.
 |      format : str
 |          Format string for text file output.
 |          Each entry in the array is formatted to text by first converting
 |          it to the closest Python type, and then using "format" % item.
 |
 |      Notes
 |      -----
 |      This is a convenience function for quick storage of array data.
 |      Information on endianness and precision is lost, so this method is not a
 |      good choice for files intended to archive data or transport data between
 |      machines with different endianness. Some of these problems can be overcome
 |      by outputting the data as text files, at the expense of speed and file
 |      size.
 |
 |      When fid is a file object, array contents are directly written to the
 |      file, bypassing the file object's ``write`` method. As a result, tofile
 |      cannot be used with files objects supporting compression (e.g., GzipFile)
 |      or file-like objects that do not support ``fileno()`` (e.g., BytesIO).
 |
 |  tolist(...)
 |      a.tolist()
 |
 |      Return the array as an ``a.ndim``-levels deep nested list of Python scalars.
 |
 |      Return a copy of the array data as a (nested) Python list.
 |      Data items are converted to the nearest compatible builtin Python type, via
 |      the `~numpy.ndarray.item` function.
 |
 |      If ``a.ndim`` is 0, then since the depth of the nested list is 0, it will
 |      not be a list at all, but a simple Python scalar.
 |
 |      Parameters
 |      ----------
 |      none
 |
 |      Returns
 |      -------
 |      y : object, or list of object, or list of list of object, or ...
 |          The possibly nested list of array elements.
 |
 |      Notes
 |      -----
 |      The array may be recreated via ``a = np.array(a.tolist())``, although this
 |      may sometimes lose precision.
 |
 |      Examples
 |      --------
 |      For a 1D array, ``a.tolist()`` is almost the same as ``list(a)``,
 |      except that ``tolist`` changes numpy scalars to Python scalars:
 |
 |      >>> import numpy as np
 |      >>> a = np.uint32([1, 2])
 |      >>> a_list = list(a)
 |      >>> a_list
 |      [1, 2]
 |      >>> type(a_list[0])
 |      <class 'numpy.uint32'>
 |      >>> a_tolist = a.tolist()
 |      >>> a_tolist
 |      [1, 2]
 |      >>> type(a_tolist[0])
 |      <class 'int'>
 |
 |      Additionally, for a 2D array, ``tolist`` applies recursively:
 |
 |      >>> a = np.array([[1, 2], [3, 4]])
 |      >>> list(a)
 |      [array([1, 2]), array([3, 4])]
 |      >>> a.tolist()
 |      [[1, 2], [3, 4]]
 |
 |      The base case for this recursion is a 0D array:
 |
 |      >>> a = np.array(1)
 |      >>> list(a)
 |      Traceback (most recent call last):
 |        ...
 |      TypeError: iteration over a 0-d array
 |      >>> a.tolist()
 |      1
 |
 |  tostring(...)
 |      a.tostring(order='C')
 |
 |      A compatibility alias for `~ndarray.tobytes`, with exactly the same
 |      behavior.
 |
 |      Despite its name, it returns :class:`bytes` not :class:`str`\ s.
 |
 |      .. deprecated:: 1.19.0
 |
 |  trace(...)
 |      a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)
 |
 |      Return the sum along diagonals of the array.
 |
 |      Refer to `numpy.trace` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.trace : equivalent function
 |
 |  transpose(...)
 |      a.transpose(*axes)
 |
 |      Returns a view of the array with axes transposed.
 |
 |      Refer to `numpy.transpose` for full documentation.
 |
 |      Parameters
 |      ----------
 |      axes : None, tuple of ints, or `n` ints
 |
 |       * None or no argument: reverses the order of the axes.
 |
 |       * tuple of ints: `i` in the `j`-th place in the tuple means that the
 |         array's `i`-th axis becomes the transposed array's `j`-th axis.
 |
 |       * `n` ints: same as an n-tuple of the same ints (this form is
 |         intended simply as a "convenience" alternative to the tuple form).
 |
 |      Returns
 |      -------
 |      p : ndarray
 |          View of the array with its axes suitably permuted.
 |
 |      See Also
 |      --------
 |      transpose : Equivalent function.
 |      ndarray.T : Array property returning the array transposed.
 |      ndarray.reshape : Give a new shape to an array without changing its data.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1, 2], [3, 4]])
 |      >>> a
 |      array([[1, 2],
 |             [3, 4]])
 |      >>> a.transpose()
 |      array([[1, 3],
 |             [2, 4]])
 |      >>> a.transpose((1, 0))
 |      array([[1, 3],
 |             [2, 4]])
 |      >>> a.transpose(1, 0)
 |      array([[1, 3],
 |             [2, 4]])
 |
 |      >>> a = np.array([1, 2, 3, 4])
 |      >>> a
 |      array([1, 2, 3, 4])
 |      >>> a.transpose()
 |      array([1, 2, 3, 4])
 |
 |  var(...)
 |      a.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)
 |
 |      Returns the variance of the array elements, along given axis.
 |
 |      Refer to `numpy.var` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.var : equivalent function
 |
 |  view(...)
 |      a.view([dtype][, type])
 |
 |      New view of array with the same data.
 |
 |      .. note::
 |          Passing None for ``dtype`` is different from omitting the parameter,
 |          since the former invokes ``dtype(None)`` which is an alias for
 |          ``dtype('float64')``.
 |
 |      Parameters
 |      ----------
 |      dtype : data-type or ndarray sub-class, optional
 |          Data-type descriptor of the returned view, e.g., float32 or int16.
 |          Omitting it results in the view having the same data-type as `a`.
 |          This argument can also be specified as an ndarray sub-class, which
 |          then specifies the type of the returned object (this is equivalent to
 |          setting the ``type`` parameter).
 |      type : Python type, optional
 |          Type of the returned view, e.g., ndarray or matrix.  Again, omission
 |          of the parameter results in type preservation.
 |
 |      Notes
 |      -----
 |      ``a.view()`` is used two different ways:
 |
 |      ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view
 |      of the array's memory with a different data-type.  This can cause a
 |      reinterpretation of the bytes of memory.
 |
 |      ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just
 |      returns an instance of `ndarray_subclass` that looks at the same array
 |      (same shape, dtype, etc.)  This does not cause a reinterpretation of the
 |      memory.
 |
 |      For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of
 |      bytes per entry than the previous dtype (for example, converting a regular
 |      array to a structured array), then the last axis of ``a`` must be
 |      contiguous. This axis will be resized in the result.
 |
 |      .. versionchanged:: 1.23.0
 |         Only the last axis needs to be contiguous. Previously, the entire array
 |         had to be C-contiguous.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([(-1, 2)], dtype=[('a', np.int8), ('b', np.int8)])
 |
 |      Viewing array data using a different type and dtype:
 |
 |      >>> nonneg = np.dtype([("a", np.uint8), ("b", np.uint8)])
 |      >>> y = x.view(dtype=nonneg, type=np.recarray)
 |      >>> x["a"]
 |      array([-1], dtype=int8)
 |      >>> y.a
 |      array([255], dtype=uint8)
 |
 |      Creating a view on a structured array so it can be used in calculations
 |
 |      >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])
 |      >>> xv = x.view(dtype=np.int8).reshape(-1,2)
 |      >>> xv
 |      array([[1, 2],
 |             [3, 4]], dtype=int8)
 |      >>> xv.mean(0)
 |      array([2.,  3.])
 |
 |      Making changes to the view changes the underlying array
 |
 |      >>> xv[0,1] = 20
 |      >>> x
 |      array([(1, 20), (3,  4)], dtype=[('a', 'i1'), ('b', 'i1')])
 |
 |      Using a view to convert an array to a recarray:
 |
 |      >>> z = x.view(np.recarray)
 |      >>> z.a
 |      array([1, 3], dtype=int8)
 |
 |      Views share data:
 |
 |      >>> x[0] = (9, 10)
 |      >>> z[0]
 |      np.record((9, 10), dtype=[('a', 'i1'), ('b', 'i1')])
 |
 |      Views that change the dtype size (bytes per entry) should normally be
 |      avoided on arrays defined by slices, transposes, fortran-ordering, etc.:
 |
 |      >>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16)
 |      >>> y = x[:, ::2]
 |      >>> y
 |      array([[1, 3],
 |             [4, 6]], dtype=int16)
 |      >>> y.view(dtype=[('width', np.int16), ('length', np.int16)])
 |      Traceback (most recent call last):
 |          ...
 |      ValueError: To change to a dtype of a different size, the last axis must be contiguous
 |      >>> z = y.copy()
 |      >>> z.view(dtype=[('width', np.int16), ('length', np.int16)])
 |      array([[(1, 3)],
 |             [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])
 |
 |      However, views that change dtype are totally fine for arrays with a
 |      contiguous last axis, even if the rest of the axes are not C-contiguous:
 |
 |      >>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4)
 |      >>> x.transpose(1, 0, 2).view(np.int16)
 |      array([[[ 256,  770],
 |              [3340, 3854]],
 |      <BLANKLINE>
 |             [[1284, 1798],
 |              [4368, 4882]],
 |      <BLANKLINE>
 |             [[2312, 2826],
 |              [5396, 5910]]], dtype=int16)
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from ndarray:
 |
 |  __class_getitem__(...)
 |      a.__class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.ndarray` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.ndarray` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.ndarray[Any, np.dtype[Any]]
 |      numpy.ndarray[typing.Any, numpy.dtype[typing.Any]]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |      numpy.typing.NDArray : An ndarray alias :term:`generic <generic type>`
 |                          w.r.t. its `dtype.type <numpy.dtype.type>`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from ndarray:
 |
 |  T
 |      View of the transposed array.
 |
 |      Same as ``self.transpose()``.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1, 2], [3, 4]])
 |      >>> a
 |      array([[1, 2],
 |             [3, 4]])
 |      >>> a.T
 |      array([[1, 3],
 |             [2, 4]])
 |
 |      >>> a = np.array([1, 2, 3, 4])
 |      >>> a
 |      array([1, 2, 3, 4])
 |      >>> a.T
 |      array([1, 2, 3, 4])
 |
 |      See Also
 |      --------
 |      transpose
 |
 |  __array_interface__
 |      Array protocol: Python side.
 |
 |  __array_struct__
 |      Array protocol: C-struct side.
 |
 |  base
 |      Base object if memory is from some other object.
 |
 |      Examples
 |      --------
 |      The base of an array that owns its memory is None:
 |
 |      >>> import numpy as np
 |      >>> x = np.array([1,2,3,4])
 |      >>> x.base is None
 |      True
 |
 |      Slicing creates a view, whose memory is shared with x:
 |
 |      >>> y = x[2:]
 |      >>> y.base is x
 |      True
 |
 |  ctypes
 |      An object to simplify the interaction of the array with the ctypes
 |      module.
 |
 |      This attribute creates an object that makes it easier to use arrays
 |      when calling shared libraries with the ctypes module. The returned
 |      object has, among others, data, shape, and strides attributes (see
 |      Notes below) which themselves return ctypes objects that can be used
 |      as arguments to a shared library.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      c : Python object
 |          Possessing attributes data, shape, strides, etc.
 |
 |      See Also
 |      --------
 |      numpy.ctypeslib
 |
 |      Notes
 |      -----
 |      Below are the public attributes of this object which were documented
 |      in "Guide to NumPy" (we have omitted undocumented public attributes,
 |      as well as documented private attributes):
 |
 |      .. autoattribute:: numpy._core._internal._ctypes.data
 |          :noindex:
 |
 |      .. autoattribute:: numpy._core._internal._ctypes.shape
 |          :noindex:
 |
 |      .. autoattribute:: numpy._core._internal._ctypes.strides
 |          :noindex:
 |
 |      .. automethod:: numpy._core._internal._ctypes.data_as
 |          :noindex:
 |
 |      .. automethod:: numpy._core._internal._ctypes.shape_as
 |          :noindex:
 |
 |      .. automethod:: numpy._core._internal._ctypes.strides_as
 |          :noindex:
 |
 |      If the ctypes module is not available, then the ctypes attribute
 |      of array objects still returns something useful, but ctypes objects
 |      are not returned and errors may be raised instead. In particular,
 |      the object will still have the ``as_parameter`` attribute which will
 |      return an integer equal to the data attribute.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> import ctypes
 |      >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)
 |      >>> x
 |      array([[0, 1],
 |             [2, 3]], dtype=int32)
 |      >>> x.ctypes.data
 |      31962608 # may vary
 |      >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))
 |      <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary
 |      >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents
 |      c_uint(0)
 |      >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents
 |      c_ulong(4294967296)
 |      >>> x.ctypes.shape
 |      <numpy._core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary
 |      >>> x.ctypes.strides
 |      <numpy._core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary
 |
 |  data
 |      Python buffer object pointing to the start of the array's data.
 |
 |  device
 |
 |  dtype
 |      Data-type of the array's elements.
 |
 |      .. warning::
 |
 |          Setting ``arr.dtype`` is discouraged and may be deprecated in the
 |          future.  Setting will replace the ``dtype`` without modifying the
 |          memory (see also `ndarray.view` and `ndarray.astype`).
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      d : numpy dtype object
 |
 |      See Also
 |      --------
 |      ndarray.astype : Cast the values contained in the array to a new data-type.
 |      ndarray.view : Create a view of the same data but a different data-type.
 |      numpy.dtype
 |
 |      Examples
 |      --------
 |      >>> x
 |      array([[0, 1],
 |             [2, 3]])
 |      >>> x.dtype
 |      dtype('int32')
 |      >>> type(x.dtype)
 |      <type 'numpy.dtype'>
 |
 |  flags
 |      Information about the memory layout of the array.
 |
 |      Attributes
 |      ----------
 |      C_CONTIGUOUS (C)
 |          The data is in a single, C-style contiguous segment.
 |      F_CONTIGUOUS (F)
 |          The data is in a single, Fortran-style contiguous segment.
 |      OWNDATA (O)
 |          The array owns the memory it uses or borrows it from another object.
 |      WRITEABLE (W)
 |          The data area can be written to.  Setting this to False locks
 |          the data, making it read-only.  A view (slice, etc.) inherits WRITEABLE
 |          from its base array at creation time, but a view of a writeable
 |          array may be subsequently locked while the base array remains writeable.
 |          (The opposite is not true, in that a view of a locked array may not
 |          be made writeable.  However, currently, locking a base object does not
 |          lock any views that already reference it, so under that circumstance it
 |          is possible to alter the contents of a locked array via a previously
 |          created writeable view onto it.)  Attempting to change a non-writeable
 |          array raises a RuntimeError exception.
 |      ALIGNED (A)
 |          The data and all elements are aligned appropriately for the hardware.
 |      WRITEBACKIFCOPY (X)
 |          This array is a copy of some other array. The C-API function
 |          PyArray_ResolveWritebackIfCopy must be called before deallocating
 |          to the base array will be updated with the contents of this array.
 |      FNC
 |          F_CONTIGUOUS and not C_CONTIGUOUS.
 |      FORC
 |          F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).
 |      BEHAVED (B)
 |          ALIGNED and WRITEABLE.
 |      CARRAY (CA)
 |          BEHAVED and C_CONTIGUOUS.
 |      FARRAY (FA)
 |          BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.
 |
 |      Notes
 |      -----
 |      The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``),
 |      or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag
 |      names are only supported in dictionary access.
 |
 |      Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be
 |      changed by the user, via direct assignment to the attribute or dictionary
 |      entry, or by calling `ndarray.setflags`.
 |
 |      The array flags cannot be set arbitrarily:
 |
 |      - WRITEBACKIFCOPY can only be set ``False``.
 |      - ALIGNED can only be set ``True`` if the data is truly aligned.
 |      - WRITEABLE can only be set ``True`` if the array owns its own memory
 |        or the ultimate owner of the memory exposes a writeable buffer
 |        interface or is a string.
 |
 |      Arrays can be both C-style and Fortran-style contiguous simultaneously.
 |      This is clear for 1-dimensional arrays, but can also be true for higher
 |      dimensional arrays.
 |
 |      Even for contiguous arrays a stride for a given dimension
 |      ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1``
 |      or the array has no elements.
 |      It does *not* generally hold that ``self.strides[-1] == self.itemsize``
 |      for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for
 |      Fortran-style contiguous arrays is true.
 |
 |  flat
 |      A 1-D iterator over the array.
 |
 |      This is a `numpy.flatiter` instance, which acts similarly to, but is not
 |      a subclass of, Python's built-in iterator object.
 |
 |      See Also
 |      --------
 |      flatten : Return a copy of the array collapsed into one dimension.
 |
 |      flatiter
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.arange(1, 7).reshape(2, 3)
 |      >>> x
 |      array([[1, 2, 3],
 |             [4, 5, 6]])
 |      >>> x.flat[3]
 |      4
 |      >>> x.T
 |      array([[1, 4],
 |             [2, 5],
 |             [3, 6]])
 |      >>> x.T.flat[3]
 |      5
 |      >>> type(x.flat)
 |      <class 'numpy.flatiter'>
 |
 |      An assignment example:
 |
 |      >>> x.flat = 3; x
 |      array([[3, 3, 3],
 |             [3, 3, 3]])
 |      >>> x.flat[[1,4]] = 1; x
 |      array([[3, 1, 3],
 |             [3, 1, 3]])
 |
 |  imag
 |      The imaginary part of the array.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.sqrt([1+0j, 0+1j])
 |      >>> x.imag
 |      array([ 0.        ,  0.70710678])
 |      >>> x.imag.dtype
 |      dtype('float64')
 |
 |  itemset
 |
 |  itemsize
 |      Length of one array element in bytes.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1,2,3], dtype=np.float64)
 |      >>> x.itemsize
 |      8
 |      >>> x = np.array([1,2,3], dtype=np.complex128)
 |      >>> x.itemsize
 |      16
 |
 |  mT
 |      View of the matrix transposed array.
 |
 |      The matrix transpose is the transpose of the last two dimensions, even
 |      if the array is of higher dimension.
 |
 |      .. versionadded:: 2.0
 |
 |      Raises
 |      ------
 |      ValueError
 |          If the array is of dimension less than 2.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1, 2], [3, 4]])
 |      >>> a
 |      array([[1, 2],
 |             [3, 4]])
 |      >>> a.mT
 |      array([[1, 3],
 |             [2, 4]])
 |
 |      >>> a = np.arange(8).reshape((2, 2, 2))
 |      >>> a
 |      array([[[0, 1],
 |              [2, 3]],
 |      <BLANKLINE>
 |             [[4, 5],
 |              [6, 7]]])
 |      >>> a.mT
 |      array([[[0, 2],
 |              [1, 3]],
 |      <BLANKLINE>
 |             [[4, 6],
 |              [5, 7]]])
 |
 |  nbytes
 |      Total bytes consumed by the elements of the array.
 |
 |      Notes
 |      -----
 |      Does not include memory consumed by non-element attributes of the
 |      array object.
 |
 |      See Also
 |      --------
 |      sys.getsizeof
 |          Memory consumed by the object itself without parents in case view.
 |          This does include memory consumed by non-element attributes.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.zeros((3,5,2), dtype=np.complex128)
 |      >>> x.nbytes
 |      480
 |      >>> np.prod(x.shape) * x.itemsize
 |      480
 |
 |  ndim
 |      Number of array dimensions.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 3])
 |      >>> x.ndim
 |      1
 |      >>> y = np.zeros((2, 3, 4))
 |      >>> y.ndim
 |      3
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the array.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.sqrt([1+0j, 0+1j])
 |      >>> x.real
 |      array([ 1.        ,  0.70710678])
 |      >>> x.real.dtype
 |      dtype('float64')
 |
 |      See Also
 |      --------
 |      numpy.real : equivalent function
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |      The shape property is usually used to get the current shape of an array,
 |      but may also be used to reshape the array in-place by assigning a tuple of
 |      array dimensions to it.  As with `numpy.reshape`, one of the new shape
 |      dimensions can be -1, in which case its value is inferred from the size of
 |      the array and the remaining dimensions. Reshaping an array in-place will
 |      fail if a copy is required.
 |
 |      .. warning::
 |
 |          Setting ``arr.shape`` is discouraged and may be deprecated in the
 |          future.  Using `ndarray.reshape` is the preferred approach.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 3, 4])
 |      >>> x.shape
 |      (4,)
 |      >>> y = np.zeros((2, 3, 4))
 |      >>> y.shape
 |      (2, 3, 4)
 |      >>> y.shape = (3, 8)
 |      >>> y
 |      array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
 |             [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
 |             [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])
 |      >>> y.shape = (3, 6)
 |      Traceback (most recent call last):
 |        File "<stdin>", line 1, in <module>
 |      ValueError: total size of new array must be unchanged
 |      >>> np.zeros((4,2))[::2].shape = (-1,)
 |      Traceback (most recent call last):
 |        File "<stdin>", line 1, in <module>
 |      AttributeError: Incompatible shape for in-place modification. Use
 |      `.reshape()` to make a copy with the desired shape.
 |
 |      See Also
 |      --------
 |      numpy.shape : Equivalent getter function.
 |      numpy.reshape : Function similar to setting ``shape``.
 |      ndarray.reshape : Method similar to setting ``shape``.
 |
 |  size
 |      Number of elements in the array.
 |
 |      Equal to ``np.prod(a.shape)``, i.e., the product of the array's
 |      dimensions.
 |
 |      Notes
 |      -----
 |      `a.size` returns a standard arbitrary precision Python integer. This
 |      may not be the case with other methods of obtaining the same value
 |      (like the suggested ``np.prod(a.shape)``, which returns an instance
 |      of ``np.int_``), and may be relevant if the value is used further in
 |      calculations that may overflow a fixed size integer type.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.zeros((3, 5, 2), dtype=np.complex128)
 |      >>> x.size
 |      30
 |      >>> np.prod(x.shape)
 |      30
 |
 |  strides
 |      Tuple of bytes to step in each dimension when traversing an array.
 |
 |      The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a`
 |      is::
 |
 |          offset = sum(np.array(i) * a.strides)
 |
 |      A more detailed explanation of strides can be found in
 |      :ref:`arrays.ndarray`.
 |
 |      .. warning::
 |
 |          Setting ``arr.strides`` is discouraged and may be deprecated in the
 |          future.  `numpy.lib.stride_tricks.as_strided` should be preferred
 |          to create a new view of the same data in a safer way.
 |
 |      Notes
 |      -----
 |      Imagine an array of 32-bit integers (each 4 bytes)::
 |
 |        x = np.array([[0, 1, 2, 3, 4],
 |                      [5, 6, 7, 8, 9]], dtype=np.int32)
 |
 |      This array is stored in memory as 40 bytes, one after the other
 |      (known as a contiguous block of memory).  The strides of an array tell
 |      us how many bytes we have to skip in memory to move to the next position
 |      along a certain axis.  For example, we have to skip 4 bytes (1 value) to
 |      move to the next column, but 20 bytes (5 values) to get to the same
 |      position in the next row.  As such, the strides for the array `x` will be
 |      ``(20, 4)``.
 |
 |      See Also
 |      --------
 |      numpy.lib.stride_tricks.as_strided
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> y = np.reshape(np.arange(2*3*4), (2,3,4))
 |      >>> y
 |      array([[[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]],
 |             [[12, 13, 14, 15],
 |              [16, 17, 18, 19],
 |              [20, 21, 22, 23]]])
 |      >>> y.strides
 |      (48, 16, 4)
 |      >>> y[1,1,1]
 |      17
 |      >>> offset=sum(y.strides * np.array((1,1,1)))
 |      >>> offset/y.itemsize
 |      17
 |
 |      >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)
 |      >>> x.strides
 |      (32, 4, 224, 1344)
 |      >>> i = np.array([3,5,2,2])
 |      >>> offset = sum(i * x.strides)
 |      >>> x[3,5,2,2]
 |      813
 |      >>> offset / x.itemsize
 |      813
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes inherited from ndarray:
 |
 |  __hash__ = None

Python Library Documentation: function meshgrid in module autograd.tracer

meshgrid(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return a tuple of coordinate matrices from coordinate vectors.

    Make N-D coordinate arrays for vectorized evaluations of
    N-D scalar/vector fields over N-D grids, given
    one-dimensional coordinate arrays x1, x2,..., xn.

    .. versionchanged:: 1.9
       1-D and 0-D cases are allowed.

    Parameters
    ----------
    x1, x2,..., xn : array_like
        1-D arrays representing the coordinates of a grid.
    indexing : {'xy', 'ij'}, optional
        Cartesian ('xy', default) or matrix ('ij') indexing of output.
        See Notes for more details.

        .. versionadded:: 1.7.0
    sparse : bool, optional
        If True the shape of the returned coordinate array for dimension *i*
        is reduced from ``(N1, ..., Ni, ... Nn)`` to
        ``(1, ..., 1, Ni, 1, ..., 1)``.  These sparse coordinate grids are
        intended to be use with :ref:`basics.broadcasting`.  When all
        coordinates are used in an expression, broadcasting still leads to a
        fully-dimensonal result array.

        Default is False.

        .. versionadded:: 1.7.0
    copy : bool, optional
        If False, a view into the original arrays are returned in order to
        conserve memory.  Default is True.  Please note that
        ``sparse=False, copy=False`` will likely return non-contiguous
        arrays.  Furthermore, more than one element of a broadcast array
        may refer to a single memory location.  If you need to write to the
        arrays, make copies first.

        .. versionadded:: 1.7.0

    Returns
    -------
    X1, X2,..., XN : tuple of ndarrays
        For vectors `x1`, `x2`,..., `xn` with lengths ``Ni=len(xi)``,
        returns ``(N1, N2, N3,..., Nn)`` shaped arrays if indexing='ij'
        or ``(N2, N1, N3,..., Nn)`` shaped arrays if indexing='xy'
        with the elements of `xi` repeated to fill the matrix along
        the first dimension for `x1`, the second for `x2` and so on.

    Notes
    -----
    This function supports both indexing conventions through the indexing
    keyword argument.  Giving the string 'ij' returns a meshgrid with
    matrix indexing, while 'xy' returns a meshgrid with Cartesian indexing.
    In the 2-D case with inputs of length M and N, the outputs are of shape
    (N, M) for 'xy' indexing and (M, N) for 'ij' indexing.  In the 3-D case
    with inputs of length M, N and P, outputs are of shape (N, M, P) for
    'xy' indexing and (M, N, P) for 'ij' indexing.  The difference is
    illustrated by the following code snippet::

        xv, yv = np.meshgrid(x, y, indexing='ij')
        for i in range(nx):
            for j in range(ny):
                # treat xv[i,j], yv[i,j]

        xv, yv = np.meshgrid(x, y, indexing='xy')
        for i in range(nx):
            for j in range(ny):
                # treat xv[j,i], yv[j,i]

    In the 1-D and 0-D case, the indexing and sparse keywords have no effect.

    See Also
    --------
    mgrid : Construct a multi-dimensional "meshgrid" using indexing notation.
    ogrid : Construct an open multi-dimensional "meshgrid" using indexing
            notation.
    :ref:`how-to-index`

    Examples
    --------
    >>> import numpy as np
    >>> nx, ny = (3, 2)
    >>> x = np.linspace(0, 1, nx)
    >>> y = np.linspace(0, 1, ny)
    >>> xv, yv = np.meshgrid(x, y)
    >>> xv
    array([[0. , 0.5, 1. ],
           [0. , 0.5, 1. ]])
    >>> yv
    array([[0.,  0.,  0.],
           [1.,  1.,  1.]])

    The result of `meshgrid` is a coordinate grid:

    >>> import matplotlib.pyplot as plt
    >>> plt.plot(xv, yv, marker='o', color='k', linestyle='none')
    >>> plt.show()

    You can create sparse output arrays to save memory and computation time.

    >>> xv, yv = np.meshgrid(x, y, sparse=True)
    >>> xv
    array([[0. ,  0.5,  1. ]])
    >>> yv
    array([[0.],
           [1.]])

    `meshgrid` is very useful to evaluate functions on a grid. If the
    function depends on all coordinates, both dense and sparse outputs can be
    used.

    >>> x = np.linspace(-5, 5, 101)
    >>> y = np.linspace(-5, 5, 101)
    >>> # full coordinate arrays
    >>> xx, yy = np.meshgrid(x, y)
    >>> zz = np.sqrt(xx**2 + yy**2)
    >>> xx.shape, yy.shape, zz.shape
    ((101, 101), (101, 101), (101, 101))
    >>> # sparse coordinate arrays
    >>> xs, ys = np.meshgrid(x, y, sparse=True)
    >>> zs = np.sqrt(xs**2 + ys**2)
    >>> xs.shape, ys.shape, zs.shape
    ((1, 101), (101, 1), (101, 101))
    >>> np.array_equal(zz, zs)
    True

    >>> h = plt.contourf(x, y, zs)
    >>> plt.axis('scaled')
    >>> plt.colorbar()
    >>> plt.show()

Python Library Documentation: function metadata in module autograd.tracer

metadata(*args, **kwargs)
    None

Python Library Documentation: function min in module autograd.tracer

min(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the minimum of an array or minimum along an axis.

    Parameters
    ----------
    a : array_like
        Input data.
    axis : None or int or tuple of ints, optional
        Axis or axes along which to operate.  By default, flattened input is
        used.

        .. versionadded:: 1.7.0

        If this is a tuple of ints, the minimum is selected over multiple axes,
        instead of a single axis or all the axes as before.
    out : ndarray, optional
        Alternative output array in which to place the result.  Must
        be of the same shape and buffer length as the expected output.
        See :ref:`ufuncs-output-type` for more details.

    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the input array.

        If the default value is passed, then `keepdims` will not be
        passed through to the ``min`` method of sub-classes of
        `ndarray`, however any non-default value will be.  If the
        sub-class' method does not implement `keepdims` any
        exceptions will be raised.

    initial : scalar, optional
        The maximum value of an output element. Must be present to allow
        computation on empty slice. See `~numpy.ufunc.reduce` for details.

        .. versionadded:: 1.15.0

    where : array_like of bool, optional
        Elements to compare for the minimum. See `~numpy.ufunc.reduce`
        for details.

        .. versionadded:: 1.17.0

    Returns
    -------
    min : ndarray or scalar
        Minimum of `a`. If `axis` is None, the result is a scalar value.
        If `axis` is an int, the result is an array of dimension
        ``a.ndim - 1``.  If `axis` is a tuple, the result is an array of
        dimension ``a.ndim - len(axis)``.

    See Also
    --------
    amax :
        The maximum value of an array along a given axis, propagating any NaNs.
    nanmin :
        The minimum value of an array along a given axis, ignoring any NaNs.
    minimum :
        Element-wise minimum of two arrays, propagating any NaNs.
    fmin :
        Element-wise minimum of two arrays, ignoring any NaNs.
    argmin :
        Return the indices of the minimum values.

    nanmax, maximum, fmax

    Notes
    -----
    NaN values are propagated, that is if at least one item is NaN, the
    corresponding min value will be NaN as well. To ignore NaN values
    (MATLAB behavior), please use nanmin.

    Don't use `~numpy.min` for element-wise comparison of 2 arrays; when
    ``a.shape[0]`` is 2, ``minimum(a[0], a[1])`` is faster than
    ``min(a, axis=0)``.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.arange(4).reshape((2,2))
    >>> a
    array([[0, 1],
           [2, 3]])
    >>> np.min(a)           # Minimum of the flattened array
    0
    >>> np.min(a, axis=0)   # Minima along the first axis
    array([0, 1])
    >>> np.min(a, axis=1)   # Minima along the second axis
    array([0, 2])
    >>> np.min(a, where=[False, True], initial=10, axis=0)
    array([10,  1])

    >>> b = np.arange(5, dtype=float)
    >>> b[2] = np.nan
    >>> np.min(b)
    np.float64(nan)
    >>> np.min(b, where=~np.isnan(b), initial=10)
    0.0
    >>> np.nanmin(b)
    0.0

    >>> np.min([[-50], [10]], axis=-1, initial=0)
    array([-50,   0])

    Notice that the initial value is used as one of the elements for which the
    minimum is determined, unlike for the default argument Python's max
    function, which is only used for empty iterables.

    Notice that this isn't the same as Python's ``default`` argument.

    >>> np.min([6], initial=5)
    5
    >>> min([6], default=5)
    6

Python Library Documentation: function min_scalar_type in module autograd.tracer

min_scalar_type(*args, called_by_autograd_dispatcher=False, **kwargs)
    min_scalar_type(a, /)

    For scalar ``a``, returns the data type with the smallest size
    and smallest scalar kind which can hold its value.  For non-scalar
    array ``a``, returns the vector's dtype unmodified.

    Floating point values are not demoted to integers,
    and complex values are not demoted to floats.

    Parameters
    ----------
    a : scalar or array_like
        The value whose minimal data type is to be found.

    Returns
    -------
    out : dtype
        The minimal data type.

    Notes
    -----
    .. versionadded:: 1.6.0

    See Also
    --------
    result_type, promote_types, dtype, can_cast

    Examples
    --------
    >>> import numpy as np
    >>> np.min_scalar_type(10)
    dtype('uint8')

    >>> np.min_scalar_type(-260)
    dtype('int16')

    >>> np.min_scalar_type(3.1)
    dtype('float16')

    >>> np.min_scalar_type(1e50)
    dtype('float64')

    >>> np.min_scalar_type(np.arange(4,dtype='f8'))
    dtype('float64')

Python Library Documentation: function minimum in module autograd.tracer

minimum(*args, called_by_autograd_dispatcher=False, **kwargs)
    minimum(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Element-wise minimum of array elements.

    Compare two arrays and return a new array containing the element-wise
    minima. If one of the elements being compared is a NaN, then that
    element is returned. If both elements are NaNs then the first is
    returned. The latter distinction is important for complex NaNs, which
    are defined as at least one of the real or imaginary parts being a NaN.
    The net effect is that NaNs are propagated.

    Parameters
    ----------
    x1, x2 : array_like
        The arrays holding the elements to be compared.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray or scalar
        The minimum of `x1` and `x2`, element-wise.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    maximum :
        Element-wise maximum of two arrays, propagates NaNs.
    fmin :
        Element-wise minimum of two arrays, ignores NaNs.
    amin :
        The minimum value of an array along a given axis, propagates NaNs.
    nanmin :
        The minimum value of an array along a given axis, ignores NaNs.

    fmax, amax, nanmax

    Notes
    -----
    The minimum is equivalent to ``np.where(x1 <= x2, x1, x2)`` when
    neither x1 nor x2 are NaNs, but it is faster and does proper
    broadcasting.

    Examples
    --------
    >>> import numpy as np
    >>> np.minimum([2, 3, 4], [1, 5, 2])
    array([1, 3, 2])

    >>> np.minimum(np.eye(2), [0.5, 2]) # broadcasting
    array([[ 0.5,  0. ],
           [ 0. ,  1. ]])

    >>> np.minimum([np.nan, 0, np.nan],[0, np.nan, np.nan])
    array([nan, nan, nan])
    >>> np.minimum(-np.inf, 1)
    -inf

Python Library Documentation: function mintypecode in module autograd.tracer

mintypecode(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the character for the minimum-size type to which given types can
    be safely cast.

    The returned type character must represent the smallest size dtype such
    that an array of the returned type can handle the data from an array of
    all types in `typechars` (or if `typechars` is an array, then its
    dtype.char).

    Parameters
    ----------
    typechars : list of str or array_like
        If a list of strings, each string should represent a dtype.
        If array_like, the character representation of the array dtype is used.
    typeset : str or list of str, optional
        The set of characters that the returned character is chosen from.
        The default set is 'GDFgdf'.
    default : str, optional
        The default character, this is returned if none of the characters in
        `typechars` matches a character in `typeset`.

    Returns
    -------
    typechar : str
        The character representing the minimum-size type that was found.

    See Also
    --------
    dtype

    Examples
    --------
    >>> import numpy as np
    >>> np.mintypecode(['d', 'f', 'S'])
    'd'
    >>> x = np.array([1.1, 2-3.j])
    >>> np.mintypecode(x)
    'D'

    >>> np.mintypecode('abceh', default='G')
    'G'

Python Library Documentation: function remainder in module autograd.tracer

remainder(*args, called_by_autograd_dispatcher=False, **kwargs)
    remainder(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Returns the element-wise remainder of division.

    Computes the remainder complementary to the `floor_divide` function.  It is
    equivalent to the Python modulus operator ``x1 % x2`` and has the same sign
    as the divisor `x2`. The MATLAB function equivalent to ``np.remainder``
    is ``mod``.

    .. warning::

        This should not be confused with:

        * Python 3.7's `math.remainder` and C's ``remainder``, which
          computes the IEEE remainder, which are the complement to
          ``round(x1 / x2)``.
        * The MATLAB ``rem`` function and or the C ``%`` operator which is the
          complement to ``int(x1 / x2)``.

    Parameters
    ----------
    x1 : array_like
        Dividend array.
    x2 : array_like
        Divisor array.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The element-wise remainder of the quotient ``floor_divide(x1, x2)``.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    floor_divide : Equivalent of Python ``//`` operator.
    divmod : Simultaneous floor division and remainder.
    fmod : Equivalent of the MATLAB ``rem`` function.
    divide, floor

    Notes
    -----
    Returns 0 when `x2` is 0 and both `x1` and `x2` are (arrays of)
    integers.
    ``mod`` is an alias of ``remainder``.

    Examples
    --------
    >>> import numpy as np
    >>> np.remainder([4, 7], [2, 3])
    array([0, 1])
    >>> np.remainder(np.arange(7), 5)
    array([0, 1, 2, 3, 4, 0, 1])

    The ``%`` operator can be used as a shorthand for ``np.remainder`` on
    ndarrays.

    >>> x1 = np.arange(7)
    >>> x1 % 5
    array([0, 1, 2, 3, 4, 0, 1])

Python Library Documentation: function modf in module autograd.tracer

modf(*args, called_by_autograd_dispatcher=False, **kwargs)
    modf(x[, out1, out2], / [, out=(None, None)], *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the fractional and integral parts of an array, element-wise.

    The fractional and integral parts are negative if the given number is
    negative.

    Parameters
    ----------
    x : array_like
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y1 : ndarray
        Fractional part of `x`.
        This is a scalar if `x` is a scalar.
    y2 : ndarray
        Integral part of `x`.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    For integer input the return values are floats.

    See Also
    --------
    divmod : ``divmod(x, 1)`` is equivalent to ``modf`` with the return values
             switched, except it always has a positive remainder.

    Examples
    --------
    >>> import numpy as np
    >>> np.modf([0, 3.5])
    (array([ 0. ,  0.5]), array([ 0.,  3.]))
    >>> np.modf(-0.5)
    (-0.5, -0)

Python Library Documentation: function moveaxis in module autograd.tracer

moveaxis(*args, called_by_autograd_dispatcher=False, **kwargs)
    Move axes of an array to new positions.

    Other axes remain in their original order.

    .. versionadded:: 1.11.0

    Parameters
    ----------
    a : np.ndarray
        The array whose axes should be reordered.
    source : int or sequence of int
        Original positions of the axes to move. These must be unique.
    destination : int or sequence of int
        Destination positions for each of the original axes. These must also be
        unique.

    Returns
    -------
    result : np.ndarray
        Array with moved axes. This array is a view of the input array.

    See Also
    --------
    transpose : Permute the dimensions of an array.
    swapaxes : Interchange two axes of an array.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.zeros((3, 4, 5))
    >>> np.moveaxis(x, 0, -1).shape
    (4, 5, 3)
    >>> np.moveaxis(x, -1, 0).shape
    (5, 3, 4)

    These all achieve the same result:

    >>> np.transpose(x).shape
    (5, 4, 3)
    >>> np.swapaxes(x, 0, -1).shape
    (5, 4, 3)
    >>> np.moveaxis(x, [0, 1], [-1, -2]).shape
    (5, 4, 3)
    >>> np.moveaxis(x, [0, 1, 2], [-1, -2, -3]).shape
    (5, 4, 3)

Python Library Documentation: function multiply in module autograd.tracer

multiply(*args, called_by_autograd_dispatcher=False, **kwargs)
    multiply(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Multiply arguments element-wise.

    Parameters
    ----------
    x1, x2 : array_like
        Input arrays to be multiplied.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The product of `x1` and `x2`, element-wise.
        This is a scalar if both `x1` and `x2` are scalars.

    Notes
    -----
    Equivalent to `x1` * `x2` in terms of array broadcasting.

    Examples
    --------
    >>> import numpy as np
    >>> np.multiply(2.0, 4.0)
    8.0

    >>> x1 = np.arange(9.0).reshape((3, 3))
    >>> x2 = np.arange(3.0)
    >>> np.multiply(x1, x2)
    array([[  0.,   1.,   4.],
           [  0.,   4.,  10.],
           [  0.,   7.,  16.]])

    The ``*`` operator can be used as a shorthand for ``np.multiply`` on
    ndarrays.

    >>> x1 = np.arange(9.0).reshape((3, 3))
    >>> x2 = np.arange(3.0)
    >>> x1 * x2
    array([[  0.,   1.,   4.],
           [  0.,   4.,  10.],
           [  0.,   7.,  16.]])

Python Library Documentation: float object

class float(object)
 |  float(x=0, /)
 |
 |  Convert a string or number to a floating-point number, if possible.
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __ceil__(self, /)
 |      Return the ceiling as an Integral.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floor__(self, /)
 |      Return the floor as an Integral.
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(self, format_spec, /)
 |      Formats the float according to format_spec.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getnewargs__(self, /)
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __round__(self, ndigits=None, /)
 |      Return the Integral closest to x, rounding half toward even.
 |
 |      When an argument is passed, work like built-in round(x, ndigits).
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __trunc__(self, /)
 |      Return the Integral closest to x between 0 and x.
 |
 |  as_integer_ratio(self, /)
 |      Return a pair of integers, whose ratio is exactly equal to the original float.
 |
 |      The ratio is in lowest terms and has a positive denominator.  Raise
 |      OverflowError on infinities and a ValueError on NaNs.
 |
 |      >>> (10.0).as_integer_ratio()
 |      (10, 1)
 |      >>> (0.0).as_integer_ratio()
 |      (0, 1)
 |      >>> (-.25).as_integer_ratio()
 |      (-1, 4)
 |
 |  conjugate(self, /)
 |      Return self, the complex conjugate of any float.
 |
 |  hex(self, /)
 |      Return a hexadecimal representation of a floating-point number.
 |
 |      >>> (-0.1).hex()
 |      '-0x1.999999999999ap-4'
 |      >>> 3.14159.hex()
 |      '0x1.921f9f01b866ep+1'
 |
 |  is_integer(self, /)
 |      Return True if the float is an integer.
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __getformat__(typestr, /)
 |      You probably don't want to use this function.
 |
 |        typestr
 |          Must be 'double' or 'float'.
 |
 |      It exists mainly to be used in Python's test suite.
 |
 |      This function returns whichever of 'unknown', 'IEEE, big-endian' or 'IEEE,
 |      little-endian' best describes the format of floating-point numbers used by the
 |      C type named by typestr.
 |
 |  fromhex(string, /)
 |      Create a floating-point number from a hexadecimal string.
 |
 |      >>> float.fromhex('0x1.ffffp10')
 |      2047.984375
 |      >>> float.fromhex('-0x1p-1074')
 |      -5e-324
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  imag
 |      the imaginary part of a complex number
 |
 |  real
 |      the real part of a complex number

Python Library Documentation: function nan_to_num in module autograd.tracer

nan_to_num(*args, called_by_autograd_dispatcher=False, **kwargs)
    Replace NaN with zero and infinity with large finite numbers (default
    behaviour) or with the numbers defined by the user using the `nan`,
    `posinf` and/or `neginf` keywords.

    If `x` is inexact, NaN is replaced by zero or by the user defined value in
    `nan` keyword, infinity is replaced by the largest finite floating point
    values representable by ``x.dtype`` or by the user defined value in
    `posinf` keyword and -infinity is replaced by the most negative finite
    floating point values representable by ``x.dtype`` or by the user defined
    value in `neginf` keyword.

    For complex dtypes, the above is applied to each of the real and
    imaginary components of `x` separately.

    If `x` is not inexact, then no replacements are made.

    Parameters
    ----------
    x : scalar or array_like
        Input data.
    copy : bool, optional
        Whether to create a copy of `x` (True) or to replace values
        in-place (False). The in-place operation only occurs if
        casting to an array does not require a copy.
        Default is True.

        .. versionadded:: 1.13
    nan : int, float, optional
        Value to be used to fill NaN values. If no value is passed
        then NaN values will be replaced with 0.0.

        .. versionadded:: 1.17
    posinf : int, float, optional
        Value to be used to fill positive infinity values. If no value is
        passed then positive infinity values will be replaced with a very
        large number.

        .. versionadded:: 1.17
    neginf : int, float, optional
        Value to be used to fill negative infinity values. If no value is
        passed then negative infinity values will be replaced with a very
        small (or negative) number.

        .. versionadded:: 1.17



    Returns
    -------
    out : ndarray
        `x`, with the non-finite values replaced. If `copy` is False, this may
        be `x` itself.

    See Also
    --------
    isinf : Shows which elements are positive or negative infinity.
    isneginf : Shows which elements are negative infinity.
    isposinf : Shows which elements are positive infinity.
    isnan : Shows which elements are Not a Number (NaN).
    isfinite : Shows which elements are finite (not NaN, not infinity)

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754). This means that Not a Number is not equivalent to infinity.

    Examples
    --------
    >>> import numpy as np
    >>> np.nan_to_num(np.inf)
    1.7976931348623157e+308
    >>> np.nan_to_num(-np.inf)
    -1.7976931348623157e+308
    >>> np.nan_to_num(np.nan)
    0.0
    >>> x = np.array([np.inf, -np.inf, np.nan, -128, 128])
    >>> np.nan_to_num(x)
    array([ 1.79769313e+308, -1.79769313e+308,  0.00000000e+000, # may vary
           -1.28000000e+002,  1.28000000e+002])
    >>> np.nan_to_num(x, nan=-9999, posinf=33333333, neginf=33333333)
    array([ 3.3333333e+07,  3.3333333e+07, -9.9990000e+03,
           -1.2800000e+02,  1.2800000e+02])
    >>> y = np.array([complex(np.inf, np.nan), np.nan, complex(np.nan, np.inf)])
    array([  1.79769313e+308,  -1.79769313e+308,   0.00000000e+000, # may vary
         -1.28000000e+002,   1.28000000e+002])
    >>> np.nan_to_num(y)
    array([  1.79769313e+308 +0.00000000e+000j, # may vary
             0.00000000e+000 +0.00000000e+000j,
             0.00000000e+000 +1.79769313e+308j])
    >>> np.nan_to_num(y, nan=111111, posinf=222222)
    array([222222.+111111.j, 111111.     +0.j, 111111.+222222.j])

Python Library Documentation: function nanargmax in module autograd.tracer

nanargmax(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the indices of the maximum values in the specified axis ignoring
    NaNs. For all-NaN slices ``ValueError`` is raised. Warning: the
    results cannot be trusted if a slice contains only NaNs and -Infs.


    Parameters
    ----------
    a : array_like
        Input data.
    axis : int, optional
        Axis along which to operate.  By default flattened input is used.
    out : array, optional
        If provided, the result will be inserted into this array. It should
        be of the appropriate shape and dtype.

        .. versionadded:: 1.22.0
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the array.

        .. versionadded:: 1.22.0

    Returns
    -------
    index_array : ndarray
        An array of indices or a single index value.

    See Also
    --------
    argmax, nanargmin

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[np.nan, 4], [2, 3]])
    >>> np.argmax(a)
    0
    >>> np.nanargmax(a)
    1
    >>> np.nanargmax(a, axis=0)
    array([1, 0])
    >>> np.nanargmax(a, axis=1)
    array([1, 1])

Python Library Documentation: function nanargmin in module autograd.tracer

nanargmin(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the indices of the minimum values in the specified axis ignoring
    NaNs. For all-NaN slices ``ValueError`` is raised. Warning: the results
    cannot be trusted if a slice contains only NaNs and Infs.

    Parameters
    ----------
    a : array_like
        Input data.
    axis : int, optional
        Axis along which to operate.  By default flattened input is used.
    out : array, optional
        If provided, the result will be inserted into this array. It should
        be of the appropriate shape and dtype.

        .. versionadded:: 1.22.0
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the array.

        .. versionadded:: 1.22.0

    Returns
    -------
    index_array : ndarray
        An array of indices or a single index value.

    See Also
    --------
    argmin, nanargmax

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[np.nan, 4], [2, 3]])
    >>> np.argmin(a)
    0
    >>> np.nanargmin(a)
    2
    >>> np.nanargmin(a, axis=0)
    array([1, 1])
    >>> np.nanargmin(a, axis=1)
    array([1, 0])

Python Library Documentation: function nancumprod in module autograd.tracer

nancumprod(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the cumulative product of array elements over a given axis treating Not a
    Numbers (NaNs) as one.  The cumulative product does not change when NaNs are
    encountered and leading NaNs are replaced by ones.

    Ones are returned for slices that are all-NaN or empty.

    .. versionadded:: 1.12.0

    Parameters
    ----------
    a : array_like
        Input array.
    axis : int, optional
        Axis along which the cumulative product is computed.  By default
        the input is flattened.
    dtype : dtype, optional
        Type of the returned array, as well as of the accumulator in which
        the elements are multiplied.  If *dtype* is not specified, it
        defaults to the dtype of `a`, unless `a` has an integer dtype with
        a precision less than that of the default platform integer.  In
        that case, the default platform integer is used instead.
    out : ndarray, optional
        Alternative output array in which to place the result. It must
        have the same shape and buffer length as the expected output
        but the type of the resulting values will be cast if necessary.

    Returns
    -------
    nancumprod : ndarray
        A new array holding the result is returned unless `out` is
        specified, in which case it is returned.

    See Also
    --------
    numpy.cumprod : Cumulative product across array propagating NaNs.
    isnan : Show which elements are NaN.

    Examples
    --------
    >>> import numpy as np
    >>> np.nancumprod(1)
    array([1])
    >>> np.nancumprod([1])
    array([1])
    >>> np.nancumprod([1, np.nan])
    array([1.,  1.])
    >>> a = np.array([[1, 2], [3, np.nan]])
    >>> np.nancumprod(a)
    array([1.,  2.,  6.,  6.])
    >>> np.nancumprod(a, axis=0)
    array([[1.,  2.],
           [3.,  2.]])
    >>> np.nancumprod(a, axis=1)
    array([[1.,  2.],
           [3.,  3.]])

Python Library Documentation: function nancumsum in module autograd.tracer

nancumsum(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the cumulative sum of array elements over a given axis treating Not a
    Numbers (NaNs) as zero.  The cumulative sum does not change when NaNs are
    encountered and leading NaNs are replaced by zeros.

    Zeros are returned for slices that are all-NaN or empty.

    .. versionadded:: 1.12.0

    Parameters
    ----------
    a : array_like
        Input array.
    axis : int, optional
        Axis along which the cumulative sum is computed. The default
        (None) is to compute the cumsum over the flattened array.
    dtype : dtype, optional
        Type of the returned array and of the accumulator in which the
        elements are summed.  If `dtype` is not specified, it defaults
        to the dtype of `a`, unless `a` has an integer dtype with a
        precision less than that of the default platform integer.  In
        that case, the default platform integer is used.
    out : ndarray, optional
        Alternative output array in which to place the result. It must
        have the same shape and buffer length as the expected output
        but the type will be cast if necessary. See :ref:`ufuncs-output-type` for
        more details.

    Returns
    -------
    nancumsum : ndarray.
        A new array holding the result is returned unless `out` is
        specified, in which it is returned. The result has the same
        size as `a`, and the same shape as `a` if `axis` is not None
        or `a` is a 1-d array.

    See Also
    --------
    numpy.cumsum : Cumulative sum across array propagating NaNs.
    isnan : Show which elements are NaN.

    Examples
    --------
    >>> import numpy as np
    >>> np.nancumsum(1)
    array([1])
    >>> np.nancumsum([1])
    array([1])
    >>> np.nancumsum([1, np.nan])
    array([1.,  1.])
    >>> a = np.array([[1, 2], [3, np.nan]])
    >>> np.nancumsum(a)
    array([1.,  3.,  6.,  6.])
    >>> np.nancumsum(a, axis=0)
    array([[1.,  2.],
           [4.,  2.]])
    >>> np.nancumsum(a, axis=1)
    array([[1.,  3.],
           [3.,  3.]])

Python Library Documentation: function nanmax in module autograd.tracer

nanmax(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the maximum of an array or maximum along an axis, ignoring any
    NaNs.  When all-NaN slices are encountered a ``RuntimeWarning`` is
    raised and NaN is returned for that slice.

    Parameters
    ----------
    a : array_like
        Array containing numbers whose maximum is desired. If `a` is not an
        array, a conversion is attempted.
    axis : {int, tuple of int, None}, optional
        Axis or axes along which the maximum is computed. The default is to compute
        the maximum of the flattened array.
    out : ndarray, optional
        Alternate output array in which to place the result.  The default
        is ``None``; if provided, it must have the same shape as the
        expected output, but the type will be cast if necessary. See
        :ref:`ufuncs-output-type` for more details.

        .. versionadded:: 1.8.0
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the original `a`.

        If the value is anything but the default, then
        `keepdims` will be passed through to the `max` method
        of sub-classes of `ndarray`.  If the sub-classes methods
        does not implement `keepdims` any exceptions will be raised.

        .. versionadded:: 1.8.0
    initial : scalar, optional
        The minimum value of an output element. Must be present to allow
        computation on empty slice. See `~numpy.ufunc.reduce` for details.

        .. versionadded:: 1.22.0
    where : array_like of bool, optional
        Elements to compare for the maximum. See `~numpy.ufunc.reduce`
        for details.

        .. versionadded:: 1.22.0

    Returns
    -------
    nanmax : ndarray
        An array with the same shape as `a`, with the specified axis removed.
        If `a` is a 0-d array, or if axis is None, an ndarray scalar is
        returned.  The same dtype as `a` is returned.

    See Also
    --------
    nanmin :
        The minimum value of an array along a given axis, ignoring any NaNs.
    amax :
        The maximum value of an array along a given axis, propagating any NaNs.
    fmax :
        Element-wise maximum of two arrays, ignoring any NaNs.
    maximum :
        Element-wise maximum of two arrays, propagating any NaNs.
    isnan :
        Shows which elements are Not a Number (NaN).
    isfinite:
        Shows which elements are neither NaN nor infinity.

    amin, fmin, minimum

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754). This means that Not a Number is not equivalent to infinity.
    Positive infinity is treated as a very large number and negative
    infinity is treated as a very small (i.e. negative) number.

    If the input has a integer type the function is equivalent to np.max.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[1, 2], [3, np.nan]])
    >>> np.nanmax(a)
    3.0
    >>> np.nanmax(a, axis=0)
    array([3.,  2.])
    >>> np.nanmax(a, axis=1)
    array([2.,  3.])

    When positive infinity and negative infinity are present:

    >>> np.nanmax([1, 2, np.nan, -np.inf])
    2.0
    >>> np.nanmax([1, 2, np.nan, np.inf])
    inf

Python Library Documentation: function nanmean in module autograd.tracer

nanmean(*args, called_by_autograd_dispatcher=False, **kwargs)
    Compute the arithmetic mean along the specified axis, ignoring NaNs.

    Returns the average of the array elements.  The average is taken over
    the flattened array by default, otherwise over the specified axis.
    `float64` intermediate and return values are used for integer inputs.

    For all-NaN slices, NaN is returned and a `RuntimeWarning` is raised.

    .. versionadded:: 1.8.0

    Parameters
    ----------
    a : array_like
        Array containing numbers whose mean is desired. If `a` is not an
        array, a conversion is attempted.
    axis : {int, tuple of int, None}, optional
        Axis or axes along which the means are computed. The default is to compute
        the mean of the flattened array.
    dtype : data-type, optional
        Type to use in computing the mean.  For integer inputs, the default
        is `float64`; for inexact inputs, it is the same as the input
        dtype.
    out : ndarray, optional
        Alternate output array in which to place the result.  The default
        is ``None``; if provided, it must have the same shape as the
        expected output, but the type will be cast if necessary.
        See :ref:`ufuncs-output-type` for more details.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the original `a`.

        If the value is anything but the default, then
        `keepdims` will be passed through to the `mean` or `sum` methods
        of sub-classes of `ndarray`.  If the sub-classes methods
        does not implement `keepdims` any exceptions will be raised.
    where : array_like of bool, optional
        Elements to include in the mean. See `~numpy.ufunc.reduce` for details.

        .. versionadded:: 1.22.0

    Returns
    -------
    m : ndarray, see dtype parameter above
        If `out=None`, returns a new array containing the mean values,
        otherwise a reference to the output array is returned. Nan is
        returned for slices that contain only NaNs.

    See Also
    --------
    average : Weighted average
    mean : Arithmetic mean taken while not ignoring NaNs
    var, nanvar

    Notes
    -----
    The arithmetic mean is the sum of the non-NaN elements along the axis
    divided by the number of non-NaN elements.

    Note that for floating-point input, the mean is computed using the same
    precision the input has.  Depending on the input data, this can cause
    the results to be inaccurate, especially for `float32`.  Specifying a
    higher-precision accumulator using the `dtype` keyword can alleviate
    this issue.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[1, np.nan], [3, 4]])
    >>> np.nanmean(a)
    2.6666666666666665
    >>> np.nanmean(a, axis=0)
    array([2.,  4.])
    >>> np.nanmean(a, axis=1)
    array([1.,  3.5]) # may vary

Python Library Documentation: function nanmedian in module autograd.tracer

nanmedian(*args, called_by_autograd_dispatcher=False, **kwargs)
    Compute the median along the specified axis, while ignoring NaNs.

    Returns the median of the array elements.

    .. versionadded:: 1.9.0

    Parameters
    ----------
    a : array_like
        Input array or object that can be converted to an array.
    axis : {int, sequence of int, None}, optional
        Axis or axes along which the medians are computed. The default
        is to compute the median along a flattened version of the array.
        A sequence of axes is supported since version 1.9.0.
    out : ndarray, optional
        Alternative output array in which to place the result. It must
        have the same shape and buffer length as the expected output,
        but the type (of the output) will be cast if necessary.
    overwrite_input : bool, optional
       If True, then allow use of memory of input array `a` for
       calculations. The input array will be modified by the call to
       `median`. This will save memory when you do not need to preserve
       the contents of the input array. Treat the input as undefined,
       but it will probably be fully or partially sorted. Default is
       False. If `overwrite_input` is ``True`` and `a` is not already an
       `ndarray`, an error will be raised.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the original `a`.

        If this is anything but the default value it will be passed
        through (in the special case of an empty array) to the
        `mean` function of the underlying array.  If the array is
        a sub-class and `mean` does not have the kwarg `keepdims` this
        will raise a RuntimeError.

    Returns
    -------
    median : ndarray
        A new array holding the result. If the input contains integers
        or floats smaller than ``float64``, then the output data-type is
        ``np.float64``.  Otherwise, the data-type of the output is the
        same as that of the input. If `out` is specified, that array is
        returned instead.

    See Also
    --------
    mean, median, percentile

    Notes
    -----
    Given a vector ``V`` of length ``N``, the median of ``V`` is the
    middle value of a sorted copy of ``V``, ``V_sorted`` - i.e.,
    ``V_sorted[(N-1)/2]``, when ``N`` is odd and the average of the two
    middle values of ``V_sorted`` when ``N`` is even.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[10.0, 7, 4], [3, 2, 1]])
    >>> a[0, 1] = np.nan
    >>> a
    array([[10., nan,  4.],
           [ 3.,  2.,  1.]])
    >>> np.median(a)
    np.float64(nan)
    >>> np.nanmedian(a)
    3.0
    >>> np.nanmedian(a, axis=0)
    array([6.5, 2. , 2.5])
    >>> np.median(a, axis=1)
    array([nan,  2.])
    >>> b = a.copy()
    >>> np.nanmedian(b, axis=1, overwrite_input=True)
    array([7.,  2.])
    >>> assert not np.all(a==b)
    >>> b = a.copy()
    >>> np.nanmedian(b, axis=None, overwrite_input=True)
    3.0
    >>> assert not np.all(a==b)

Python Library Documentation: function nanmin in module autograd.tracer

nanmin(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return minimum of an array or minimum along an axis, ignoring any NaNs.
    When all-NaN slices are encountered a ``RuntimeWarning`` is raised and
    Nan is returned for that slice.

    Parameters
    ----------
    a : array_like
        Array containing numbers whose minimum is desired. If `a` is not an
        array, a conversion is attempted.
    axis : {int, tuple of int, None}, optional
        Axis or axes along which the minimum is computed. The default is to compute
        the minimum of the flattened array.
    out : ndarray, optional
        Alternate output array in which to place the result.  The default
        is ``None``; if provided, it must have the same shape as the
        expected output, but the type will be cast if necessary. See
        :ref:`ufuncs-output-type` for more details.

        .. versionadded:: 1.8.0
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the original `a`.

        If the value is anything but the default, then
        `keepdims` will be passed through to the `min` method
        of sub-classes of `ndarray`.  If the sub-classes methods
        does not implement `keepdims` any exceptions will be raised.

        .. versionadded:: 1.8.0
    initial : scalar, optional
        The maximum value of an output element. Must be present to allow
        computation on empty slice. See `~numpy.ufunc.reduce` for details.

        .. versionadded:: 1.22.0
    where : array_like of bool, optional
        Elements to compare for the minimum. See `~numpy.ufunc.reduce`
        for details.

        .. versionadded:: 1.22.0

    Returns
    -------
    nanmin : ndarray
        An array with the same shape as `a`, with the specified axis
        removed.  If `a` is a 0-d array, or if axis is None, an ndarray
        scalar is returned.  The same dtype as `a` is returned.

    See Also
    --------
    nanmax :
        The maximum value of an array along a given axis, ignoring any NaNs.
    amin :
        The minimum value of an array along a given axis, propagating any NaNs.
    fmin :
        Element-wise minimum of two arrays, ignoring any NaNs.
    minimum :
        Element-wise minimum of two arrays, propagating any NaNs.
    isnan :
        Shows which elements are Not a Number (NaN).
    isfinite:
        Shows which elements are neither NaN nor infinity.

    amax, fmax, maximum

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754). This means that Not a Number is not equivalent to infinity.
    Positive infinity is treated as a very large number and negative
    infinity is treated as a very small (i.e. negative) number.

    If the input has a integer type the function is equivalent to np.min.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[1, 2], [3, np.nan]])
    >>> np.nanmin(a)
    1.0
    >>> np.nanmin(a, axis=0)
    array([1.,  2.])
    >>> np.nanmin(a, axis=1)
    array([1.,  3.])

    When positive infinity and negative infinity are present:

    >>> np.nanmin([1, 2, np.nan, np.inf])
    1.0
    >>> np.nanmin([1, 2, np.nan, -np.inf])
    -inf

Python Library Documentation: function nanpercentile in module autograd.tracer

nanpercentile(*args, called_by_autograd_dispatcher=False, **kwargs)
    Compute the qth percentile of the data along the specified axis,
    while ignoring nan values.

    Returns the qth percentile(s) of the array elements.

    .. versionadded:: 1.9.0

    Parameters
    ----------
    a : array_like
        Input array or object that can be converted to an array, containing
        nan values to be ignored.
    q : array_like of float
        Percentile or sequence of percentiles to compute, which must be
        between 0 and 100 inclusive.
    axis : {int, tuple of int, None}, optional
        Axis or axes along which the percentiles are computed. The default
        is to compute the percentile(s) along a flattened version of the
        array.
    out : ndarray, optional
        Alternative output array in which to place the result. It must have
        the same shape and buffer length as the expected output, but the
        type (of the output) will be cast if necessary.
    overwrite_input : bool, optional
        If True, then allow the input array `a` to be modified by
        intermediate calculations, to save memory. In this case, the
        contents of the input `a` after this function completes is
        undefined.
    method : str, optional
        This parameter specifies the method to use for estimating the
        percentile.  There are many different methods, some unique to NumPy.
        See the notes for explanation.  The options sorted by their R type
        as summarized in the H&F paper [1]_ are:

        1. 'inverted_cdf'
        2. 'averaged_inverted_cdf'
        3. 'closest_observation'
        4. 'interpolated_inverted_cdf'
        5. 'hazen'
        6. 'weibull'
        7. 'linear'  (default)
        8. 'median_unbiased'
        9. 'normal_unbiased'

        The first three methods are discontinuous.  NumPy further defines the
        following discontinuous variations of the default 'linear' (7.) option:

        * 'lower'
        * 'higher',
        * 'midpoint'
        * 'nearest'

        .. versionchanged:: 1.22.0
            This argument was previously called "interpolation" and only
            offered the "linear" default and last four options.

    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left in
        the result as dimensions with size one. With this option, the
        result will broadcast correctly against the original array `a`.

        If this is anything but the default value it will be passed
        through (in the special case of an empty array) to the
        `mean` function of the underlying array.  If the array is
        a sub-class and `mean` does not have the kwarg `keepdims` this
        will raise a RuntimeError.

    weights : array_like, optional
        An array of weights associated with the values in `a`. Each value in
        `a` contributes to the percentile according to its associated weight.
        The weights array can either be 1-D (in which case its length must be
        the size of `a` along the given axis) or of the same shape as `a`.
        If `weights=None`, then all data in `a` are assumed to have a
        weight equal to one.
        Only `method="inverted_cdf"` supports weights.

        .. versionadded:: 2.0.0

    interpolation : str, optional
        Deprecated name for the method keyword argument.

        .. deprecated:: 1.22.0

    Returns
    -------
    percentile : scalar or ndarray
        If `q` is a single percentile and `axis=None`, then the result
        is a scalar. If multiple percentiles are given, first axis of
        the result corresponds to the percentiles. The other axes are
        the axes that remain after the reduction of `a`. If the input
        contains integers or floats smaller than ``float64``, the output
        data-type is ``float64``. Otherwise, the output data-type is the
        same as that of the input. If `out` is specified, that array is
        returned instead.

    See Also
    --------
    nanmean
    nanmedian : equivalent to ``nanpercentile(..., 50)``
    percentile, median, mean
    nanquantile : equivalent to nanpercentile, except q in range [0, 1].

    Notes
    -----
    The behavior of `numpy.nanpercentile` with percentage `q` is that of
    `numpy.quantile` with argument ``q/100`` (ignoring nan values).
    For more information, please see `numpy.quantile`.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[10., 7., 4.], [3., 2., 1.]])
    >>> a[0][1] = np.nan
    >>> a
    array([[10.,  nan,   4.],
          [ 3.,   2.,   1.]])
    >>> np.percentile(a, 50)
    np.float64(nan)
    >>> np.nanpercentile(a, 50)
    3.0
    >>> np.nanpercentile(a, 50, axis=0)
    array([6.5, 2. , 2.5])
    >>> np.nanpercentile(a, 50, axis=1, keepdims=True)
    array([[7.],
           [2.]])
    >>> m = np.nanpercentile(a, 50, axis=0)
    >>> out = np.zeros_like(m)
    >>> np.nanpercentile(a, 50, axis=0, out=out)
    array([6.5, 2. , 2.5])
    >>> m
    array([6.5,  2. ,  2.5])

    >>> b = a.copy()
    >>> np.nanpercentile(b, 50, axis=1, overwrite_input=True)
    array([7., 2.])
    >>> assert not np.all(a==b)

    References
    ----------
    .. [1] R. J. Hyndman and Y. Fan,
       "Sample quantiles in statistical packages,"
       The American Statistician, 50(4), pp. 361-365, 1996

Python Library Documentation: function nanprod in module autograd.tracer

nanprod(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the product of array elements over a given axis treating Not a
    Numbers (NaNs) as ones.

    One is returned for slices that are all-NaN or empty.

    .. versionadded:: 1.10.0

    Parameters
    ----------
    a : array_like
        Array containing numbers whose product is desired. If `a` is not an
        array, a conversion is attempted.
    axis : {int, tuple of int, None}, optional
        Axis or axes along which the product is computed. The default is to compute
        the product of the flattened array.
    dtype : data-type, optional
        The type of the returned array and of the accumulator in which the
        elements are summed.  By default, the dtype of `a` is used.  An
        exception is when `a` has an integer type with less precision than
        the platform (u)intp. In that case, the default will be either
        (u)int32 or (u)int64 depending on whether the platform is 32 or 64
        bits. For inexact inputs, dtype must be inexact.
    out : ndarray, optional
        Alternate output array in which to place the result.  The default
        is ``None``. If provided, it must have the same shape as the
        expected output, but the type will be cast if necessary. See
        :ref:`ufuncs-output-type` for more details. The casting of NaN to integer
        can yield unexpected results.
    keepdims : bool, optional
        If True, the axes which are reduced are left in the result as
        dimensions with size one. With this option, the result will
        broadcast correctly against the original `arr`.
    initial : scalar, optional
        The starting value for this product. See `~numpy.ufunc.reduce`
        for details.

        .. versionadded:: 1.22.0
    where : array_like of bool, optional
        Elements to include in the product. See `~numpy.ufunc.reduce`
        for details.

        .. versionadded:: 1.22.0

    Returns
    -------
    nanprod : ndarray
        A new array holding the result is returned unless `out` is
        specified, in which case it is returned.

    See Also
    --------
    numpy.prod : Product across array propagating NaNs.
    isnan : Show which elements are NaN.

    Examples
    --------
    >>> import numpy as np
    >>> np.nanprod(1)
    1
    >>> np.nanprod([1])
    1
    >>> np.nanprod([1, np.nan])
    1.0
    >>> a = np.array([[1, 2], [3, np.nan]])
    >>> np.nanprod(a)
    6.0
    >>> np.nanprod(a, axis=0)
    array([3., 2.])

Python Library Documentation: function nanquantile in module autograd.tracer

nanquantile(*args, called_by_autograd_dispatcher=False, **kwargs)
    Compute the qth quantile of the data along the specified axis,
    while ignoring nan values.
    Returns the qth quantile(s) of the array elements.

    .. versionadded:: 1.15.0

    Parameters
    ----------
    a : array_like
        Input array or object that can be converted to an array, containing
        nan values to be ignored
    q : array_like of float
        Probability or sequence of probabilities for the quantiles to compute.
        Values must be between 0 and 1 inclusive.
    axis : {int, tuple of int, None}, optional
        Axis or axes along which the quantiles are computed. The
        default is to compute the quantile(s) along a flattened
        version of the array.
    out : ndarray, optional
        Alternative output array in which to place the result. It must
        have the same shape and buffer length as the expected output,
        but the type (of the output) will be cast if necessary.
    overwrite_input : bool, optional
        If True, then allow the input array `a` to be modified by intermediate
        calculations, to save memory. In this case, the contents of the input
        `a` after this function completes is undefined.
    method : str, optional
        This parameter specifies the method to use for estimating the
        quantile.  There are many different methods, some unique to NumPy.
        See the notes for explanation.  The options sorted by their R type
        as summarized in the H&F paper [1]_ are:

        1. 'inverted_cdf'
        2. 'averaged_inverted_cdf'
        3. 'closest_observation'
        4. 'interpolated_inverted_cdf'
        5. 'hazen'
        6. 'weibull'
        7. 'linear'  (default)
        8. 'median_unbiased'
        9. 'normal_unbiased'

        The first three methods are discontinuous.  NumPy further defines the
        following discontinuous variations of the default 'linear' (7.) option:

        * 'lower'
        * 'higher',
        * 'midpoint'
        * 'nearest'

        .. versionchanged:: 1.22.0
            This argument was previously called "interpolation" and only
            offered the "linear" default and last four options.

    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left in
        the result as dimensions with size one. With this option, the
        result will broadcast correctly against the original array `a`.

        If this is anything but the default value it will be passed
        through (in the special case of an empty array) to the
        `mean` function of the underlying array.  If the array is
        a sub-class and `mean` does not have the kwarg `keepdims` this
        will raise a RuntimeError.

    weights : array_like, optional
        An array of weights associated with the values in `a`. Each value in
        `a` contributes to the quantile according to its associated weight.
        The weights array can either be 1-D (in which case its length must be
        the size of `a` along the given axis) or of the same shape as `a`.
        If `weights=None`, then all data in `a` are assumed to have a
        weight equal to one.
        Only `method="inverted_cdf"` supports weights.

        .. versionadded:: 2.0.0

    interpolation : str, optional
        Deprecated name for the method keyword argument.

        .. deprecated:: 1.22.0

    Returns
    -------
    quantile : scalar or ndarray
        If `q` is a single probability and `axis=None`, then the result
        is a scalar. If multiple probability levels are given, first axis of
        the result corresponds to the quantiles. The other axes are
        the axes that remain after the reduction of `a`. If the input
        contains integers or floats smaller than ``float64``, the output
        data-type is ``float64``. Otherwise, the output data-type is the
        same as that of the input. If `out` is specified, that array is
        returned instead.

    See Also
    --------
    quantile
    nanmean, nanmedian
    nanmedian : equivalent to ``nanquantile(..., 0.5)``
    nanpercentile : same as nanquantile, but with q in the range [0, 100].

    Notes
    -----
    The behavior of `numpy.nanquantile` is the same as that of
    `numpy.quantile` (ignoring nan values).
    For more information, please see `numpy.quantile`.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[10., 7., 4.], [3., 2., 1.]])
    >>> a[0][1] = np.nan
    >>> a
    array([[10.,  nan,   4.],
          [ 3.,   2.,   1.]])
    >>> np.quantile(a, 0.5)
    np.float64(nan)
    >>> np.nanquantile(a, 0.5)
    3.0
    >>> np.nanquantile(a, 0.5, axis=0)
    array([6.5, 2. , 2.5])
    >>> np.nanquantile(a, 0.5, axis=1, keepdims=True)
    array([[7.],
           [2.]])
    >>> m = np.nanquantile(a, 0.5, axis=0)
    >>> out = np.zeros_like(m)
    >>> np.nanquantile(a, 0.5, axis=0, out=out)
    array([6.5, 2. , 2.5])
    >>> m
    array([6.5,  2. ,  2.5])
    >>> b = a.copy()
    >>> np.nanquantile(b, 0.5, axis=1, overwrite_input=True)
    array([7., 2.])
    >>> assert not np.all(a==b)

    References
    ----------
    .. [1] R. J. Hyndman and Y. Fan,
       "Sample quantiles in statistical packages,"
       The American Statistician, 50(4), pp. 361-365, 1996

Python Library Documentation: function nanstd in module autograd.tracer

nanstd(*args, called_by_autograd_dispatcher=False, **kwargs)
    Compute the standard deviation along the specified axis, while
    ignoring NaNs.

    Returns the standard deviation, a measure of the spread of a
    distribution, of the non-NaN array elements. The standard deviation is
    computed for the flattened array by default, otherwise over the
    specified axis.

    For all-NaN slices or slices with zero degrees of freedom, NaN is
    returned and a `RuntimeWarning` is raised.

    .. versionadded:: 1.8.0

    Parameters
    ----------
    a : array_like
        Calculate the standard deviation of the non-NaN values.
    axis : {int, tuple of int, None}, optional
        Axis or axes along which the standard deviation is computed. The default is
        to compute the standard deviation of the flattened array.
    dtype : dtype, optional
        Type to use in computing the standard deviation. For arrays of
        integer type the default is float64, for arrays of float types it
        is the same as the array type.
    out : ndarray, optional
        Alternative output array in which to place the result. It must have
        the same shape as the expected output but the type (of the
        calculated values) will be cast if necessary.
    ddof : {int, float}, optional
        Means Delta Degrees of Freedom.  The divisor used in calculations
        is ``N - ddof``, where ``N`` represents the number of non-NaN
        elements.  By default `ddof` is zero.

    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the original `a`.

        If this value is anything but the default it is passed through
        as-is to the relevant functions of the sub-classes.  If these
        functions do not have a `keepdims` kwarg, a RuntimeError will
        be raised.
    where : array_like of bool, optional
        Elements to include in the standard deviation.
        See `~numpy.ufunc.reduce` for details.

        .. versionadded:: 1.22.0

    mean : array_like, optional
        Provide the mean to prevent its recalculation. The mean should have
        a shape as if it was calculated with ``keepdims=True``.
        The axis for the calculation of the mean should be the same as used in
        the call to this std function.

        .. versionadded:: 1.26.0

    correction : {int, float}, optional
        Array API compatible name for the ``ddof`` parameter. Only one of them
        can be provided at the same time.

        .. versionadded:: 2.0.0

    Returns
    -------
    standard_deviation : ndarray, see dtype parameter above.
        If `out` is None, return a new array containing the standard
        deviation, otherwise return a reference to the output array. If
        ddof is >= the number of non-NaN elements in a slice or the slice
        contains only NaNs, then the result for that slice is NaN.

    See Also
    --------
    var, mean, std
    nanvar, nanmean
    :ref:`ufuncs-output-type`

    Notes
    -----
    The standard deviation is the square root of the average of the squared
    deviations from the mean: ``std = sqrt(mean(abs(x - x.mean())**2))``.

    The average squared deviation is normally calculated as
    ``x.sum() / N``, where ``N = len(x)``.  If, however, `ddof` is
    specified, the divisor ``N - ddof`` is used instead. In standard
    statistical practice, ``ddof=1`` provides an unbiased estimator of the
    variance of the infinite population. ``ddof=0`` provides a maximum
    likelihood estimate of the variance for normally distributed variables.
    The standard deviation computed in this function is the square root of
    the estimated variance, so even with ``ddof=1``, it will not be an
    unbiased estimate of the standard deviation per se.

    Note that, for complex numbers, `std` takes the absolute value before
    squaring, so that the result is always real and nonnegative.

    For floating-point input, the *std* is computed using the same
    precision the input has. Depending on the input data, this can cause
    the results to be inaccurate, especially for float32 (see example
    below).  Specifying a higher-accuracy accumulator using the `dtype`
    keyword can alleviate this issue.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[1, np.nan], [3, 4]])
    >>> np.nanstd(a)
    1.247219128924647
    >>> np.nanstd(a, axis=0)
    array([1., 0.])
    >>> np.nanstd(a, axis=1)
    array([0.,  0.5]) # may vary

Python Library Documentation: function nansum in module autograd.tracer

nansum(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the sum of array elements over a given axis treating Not a
    Numbers (NaNs) as zero.

    In NumPy versions <= 1.9.0 Nan is returned for slices that are all-NaN or
    empty. In later versions zero is returned.

    Parameters
    ----------
    a : array_like
        Array containing numbers whose sum is desired. If `a` is not an
        array, a conversion is attempted.
    axis : {int, tuple of int, None}, optional
        Axis or axes along which the sum is computed. The default is to compute the
        sum of the flattened array.
    dtype : data-type, optional
        The type of the returned array and of the accumulator in which the
        elements are summed.  By default, the dtype of `a` is used.  An
        exception is when `a` has an integer type with less precision than
        the platform (u)intp. In that case, the default will be either
        (u)int32 or (u)int64 depending on whether the platform is 32 or 64
        bits. For inexact inputs, dtype must be inexact.

        .. versionadded:: 1.8.0
    out : ndarray, optional
        Alternate output array in which to place the result.  The default
        is ``None``. If provided, it must have the same shape as the
        expected output, but the type will be cast if necessary.  See
        :ref:`ufuncs-output-type` for more details. The casting of NaN to integer
        can yield unexpected results.

        .. versionadded:: 1.8.0
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the original `a`.


        If the value is anything but the default, then
        `keepdims` will be passed through to the `mean` or `sum` methods
        of sub-classes of `ndarray`.  If the sub-classes methods
        does not implement `keepdims` any exceptions will be raised.

        .. versionadded:: 1.8.0
    initial : scalar, optional
        Starting value for the sum. See `~numpy.ufunc.reduce` for details.

        .. versionadded:: 1.22.0
    where : array_like of bool, optional
        Elements to include in the sum. See `~numpy.ufunc.reduce` for details.

        .. versionadded:: 1.22.0

    Returns
    -------
    nansum : ndarray.
        A new array holding the result is returned unless `out` is
        specified, in which it is returned. The result has the same
        size as `a`, and the same shape as `a` if `axis` is not None
        or `a` is a 1-d array.

    See Also
    --------
    numpy.sum : Sum across array propagating NaNs.
    isnan : Show which elements are NaN.
    isfinite : Show which elements are not NaN or +/-inf.

    Notes
    -----
    If both positive and negative infinity are present, the sum will be Not
    A Number (NaN).

    Examples
    --------
    >>> import numpy as np
    >>> np.nansum(1)
    1
    >>> np.nansum([1])
    1
    >>> np.nansum([1, np.nan])
    1.0
    >>> a = np.array([[1, 1], [1, np.nan]])
    >>> np.nansum(a)
    3.0
    >>> np.nansum(a, axis=0)
    array([2.,  1.])
    >>> np.nansum([1, np.nan, np.inf])
    inf
    >>> np.nansum([1, np.nan, -np.inf])
    -inf
    >>> from numpy.testing import suppress_warnings
    >>> with np.errstate(invalid="ignore"):
    ...     np.nansum([1, np.nan, np.inf, -np.inf]) # both +/- infinity present
    np.float64(nan)

Python Library Documentation: function nanvar in module autograd.tracer

nanvar(*args, called_by_autograd_dispatcher=False, **kwargs)
    Compute the variance along the specified axis, while ignoring NaNs.

    Returns the variance of the array elements, a measure of the spread of
    a distribution.  The variance is computed for the flattened array by
    default, otherwise over the specified axis.

    For all-NaN slices or slices with zero degrees of freedom, NaN is
    returned and a `RuntimeWarning` is raised.

    .. versionadded:: 1.8.0

    Parameters
    ----------
    a : array_like
        Array containing numbers whose variance is desired.  If `a` is not an
        array, a conversion is attempted.
    axis : {int, tuple of int, None}, optional
        Axis or axes along which the variance is computed.  The default is to compute
        the variance of the flattened array.
    dtype : data-type, optional
        Type to use in computing the variance.  For arrays of integer type
        the default is `float64`; for arrays of float types it is the same as
        the array type.
    out : ndarray, optional
        Alternate output array in which to place the result.  It must have
        the same shape as the expected output, but the type is cast if
        necessary.
    ddof : {int, float}, optional
        "Delta Degrees of Freedom": the divisor used in the calculation is
        ``N - ddof``, where ``N`` represents the number of non-NaN
        elements. By default `ddof` is zero.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the original `a`.
    where : array_like of bool, optional
        Elements to include in the variance. See `~numpy.ufunc.reduce` for
        details.

        .. versionadded:: 1.22.0

    mean : array_like, optional
        Provide the mean to prevent its recalculation. The mean should have
        a shape as if it was calculated with ``keepdims=True``.
        The axis for the calculation of the mean should be the same as used in
        the call to this var function.

        .. versionadded:: 1.26.0

    correction : {int, float}, optional
        Array API compatible name for the ``ddof`` parameter. Only one of them
        can be provided at the same time.

        .. versionadded:: 2.0.0

    Returns
    -------
    variance : ndarray, see dtype parameter above
        If `out` is None, return a new array containing the variance,
        otherwise return a reference to the output array. If ddof is >= the
        number of non-NaN elements in a slice or the slice contains only
        NaNs, then the result for that slice is NaN.

    See Also
    --------
    std : Standard deviation
    mean : Average
    var : Variance while not ignoring NaNs
    nanstd, nanmean
    :ref:`ufuncs-output-type`

    Notes
    -----
    The variance is the average of the squared deviations from the mean,
    i.e.,  ``var = mean(abs(x - x.mean())**2)``.

    The mean is normally calculated as ``x.sum() / N``, where ``N = len(x)``.
    If, however, `ddof` is specified, the divisor ``N - ddof`` is used
    instead.  In standard statistical practice, ``ddof=1`` provides an
    unbiased estimator of the variance of a hypothetical infinite
    population.  ``ddof=0`` provides a maximum likelihood estimate of the
    variance for normally distributed variables.

    Note that for complex numbers, the absolute value is taken before
    squaring, so that the result is always real and nonnegative.

    For floating-point input, the variance is computed using the same
    precision the input has.  Depending on the input data, this can cause
    the results to be inaccurate, especially for `float32` (see example
    below).  Specifying a higher-accuracy accumulator using the ``dtype``
    keyword can alleviate this issue.

    For this function to work on sub-classes of ndarray, they must define
    `sum` with the kwarg `keepdims`

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[1, np.nan], [3, 4]])
    >>> np.nanvar(a)
    1.5555555555555554
    >>> np.nanvar(a, axis=0)
    array([1.,  0.])
    >>> np.nanvar(a, axis=1)
    array([0.,  0.25])  # may vary

Python Library Documentation: class ndarray in module numpy

class ndarray(builtins.object)
 |  ndarray(shape, dtype=float, buffer=None, offset=0,
 |          strides=None, order=None)
 |
 |  An array object represents a multidimensional, homogeneous array
 |  of fixed-size items.  An associated data-type object describes the
 |  format of each element in the array (its byte-order, how many bytes it
 |  occupies in memory, whether it is an integer, a floating point number,
 |  or something else, etc.)
 |
 |  Arrays should be constructed using `array`, `zeros` or `empty` (refer
 |  to the See Also section below).  The parameters given here refer to
 |  a low-level method (`ndarray(...)`) for instantiating an array.
 |
 |  For more information, refer to the `numpy` module and examine the
 |  methods and attributes of an array.
 |
 |  Parameters
 |  ----------
 |  (for the __new__ method; see Notes below)
 |
 |  shape : tuple of ints
 |      Shape of created array.
 |  dtype : data-type, optional
 |      Any object that can be interpreted as a numpy data type.
 |  buffer : object exposing buffer interface, optional
 |      Used to fill the array with data.
 |  offset : int, optional
 |      Offset of array data in buffer.
 |  strides : tuple of ints, optional
 |      Strides of data in memory.
 |  order : {'C', 'F'}, optional
 |      Row-major (C-style) or column-major (Fortran-style) order.
 |
 |  Attributes
 |  ----------
 |  T : ndarray
 |      Transpose of the array.
 |  data : buffer
 |      The array's elements, in memory.
 |  dtype : dtype object
 |      Describes the format of the elements in the array.
 |  flags : dict
 |      Dictionary containing information related to memory use, e.g.,
 |      'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
 |  flat : numpy.flatiter object
 |      Flattened version of the array as an iterator.  The iterator
 |      allows assignments, e.g., ``x.flat = 3`` (See `ndarray.flat` for
 |      assignment examples; TODO).
 |  imag : ndarray
 |      Imaginary part of the array.
 |  real : ndarray
 |      Real part of the array.
 |  size : int
 |      Number of elements in the array.
 |  itemsize : int
 |      The memory use of each array element in bytes.
 |  nbytes : int
 |      The total number of bytes required to store the array data,
 |      i.e., ``itemsize * size``.
 |  ndim : int
 |      The array's number of dimensions.
 |  shape : tuple of ints
 |      Shape of the array.
 |  strides : tuple of ints
 |      The step-size required to move from one element to the next in
 |      memory. For example, a contiguous ``(3, 4)`` array of type
 |      ``int16`` in C-order has strides ``(8, 2)``.  This implies that
 |      to move from element to element in memory requires jumps of 2 bytes.
 |      To move from row-to-row, one needs to jump 8 bytes at a time
 |      (``2 * 4``).
 |  ctypes : ctypes object
 |      Class containing properties of the array needed for interaction
 |      with ctypes.
 |  base : ndarray
 |      If the array is a view into another array, that array is its `base`
 |      (unless that array is also a view).  The `base` array is where the
 |      array data is actually stored.
 |
 |  See Also
 |  --------
 |  array : Construct an array.
 |  zeros : Create an array, each element of which is zero.
 |  empty : Create an array, but leave its allocated memory unchanged (i.e.,
 |          it contains "garbage").
 |  dtype : Create a data-type.
 |  numpy.typing.NDArray : An ndarray alias :term:`generic <generic type>`
 |                         w.r.t. its `dtype.type <numpy.dtype.type>`.
 |
 |  Notes
 |  -----
 |  There are two modes of creating an array using ``__new__``:
 |
 |  1. If `buffer` is None, then only `shape`, `dtype`, and `order`
 |     are used.
 |  2. If `buffer` is an object exposing the buffer interface, then
 |     all keywords are interpreted.
 |
 |  No ``__init__`` method is needed because the array is fully initialized
 |  after the ``__new__`` method.
 |
 |  Examples
 |  --------
 |  These examples illustrate the low-level `ndarray` constructor.  Refer
 |  to the `See Also` section above for easier ways of constructing an
 |  ndarray.
 |
 |  First mode, `buffer` is None:
 |
 |  >>> import numpy as np
 |  >>> np.ndarray(shape=(2,2), dtype=float, order='F')
 |  array([[0.0e+000, 0.0e+000], # random
 |         [     nan, 2.5e-323]])
 |
 |  Second mode:
 |
 |  >>> np.ndarray((2,), buffer=np.array([1,2,3]),
 |  ...            offset=np.int_().itemsize,
 |  ...            dtype=int) # offset = 1*itemsize, i.e. skip first element
 |  array([2, 3])
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      a.__array__([dtype], *, copy=None)
 |
 |      For ``dtype`` parameter it returns a new reference to self if
 |      ``dtype`` is not given or it matches array's data type.
 |      A new array of provided data type is returned if ``dtype``
 |      is different from the current data type of the array.
 |      For ``copy`` parameter it returns a new reference to self if
 |      ``copy=False`` or ``copy=None`` and copying isn't enforced by ``dtype``
 |      parameter. The method returns a new array for ``copy=True``, regardless of
 |      ``dtype`` parameter.
 |
 |      A more detailed explanation of the ``__array__`` interface
 |      can be found in :ref:`dunder_array.interface`.
 |
 |  __array_finalize__(...)
 |      a.__array_finalize__(obj, /)
 |
 |      Present so subclasses can call super. Does nothing.
 |
 |  __array_function__(...)
 |
 |  __array_namespace__(...)
 |
 |  __array_ufunc__(...)
 |
 |  __array_wrap__(...)
 |      a.__array_wrap__(array[, context], /)
 |
 |      Returns a view of `array` with the same type as self.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __complex__(...)
 |
 |  __contains__(self, key, /)
 |      Return bool(key in self).
 |
 |  __copy__(...)
 |      a.__copy__()
 |
 |      Used if :func:`copy.copy` is called on an array. Returns a copy of the array.
 |
 |      Equivalent to ``a.copy(order='K')``.
 |
 |  __deepcopy__(...)
 |      a.__deepcopy__(memo, /)
 |
 |      Used if :func:`copy.deepcopy` is called on an array.
 |
 |  __delitem__(self, key, /)
 |      Delete self[key].
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __dlpack__(...)
 |      a.__dlpack__(*, stream=None, max_version=None, dl_device=None, copy=None)
 |
 |      DLPack Protocol: Part of the Array API.
 |
 |  __dlpack_device__(...)
 |      a.__dlpack_device__()
 |
 |      DLPack Protocol: Part of the Array API.
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      Default object formatter.
 |
 |      Return str(self) if format_spec is empty. Raise TypeError otherwise.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __iadd__(self, value, /)
 |      Return self+=value.
 |
 |  __iand__(self, value, /)
 |      Return self&=value.
 |
 |  __ifloordiv__(self, value, /)
 |      Return self//=value.
 |
 |  __ilshift__(self, value, /)
 |      Return self<<=value.
 |
 |  __imatmul__(self, value, /)
 |      Return self@=value.
 |
 |  __imod__(self, value, /)
 |      Return self%=value.
 |
 |  __imul__(self, value, /)
 |      Return self*=value.
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __ior__(self, value, /)
 |      Return self|=value.
 |
 |  __ipow__(self, value, /)
 |      Return self**=value.
 |
 |  __irshift__(self, value, /)
 |      Return self>>=value.
 |
 |  __isub__(self, value, /)
 |      Return self-=value.
 |
 |  __iter__(self, /)
 |      Implement iter(self).
 |
 |  __itruediv__(self, value, /)
 |      Return self/=value.
 |
 |  __ixor__(self, value, /)
 |      Return self^=value.
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __matmul__(self, value, /)
 |      Return self@value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      a.__reduce__()
 |
 |      For pickling.
 |
 |  __reduce_ex__(...)
 |      Helper for pickle.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmatmul__(self, value, /)
 |      Return value@self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setitem__(self, key, value, /)
 |      Set self[key] to value.
 |
 |  __setstate__(...)
 |      a.__setstate__(state, /)
 |
 |      For unpickling.
 |
 |      The `state` argument must be a sequence that contains the following
 |      elements:
 |
 |      Parameters
 |      ----------
 |      version : int
 |          optional pickle version. If omitted defaults to 0.
 |      shape : tuple
 |      dtype : data-type
 |      isFortran : bool
 |      rawdata : string or list
 |          a binary string with the data (or a list if 'a' is an object array)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      a.all(axis=None, out=None, keepdims=False, *, where=True)
 |
 |      Returns True if all elements evaluate to True.
 |
 |      Refer to `numpy.all` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.all : equivalent function
 |
 |  any(...)
 |      a.any(axis=None, out=None, keepdims=False, *, where=True)
 |
 |      Returns True if any of the elements of `a` evaluate to True.
 |
 |      Refer to `numpy.any` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.any : equivalent function
 |
 |  argmax(...)
 |      a.argmax(axis=None, out=None, *, keepdims=False)
 |
 |      Return indices of the maximum values along the given axis.
 |
 |      Refer to `numpy.argmax` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.argmax : equivalent function
 |
 |  argmin(...)
 |      a.argmin(axis=None, out=None, *, keepdims=False)
 |
 |      Return indices of the minimum values along the given axis.
 |
 |      Refer to `numpy.argmin` for detailed documentation.
 |
 |      See Also
 |      --------
 |      numpy.argmin : equivalent function
 |
 |  argpartition(...)
 |      a.argpartition(kth, axis=-1, kind='introselect', order=None)
 |
 |      Returns the indices that would partition this array.
 |
 |      Refer to `numpy.argpartition` for full documentation.
 |
 |      .. versionadded:: 1.8.0
 |
 |      See Also
 |      --------
 |      numpy.argpartition : equivalent function
 |
 |  argsort(...)
 |      a.argsort(axis=-1, kind=None, order=None)
 |
 |      Returns the indices that would sort this array.
 |
 |      Refer to `numpy.argsort` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.argsort : equivalent function
 |
 |  astype(...)
 |      a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True)
 |
 |      Copy of the array, cast to a specified type.
 |
 |      Parameters
 |      ----------
 |      dtype : str or dtype
 |          Typecode or data-type to which the array is cast.
 |      order : {'C', 'F', 'A', 'K'}, optional
 |          Controls the memory layout order of the result.
 |          'C' means C order, 'F' means Fortran order, 'A'
 |          means 'F' order if all the arrays are Fortran contiguous,
 |          'C' order otherwise, and 'K' means as close to the
 |          order the array elements appear in memory as possible.
 |          Default is 'K'.
 |      casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
 |          Controls what kind of data casting may occur. Defaults to 'unsafe'
 |          for backwards compatibility.
 |
 |          * 'no' means the data types should not be cast at all.
 |          * 'equiv' means only byte-order changes are allowed.
 |          * 'safe' means only casts which can preserve values are allowed.
 |          * 'same_kind' means only safe casts or casts within a kind,
 |            like float64 to float32, are allowed.
 |          * 'unsafe' means any data conversions may be done.
 |      subok : bool, optional
 |          If True, then sub-classes will be passed-through (default), otherwise
 |          the returned array will be forced to be a base-class array.
 |      copy : bool, optional
 |          By default, astype always returns a newly allocated array. If this
 |          is set to false, and the `dtype`, `order`, and `subok`
 |          requirements are satisfied, the input array is returned instead
 |          of a copy.
 |
 |      Returns
 |      -------
 |      arr_t : ndarray
 |          Unless `copy` is False and the other conditions for returning the input
 |          array are satisfied (see description for `copy` input parameter), `arr_t`
 |          is a new array of the same shape as the input array, with dtype, order
 |          given by `dtype`, `order`.
 |
 |      Notes
 |      -----
 |      .. versionchanged:: 1.17.0
 |         Casting between a simple data type and a structured one is possible only
 |         for "unsafe" casting.  Casting to multiple fields is allowed, but
 |         casting from multiple fields is not.
 |
 |      .. versionchanged:: 1.9.0
 |         Casting from numeric to string types in 'safe' casting mode requires
 |         that the string dtype length is long enough to store the max
 |         integer/float value converted.
 |
 |      Raises
 |      ------
 |      ComplexWarning
 |          When casting from complex to float or int. To avoid this,
 |          one should use ``a.real.astype(t)``.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 2.5])
 |      >>> x
 |      array([1. ,  2. ,  2.5])
 |
 |      >>> x.astype(int)
 |      array([1, 2, 2])
 |
 |  byteswap(...)
 |      a.byteswap(inplace=False)
 |
 |      Swap the bytes of the array elements
 |
 |      Toggle between low-endian and big-endian data representation by
 |      returning a byteswapped array, optionally swapped in-place.
 |      Arrays of byte-strings are not swapped. The real and imaginary
 |      parts of a complex number are swapped individually.
 |
 |      Parameters
 |      ----------
 |      inplace : bool, optional
 |          If ``True``, swap bytes in-place, default is ``False``.
 |
 |      Returns
 |      -------
 |      out : ndarray
 |          The byteswapped array. If `inplace` is ``True``, this is
 |          a view to self.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> A = np.array([1, 256, 8755], dtype=np.int16)
 |      >>> list(map(hex, A))
 |      ['0x1', '0x100', '0x2233']
 |      >>> A.byteswap(inplace=True)
 |      array([  256,     1, 13090], dtype=int16)
 |      >>> list(map(hex, A))
 |      ['0x100', '0x1', '0x3322']
 |
 |      Arrays of byte-strings are not swapped
 |
 |      >>> A = np.array([b'ceg', b'fac'])
 |      >>> A.byteswap()
 |      array([b'ceg', b'fac'], dtype='|S3')
 |
 |      ``A.view(A.dtype.newbyteorder()).byteswap()`` produces an array with
 |      the same values but different representation in memory
 |
 |      >>> A = np.array([1, 2, 3])
 |      >>> A.view(np.uint8)
 |      array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,
 |             0, 0], dtype=uint8)
 |      >>> A.view(A.dtype.newbyteorder()).byteswap(inplace=True)
 |      array([1, 2, 3])
 |      >>> A.view(np.uint8)
 |      array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0,
 |             0, 3], dtype=uint8)
 |
 |  choose(...)
 |      a.choose(choices, out=None, mode='raise')
 |
 |      Use an index array to construct a new array from a set of choices.
 |
 |      Refer to `numpy.choose` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.choose : equivalent function
 |
 |  clip(...)
 |      a.clip(min=None, max=None, out=None, **kwargs)
 |
 |      Return an array whose values are limited to ``[min, max]``.
 |      One of max or min must be given.
 |
 |      Refer to `numpy.clip` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.clip : equivalent function
 |
 |  compress(...)
 |      a.compress(condition, axis=None, out=None)
 |
 |      Return selected slices of this array along given axis.
 |
 |      Refer to `numpy.compress` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.compress : equivalent function
 |
 |  conj(...)
 |      a.conj()
 |
 |      Complex-conjugate all elements.
 |
 |      Refer to `numpy.conjugate` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.conjugate : equivalent function
 |
 |  conjugate(...)
 |      a.conjugate()
 |
 |      Return the complex conjugate, element-wise.
 |
 |      Refer to `numpy.conjugate` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.conjugate : equivalent function
 |
 |  copy(...)
 |      a.copy(order='C')
 |
 |      Return a copy of the array.
 |
 |      Parameters
 |      ----------
 |      order : {'C', 'F', 'A', 'K'}, optional
 |          Controls the memory layout of the copy. 'C' means C-order,
 |          'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
 |          'C' otherwise. 'K' means match the layout of `a` as closely
 |          as possible. (Note that this function and :func:`numpy.copy` are very
 |          similar but have different default values for their order=
 |          arguments, and this function always passes sub-classes through.)
 |
 |      See also
 |      --------
 |      numpy.copy : Similar function with different default behavior
 |      numpy.copyto
 |
 |      Notes
 |      -----
 |      This function is the preferred method for creating an array copy.  The
 |      function :func:`numpy.copy` is similar, but it defaults to using order 'K',
 |      and will not pass sub-classes through by default.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([[1,2,3],[4,5,6]], order='F')
 |
 |      >>> y = x.copy()
 |
 |      >>> x.fill(0)
 |
 |      >>> x
 |      array([[0, 0, 0],
 |             [0, 0, 0]])
 |
 |      >>> y
 |      array([[1, 2, 3],
 |             [4, 5, 6]])
 |
 |      >>> y.flags['C_CONTIGUOUS']
 |      True
 |
 |      For arrays containing Python objects (e.g. dtype=object),
 |      the copy is a shallow one. The new array will contain the
 |      same object which may lead to surprises if that object can
 |      be modified (is mutable):
 |
 |      >>> a = np.array([1, 'm', [2, 3, 4]], dtype=object)
 |      >>> b = a.copy()
 |      >>> b[2][0] = 10
 |      >>> a
 |      array([1, 'm', list([10, 3, 4])], dtype=object)
 |
 |      To ensure all elements within an ``object`` array are copied,
 |      use `copy.deepcopy`:
 |
 |      >>> import copy
 |      >>> a = np.array([1, 'm', [2, 3, 4]], dtype=object)
 |      >>> c = copy.deepcopy(a)
 |      >>> c[2][0] = 10
 |      >>> c
 |      array([1, 'm', list([10, 3, 4])], dtype=object)
 |      >>> a
 |      array([1, 'm', list([2, 3, 4])], dtype=object)
 |
 |  cumprod(...)
 |      a.cumprod(axis=None, dtype=None, out=None)
 |
 |      Return the cumulative product of the elements along the given axis.
 |
 |      Refer to `numpy.cumprod` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.cumprod : equivalent function
 |
 |  cumsum(...)
 |      a.cumsum(axis=None, dtype=None, out=None)
 |
 |      Return the cumulative sum of the elements along the given axis.
 |
 |      Refer to `numpy.cumsum` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.cumsum : equivalent function
 |
 |  diagonal(...)
 |      a.diagonal(offset=0, axis1=0, axis2=1)
 |
 |      Return specified diagonals. In NumPy 1.9 the returned array is a
 |      read-only view instead of a copy as in previous NumPy versions.  In
 |      a future version the read-only restriction will be removed.
 |
 |      Refer to :func:`numpy.diagonal` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.diagonal : equivalent function
 |
 |  dot(...)
 |
 |  dump(...)
 |      a.dump(file)
 |
 |      Dump a pickle of the array to the specified file.
 |      The array can be read back with pickle.load or numpy.load.
 |
 |      Parameters
 |      ----------
 |      file : str or Path
 |          A string naming the dump file.
 |
 |          .. versionchanged:: 1.17.0
 |              `pathlib.Path` objects are now accepted.
 |
 |  dumps(...)
 |      a.dumps()
 |
 |      Returns the pickle of the array as a string.
 |      pickle.loads will convert the string back to an array.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |  fill(...)
 |      a.fill(value)
 |
 |      Fill the array with a scalar value.
 |
 |      Parameters
 |      ----------
 |      value : scalar
 |          All elements of `a` will be assigned this value.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([1, 2])
 |      >>> a.fill(0)
 |      >>> a
 |      array([0, 0])
 |      >>> a = np.empty(2)
 |      >>> a.fill(1)
 |      >>> a
 |      array([1.,  1.])
 |
 |      Fill expects a scalar value and always behaves the same as assigning
 |      to a single array element.  The following is a rare example where this
 |      distinction is important:
 |
 |      >>> a = np.array([None, None], dtype=object)
 |      >>> a[0] = np.array(3)
 |      >>> a
 |      array([array(3), None], dtype=object)
 |      >>> a.fill(np.array(3))
 |      >>> a
 |      array([array(3), array(3)], dtype=object)
 |
 |      Where other forms of assignments will unpack the array being assigned:
 |
 |      >>> a[...] = np.array(3)
 |      >>> a
 |      array([3, 3], dtype=object)
 |
 |  flatten(...)
 |      a.flatten(order='C')
 |
 |      Return a copy of the array collapsed into one dimension.
 |
 |      Parameters
 |      ----------
 |      order : {'C', 'F', 'A', 'K'}, optional
 |          'C' means to flatten in row-major (C-style) order.
 |          'F' means to flatten in column-major (Fortran-
 |          style) order. 'A' means to flatten in column-major
 |          order if `a` is Fortran *contiguous* in memory,
 |          row-major order otherwise. 'K' means to flatten
 |          `a` in the order the elements occur in memory.
 |          The default is 'C'.
 |
 |      Returns
 |      -------
 |      y : ndarray
 |          A copy of the input array, flattened to one dimension.
 |
 |      See Also
 |      --------
 |      ravel : Return a flattened array.
 |      flat : A 1-D flat iterator over the array.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1,2], [3,4]])
 |      >>> a.flatten()
 |      array([1, 2, 3, 4])
 |      >>> a.flatten('F')
 |      array([1, 3, 2, 4])
 |
 |  getfield(...)
 |      a.getfield(dtype, offset=0)
 |
 |      Returns a field of the given array as a certain type.
 |
 |      A field is a view of the array data with a given data-type. The values in
 |      the view are determined by the given type and the offset into the current
 |      array in bytes. The offset needs to be such that the view dtype fits in the
 |      array dtype; for example an array of dtype complex128 has 16-byte elements.
 |      If taking a view with a 32-bit integer (4 bytes), the offset needs to be
 |      between 0 and 12 bytes.
 |
 |      Parameters
 |      ----------
 |      dtype : str or dtype
 |          The data type of the view. The dtype size of the view can not be larger
 |          than that of the array itself.
 |      offset : int
 |          Number of bytes to skip before beginning the element view.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.diag([1.+1.j]*2)
 |      >>> x[1, 1] = 2 + 4.j
 |      >>> x
 |      array([[1.+1.j,  0.+0.j],
 |             [0.+0.j,  2.+4.j]])
 |      >>> x.getfield(np.float64)
 |      array([[1.,  0.],
 |             [0.,  2.]])
 |
 |      By choosing an offset of 8 bytes we can select the complex part of the
 |      array for our view:
 |
 |      >>> x.getfield(np.float64, offset=8)
 |      array([[1.,  0.],
 |             [0.,  4.]])
 |
 |  item(...)
 |      a.item(*args)
 |
 |      Copy an element of an array to a standard Python scalar and return it.
 |
 |      Parameters
 |      ----------
 |      \*args : Arguments (variable number and type)
 |
 |          * none: in this case, the method only works for arrays
 |            with one element (`a.size == 1`), which element is
 |            copied into a standard Python scalar object and returned.
 |
 |          * int_type: this argument is interpreted as a flat index into
 |            the array, specifying which element to copy and return.
 |
 |          * tuple of int_types: functions as does a single int_type argument,
 |            except that the argument is interpreted as an nd-index into the
 |            array.
 |
 |      Returns
 |      -------
 |      z : Standard Python scalar object
 |          A copy of the specified element of the array as a suitable
 |          Python scalar
 |
 |      Notes
 |      -----
 |      When the data type of `a` is longdouble or clongdouble, item() returns
 |      a scalar array object because there is no available Python scalar that
 |      would not lose information. Void arrays return a buffer object for item(),
 |      unless fields are defined, in which case a tuple is returned.
 |
 |      `item` is very similar to a[args], except, instead of an array scalar,
 |      a standard Python scalar is returned. This can be useful for speeding up
 |      access to elements of the array and doing arithmetic on elements of the
 |      array using Python's optimized math.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.random.seed(123)
 |      >>> x = np.random.randint(9, size=(3, 3))
 |      >>> x
 |      array([[2, 2, 6],
 |             [1, 3, 6],
 |             [1, 0, 1]])
 |      >>> x.item(3)
 |      1
 |      >>> x.item(7)
 |      0
 |      >>> x.item((0, 1))
 |      2
 |      >>> x.item((2, 2))
 |      1
 |
 |      For an array with object dtype, elements are returned as-is.
 |
 |      >>> a = np.array([np.int64(1)], dtype=object)
 |      >>> a.item() #return np.int64
 |      np.int64(1)
 |
 |  max(...)
 |      a.max(axis=None, out=None, keepdims=False, initial=<no value>, where=True)
 |
 |      Return the maximum along a given axis.
 |
 |      Refer to `numpy.amax` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.amax : equivalent function
 |
 |  mean(...)
 |      a.mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True)
 |
 |      Returns the average of the array elements along given axis.
 |
 |      Refer to `numpy.mean` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.mean : equivalent function
 |
 |  min(...)
 |      a.min(axis=None, out=None, keepdims=False, initial=<no value>, where=True)
 |
 |      Return the minimum along a given axis.
 |
 |      Refer to `numpy.amin` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.amin : equivalent function
 |
 |  nonzero(...)
 |      a.nonzero()
 |
 |      Return the indices of the elements that are non-zero.
 |
 |      Refer to `numpy.nonzero` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.nonzero : equivalent function
 |
 |  partition(...)
 |      a.partition(kth, axis=-1, kind='introselect', order=None)
 |
 |      Partially sorts the elements in the array in such a way that the value of
 |      the element in k-th position is in the position it would be in a sorted
 |      array. In the output array, all elements smaller than the k-th element
 |      are located to the left of this element and all equal or greater are
 |      located to its right. The ordering of the elements in the two partitions
 |      on the either side of the k-th element in the output array is undefined.
 |
 |      .. versionadded:: 1.8.0
 |
 |      Parameters
 |      ----------
 |      kth : int or sequence of ints
 |          Element index to partition by. The kth element value will be in its
 |          final sorted position and all smaller elements will be moved before it
 |          and all equal or greater elements behind it.
 |          The order of all elements in the partitions is undefined.
 |          If provided with a sequence of kth it will partition all elements
 |          indexed by kth of them into their sorted position at once.
 |
 |          .. deprecated:: 1.22.0
 |              Passing booleans as index is deprecated.
 |      axis : int, optional
 |          Axis along which to sort. Default is -1, which means sort along the
 |          last axis.
 |      kind : {'introselect'}, optional
 |          Selection algorithm. Default is 'introselect'.
 |      order : str or list of str, optional
 |          When `a` is an array with fields defined, this argument specifies
 |          which fields to compare first, second, etc. A single field can
 |          be specified as a string, and not all fields need to be specified,
 |          but unspecified fields will still be used, in the order in which
 |          they come up in the dtype, to break ties.
 |
 |      See Also
 |      --------
 |      numpy.partition : Return a partitioned copy of an array.
 |      argpartition : Indirect partition.
 |      sort : Full sort.
 |
 |      Notes
 |      -----
 |      See ``np.partition`` for notes on the different algorithms.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([3, 4, 2, 1])
 |      >>> a.partition(3)
 |      >>> a
 |      array([2, 1, 3, 4]) # may vary
 |
 |      >>> a.partition((1, 3))
 |      >>> a
 |      array([1, 2, 3, 4])
 |
 |  prod(...)
 |      a.prod(axis=None, dtype=None, out=None, keepdims=False,
 |          initial=1, where=True)
 |
 |      Return the product of the array elements over the given axis
 |
 |      Refer to `numpy.prod` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.prod : equivalent function
 |
 |  put(...)
 |      a.put(indices, values, mode='raise')
 |
 |      Set ``a.flat[n] = values[n]`` for all `n` in indices.
 |
 |      Refer to `numpy.put` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.put : equivalent function
 |
 |  ravel(...)
 |      a.ravel([order])
 |
 |      Return a flattened array.
 |
 |      Refer to `numpy.ravel` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.ravel : equivalent function
 |
 |      ndarray.flat : a flat iterator on the array.
 |
 |  repeat(...)
 |      a.repeat(repeats, axis=None)
 |
 |      Repeat elements of an array.
 |
 |      Refer to `numpy.repeat` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.repeat : equivalent function
 |
 |  reshape(...)
 |      a.reshape(shape, /, *, order='C', copy=None)
 |
 |      Returns an array containing the same data with a new shape.
 |
 |      Refer to `numpy.reshape` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.reshape : equivalent function
 |
 |      Notes
 |      -----
 |      Unlike the free function `numpy.reshape`, this method on `ndarray` allows
 |      the elements of the shape parameter to be passed in as separate arguments.
 |      For example, ``a.reshape(10, 11)`` is equivalent to
 |      ``a.reshape((10, 11))``.
 |
 |  resize(...)
 |      a.resize(new_shape, refcheck=True)
 |
 |      Change shape and size of array in-place.
 |
 |      Parameters
 |      ----------
 |      new_shape : tuple of ints, or `n` ints
 |          Shape of resized array.
 |      refcheck : bool, optional
 |          If False, reference count will not be checked. Default is True.
 |
 |      Returns
 |      -------
 |      None
 |
 |      Raises
 |      ------
 |      ValueError
 |          If `a` does not own its own data or references or views to it exist,
 |          and the data memory must be changed.
 |          PyPy only: will always raise if the data memory must be changed, since
 |          there is no reliable way to determine if references or views to it
 |          exist.
 |
 |      SystemError
 |          If the `order` keyword argument is specified. This behaviour is a
 |          bug in NumPy.
 |
 |      See Also
 |      --------
 |      resize : Return a new array with the specified shape.
 |
 |      Notes
 |      -----
 |      This reallocates space for the data area if necessary.
 |
 |      Only contiguous arrays (data elements consecutive in memory) can be
 |      resized.
 |
 |      The purpose of the reference count check is to make sure you
 |      do not use this array as a buffer for another Python object and then
 |      reallocate the memory. However, reference counts can increase in
 |      other ways so if you are sure that you have not shared the memory
 |      for this array with another Python object, then you may safely set
 |      `refcheck` to False.
 |
 |      Examples
 |      --------
 |      Shrinking an array: array is flattened (in the order that the data are
 |      stored in memory), resized, and reshaped:
 |
 |      >>> import numpy as np
 |
 |      >>> a = np.array([[0, 1], [2, 3]], order='C')
 |      >>> a.resize((2, 1))
 |      >>> a
 |      array([[0],
 |             [1]])
 |
 |      >>> a = np.array([[0, 1], [2, 3]], order='F')
 |      >>> a.resize((2, 1))
 |      >>> a
 |      array([[0],
 |             [2]])
 |
 |      Enlarging an array: as above, but missing entries are filled with zeros:
 |
 |      >>> b = np.array([[0, 1], [2, 3]])
 |      >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple
 |      >>> b
 |      array([[0, 1, 2],
 |             [3, 0, 0]])
 |
 |      Referencing an array prevents resizing...
 |
 |      >>> c = a
 |      >>> a.resize((1, 1))
 |      Traceback (most recent call last):
 |      ...
 |      ValueError: cannot resize an array that references or is referenced ...
 |
 |      Unless `refcheck` is False:
 |
 |      >>> a.resize((1, 1), refcheck=False)
 |      >>> a
 |      array([[0]])
 |      >>> c
 |      array([[0]])
 |
 |  round(...)
 |      a.round(decimals=0, out=None)
 |
 |      Return `a` with each element rounded to the given number of decimals.
 |
 |      Refer to `numpy.around` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.around : equivalent function
 |
 |  searchsorted(...)
 |      a.searchsorted(v, side='left', sorter=None)
 |
 |      Find indices where elements of v should be inserted in a to maintain order.
 |
 |      For full documentation, see `numpy.searchsorted`
 |
 |      See Also
 |      --------
 |      numpy.searchsorted : equivalent function
 |
 |  setfield(...)
 |      a.setfield(val, dtype, offset=0)
 |
 |      Put a value into a specified place in a field defined by a data-type.
 |
 |      Place `val` into `a`'s field defined by `dtype` and beginning `offset`
 |      bytes into the field.
 |
 |      Parameters
 |      ----------
 |      val : object
 |          Value to be placed in field.
 |      dtype : dtype object
 |          Data-type of the field in which to place `val`.
 |      offset : int, optional
 |          The number of bytes into the field at which to place `val`.
 |
 |      Returns
 |      -------
 |      None
 |
 |      See Also
 |      --------
 |      getfield
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.eye(3)
 |      >>> x.getfield(np.float64)
 |      array([[1.,  0.,  0.],
 |             [0.,  1.,  0.],
 |             [0.,  0.,  1.]])
 |      >>> x.setfield(3, np.int32)
 |      >>> x.getfield(np.int32)
 |      array([[3, 3, 3],
 |             [3, 3, 3],
 |             [3, 3, 3]], dtype=int32)
 |      >>> x
 |      array([[1.0e+000, 1.5e-323, 1.5e-323],
 |             [1.5e-323, 1.0e+000, 1.5e-323],
 |             [1.5e-323, 1.5e-323, 1.0e+000]])
 |      >>> x.setfield(np.eye(3), np.int32)
 |      >>> x
 |      array([[1.,  0.,  0.],
 |             [0.,  1.,  0.],
 |             [0.,  0.,  1.]])
 |
 |  setflags(...)
 |      a.setflags(write=None, align=None, uic=None)
 |
 |      Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY,
 |      respectively.
 |
 |      These Boolean-valued flags affect how numpy interprets the memory
 |      area used by `a` (see Notes below). The ALIGNED flag can only
 |      be set to True if the data is actually aligned according to the type.
 |      The WRITEBACKIFCOPY flag can never be set
 |      to True. The flag WRITEABLE can only be set to True if the array owns its
 |      own memory, or the ultimate owner of the memory exposes a writeable buffer
 |      interface, or is a string. (The exception for string is made so that
 |      unpickling can be done without copying memory.)
 |
 |      Parameters
 |      ----------
 |      write : bool, optional
 |          Describes whether or not `a` can be written to.
 |      align : bool, optional
 |          Describes whether or not `a` is aligned properly for its type.
 |      uic : bool, optional
 |          Describes whether or not `a` is a copy of another "base" array.
 |
 |      Notes
 |      -----
 |      Array flags provide information about how the memory area used
 |      for the array is to be interpreted. There are 7 Boolean flags
 |      in use, only three of which can be changed by the user:
 |      WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.
 |
 |      WRITEABLE (W) the data area can be written to;
 |
 |      ALIGNED (A) the data and strides are aligned appropriately for the hardware
 |      (as determined by the compiler);
 |
 |      WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced
 |      by .base). When the C-API function PyArray_ResolveWritebackIfCopy is
 |      called, the base array will be updated with the contents of this array.
 |
 |      All flags can be accessed using the single (upper case) letter as well
 |      as the full name.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> y = np.array([[3, 1, 7],
 |      ...               [2, 0, 0],
 |      ...               [8, 5, 9]])
 |      >>> y
 |      array([[3, 1, 7],
 |             [2, 0, 0],
 |             [8, 5, 9]])
 |      >>> y.flags
 |        C_CONTIGUOUS : True
 |        F_CONTIGUOUS : False
 |        OWNDATA : True
 |        WRITEABLE : True
 |        ALIGNED : True
 |        WRITEBACKIFCOPY : False
 |      >>> y.setflags(write=0, align=0)
 |      >>> y.flags
 |        C_CONTIGUOUS : True
 |        F_CONTIGUOUS : False
 |        OWNDATA : True
 |        WRITEABLE : False
 |        ALIGNED : False
 |        WRITEBACKIFCOPY : False
 |      >>> y.setflags(uic=1)
 |      Traceback (most recent call last):
 |        File "<stdin>", line 1, in <module>
 |      ValueError: cannot set WRITEBACKIFCOPY flag to True
 |
 |  sort(...)
 |      a.sort(axis=-1, kind=None, order=None)
 |
 |      Sort an array in-place. Refer to `numpy.sort` for full documentation.
 |
 |      Parameters
 |      ----------
 |      axis : int, optional
 |          Axis along which to sort. Default is -1, which means sort along the
 |          last axis.
 |      kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
 |          Sorting algorithm. The default is 'quicksort'. Note that both 'stable'
 |          and 'mergesort' use timsort under the covers and, in general, the
 |          actual implementation will vary with datatype. The 'mergesort' option
 |          is retained for backwards compatibility.
 |
 |          .. versionchanged:: 1.15.0
 |             The 'stable' option was added.
 |
 |      order : str or list of str, optional
 |          When `a` is an array with fields defined, this argument specifies
 |          which fields to compare first, second, etc.  A single field can
 |          be specified as a string, and not all fields need be specified,
 |          but unspecified fields will still be used, in the order in which
 |          they come up in the dtype, to break ties.
 |
 |      See Also
 |      --------
 |      numpy.sort : Return a sorted copy of an array.
 |      numpy.argsort : Indirect sort.
 |      numpy.lexsort : Indirect stable sort on multiple keys.
 |      numpy.searchsorted : Find elements in sorted array.
 |      numpy.partition: Partial sort.
 |
 |      Notes
 |      -----
 |      See `numpy.sort` for notes on the different sorting algorithms.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1,4], [3,1]])
 |      >>> a.sort(axis=1)
 |      >>> a
 |      array([[1, 4],
 |             [1, 3]])
 |      >>> a.sort(axis=0)
 |      >>> a
 |      array([[1, 3],
 |             [1, 4]])
 |
 |      Use the `order` keyword to specify a field to use when sorting a
 |      structured array:
 |
 |      >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])
 |      >>> a.sort(order='y')
 |      >>> a
 |      array([(b'c', 1), (b'a', 2)],
 |            dtype=[('x', 'S1'), ('y', '<i8')])
 |
 |  squeeze(...)
 |      a.squeeze(axis=None)
 |
 |      Remove axes of length one from `a`.
 |
 |      Refer to `numpy.squeeze` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.squeeze : equivalent function
 |
 |  std(...)
 |      a.std(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)
 |
 |      Returns the standard deviation of the array elements along given axis.
 |
 |      Refer to `numpy.std` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.std : equivalent function
 |
 |  sum(...)
 |      a.sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)
 |
 |      Return the sum of the array elements over the given axis.
 |
 |      Refer to `numpy.sum` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.sum : equivalent function
 |
 |  swapaxes(...)
 |      a.swapaxes(axis1, axis2)
 |
 |      Return a view of the array with `axis1` and `axis2` interchanged.
 |
 |      Refer to `numpy.swapaxes` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.swapaxes : equivalent function
 |
 |  take(...)
 |      a.take(indices, axis=None, out=None, mode='raise')
 |
 |      Return an array formed from the elements of `a` at the given indices.
 |
 |      Refer to `numpy.take` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.take : equivalent function
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |      a.tobytes(order='C')
 |
 |      Construct Python bytes containing the raw data bytes in the array.
 |
 |      Constructs Python bytes showing a copy of the raw contents of
 |      data memory. The bytes object is produced in C-order by default.
 |      This behavior is controlled by the ``order`` parameter.
 |
 |      .. versionadded:: 1.9.0
 |
 |      Parameters
 |      ----------
 |      order : {'C', 'F', 'A'}, optional
 |          Controls the memory layout of the bytes object. 'C' means C-order,
 |          'F' means F-order, 'A' (short for *Any*) means 'F' if `a` is
 |          Fortran contiguous, 'C' otherwise. Default is 'C'.
 |
 |      Returns
 |      -------
 |      s : bytes
 |          Python bytes exhibiting a copy of `a`'s raw data.
 |
 |      See also
 |      --------
 |      frombuffer
 |          Inverse of this operation, construct a 1-dimensional array from Python
 |          bytes.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([[0, 1], [2, 3]], dtype='<u2')
 |      >>> x.tobytes()
 |      b'\x00\x00\x01\x00\x02\x00\x03\x00'
 |      >>> x.tobytes('C') == x.tobytes()
 |      True
 |      >>> x.tobytes('F')
 |      b'\x00\x00\x02\x00\x01\x00\x03\x00'
 |
 |  tofile(...)
 |      a.tofile(fid, sep="", format="%s")
 |
 |      Write array to a file as text or binary (default).
 |
 |      Data is always written in 'C' order, independent of the order of `a`.
 |      The data produced by this method can be recovered using the function
 |      fromfile().
 |
 |      Parameters
 |      ----------
 |      fid : file or str or Path
 |          An open file object, or a string containing a filename.
 |
 |          .. versionchanged:: 1.17.0
 |              `pathlib.Path` objects are now accepted.
 |
 |      sep : str
 |          Separator between array items for text output.
 |          If "" (empty), a binary file is written, equivalent to
 |          ``file.write(a.tobytes())``.
 |      format : str
 |          Format string for text file output.
 |          Each entry in the array is formatted to text by first converting
 |          it to the closest Python type, and then using "format" % item.
 |
 |      Notes
 |      -----
 |      This is a convenience function for quick storage of array data.
 |      Information on endianness and precision is lost, so this method is not a
 |      good choice for files intended to archive data or transport data between
 |      machines with different endianness. Some of these problems can be overcome
 |      by outputting the data as text files, at the expense of speed and file
 |      size.
 |
 |      When fid is a file object, array contents are directly written to the
 |      file, bypassing the file object's ``write`` method. As a result, tofile
 |      cannot be used with files objects supporting compression (e.g., GzipFile)
 |      or file-like objects that do not support ``fileno()`` (e.g., BytesIO).
 |
 |  tolist(...)
 |      a.tolist()
 |
 |      Return the array as an ``a.ndim``-levels deep nested list of Python scalars.
 |
 |      Return a copy of the array data as a (nested) Python list.
 |      Data items are converted to the nearest compatible builtin Python type, via
 |      the `~numpy.ndarray.item` function.
 |
 |      If ``a.ndim`` is 0, then since the depth of the nested list is 0, it will
 |      not be a list at all, but a simple Python scalar.
 |
 |      Parameters
 |      ----------
 |      none
 |
 |      Returns
 |      -------
 |      y : object, or list of object, or list of list of object, or ...
 |          The possibly nested list of array elements.
 |
 |      Notes
 |      -----
 |      The array may be recreated via ``a = np.array(a.tolist())``, although this
 |      may sometimes lose precision.
 |
 |      Examples
 |      --------
 |      For a 1D array, ``a.tolist()`` is almost the same as ``list(a)``,
 |      except that ``tolist`` changes numpy scalars to Python scalars:
 |
 |      >>> import numpy as np
 |      >>> a = np.uint32([1, 2])
 |      >>> a_list = list(a)
 |      >>> a_list
 |      [1, 2]
 |      >>> type(a_list[0])
 |      <class 'numpy.uint32'>
 |      >>> a_tolist = a.tolist()
 |      >>> a_tolist
 |      [1, 2]
 |      >>> type(a_tolist[0])
 |      <class 'int'>
 |
 |      Additionally, for a 2D array, ``tolist`` applies recursively:
 |
 |      >>> a = np.array([[1, 2], [3, 4]])
 |      >>> list(a)
 |      [array([1, 2]), array([3, 4])]
 |      >>> a.tolist()
 |      [[1, 2], [3, 4]]
 |
 |      The base case for this recursion is a 0D array:
 |
 |      >>> a = np.array(1)
 |      >>> list(a)
 |      Traceback (most recent call last):
 |        ...
 |      TypeError: iteration over a 0-d array
 |      >>> a.tolist()
 |      1
 |
 |  tostring(...)
 |      a.tostring(order='C')
 |
 |      A compatibility alias for `~ndarray.tobytes`, with exactly the same
 |      behavior.
 |
 |      Despite its name, it returns :class:`bytes` not :class:`str`\ s.
 |
 |      .. deprecated:: 1.19.0
 |
 |  trace(...)
 |      a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)
 |
 |      Return the sum along diagonals of the array.
 |
 |      Refer to `numpy.trace` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.trace : equivalent function
 |
 |  transpose(...)
 |      a.transpose(*axes)
 |
 |      Returns a view of the array with axes transposed.
 |
 |      Refer to `numpy.transpose` for full documentation.
 |
 |      Parameters
 |      ----------
 |      axes : None, tuple of ints, or `n` ints
 |
 |       * None or no argument: reverses the order of the axes.
 |
 |       * tuple of ints: `i` in the `j`-th place in the tuple means that the
 |         array's `i`-th axis becomes the transposed array's `j`-th axis.
 |
 |       * `n` ints: same as an n-tuple of the same ints (this form is
 |         intended simply as a "convenience" alternative to the tuple form).
 |
 |      Returns
 |      -------
 |      p : ndarray
 |          View of the array with its axes suitably permuted.
 |
 |      See Also
 |      --------
 |      transpose : Equivalent function.
 |      ndarray.T : Array property returning the array transposed.
 |      ndarray.reshape : Give a new shape to an array without changing its data.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1, 2], [3, 4]])
 |      >>> a
 |      array([[1, 2],
 |             [3, 4]])
 |      >>> a.transpose()
 |      array([[1, 3],
 |             [2, 4]])
 |      >>> a.transpose((1, 0))
 |      array([[1, 3],
 |             [2, 4]])
 |      >>> a.transpose(1, 0)
 |      array([[1, 3],
 |             [2, 4]])
 |
 |      >>> a = np.array([1, 2, 3, 4])
 |      >>> a
 |      array([1, 2, 3, 4])
 |      >>> a.transpose()
 |      array([1, 2, 3, 4])
 |
 |  var(...)
 |      a.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)
 |
 |      Returns the variance of the array elements, along given axis.
 |
 |      Refer to `numpy.var` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.var : equivalent function
 |
 |  view(...)
 |      a.view([dtype][, type])
 |
 |      New view of array with the same data.
 |
 |      .. note::
 |          Passing None for ``dtype`` is different from omitting the parameter,
 |          since the former invokes ``dtype(None)`` which is an alias for
 |          ``dtype('float64')``.
 |
 |      Parameters
 |      ----------
 |      dtype : data-type or ndarray sub-class, optional
 |          Data-type descriptor of the returned view, e.g., float32 or int16.
 |          Omitting it results in the view having the same data-type as `a`.
 |          This argument can also be specified as an ndarray sub-class, which
 |          then specifies the type of the returned object (this is equivalent to
 |          setting the ``type`` parameter).
 |      type : Python type, optional
 |          Type of the returned view, e.g., ndarray or matrix.  Again, omission
 |          of the parameter results in type preservation.
 |
 |      Notes
 |      -----
 |      ``a.view()`` is used two different ways:
 |
 |      ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view
 |      of the array's memory with a different data-type.  This can cause a
 |      reinterpretation of the bytes of memory.
 |
 |      ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just
 |      returns an instance of `ndarray_subclass` that looks at the same array
 |      (same shape, dtype, etc.)  This does not cause a reinterpretation of the
 |      memory.
 |
 |      For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of
 |      bytes per entry than the previous dtype (for example, converting a regular
 |      array to a structured array), then the last axis of ``a`` must be
 |      contiguous. This axis will be resized in the result.
 |
 |      .. versionchanged:: 1.23.0
 |         Only the last axis needs to be contiguous. Previously, the entire array
 |         had to be C-contiguous.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([(-1, 2)], dtype=[('a', np.int8), ('b', np.int8)])
 |
 |      Viewing array data using a different type and dtype:
 |
 |      >>> nonneg = np.dtype([("a", np.uint8), ("b", np.uint8)])
 |      >>> y = x.view(dtype=nonneg, type=np.recarray)
 |      >>> x["a"]
 |      array([-1], dtype=int8)
 |      >>> y.a
 |      array([255], dtype=uint8)
 |
 |      Creating a view on a structured array so it can be used in calculations
 |
 |      >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])
 |      >>> xv = x.view(dtype=np.int8).reshape(-1,2)
 |      >>> xv
 |      array([[1, 2],
 |             [3, 4]], dtype=int8)
 |      >>> xv.mean(0)
 |      array([2.,  3.])
 |
 |      Making changes to the view changes the underlying array
 |
 |      >>> xv[0,1] = 20
 |      >>> x
 |      array([(1, 20), (3,  4)], dtype=[('a', 'i1'), ('b', 'i1')])
 |
 |      Using a view to convert an array to a recarray:
 |
 |      >>> z = x.view(np.recarray)
 |      >>> z.a
 |      array([1, 3], dtype=int8)
 |
 |      Views share data:
 |
 |      >>> x[0] = (9, 10)
 |      >>> z[0]
 |      np.record((9, 10), dtype=[('a', 'i1'), ('b', 'i1')])
 |
 |      Views that change the dtype size (bytes per entry) should normally be
 |      avoided on arrays defined by slices, transposes, fortran-ordering, etc.:
 |
 |      >>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16)
 |      >>> y = x[:, ::2]
 |      >>> y
 |      array([[1, 3],
 |             [4, 6]], dtype=int16)
 |      >>> y.view(dtype=[('width', np.int16), ('length', np.int16)])
 |      Traceback (most recent call last):
 |          ...
 |      ValueError: To change to a dtype of a different size, the last axis must be contiguous
 |      >>> z = y.copy()
 |      >>> z.view(dtype=[('width', np.int16), ('length', np.int16)])
 |      array([[(1, 3)],
 |             [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])
 |
 |      However, views that change dtype are totally fine for arrays with a
 |      contiguous last axis, even if the rest of the axes are not C-contiguous:
 |
 |      >>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4)
 |      >>> x.transpose(1, 0, 2).view(np.int16)
 |      array([[[ 256,  770],
 |              [3340, 3854]],
 |      <BLANKLINE>
 |             [[1284, 1798],
 |              [4368, 4882]],
 |      <BLANKLINE>
 |             [[2312, 2826],
 |              [5396, 5910]]], dtype=int16)
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      a.__class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.ndarray` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.ndarray` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.ndarray[Any, np.dtype[Any]]
 |      numpy.ndarray[typing.Any, numpy.dtype[typing.Any]]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |      numpy.typing.NDArray : An ndarray alias :term:`generic <generic type>`
 |                          w.r.t. its `dtype.type <numpy.dtype.type>`.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  T
 |      View of the transposed array.
 |
 |      Same as ``self.transpose()``.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1, 2], [3, 4]])
 |      >>> a
 |      array([[1, 2],
 |             [3, 4]])
 |      >>> a.T
 |      array([[1, 3],
 |             [2, 4]])
 |
 |      >>> a = np.array([1, 2, 3, 4])
 |      >>> a
 |      array([1, 2, 3, 4])
 |      >>> a.T
 |      array([1, 2, 3, 4])
 |
 |      See Also
 |      --------
 |      transpose
 |
 |  __array_interface__
 |      Array protocol: Python side.
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: C-struct side.
 |
 |  base
 |      Base object if memory is from some other object.
 |
 |      Examples
 |      --------
 |      The base of an array that owns its memory is None:
 |
 |      >>> import numpy as np
 |      >>> x = np.array([1,2,3,4])
 |      >>> x.base is None
 |      True
 |
 |      Slicing creates a view, whose memory is shared with x:
 |
 |      >>> y = x[2:]
 |      >>> y.base is x
 |      True
 |
 |  ctypes
 |      An object to simplify the interaction of the array with the ctypes
 |      module.
 |
 |      This attribute creates an object that makes it easier to use arrays
 |      when calling shared libraries with the ctypes module. The returned
 |      object has, among others, data, shape, and strides attributes (see
 |      Notes below) which themselves return ctypes objects that can be used
 |      as arguments to a shared library.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      c : Python object
 |          Possessing attributes data, shape, strides, etc.
 |
 |      See Also
 |      --------
 |      numpy.ctypeslib
 |
 |      Notes
 |      -----
 |      Below are the public attributes of this object which were documented
 |      in "Guide to NumPy" (we have omitted undocumented public attributes,
 |      as well as documented private attributes):
 |
 |      .. autoattribute:: numpy._core._internal._ctypes.data
 |          :noindex:
 |
 |      .. autoattribute:: numpy._core._internal._ctypes.shape
 |          :noindex:
 |
 |      .. autoattribute:: numpy._core._internal._ctypes.strides
 |          :noindex:
 |
 |      .. automethod:: numpy._core._internal._ctypes.data_as
 |          :noindex:
 |
 |      .. automethod:: numpy._core._internal._ctypes.shape_as
 |          :noindex:
 |
 |      .. automethod:: numpy._core._internal._ctypes.strides_as
 |          :noindex:
 |
 |      If the ctypes module is not available, then the ctypes attribute
 |      of array objects still returns something useful, but ctypes objects
 |      are not returned and errors may be raised instead. In particular,
 |      the object will still have the ``as_parameter`` attribute which will
 |      return an integer equal to the data attribute.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> import ctypes
 |      >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)
 |      >>> x
 |      array([[0, 1],
 |             [2, 3]], dtype=int32)
 |      >>> x.ctypes.data
 |      31962608 # may vary
 |      >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))
 |      <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary
 |      >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents
 |      c_uint(0)
 |      >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents
 |      c_ulong(4294967296)
 |      >>> x.ctypes.shape
 |      <numpy._core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary
 |      >>> x.ctypes.strides
 |      <numpy._core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary
 |
 |  data
 |      Python buffer object pointing to the start of the array's data.
 |
 |  device
 |
 |  dtype
 |      Data-type of the array's elements.
 |
 |      .. warning::
 |
 |          Setting ``arr.dtype`` is discouraged and may be deprecated in the
 |          future.  Setting will replace the ``dtype`` without modifying the
 |          memory (see also `ndarray.view` and `ndarray.astype`).
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      d : numpy dtype object
 |
 |      See Also
 |      --------
 |      ndarray.astype : Cast the values contained in the array to a new data-type.
 |      ndarray.view : Create a view of the same data but a different data-type.
 |      numpy.dtype
 |
 |      Examples
 |      --------
 |      >>> x
 |      array([[0, 1],
 |             [2, 3]])
 |      >>> x.dtype
 |      dtype('int32')
 |      >>> type(x.dtype)
 |      <type 'numpy.dtype'>
 |
 |  flags
 |      Information about the memory layout of the array.
 |
 |      Attributes
 |      ----------
 |      C_CONTIGUOUS (C)
 |          The data is in a single, C-style contiguous segment.
 |      F_CONTIGUOUS (F)
 |          The data is in a single, Fortran-style contiguous segment.
 |      OWNDATA (O)
 |          The array owns the memory it uses or borrows it from another object.
 |      WRITEABLE (W)
 |          The data area can be written to.  Setting this to False locks
 |          the data, making it read-only.  A view (slice, etc.) inherits WRITEABLE
 |          from its base array at creation time, but a view of a writeable
 |          array may be subsequently locked while the base array remains writeable.
 |          (The opposite is not true, in that a view of a locked array may not
 |          be made writeable.  However, currently, locking a base object does not
 |          lock any views that already reference it, so under that circumstance it
 |          is possible to alter the contents of a locked array via a previously
 |          created writeable view onto it.)  Attempting to change a non-writeable
 |          array raises a RuntimeError exception.
 |      ALIGNED (A)
 |          The data and all elements are aligned appropriately for the hardware.
 |      WRITEBACKIFCOPY (X)
 |          This array is a copy of some other array. The C-API function
 |          PyArray_ResolveWritebackIfCopy must be called before deallocating
 |          to the base array will be updated with the contents of this array.
 |      FNC
 |          F_CONTIGUOUS and not C_CONTIGUOUS.
 |      FORC
 |          F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).
 |      BEHAVED (B)
 |          ALIGNED and WRITEABLE.
 |      CARRAY (CA)
 |          BEHAVED and C_CONTIGUOUS.
 |      FARRAY (FA)
 |          BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.
 |
 |      Notes
 |      -----
 |      The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``),
 |      or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag
 |      names are only supported in dictionary access.
 |
 |      Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be
 |      changed by the user, via direct assignment to the attribute or dictionary
 |      entry, or by calling `ndarray.setflags`.
 |
 |      The array flags cannot be set arbitrarily:
 |
 |      - WRITEBACKIFCOPY can only be set ``False``.
 |      - ALIGNED can only be set ``True`` if the data is truly aligned.
 |      - WRITEABLE can only be set ``True`` if the array owns its own memory
 |        or the ultimate owner of the memory exposes a writeable buffer
 |        interface or is a string.
 |
 |      Arrays can be both C-style and Fortran-style contiguous simultaneously.
 |      This is clear for 1-dimensional arrays, but can also be true for higher
 |      dimensional arrays.
 |
 |      Even for contiguous arrays a stride for a given dimension
 |      ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1``
 |      or the array has no elements.
 |      It does *not* generally hold that ``self.strides[-1] == self.itemsize``
 |      for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for
 |      Fortran-style contiguous arrays is true.
 |
 |  flat
 |      A 1-D iterator over the array.
 |
 |      This is a `numpy.flatiter` instance, which acts similarly to, but is not
 |      a subclass of, Python's built-in iterator object.
 |
 |      See Also
 |      --------
 |      flatten : Return a copy of the array collapsed into one dimension.
 |
 |      flatiter
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.arange(1, 7).reshape(2, 3)
 |      >>> x
 |      array([[1, 2, 3],
 |             [4, 5, 6]])
 |      >>> x.flat[3]
 |      4
 |      >>> x.T
 |      array([[1, 4],
 |             [2, 5],
 |             [3, 6]])
 |      >>> x.T.flat[3]
 |      5
 |      >>> type(x.flat)
 |      <class 'numpy.flatiter'>
 |
 |      An assignment example:
 |
 |      >>> x.flat = 3; x
 |      array([[3, 3, 3],
 |             [3, 3, 3]])
 |      >>> x.flat[[1,4]] = 1; x
 |      array([[3, 1, 3],
 |             [3, 1, 3]])
 |
 |  imag
 |      The imaginary part of the array.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.sqrt([1+0j, 0+1j])
 |      >>> x.imag
 |      array([ 0.        ,  0.70710678])
 |      >>> x.imag.dtype
 |      dtype('float64')
 |
 |  itemset
 |
 |  itemsize
 |      Length of one array element in bytes.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1,2,3], dtype=np.float64)
 |      >>> x.itemsize
 |      8
 |      >>> x = np.array([1,2,3], dtype=np.complex128)
 |      >>> x.itemsize
 |      16
 |
 |  mT
 |      View of the matrix transposed array.
 |
 |      The matrix transpose is the transpose of the last two dimensions, even
 |      if the array is of higher dimension.
 |
 |      .. versionadded:: 2.0
 |
 |      Raises
 |      ------
 |      ValueError
 |          If the array is of dimension less than 2.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1, 2], [3, 4]])
 |      >>> a
 |      array([[1, 2],
 |             [3, 4]])
 |      >>> a.mT
 |      array([[1, 3],
 |             [2, 4]])
 |
 |      >>> a = np.arange(8).reshape((2, 2, 2))
 |      >>> a
 |      array([[[0, 1],
 |              [2, 3]],
 |      <BLANKLINE>
 |             [[4, 5],
 |              [6, 7]]])
 |      >>> a.mT
 |      array([[[0, 2],
 |              [1, 3]],
 |      <BLANKLINE>
 |             [[4, 6],
 |              [5, 7]]])
 |
 |  nbytes
 |      Total bytes consumed by the elements of the array.
 |
 |      Notes
 |      -----
 |      Does not include memory consumed by non-element attributes of the
 |      array object.
 |
 |      See Also
 |      --------
 |      sys.getsizeof
 |          Memory consumed by the object itself without parents in case view.
 |          This does include memory consumed by non-element attributes.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.zeros((3,5,2), dtype=np.complex128)
 |      >>> x.nbytes
 |      480
 |      >>> np.prod(x.shape) * x.itemsize
 |      480
 |
 |  ndim
 |      Number of array dimensions.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 3])
 |      >>> x.ndim
 |      1
 |      >>> y = np.zeros((2, 3, 4))
 |      >>> y.ndim
 |      3
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the array.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.sqrt([1+0j, 0+1j])
 |      >>> x.real
 |      array([ 1.        ,  0.70710678])
 |      >>> x.real.dtype
 |      dtype('float64')
 |
 |      See Also
 |      --------
 |      numpy.real : equivalent function
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |      The shape property is usually used to get the current shape of an array,
 |      but may also be used to reshape the array in-place by assigning a tuple of
 |      array dimensions to it.  As with `numpy.reshape`, one of the new shape
 |      dimensions can be -1, in which case its value is inferred from the size of
 |      the array and the remaining dimensions. Reshaping an array in-place will
 |      fail if a copy is required.
 |
 |      .. warning::
 |
 |          Setting ``arr.shape`` is discouraged and may be deprecated in the
 |          future.  Using `ndarray.reshape` is the preferred approach.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 3, 4])
 |      >>> x.shape
 |      (4,)
 |      >>> y = np.zeros((2, 3, 4))
 |      >>> y.shape
 |      (2, 3, 4)
 |      >>> y.shape = (3, 8)
 |      >>> y
 |      array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
 |             [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
 |             [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])
 |      >>> y.shape = (3, 6)
 |      Traceback (most recent call last):
 |        File "<stdin>", line 1, in <module>
 |      ValueError: total size of new array must be unchanged
 |      >>> np.zeros((4,2))[::2].shape = (-1,)
 |      Traceback (most recent call last):
 |        File "<stdin>", line 1, in <module>
 |      AttributeError: Incompatible shape for in-place modification. Use
 |      `.reshape()` to make a copy with the desired shape.
 |
 |      See Also
 |      --------
 |      numpy.shape : Equivalent getter function.
 |      numpy.reshape : Function similar to setting ``shape``.
 |      ndarray.reshape : Method similar to setting ``shape``.
 |
 |  size
 |      Number of elements in the array.
 |
 |      Equal to ``np.prod(a.shape)``, i.e., the product of the array's
 |      dimensions.
 |
 |      Notes
 |      -----
 |      `a.size` returns a standard arbitrary precision Python integer. This
 |      may not be the case with other methods of obtaining the same value
 |      (like the suggested ``np.prod(a.shape)``, which returns an instance
 |      of ``np.int_``), and may be relevant if the value is used further in
 |      calculations that may overflow a fixed size integer type.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.zeros((3, 5, 2), dtype=np.complex128)
 |      >>> x.size
 |      30
 |      >>> np.prod(x.shape)
 |      30
 |
 |  strides
 |      Tuple of bytes to step in each dimension when traversing an array.
 |
 |      The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a`
 |      is::
 |
 |          offset = sum(np.array(i) * a.strides)
 |
 |      A more detailed explanation of strides can be found in
 |      :ref:`arrays.ndarray`.
 |
 |      .. warning::
 |
 |          Setting ``arr.strides`` is discouraged and may be deprecated in the
 |          future.  `numpy.lib.stride_tricks.as_strided` should be preferred
 |          to create a new view of the same data in a safer way.
 |
 |      Notes
 |      -----
 |      Imagine an array of 32-bit integers (each 4 bytes)::
 |
 |        x = np.array([[0, 1, 2, 3, 4],
 |                      [5, 6, 7, 8, 9]], dtype=np.int32)
 |
 |      This array is stored in memory as 40 bytes, one after the other
 |      (known as a contiguous block of memory).  The strides of an array tell
 |      us how many bytes we have to skip in memory to move to the next position
 |      along a certain axis.  For example, we have to skip 4 bytes (1 value) to
 |      move to the next column, but 20 bytes (5 values) to get to the same
 |      position in the next row.  As such, the strides for the array `x` will be
 |      ``(20, 4)``.
 |
 |      See Also
 |      --------
 |      numpy.lib.stride_tricks.as_strided
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> y = np.reshape(np.arange(2*3*4), (2,3,4))
 |      >>> y
 |      array([[[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]],
 |             [[12, 13, 14, 15],
 |              [16, 17, 18, 19],
 |              [20, 21, 22, 23]]])
 |      >>> y.strides
 |      (48, 16, 4)
 |      >>> y[1,1,1]
 |      17
 |      >>> offset=sum(y.strides * np.array((1,1,1)))
 |      >>> offset/y.itemsize
 |      17
 |
 |      >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)
 |      >>> x.strides
 |      (32, 4, 224, 1344)
 |      >>> i = np.array([3,5,2,2])
 |      >>> offset = sum(i * x.strides)
 |      >>> x[3,5,2,2]
 |      813
 |      >>> offset / x.itemsize
 |      813
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes defined here:
 |
 |  __hash__ = None

Python Library Documentation: class ndenumerate in module numpy

class ndenumerate(builtins.object)
 |  ndenumerate(arr)
 |
 |  Multidimensional index iterator.
 |
 |  Return an iterator yielding pairs of array coordinates and values.
 |
 |  Parameters
 |  ----------
 |  arr : ndarray
 |    Input array.
 |
 |  See Also
 |  --------
 |  ndindex, flatiter
 |
 |  Examples
 |  --------
 |  >>> import numpy as np
 |  >>> a = np.array([[1, 2], [3, 4]])
 |  >>> for index, x in np.ndenumerate(a):
 |  ...     print(index, x)
 |  (0, 0) 1
 |  (0, 1) 2
 |  (1, 0) 3
 |  (1, 1) 4
 |
 |  Methods defined here:
 |
 |  __init__(self, arr) from numpy.lib._index_tricks_impl.ndenumerate
 |      Initialize self.  See help(type(self)) for accurate signature.
 |
 |  __iter__(self) from numpy.lib._index_tricks_impl.ndenumerate
 |
 |  __next__(self) from numpy.lib._index_tricks_impl.ndenumerate
 |      Standard iterator method, returns the index tuple and array value.
 |
 |      Returns
 |      -------
 |      coords : tuple of ints
 |          The indices of the current iteration.
 |      val : scalar
 |          The array element of the current iteration.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object

Python Library Documentation: function ndim in module autograd.tracer

ndim(*args, **kwargs)
    Return the number of dimensions of an array.

    Parameters
    ----------
    a : array_like
        Input array.  If it is not already an ndarray, a conversion is
        attempted.

    Returns
    -------
    number_of_dimensions : int
        The number of dimensions in `a`.  Scalars are zero-dimensional.

    See Also
    --------
    ndarray.ndim : equivalent method
    shape : dimensions of array
    ndarray.shape : dimensions of array

    Examples
    --------
    >>> import numpy as np
    >>> np.ndim([[1,2,3],[4,5,6]])
    2
    >>> np.ndim(np.array([[1,2,3],[4,5,6]]))
    2
    >>> np.ndim(1)
    0

Python Library Documentation: class ndindex in module numpy

class ndindex(builtins.object)
 |  ndindex(*shape)
 |
 |  An N-dimensional iterator object to index arrays.
 |
 |  Given the shape of an array, an `ndindex` instance iterates over
 |  the N-dimensional index of the array. At each iteration a tuple
 |  of indices is returned, the last dimension is iterated over first.
 |
 |  Parameters
 |  ----------
 |  shape : ints, or a single tuple of ints
 |      The size of each dimension of the array can be passed as
 |      individual parameters or as the elements of a tuple.
 |
 |  See Also
 |  --------
 |  ndenumerate, flatiter
 |
 |  Examples
 |  --------
 |  >>> import numpy as np
 |
 |  Dimensions as individual arguments
 |
 |  >>> for index in np.ndindex(3, 2, 1):
 |  ...     print(index)
 |  (0, 0, 0)
 |  (0, 1, 0)
 |  (1, 0, 0)
 |  (1, 1, 0)
 |  (2, 0, 0)
 |  (2, 1, 0)
 |
 |  Same dimensions - but in a tuple ``(3, 2, 1)``
 |
 |  >>> for index in np.ndindex((3, 2, 1)):
 |  ...     print(index)
 |  (0, 0, 0)
 |  (0, 1, 0)
 |  (1, 0, 0)
 |  (1, 1, 0)
 |  (2, 0, 0)
 |  (2, 1, 0)
 |
 |  Methods defined here:
 |
 |  __init__(self, *shape) from numpy.lib._index_tricks_impl.ndindex
 |      Initialize self.  See help(type(self)) for accurate signature.
 |
 |  __iter__(self) from numpy.lib._index_tricks_impl.ndindex
 |
 |  __next__(self) from numpy.lib._index_tricks_impl.ndindex
 |      Standard iterator method, updates the index and returns the index
 |      tuple.
 |
 |      Returns
 |      -------
 |      val : tuple of ints
 |          Returns a tuple containing the indices of the current
 |          iteration.
 |
 |  ndincr(self) from numpy.lib._index_tricks_impl.ndindex
 |      Increment the multi-dimensional index by one.
 |
 |      This method is for backward compatibility only: do not use.
 |
 |      .. deprecated:: 1.20.0
 |          This method has been advised against since numpy 1.8.0, but only
 |          started emitting DeprecationWarning as of this version.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object

Python Library Documentation: class nditer in module numpy

class nditer(builtins.object)
 |  nditer(op, flags=None, op_flags=None, op_dtypes=None, order='K',
 |      casting='safe', op_axes=None, itershape=None, buffersize=0)
 |
 |  Efficient multi-dimensional iterator object to iterate over arrays.
 |  To get started using this object, see the
 |  :ref:`introductory guide to array iteration <arrays.nditer>`.
 |
 |  Parameters
 |  ----------
 |  op : ndarray or sequence of array_like
 |      The array(s) to iterate over.
 |
 |  flags : sequence of str, optional
 |        Flags to control the behavior of the iterator.
 |
 |        * ``buffered`` enables buffering when required.
 |        * ``c_index`` causes a C-order index to be tracked.
 |        * ``f_index`` causes a Fortran-order index to be tracked.
 |        * ``multi_index`` causes a multi-index, or a tuple of indices
 |          with one per iteration dimension, to be tracked.
 |        * ``common_dtype`` causes all the operands to be converted to
 |          a common data type, with copying or buffering as necessary.
 |        * ``copy_if_overlap`` causes the iterator to determine if read
 |          operands have overlap with write operands, and make temporary
 |          copies as necessary to avoid overlap. False positives (needless
 |          copying) are possible in some cases.
 |        * ``delay_bufalloc`` delays allocation of the buffers until
 |          a reset() call is made. Allows ``allocate`` operands to
 |          be initialized before their values are copied into the buffers.
 |        * ``external_loop`` causes the ``values`` given to be
 |          one-dimensional arrays with multiple values instead of
 |          zero-dimensional arrays.
 |        * ``grow_inner`` allows the ``value`` array sizes to be made
 |          larger than the buffer size when both ``buffered`` and
 |          ``external_loop`` is used.
 |        * ``ranged`` allows the iterator to be restricted to a sub-range
 |          of the iterindex values.
 |        * ``refs_ok`` enables iteration of reference types, such as
 |          object arrays.
 |        * ``reduce_ok`` enables iteration of ``readwrite`` operands
 |          which are broadcasted, also known as reduction operands.
 |        * ``zerosize_ok`` allows `itersize` to be zero.
 |  op_flags : list of list of str, optional
 |        This is a list of flags for each operand. At minimum, one of
 |        ``readonly``, ``readwrite``, or ``writeonly`` must be specified.
 |
 |        * ``readonly`` indicates the operand will only be read from.
 |        * ``readwrite`` indicates the operand will be read from and written to.
 |        * ``writeonly`` indicates the operand will only be written to.
 |        * ``no_broadcast`` prevents the operand from being broadcasted.
 |        * ``contig`` forces the operand data to be contiguous.
 |        * ``aligned`` forces the operand data to be aligned.
 |        * ``nbo`` forces the operand data to be in native byte order.
 |        * ``copy`` allows a temporary read-only copy if required.
 |        * ``updateifcopy`` allows a temporary read-write copy if required.
 |        * ``allocate`` causes the array to be allocated if it is None
 |          in the ``op`` parameter.
 |        * ``no_subtype`` prevents an ``allocate`` operand from using a subtype.
 |        * ``arraymask`` indicates that this operand is the mask to use
 |          for selecting elements when writing to operands with the
 |          'writemasked' flag set. The iterator does not enforce this,
 |          but when writing from a buffer back to the array, it only
 |          copies those elements indicated by this mask.
 |        * ``writemasked`` indicates that only elements where the chosen
 |          ``arraymask`` operand is True will be written to.
 |        * ``overlap_assume_elementwise`` can be used to mark operands that are
 |          accessed only in the iterator order, to allow less conservative
 |          copying when ``copy_if_overlap`` is present.
 |  op_dtypes : dtype or tuple of dtype(s), optional
 |      The required data type(s) of the operands. If copying or buffering
 |      is enabled, the data will be converted to/from their original types.
 |  order : {'C', 'F', 'A', 'K'}, optional
 |      Controls the iteration order. 'C' means C order, 'F' means
 |      Fortran order, 'A' means 'F' order if all the arrays are Fortran
 |      contiguous, 'C' order otherwise, and 'K' means as close to the
 |      order the array elements appear in memory as possible. This also
 |      affects the element memory order of ``allocate`` operands, as they
 |      are allocated to be compatible with iteration order.
 |      Default is 'K'.
 |  casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
 |      Controls what kind of data casting may occur when making a copy
 |      or buffering.  Setting this to 'unsafe' is not recommended,
 |      as it can adversely affect accumulations.
 |
 |      * 'no' means the data types should not be cast at all.
 |      * 'equiv' means only byte-order changes are allowed.
 |      * 'safe' means only casts which can preserve values are allowed.
 |      * 'same_kind' means only safe casts or casts within a kind,
 |        like float64 to float32, are allowed.
 |      * 'unsafe' means any data conversions may be done.
 |  op_axes : list of list of ints, optional
 |      If provided, is a list of ints or None for each operands.
 |      The list of axes for an operand is a mapping from the dimensions
 |      of the iterator to the dimensions of the operand. A value of
 |      -1 can be placed for entries, causing that dimension to be
 |      treated as `newaxis`.
 |  itershape : tuple of ints, optional
 |      The desired shape of the iterator. This allows ``allocate`` operands
 |      with a dimension mapped by op_axes not corresponding to a dimension
 |      of a different operand to get a value not equal to 1 for that
 |      dimension.
 |  buffersize : int, optional
 |      When buffering is enabled, controls the size of the temporary
 |      buffers. Set to 0 for the default value.
 |
 |  Attributes
 |  ----------
 |  dtypes : tuple of dtype(s)
 |      The data types of the values provided in `value`. This may be
 |      different from the operand data types if buffering is enabled.
 |      Valid only before the iterator is closed.
 |  finished : bool
 |      Whether the iteration over the operands is finished or not.
 |  has_delayed_bufalloc : bool
 |      If True, the iterator was created with the ``delay_bufalloc`` flag,
 |      and no reset() function was called on it yet.
 |  has_index : bool
 |      If True, the iterator was created with either the ``c_index`` or
 |      the ``f_index`` flag, and the property `index` can be used to
 |      retrieve it.
 |  has_multi_index : bool
 |      If True, the iterator was created with the ``multi_index`` flag,
 |      and the property `multi_index` can be used to retrieve it.
 |  index
 |      When the ``c_index`` or ``f_index`` flag was used, this property
 |      provides access to the index. Raises a ValueError if accessed
 |      and ``has_index`` is False.
 |  iterationneedsapi : bool
 |      Whether iteration requires access to the Python API, for example
 |      if one of the operands is an object array.
 |  iterindex : int
 |      An index which matches the order of iteration.
 |  itersize : int
 |      Size of the iterator.
 |  itviews
 |      Structured view(s) of `operands` in memory, matching the reordered
 |      and optimized iterator access pattern. Valid only before the iterator
 |      is closed.
 |  multi_index
 |      When the ``multi_index`` flag was used, this property
 |      provides access to the index. Raises a ValueError if accessed
 |      accessed and ``has_multi_index`` is False.
 |  ndim : int
 |      The dimensions of the iterator.
 |  nop : int
 |      The number of iterator operands.
 |  operands : tuple of operand(s)
 |      The array(s) to be iterated over. Valid only before the iterator is
 |      closed.
 |  shape : tuple of ints
 |      Shape tuple, the shape of the iterator.
 |  value
 |      Value of ``operands`` at current iteration. Normally, this is a
 |      tuple of array scalars, but if the flag ``external_loop`` is used,
 |      it is a tuple of one dimensional arrays.
 |
 |  Notes
 |  -----
 |  `nditer` supersedes `flatiter`.  The iterator implementation behind
 |  `nditer` is also exposed by the NumPy C API.
 |
 |  The Python exposure supplies two iteration interfaces, one which follows
 |  the Python iterator protocol, and another which mirrors the C-style
 |  do-while pattern.  The native Python approach is better in most cases, but
 |  if you need the coordinates or index of an iterator, use the C-style pattern.
 |
 |  Examples
 |  --------
 |  Here is how we might write an ``iter_add`` function, using the
 |  Python iterator protocol:
 |
 |  >>> import numpy as np
 |
 |  >>> def iter_add_py(x, y, out=None):
 |  ...     addop = np.add
 |  ...     it = np.nditer([x, y, out], [],
 |  ...                 [['readonly'], ['readonly'], ['writeonly','allocate']])
 |  ...     with it:
 |  ...         for (a, b, c) in it:
 |  ...             addop(a, b, out=c)
 |  ...         return it.operands[2]
 |
 |  Here is the same function, but following the C-style pattern:
 |
 |  >>> def iter_add(x, y, out=None):
 |  ...    addop = np.add
 |  ...    it = np.nditer([x, y, out], [],
 |  ...                [['readonly'], ['readonly'], ['writeonly','allocate']])
 |  ...    with it:
 |  ...        while not it.finished:
 |  ...            addop(it[0], it[1], out=it[2])
 |  ...            it.iternext()
 |  ...        return it.operands[2]
 |
 |  Here is an example outer product function:
 |
 |  >>> def outer_it(x, y, out=None):
 |  ...     mulop = np.multiply
 |  ...     it = np.nditer([x, y, out], ['external_loop'],
 |  ...             [['readonly'], ['readonly'], ['writeonly', 'allocate']],
 |  ...             op_axes=[list(range(x.ndim)) + [-1] * y.ndim,
 |  ...                      [-1] * x.ndim + list(range(y.ndim)),
 |  ...                      None])
 |  ...     with it:
 |  ...         for (a, b, c) in it:
 |  ...             mulop(a, b, out=c)
 |  ...         return it.operands[2]
 |
 |  >>> a = np.arange(2)+1
 |  >>> b = np.arange(3)+1
 |  >>> outer_it(a,b)
 |  array([[1, 2, 3],
 |         [2, 4, 6]])
 |
 |  Here is an example function which operates like a "lambda" ufunc:
 |
 |  >>> def luf(lamdaexpr, *args, **kwargs):
 |  ...    '''luf(lambdaexpr, op1, ..., opn, out=None, order='K', casting='safe', buffersize=0)'''
 |  ...    nargs = len(args)
 |  ...    op = (kwargs.get('out',None),) + args
 |  ...    it = np.nditer(op, ['buffered','external_loop'],
 |  ...            [['writeonly','allocate','no_broadcast']] +
 |  ...                            [['readonly','nbo','aligned']]*nargs,
 |  ...            order=kwargs.get('order','K'),
 |  ...            casting=kwargs.get('casting','safe'),
 |  ...            buffersize=kwargs.get('buffersize',0))
 |  ...    while not it.finished:
 |  ...        it[0] = lamdaexpr(*it[1:])
 |  ...        it.iternext()
 |  ...    return it.operands[0]
 |
 |  >>> a = np.arange(5)
 |  >>> b = np.ones(5)
 |  >>> luf(lambda i,j:i*i + j/2, a, b)
 |  array([  0.5,   1.5,   4.5,   9.5,  16.5])
 |
 |  If operand flags ``"writeonly"`` or ``"readwrite"`` are used the
 |  operands may be views into the original data with the
 |  `WRITEBACKIFCOPY` flag. In this case `nditer` must be used as a
 |  context manager or the `nditer.close` method must be called before
 |  using the result. The temporary data will be written back to the
 |  original data when the :meth:`~object.__exit__` function is called
 |  but not before:
 |
 |  >>> a = np.arange(6, dtype='i4')[::-2]
 |  >>> with np.nditer(a, [],
 |  ...        [['writeonly', 'updateifcopy']],
 |  ...        casting='unsafe',
 |  ...        op_dtypes=[np.dtype('f4')]) as i:
 |  ...    x = i.operands[0]
 |  ...    x[:] = [-1, -2, -3]
 |  ...    # a still unchanged here
 |  >>> a, x
 |  (array([-1, -2, -3], dtype=int32), array([-1., -2., -3.], dtype=float32))
 |
 |  It is important to note that once the iterator is exited, dangling
 |  references (like `x` in the example) may or may not share data with
 |  the original data `a`. If writeback semantics were active, i.e. if
 |  `x.base.flags.writebackifcopy` is `True`, then exiting the iterator
 |  will sever the connection between `x` and `a`, writing to `x` will
 |  no longer write to `a`. If writeback semantics are not active, then
 |  `x.data` will still point at some part of `a.data`, and writing to
 |  one will affect the other.
 |
 |  Context management and the `close` method appeared in version 1.15.0.
 |
 |  Methods defined here:
 |
 |  __copy__(...)
 |
 |  __delitem__(self, key, /)
 |      Delete self[key].
 |
 |  __enter__(...)
 |
 |  __exit__(...)
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __init__(self, /, *args, **kwargs)
 |      Initialize self.  See help(type(self)) for accurate signature.
 |
 |  __iter__(self, /)
 |      Implement iter(self).
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  __next__(self, /)
 |      Implement next(self).
 |
 |  __setitem__(self, key, value, /)
 |      Set self[key] to value.
 |
 |  close(...)
 |      close()
 |
 |      Resolve all writeback semantics in writeable operands.
 |
 |      .. versionadded:: 1.15.0
 |
 |      See Also
 |      --------
 |
 |      :ref:`nditer-context-manager`
 |
 |  copy(...)
 |      copy()
 |
 |      Get a copy of the iterator in its current state.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.arange(10)
 |      >>> y = x + 1
 |      >>> it = np.nditer([x, y])
 |      >>> next(it)
 |      (array(0), array(1))
 |      >>> it2 = it.copy()
 |      >>> next(it2)
 |      (array(1), array(2))
 |
 |  debug_print(...)
 |      debug_print()
 |
 |      Print the current state of the `nditer` instance and debug info to stdout.
 |
 |  enable_external_loop(...)
 |      enable_external_loop()
 |
 |      When the "external_loop" was not used during construction, but
 |      is desired, this modifies the iterator to behave as if the flag
 |      was specified.
 |
 |  iternext(...)
 |      iternext()
 |
 |      Check whether iterations are left, and perform a single internal iteration
 |      without returning the result.  Used in the C-style pattern do-while
 |      pattern.  For an example, see `nditer`.
 |
 |      Returns
 |      -------
 |      iternext : bool
 |          Whether or not there are iterations left.
 |
 |  remove_axis(...)
 |      remove_axis(i, /)
 |
 |      Removes axis `i` from the iterator. Requires that the flag "multi_index"
 |      be enabled.
 |
 |  remove_multi_index(...)
 |      remove_multi_index()
 |
 |      When the "multi_index" flag was specified, this removes it, allowing
 |      the internal iteration structure to be optimized further.
 |
 |  reset(...)
 |      reset()
 |
 |      Reset the iterator to its initial state.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  dtypes
 |
 |  finished
 |
 |  has_delayed_bufalloc
 |
 |  has_index
 |
 |  has_multi_index
 |
 |  index
 |
 |  iterationneedsapi
 |
 |  iterindex
 |
 |  iterrange
 |
 |  itersize
 |
 |  itviews
 |
 |  multi_index
 |
 |  ndim
 |
 |  nop
 |
 |  operands
 |      operands[`Slice`]
 |
 |      The array(s) to be iterated over. Valid only before the iterator is closed.
 |
 |  shape
 |
 |  value

Python Library Documentation: function negative in module autograd.tracer

negative(*args, called_by_autograd_dispatcher=False, **kwargs)
    negative(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Numerical negative, element-wise.

    Parameters
    ----------
    x : array_like or scalar
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray or scalar
        Returned array or scalar: `y = -x`.
        This is a scalar if `x` is a scalar.

    Examples
    --------
    >>> import numpy as np
    >>> np.negative([1.,-1.])
    array([-1.,  1.])

    The unary ``-`` operator can be used as a shorthand for ``np.negative`` on
    ndarrays.

    >>> x1 = np.array(([1., -1.]))
    >>> -x1
    array([-1.,  1.])

Python Library Documentation: function nested_iters in module autograd.tracer

nested_iters(*args, called_by_autograd_dispatcher=False, **kwargs)
    nested_iters(op, axes, flags=None, op_flags=None, op_dtypes=None,     order="K", casting="safe", buffersize=0)

    Create nditers for use in nested loops

    Create a tuple of `nditer` objects which iterate in nested loops over
    different axes of the op argument. The first iterator is used in the
    outermost loop, the last in the innermost loop. Advancing one will change
    the subsequent iterators to point at its new element.

    Parameters
    ----------
    op : ndarray or sequence of array_like
        The array(s) to iterate over.

    axes : list of list of int
        Each item is used as an "op_axes" argument to an nditer

    flags, op_flags, op_dtypes, order, casting, buffersize (optional)
        See `nditer` parameters of the same name

    Returns
    -------
    iters : tuple of nditer
        An nditer for each item in `axes`, outermost first

    See Also
    --------
    nditer

    Examples
    --------

    Basic usage. Note how y is the "flattened" version of
    [a[:, 0, :], a[:, 1, 0], a[:, 2, :]] since we specified
    the first iter's axes as [1]

    >>> import numpy as np
    >>> a = np.arange(12).reshape(2, 3, 2)
    >>> i, j = np.nested_iters(a, [[1], [0, 2]], flags=["multi_index"])
    >>> for x in i:
    ...      print(i.multi_index)
    ...      for y in j:
    ...          print('', j.multi_index, y)
    (0,)
     (0, 0) 0
     (0, 1) 1
     (1, 0) 6
     (1, 1) 7
    (1,)
     (0, 0) 2
     (0, 1) 3
     (1, 0) 8
     (1, 1) 9
    (2,)
     (0, 0) 4
     (0, 1) 5
     (1, 0) 10
     (1, 1) 11

Python Library Documentation: NoneType object

class NoneType(object)
 |  Methods defined here:
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.

Python Library Documentation: function nextafter in module autograd.tracer

nextafter(*args, called_by_autograd_dispatcher=False, **kwargs)
    nextafter(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the next floating-point value after x1 towards x2, element-wise.

    Parameters
    ----------
    x1 : array_like
        Values to find the next representable value of.
    x2 : array_like
        The direction where to look for the next representable value of `x1`.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        The next representable values of `x1` in the direction of `x2`.
        This is a scalar if both `x1` and `x2` are scalars.

    Examples
    --------
    >>> import numpy as np
    >>> eps = np.finfo(np.float64).eps
    >>> np.nextafter(1, 2) == eps + 1
    True
    >>> np.nextafter([1, 2], [2, 1]) == [eps + 1, 2 - eps]
    array([ True,  True])

Python Library Documentation: function nonzero in module autograd.tracer

nonzero(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the indices of the elements that are non-zero.

    Returns a tuple of arrays, one for each dimension of `a`,
    containing the indices of the non-zero elements in that
    dimension. The values in `a` are always tested and returned in
    row-major, C-style order.

    To group the indices by element, rather than dimension, use `argwhere`,
    which returns a row for each non-zero element.

    .. note::

       When called on a zero-d array or scalar, ``nonzero(a)`` is treated
       as ``nonzero(atleast_1d(a))``.

       .. deprecated:: 1.17.0

          Use `atleast_1d` explicitly if this behavior is deliberate.

    Parameters
    ----------
    a : array_like
        Input array.

    Returns
    -------
    tuple_of_arrays : tuple
        Indices of elements that are non-zero.

    See Also
    --------
    flatnonzero :
        Return indices that are non-zero in the flattened version of the input
        array.
    ndarray.nonzero :
        Equivalent ndarray method.
    count_nonzero :
        Counts the number of non-zero elements in the input array.

    Notes
    -----
    While the nonzero values can be obtained with ``a[nonzero(a)]``, it is
    recommended to use ``x[x.astype(bool)]`` or ``x[x != 0]`` instead, which
    will correctly handle 0-d arrays.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([[3, 0, 0], [0, 4, 0], [5, 6, 0]])
    >>> x
    array([[3, 0, 0],
           [0, 4, 0],
           [5, 6, 0]])
    >>> np.nonzero(x)
    (array([0, 1, 2, 2]), array([0, 1, 0, 1]))

    >>> x[np.nonzero(x)]
    array([3, 4, 5, 6])
    >>> np.transpose(np.nonzero(x))
    array([[0, 0],
           [1, 1],
           [2, 0],
           [2, 1]])

    A common use for ``nonzero`` is to find the indices of an array, where
    a condition is True.  Given an array `a`, the condition `a` > 3 is a
    boolean array and since False is interpreted as 0, np.nonzero(a > 3)
    yields the indices of the `a` where the condition is true.

    >>> a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
    >>> a > 3
    array([[False, False, False],
           [ True,  True,  True],
           [ True,  True,  True]])
    >>> np.nonzero(a > 3)
    (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))

    Using this result to index `a` is equivalent to using the mask directly:

    >>> a[np.nonzero(a > 3)]
    array([4, 5, 6, 7, 8, 9])
    >>> a[a > 3]  # prefer this spelling
    array([4, 5, 6, 7, 8, 9])

    ``nonzero`` can also be called as a method of the array.

    >>> (a > 3).nonzero()
    (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))

Python Library Documentation: function not_equal in module autograd.tracer

not_equal(*args, called_by_autograd_dispatcher=False, **kwargs)
    not_equal(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return (x1 != x2) element-wise.

    Parameters
    ----------
    x1, x2 : array_like
        Input arrays.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Output array, element-wise comparison of `x1` and `x2`.
        Typically of type bool, unless ``dtype=object`` is passed.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    equal, greater, greater_equal, less, less_equal

    Examples
    --------
    >>> import numpy as np
    >>> np.not_equal([1.,2.], [1., 3.])
    array([False,  True])
    >>> np.not_equal([1, 2], [[1, 3],[1, 4]])
    array([[False,  True],
           [False,  True]])

    The ``!=`` operator can be used as a shorthand for ``np.not_equal`` on
    ndarrays.

    >>> a = np.array([1., 2.])
    >>> b = np.array([1., 3.])
    >>> a != b
    array([False,  True])

Python Library Documentation: list object

class list(object)
 |  list(iterable=(), /)
 |
 |  Built-in mutable sequence.
 |
 |  If no argument is given, the constructor creates a new empty list.
 |  The argument must be an iterable if specified.
 |
 |  Methods defined here:
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __contains__(self, key, /)
 |      Return bool(key in self).
 |
 |  __delitem__(self, key, /)
 |      Delete self[key].
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getattribute__(self, name, /)
 |      Return getattr(self, name).
 |
 |  __getitem__(self, index, /)
 |      Return self[index].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __iadd__(self, value, /)
 |      Implement self+=value.
 |
 |  __imul__(self, value, /)
 |      Implement self*=value.
 |
 |  __init__(self, /, *args, **kwargs)
 |      Initialize self.  See help(type(self)) for accurate signature.
 |
 |  __iter__(self, /)
 |      Implement iter(self).
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __reversed__(self, /)
 |      Return a reverse iterator over the list.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __setitem__(self, key, value, /)
 |      Set self[key] to value.
 |
 |  __sizeof__(self, /)
 |      Return the size of the list in memory, in bytes.
 |
 |  append(self, object, /)
 |      Append object to the end of the list.
 |
 |  clear(self, /)
 |      Remove all items from list.
 |
 |  copy(self, /)
 |      Return a shallow copy of the list.
 |
 |  count(self, value, /)
 |      Return number of occurrences of value.
 |
 |  extend(self, iterable, /)
 |      Extend list by appending elements from the iterable.
 |
 |  index(self, value, start=0, stop=9223372036854775807, /)
 |      Return first index of value.
 |
 |      Raises ValueError if the value is not present.
 |
 |  insert(self, index, object, /)
 |      Insert object before index.
 |
 |  pop(self, index=-1, /)
 |      Remove and return item at index (default last).
 |
 |      Raises IndexError if list is empty or index is out of range.
 |
 |  remove(self, value, /)
 |      Remove first occurrence of value.
 |
 |      Raises ValueError if the value is not present.
 |
 |  reverse(self, /)
 |      Reverse *IN PLACE*.
 |
 |  sort(self, /, *, key=None, reverse=False)
 |      Sort the list in ascending order and return None.
 |
 |      The sort is in-place (i.e. the list itself is modified) and stable (i.e. the
 |      order of two equal elements is maintained).
 |
 |      If a key function is given, apply it once to each list item and sort them,
 |      ascending or descending, according to their function values.
 |
 |      The reverse flag can be set to sort in descending order.
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      See PEP 585
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes defined here:
 |
 |  __hash__ = None

Python Library Documentation: function notrace_primitive in module autograd.tracer

notrace_primitive(f_raw)

Python Library Documentation: class number in module numpy

class number(generic)
 |  Abstract base class of all numeric scalar types.
 |
 |  Method resolution order:
 |      number
 |      generic
 |      builtins.object
 |
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes inherited from generic:
 |
 |  __hash__ = None

Error rendering doc: No Python documentation found for '2.1.3'.
Use help() to get the interactive help utility.
Use help(str) for help on the str class.

Python Library Documentation: class object_ in module numpy

class object_(generic)
 |  Any Python object.
 |
 |  :Character code: ``'O'``
 |
 |  Method resolution order:
 |      object_
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __call__(self, /, *args, **kwargs)
 |      Call self as a function.
 |
 |  __contains__(self, key, /)
 |      Return bool(key in self).
 |
 |  __delattr__(self, name, /)
 |      Implement delattr(self, name).
 |
 |  __delitem__(self, key, /)
 |      Delete self[key].
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getattribute__(self, name, /)
 |      Return getattr(self, name).
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __iadd__(self, value, /)
 |      Implement self+=value.
 |
 |  __imul__(self, value, /)
 |      Implement self*=value.
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __release_buffer__(self, buffer, /)
 |      Release the buffer object that exposes the underlying memory of the object.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __setattr__(self, name, value, /)
 |      Implement setattr(self, name, value).
 |
 |  __setitem__(self, key, value, /)
 |      Set self[key] to value.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: function ones in module autograd.tracer

ones(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return a new array of given shape and type, filled with ones.

    Parameters
    ----------
    shape : int or sequence of ints
        Shape of the new array, e.g., ``(2, 3)`` or ``2``.
    dtype : data-type, optional
        The desired data-type for the array, e.g., `numpy.int8`.  Default is
        `numpy.float64`.
    order : {'C', 'F'}, optional, default: C
        Whether to store multi-dimensional data in row-major
        (C-style) or column-major (Fortran-style) order in
        memory.
    device : str, optional
        The device on which to place the created array. Default: None.
        For Array-API interoperability only, so must be ``"cpu"`` if passed.

        .. versionadded:: 2.0.0
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    out : ndarray
        Array of ones with the given shape, dtype, and order.

    See Also
    --------
    ones_like : Return an array of ones with shape and type of input.
    empty : Return a new uninitialized array.
    zeros : Return a new array setting values to zero.
    full : Return a new array of given shape filled with value.

    Examples
    --------
    >>> import numpy as np
    >>> np.ones(5)
    array([1., 1., 1., 1., 1.])

    >>> np.ones((5,), dtype=int)
    array([1, 1, 1, 1, 1])

    >>> np.ones((2, 1))
    array([[1.],
           [1.]])

    >>> s = (2,2)
    >>> np.ones(s)
    array([[1.,  1.],
           [1.,  1.]])

Python Library Documentation: function ones_like in module autograd.tracer

ones_like(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return an array of ones with the same shape and type as a given array.

    Parameters
    ----------
    a : array_like
        The shape and data-type of `a` define these same attributes of
        the returned array.
    dtype : data-type, optional
        Overrides the data type of the result.

        .. versionadded:: 1.6.0
    order : {'C', 'F', 'A', or 'K'}, optional
        Overrides the memory layout of the result. 'C' means C-order,
        'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
        'C' otherwise. 'K' means match the layout of `a` as closely
        as possible.

        .. versionadded:: 1.6.0
    subok : bool, optional.
        If True, then the newly created array will use the sub-class
        type of `a`, otherwise it will be a base-class array. Defaults
        to True.
    shape : int or sequence of ints, optional.
        Overrides the shape of the result. If order='K' and the number of
        dimensions is unchanged, will try to keep order, otherwise,
        order='C' is implied.

        .. versionadded:: 1.17.0
    device : str, optional
        The device on which to place the created array. Default: None.
        For Array-API interoperability only, so must be ``"cpu"`` if passed.

        .. versionadded:: 2.0.0

    Returns
    -------
    out : ndarray
        Array of ones with the same shape and type as `a`.

    See Also
    --------
    empty_like : Return an empty array with shape and type of input.
    zeros_like : Return an array of zeros with shape and type of input.
    full_like : Return a new array with shape of input filled with value.
    ones : Return a new array setting values to one.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.arange(6)
    >>> x = x.reshape((2, 3))
    >>> x
    array([[0, 1, 2],
           [3, 4, 5]])
    >>> np.ones_like(x)
    array([[1, 1, 1],
           [1, 1, 1]])

    >>> y = np.arange(3, dtype=float)
    >>> y
    array([0., 1., 2.])
    >>> np.ones_like(y)
    array([1.,  1.,  1.])

Python Library Documentation: function outer in module autograd.tracer

outer(*args, called_by_autograd_dispatcher=False, **kwargs)
    Compute the outer product of two vectors.

    Given two vectors `a` and `b` of length ``M`` and ``N``, respectively,
    the outer product [1]_ is::

      [[a_0*b_0  a_0*b_1 ... a_0*b_{N-1} ]
       [a_1*b_0    .
       [ ...          .
       [a_{M-1}*b_0            a_{M-1}*b_{N-1} ]]

    Parameters
    ----------
    a : (M,) array_like
        First input vector.  Input is flattened if
        not already 1-dimensional.
    b : (N,) array_like
        Second input vector.  Input is flattened if
        not already 1-dimensional.
    out : (M, N) ndarray, optional
        A location where the result is stored

        .. versionadded:: 1.9.0

    Returns
    -------
    out : (M, N) ndarray
        ``out[i, j] = a[i] * b[j]``

    See also
    --------
    inner
    einsum : ``einsum('i,j->ij', a.ravel(), b.ravel())`` is the equivalent.
    ufunc.outer : A generalization to dimensions other than 1D and other
                  operations. ``np.multiply.outer(a.ravel(), b.ravel())``
                  is the equivalent.
    linalg.outer : An Array API compatible variation of ``np.outer``,
                   which accepts 1-dimensional inputs only.
    tensordot : ``np.tensordot(a.ravel(), b.ravel(), axes=((), ()))``
                is the equivalent.

    References
    ----------
    .. [1] G. H. Golub and C. F. Van Loan, *Matrix Computations*, 3rd
           ed., Baltimore, MD, Johns Hopkins University Press, 1996,
           pg. 8.

    Examples
    --------
    Make a (*very* coarse) grid for computing a Mandelbrot set:

    >>> import numpy as np
    >>> rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5))
    >>> rl
    array([[-2., -1.,  0.,  1.,  2.],
           [-2., -1.,  0.,  1.,  2.],
           [-2., -1.,  0.,  1.,  2.],
           [-2., -1.,  0.,  1.,  2.],
           [-2., -1.,  0.,  1.,  2.]])
    >>> im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,)))
    >>> im
    array([[0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j],
           [0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j],
           [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
           [0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j],
           [0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j]])
    >>> grid = rl + im
    >>> grid
    array([[-2.+2.j, -1.+2.j,  0.+2.j,  1.+2.j,  2.+2.j],
           [-2.+1.j, -1.+1.j,  0.+1.j,  1.+1.j,  2.+1.j],
           [-2.+0.j, -1.+0.j,  0.+0.j,  1.+0.j,  2.+0.j],
           [-2.-1.j, -1.-1.j,  0.-1.j,  1.-1.j,  2.-1.j],
           [-2.-2.j, -1.-2.j,  0.-2.j,  1.-2.j,  2.-2.j]])

    An example using a "vector" of letters:

    >>> x = np.array(['a', 'b', 'c'], dtype=object)
    >>> np.outer(x, [1, 2, 3])
    array([['a', 'aa', 'aaa'],
           ['b', 'bb', 'bbb'],
           ['c', 'cc', 'ccc']], dtype=object)

Python Library Documentation: function packbits in module autograd.tracer

packbits(*args, called_by_autograd_dispatcher=False, **kwargs)
    packbits(a, /, axis=None, bitorder='big')

    Packs the elements of a binary-valued array into bits in a uint8 array.

    The result is padded to full bytes by inserting zero bits at the end.

    Parameters
    ----------
    a : array_like
        An array of integers or booleans whose elements should be packed to
        bits.
    axis : int, optional
        The dimension over which bit-packing is done.
        ``None`` implies packing the flattened array.
    bitorder : {'big', 'little'}, optional
        The order of the input bits. 'big' will mimic bin(val),
        ``[0, 0, 0, 0, 0, 0, 1, 1] => 3 = 0b00000011``, 'little' will
        reverse the order so ``[1, 1, 0, 0, 0, 0, 0, 0] => 3``.
        Defaults to 'big'.

        .. versionadded:: 1.17.0

    Returns
    -------
    packed : ndarray
        Array of type uint8 whose elements represent bits corresponding to the
        logical (0 or nonzero) value of the input elements. The shape of
        `packed` has the same number of dimensions as the input (unless `axis`
        is None, in which case the output is 1-D).

    See Also
    --------
    unpackbits: Unpacks elements of a uint8 array into a binary-valued output
                array.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[[1,0,1],
    ...                [0,1,0]],
    ...               [[1,1,0],
    ...                [0,0,1]]])
    >>> b = np.packbits(a, axis=-1)
    >>> b
    array([[[160],
            [ 64]],
           [[192],
            [ 32]]], dtype=uint8)

    Note that in binary 160 = 1010 0000, 64 = 0100 0000, 192 = 1100 0000,
    and 32 = 0010 0000.

Python Library Documentation: function pad in module autograd.tracer

pad(*args, called_by_autograd_dispatcher=False, **kwargs)
    Pad an array.

    Parameters
    ----------
    array : array_like of rank N
        The array to pad.
    pad_width : {sequence, array_like, int}
        Number of values padded to the edges of each axis.
        ``((before_1, after_1), ... (before_N, after_N))`` unique pad widths
        for each axis.
        ``(before, after)`` or ``((before, after),)`` yields same before
        and after pad for each axis.
        ``(pad,)`` or ``int`` is a shortcut for before = after = pad width
        for all axes.
    mode : str or function, optional
        One of the following string values or a user supplied function.

        'constant' (default)
            Pads with a constant value.
        'edge'
            Pads with the edge values of array.
        'linear_ramp'
            Pads with the linear ramp between end_value and the
            array edge value.
        'maximum'
            Pads with the maximum value of all or part of the
            vector along each axis.
        'mean'
            Pads with the mean value of all or part of the
            vector along each axis.
        'median'
            Pads with the median value of all or part of the
            vector along each axis.
        'minimum'
            Pads with the minimum value of all or part of the
            vector along each axis.
        'reflect'
            Pads with the reflection of the vector mirrored on
            the first and last values of the vector along each
            axis.
        'symmetric'
            Pads with the reflection of the vector mirrored
            along the edge of the array.
        'wrap'
            Pads with the wrap of the vector along the axis.
            The first values are used to pad the end and the
            end values are used to pad the beginning.
        'empty'
            Pads with undefined values.

            .. versionadded:: 1.17

        <function>
            Padding function, see Notes.
    stat_length : sequence or int, optional
        Used in 'maximum', 'mean', 'median', and 'minimum'.  Number of
        values at edge of each axis used to calculate the statistic value.

        ``((before_1, after_1), ... (before_N, after_N))`` unique statistic
        lengths for each axis.

        ``(before, after)`` or ``((before, after),)`` yields same before
        and after statistic lengths for each axis.

        ``(stat_length,)`` or ``int`` is a shortcut for
        ``before = after = statistic`` length for all axes.

        Default is ``None``, to use the entire axis.
    constant_values : sequence or scalar, optional
        Used in 'constant'.  The values to set the padded values for each
        axis.

        ``((before_1, after_1), ... (before_N, after_N))`` unique pad constants
        for each axis.

        ``(before, after)`` or ``((before, after),)`` yields same before
        and after constants for each axis.

        ``(constant,)`` or ``constant`` is a shortcut for
        ``before = after = constant`` for all axes.

        Default is 0.
    end_values : sequence or scalar, optional
        Used in 'linear_ramp'.  The values used for the ending value of the
        linear_ramp and that will form the edge of the padded array.

        ``((before_1, after_1), ... (before_N, after_N))`` unique end values
        for each axis.

        ``(before, after)`` or ``((before, after),)`` yields same before
        and after end values for each axis.

        ``(constant,)`` or ``constant`` is a shortcut for
        ``before = after = constant`` for all axes.

        Default is 0.
    reflect_type : {'even', 'odd'}, optional
        Used in 'reflect', and 'symmetric'.  The 'even' style is the
        default with an unaltered reflection around the edge value.  For
        the 'odd' style, the extended part of the array is created by
        subtracting the reflected values from two times the edge value.

    Returns
    -------
    pad : ndarray
        Padded array of rank equal to `array` with shape increased
        according to `pad_width`.

    Notes
    -----
    .. versionadded:: 1.7.0

    For an array with rank greater than 1, some of the padding of later
    axes is calculated from padding of previous axes.  This is easiest to
    think about with a rank 2 array where the corners of the padded array
    are calculated by using padded values from the first axis.

    The padding function, if used, should modify a rank 1 array in-place. It
    has the following signature::

        padding_func(vector, iaxis_pad_width, iaxis, kwargs)

    where

    vector : ndarray
        A rank 1 array already padded with zeros.  Padded values are
        vector[:iaxis_pad_width[0]] and vector[-iaxis_pad_width[1]:].
    iaxis_pad_width : tuple
        A 2-tuple of ints, iaxis_pad_width[0] represents the number of
        values padded at the beginning of vector where
        iaxis_pad_width[1] represents the number of values padded at
        the end of vector.
    iaxis : int
        The axis currently being calculated.
    kwargs : dict
        Any keyword arguments the function requires.

    Examples
    --------
    >>> import numpy as np
    >>> a = [1, 2, 3, 4, 5]
    >>> np.pad(a, (2, 3), 'constant', constant_values=(4, 6))
    array([4, 4, 1, ..., 6, 6, 6])

    >>> np.pad(a, (2, 3), 'edge')
    array([1, 1, 1, ..., 5, 5, 5])

    >>> np.pad(a, (2, 3), 'linear_ramp', end_values=(5, -4))
    array([ 5,  3,  1,  2,  3,  4,  5,  2, -1, -4])

    >>> np.pad(a, (2,), 'maximum')
    array([5, 5, 1, 2, 3, 4, 5, 5, 5])

    >>> np.pad(a, (2,), 'mean')
    array([3, 3, 1, 2, 3, 4, 5, 3, 3])

    >>> np.pad(a, (2,), 'median')
    array([3, 3, 1, 2, 3, 4, 5, 3, 3])

    >>> a = [[1, 2], [3, 4]]
    >>> np.pad(a, ((3, 2), (2, 3)), 'minimum')
    array([[1, 1, 1, 2, 1, 1, 1],
           [1, 1, 1, 2, 1, 1, 1],
           [1, 1, 1, 2, 1, 1, 1],
           [1, 1, 1, 2, 1, 1, 1],
           [3, 3, 3, 4, 3, 3, 3],
           [1, 1, 1, 2, 1, 1, 1],
           [1, 1, 1, 2, 1, 1, 1]])

    >>> a = [1, 2, 3, 4, 5]
    >>> np.pad(a, (2, 3), 'reflect')
    array([3, 2, 1, 2, 3, 4, 5, 4, 3, 2])

    >>> np.pad(a, (2, 3), 'reflect', reflect_type='odd')
    array([-1,  0,  1,  2,  3,  4,  5,  6,  7,  8])

    >>> np.pad(a, (2, 3), 'symmetric')
    array([2, 1, 1, 2, 3, 4, 5, 5, 4, 3])

    >>> np.pad(a, (2, 3), 'symmetric', reflect_type='odd')
    array([0, 1, 1, 2, 3, 4, 5, 5, 6, 7])

    >>> np.pad(a, (2, 3), 'wrap')
    array([4, 5, 1, 2, 3, 4, 5, 1, 2, 3])

    >>> def pad_with(vector, pad_width, iaxis, kwargs):
    ...     pad_value = kwargs.get('padder', 10)
    ...     vector[:pad_width[0]] = pad_value
    ...     vector[-pad_width[1]:] = pad_value
    >>> a = np.arange(6)
    >>> a = a.reshape((2, 3))
    >>> np.pad(a, 2, pad_with)
    array([[10, 10, 10, 10, 10, 10, 10],
           [10, 10, 10, 10, 10, 10, 10],
           [10, 10,  0,  1,  2, 10, 10],
           [10, 10,  3,  4,  5, 10, 10],
           [10, 10, 10, 10, 10, 10, 10],
           [10, 10, 10, 10, 10, 10, 10]])
    >>> np.pad(a, 2, pad_with, padder=100)
    array([[100, 100, 100, 100, 100, 100, 100],
           [100, 100, 100, 100, 100, 100, 100],
           [100, 100,   0,   1,   2, 100, 100],
           [100, 100,   3,   4,   5, 100, 100],
           [100, 100, 100, 100, 100, 100, 100],
           [100, 100, 100, 100, 100, 100, 100]])

Python Library Documentation: function parse_einsum_input in module autograd.tracer

parse_einsum_input(*args, **kwargs)
    None

Python Library Documentation: function partition in module autograd.tracer

partition(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return a partitioned copy of an array.

    Creates a copy of the array and partially sorts it in such a way that
    the value of the element in k-th position is in the position it would be
    in a sorted array. In the output array, all elements smaller than the k-th
    element are located to the left of this element and all equal or greater
    are located to its right. The ordering of the elements in the two
    partitions on the either side of the k-th element in the output array is
    undefined.

    .. versionadded:: 1.8.0

    Parameters
    ----------
    a : array_like
        Array to be sorted.
    kth : int or sequence of ints
        Element index to partition by. The k-th value of the element
        will be in its final sorted position and all smaller elements
        will be moved before it and all equal or greater elements behind
        it. The order of all elements in the partitions is undefined. If
        provided with a sequence of k-th it will partition all elements
        indexed by k-th  of them into their sorted position at once.

        .. deprecated:: 1.22.0
            Passing booleans as index is deprecated.
    axis : int or None, optional
        Axis along which to sort. If None, the array is flattened before
        sorting. The default is -1, which sorts along the last axis.
    kind : {'introselect'}, optional
        Selection algorithm. Default is 'introselect'.
    order : str or list of str, optional
        When `a` is an array with fields defined, this argument
        specifies which fields to compare first, second, etc.  A single
        field can be specified as a string.  Not all fields need be
        specified, but unspecified fields will still be used, in the
        order in which they come up in the dtype, to break ties.

    Returns
    -------
    partitioned_array : ndarray
        Array of the same type and shape as `a`.

    See Also
    --------
    ndarray.partition : Method to sort an array in-place.
    argpartition : Indirect partition.
    sort : Full sorting

    Notes
    -----
    The various selection algorithms are characterized by their average
    speed, worst case performance, work space size, and whether they are
    stable. A stable sort keeps items with the same key in the same
    relative order. The available algorithms have the following
    properties:

    ================= ======= ============= ============ =======
       kind            speed   worst case    work space  stable
    ================= ======= ============= ============ =======
    'introselect'        1        O(n)           0         no
    ================= ======= ============= ============ =======

    All the partition algorithms make temporary copies of the data when
    partitioning along any but the last axis.  Consequently,
    partitioning along the last axis is faster and uses less space than
    partitioning along any other axis.

    The sort order for complex numbers is lexicographic. If both the
    real and imaginary parts are non-nan then the order is determined by
    the real parts except when they are equal, in which case the order
    is determined by the imaginary parts.

    The sort order of ``np.nan`` is bigger than ``np.inf``.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([7, 1, 7, 7, 1, 5, 7, 2, 3, 2, 6, 2, 3, 0])
    >>> p = np.partition(a, 4)
    >>> p
    array([0, 1, 2, 1, 2, 5, 2, 3, 3, 6, 7, 7, 7, 7]) # may vary

    ``p[4]`` is 2;  all elements in ``p[:4]`` are less than or equal
    to ``p[4]``, and all elements in ``p[5:]`` are greater than or
    equal to ``p[4]``.  The partition is::

        [0, 1, 2, 1], [2], [5, 2, 3, 3, 6, 7, 7, 7, 7]

    The next example shows the use of multiple values passed to `kth`.

    >>> p2 = np.partition(a, (4, 8))
    >>> p2
    array([0, 1, 2, 1, 2, 3, 3, 2, 5, 6, 7, 7, 7, 7])

    ``p2[4]`` is 2  and ``p2[8]`` is 5.  All elements in ``p2[:4]``
    are less than or equal to ``p2[4]``, all elements in ``p2[5:8]``
    are greater than or equal to ``p2[4]`` and less than or equal to
    ``p2[8]``, and all elements in ``p2[9:]`` are greater than or
    equal to ``p2[8]``.  The partition is::

        [0, 1, 2, 1], [2], [3, 3, 2], [5], [6, 7, 7, 7, 7]

Python Library Documentation: function percentile in module autograd.tracer

percentile(*args, called_by_autograd_dispatcher=False, **kwargs)
    Compute the q-th percentile of the data along the specified axis.

    Returns the q-th percentile(s) of the array elements.

    Parameters
    ----------
    a : array_like of real numbers
        Input array or object that can be converted to an array.
    q : array_like of float
        Percentage or sequence of percentages for the percentiles to compute.
        Values must be between 0 and 100 inclusive.
    axis : {int, tuple of int, None}, optional
        Axis or axes along which the percentiles are computed. The
        default is to compute the percentile(s) along a flattened
        version of the array.

        .. versionchanged:: 1.9.0
            A tuple of axes is supported
    out : ndarray, optional
        Alternative output array in which to place the result. It must
        have the same shape and buffer length as the expected output,
        but the type (of the output) will be cast if necessary.
    overwrite_input : bool, optional
        If True, then allow the input array `a` to be modified by intermediate
        calculations, to save memory. In this case, the contents of the input
        `a` after this function completes is undefined.
    method : str, optional
        This parameter specifies the method to use for estimating the
        percentile.  There are many different methods, some unique to NumPy.
        See the notes for explanation.  The options sorted by their R type
        as summarized in the H&F paper [1]_ are:

        1. 'inverted_cdf'
        2. 'averaged_inverted_cdf'
        3. 'closest_observation'
        4. 'interpolated_inverted_cdf'
        5. 'hazen'
        6. 'weibull'
        7. 'linear'  (default)
        8. 'median_unbiased'
        9. 'normal_unbiased'

        The first three methods are discontinuous.  NumPy further defines the
        following discontinuous variations of the default 'linear' (7.) option:

        * 'lower'
        * 'higher',
        * 'midpoint'
        * 'nearest'

        .. versionchanged:: 1.22.0
            This argument was previously called "interpolation" and only
            offered the "linear" default and last four options.

    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left in
        the result as dimensions with size one. With this option, the
        result will broadcast correctly against the original array `a`.

        .. versionadded:: 1.9.0

     weights : array_like, optional
        An array of weights associated with the values in `a`. Each value in
        `a` contributes to the percentile according to its associated weight.
        The weights array can either be 1-D (in which case its length must be
        the size of `a` along the given axis) or of the same shape as `a`.
        If `weights=None`, then all data in `a` are assumed to have a
        weight equal to one.
        Only `method="inverted_cdf"` supports weights.
        See the notes for more details.

        .. versionadded:: 2.0.0

    interpolation : str, optional
        Deprecated name for the method keyword argument.

        .. deprecated:: 1.22.0

    Returns
    -------
    percentile : scalar or ndarray
        If `q` is a single percentile and `axis=None`, then the result
        is a scalar. If multiple percentiles are given, first axis of
        the result corresponds to the percentiles. The other axes are
        the axes that remain after the reduction of `a`. If the input
        contains integers or floats smaller than ``float64``, the output
        data-type is ``float64``. Otherwise, the output data-type is the
        same as that of the input. If `out` is specified, that array is
        returned instead.

    See Also
    --------
    mean
    median : equivalent to ``percentile(..., 50)``
    nanpercentile
    quantile : equivalent to percentile, except q in the range [0, 1].

    Notes
    -----
    The behavior of `numpy.percentile` with percentage `q` is
    that of `numpy.quantile` with argument ``q/100``.
    For more information, please see `numpy.quantile`.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[10, 7, 4], [3, 2, 1]])
    >>> a
    array([[10,  7,  4],
           [ 3,  2,  1]])
    >>> np.percentile(a, 50)
    3.5
    >>> np.percentile(a, 50, axis=0)
    array([6.5, 4.5, 2.5])
    >>> np.percentile(a, 50, axis=1)
    array([7.,  2.])
    >>> np.percentile(a, 50, axis=1, keepdims=True)
    array([[7.],
           [2.]])

    >>> m = np.percentile(a, 50, axis=0)
    >>> out = np.zeros_like(m)
    >>> np.percentile(a, 50, axis=0, out=out)
    array([6.5, 4.5, 2.5])
    >>> m
    array([6.5, 4.5, 2.5])

    >>> b = a.copy()
    >>> np.percentile(b, 50, axis=1, overwrite_input=True)
    array([7.,  2.])
    >>> assert not np.all(a == b)

    The different methods can be visualized graphically:

    .. plot::

        import matplotlib.pyplot as plt

        a = np.arange(4)
        p = np.linspace(0, 100, 6001)
        ax = plt.gca()
        lines = [
            ('linear', '-', 'C0'),
            ('inverted_cdf', ':', 'C1'),
            # Almost the same as `inverted_cdf`:
            ('averaged_inverted_cdf', '-.', 'C1'),
            ('closest_observation', ':', 'C2'),
            ('interpolated_inverted_cdf', '--', 'C1'),
            ('hazen', '--', 'C3'),
            ('weibull', '-.', 'C4'),
            ('median_unbiased', '--', 'C5'),
            ('normal_unbiased', '-.', 'C6'),
            ]
        for method, style, color in lines:
            ax.plot(
                p, np.percentile(a, p, method=method),
                label=method, linestyle=style, color=color)
        ax.set(
            title='Percentiles for different methods and data: ' + str(a),
            xlabel='Percentile',
            ylabel='Estimated percentile value',
            yticks=a)
        ax.legend(bbox_to_anchor=(1.03, 1))
        plt.tight_layout()
        plt.show()

    References
    ----------
    .. [1] R. J. Hyndman and Y. Fan,
       "Sample quantiles in statistical packages,"
       The American Statistician, 50(4), pp. 361-365, 1996

Python Library Documentation: function transpose in module autograd.tracer

transpose(*args, called_by_autograd_dispatcher=False, **kwargs)
    Returns an array with axes transposed.

    For a 1-D array, this returns an unchanged view of the original array, as a
    transposed vector is simply the same vector.
    To convert a 1-D array into a 2-D column vector, an additional dimension
    must be added, e.g., ``np.atleast_2d(a).T`` achieves this, as does
    ``a[:, np.newaxis]``.
    For a 2-D array, this is the standard matrix transpose.
    For an n-D array, if axes are given, their order indicates how the
    axes are permuted (see Examples). If axes are not provided, then
    ``transpose(a).shape == a.shape[::-1]``.

    Parameters
    ----------
    a : array_like
        Input array.
    axes : tuple or list of ints, optional
        If specified, it must be a tuple or list which contains a permutation
        of [0,1,...,N-1] where N is the number of axes of `a`. The `i`'th axis
        of the returned array will correspond to the axis numbered ``axes[i]``
        of the input. If not specified, defaults to ``range(a.ndim)[::-1]``,
        which reverses the order of the axes.

    Returns
    -------
    p : ndarray
        `a` with its axes permuted. A view is returned whenever possible.

    See Also
    --------
    ndarray.transpose : Equivalent method.
    moveaxis : Move axes of an array to new positions.
    argsort : Return the indices that would sort an array.

    Notes
    -----
    Use ``transpose(a, argsort(axes))`` to invert the transposition of tensors
    when using the `axes` keyword argument.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[1, 2], [3, 4]])
    >>> a
    array([[1, 2],
           [3, 4]])
    >>> np.transpose(a)
    array([[1, 3],
           [2, 4]])

    >>> a = np.array([1, 2, 3, 4])
    >>> a
    array([1, 2, 3, 4])
    >>> np.transpose(a)
    array([1, 2, 3, 4])

    >>> a = np.ones((1, 2, 3))
    >>> np.transpose(a, (1, 0, 2)).shape
    (2, 1, 3)

    >>> a = np.ones((2, 3, 4, 5))
    >>> np.transpose(a).shape
    (5, 4, 3, 2)

Python Library Documentation: float object

class float(object)
 |  float(x=0, /)
 |
 |  Convert a string or number to a floating-point number, if possible.
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __ceil__(self, /)
 |      Return the ceiling as an Integral.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floor__(self, /)
 |      Return the floor as an Integral.
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(self, format_spec, /)
 |      Formats the float according to format_spec.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getnewargs__(self, /)
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __round__(self, ndigits=None, /)
 |      Return the Integral closest to x, rounding half toward even.
 |
 |      When an argument is passed, work like built-in round(x, ndigits).
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __trunc__(self, /)
 |      Return the Integral closest to x between 0 and x.
 |
 |  as_integer_ratio(self, /)
 |      Return a pair of integers, whose ratio is exactly equal to the original float.
 |
 |      The ratio is in lowest terms and has a positive denominator.  Raise
 |      OverflowError on infinities and a ValueError on NaNs.
 |
 |      >>> (10.0).as_integer_ratio()
 |      (10, 1)
 |      >>> (0.0).as_integer_ratio()
 |      (0, 1)
 |      >>> (-.25).as_integer_ratio()
 |      (-1, 4)
 |
 |  conjugate(self, /)
 |      Return self, the complex conjugate of any float.
 |
 |  hex(self, /)
 |      Return a hexadecimal representation of a floating-point number.
 |
 |      >>> (-0.1).hex()
 |      '-0x1.999999999999ap-4'
 |      >>> 3.14159.hex()
 |      '0x1.921f9f01b866ep+1'
 |
 |  is_integer(self, /)
 |      Return True if the float is an integer.
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __getformat__(typestr, /)
 |      You probably don't want to use this function.
 |
 |        typestr
 |          Must be 'double' or 'float'.
 |
 |      It exists mainly to be used in Python's test suite.
 |
 |      This function returns whichever of 'unknown', 'IEEE, big-endian' or 'IEEE,
 |      little-endian' best describes the format of floating-point numbers used by the
 |      C type named by typestr.
 |
 |  fromhex(string, /)
 |      Create a floating-point number from a hexadecimal string.
 |
 |      >>> float.fromhex('0x1.ffffp10')
 |      2047.984375
 |      >>> float.fromhex('-0x1p-1074')
 |      -5e-324
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  imag
 |      the imaginary part of a complex number
 |
 |  real
 |      the real part of a complex number

Python Library Documentation: function piecewise in module autograd.tracer

piecewise(*args, called_by_autograd_dispatcher=False, **kwargs)
    Evaluate a piecewise-defined function.

    Given a set of conditions and corresponding functions, evaluate each
    function on the input data wherever its condition is true.

    Parameters
    ----------
    x : ndarray or scalar
        The input domain.
    condlist : list of bool arrays or bool scalars
        Each boolean array corresponds to a function in `funclist`.  Wherever
        `condlist[i]` is True, `funclist[i](x)` is used as the output value.

        Each boolean array in `condlist` selects a piece of `x`,
        and should therefore be of the same shape as `x`.

        The length of `condlist` must correspond to that of `funclist`.
        If one extra function is given, i.e. if
        ``len(funclist) == len(condlist) + 1``, then that extra function
        is the default value, used wherever all conditions are false.
    funclist : list of callables, f(x,*args,**kw), or scalars
        Each function is evaluated over `x` wherever its corresponding
        condition is True.  It should take a 1d array as input and give an 1d
        array or a scalar value as output.  If, instead of a callable,
        a scalar is provided then a constant function (``lambda x: scalar``) is
        assumed.
    args : tuple, optional
        Any further arguments given to `piecewise` are passed to the functions
        upon execution, i.e., if called ``piecewise(..., ..., 1, 'a')``, then
        each function is called as ``f(x, 1, 'a')``.
    kw : dict, optional
        Keyword arguments used in calling `piecewise` are passed to the
        functions upon execution, i.e., if called
        ``piecewise(..., ..., alpha=1)``, then each function is called as
        ``f(x, alpha=1)``.

    Returns
    -------
    out : ndarray
        The output is the same shape and type as x and is found by
        calling the functions in `funclist` on the appropriate portions of `x`,
        as defined by the boolean arrays in `condlist`.  Portions not covered
        by any condition have a default value of 0.


    See Also
    --------
    choose, select, where

    Notes
    -----
    This is similar to choose or select, except that functions are
    evaluated on elements of `x` that satisfy the corresponding condition from
    `condlist`.

    The result is::

            |--
            |funclist[0](x[condlist[0]])
      out = |funclist[1](x[condlist[1]])
            |...
            |funclist[n2](x[condlist[n2]])
            |--

    Examples
    --------
    >>> import numpy as np

    Define the signum function, which is -1 for ``x < 0`` and +1 for ``x >= 0``.

    >>> x = np.linspace(-2.5, 2.5, 6)
    >>> np.piecewise(x, [x < 0, x >= 0], [-1, 1])
    array([-1., -1., -1.,  1.,  1.,  1.])

    Define the absolute value, which is ``-x`` for ``x <0`` and ``x`` for
    ``x >= 0``.

    >>> np.piecewise(x, [x < 0, x >= 0], [lambda x: -x, lambda x: x])
    array([2.5,  1.5,  0.5,  0.5,  1.5,  2.5])

    Apply the same function to a scalar value.

    >>> y = -2
    >>> np.piecewise(y, [y < 0, y >= 0], [lambda x: -x, lambda x: x])
    array(2)

Python Library Documentation: function place in module autograd.tracer

place(*args, called_by_autograd_dispatcher=False, **kwargs)
    Change elements of an array based on conditional and input values.

    Similar to ``np.copyto(arr, vals, where=mask)``, the difference is that
    `place` uses the first N elements of `vals`, where N is the number of
    True values in `mask`, while `copyto` uses the elements where `mask`
    is True.

    Note that `extract` does the exact opposite of `place`.

    Parameters
    ----------
    arr : ndarray
        Array to put data into.
    mask : array_like
        Boolean mask array. Must have the same size as `a`.
    vals : 1-D sequence
        Values to put into `a`. Only the first N elements are used, where
        N is the number of True values in `mask`. If `vals` is smaller
        than N, it will be repeated, and if elements of `a` are to be masked,
        this sequence must be non-empty.

    See Also
    --------
    copyto, put, take, extract

    Examples
    --------
    >>> import numpy as np
    >>> arr = np.arange(6).reshape(2, 3)
    >>> np.place(arr, arr>2, [44, 55])
    >>> arr
    array([[ 0,  1,  2],
           [44, 55, 44]])

Python Library Documentation: function poly in module autograd.tracer

poly(*args, called_by_autograd_dispatcher=False, **kwargs)
    Find the coefficients of a polynomial with the given sequence of roots.

    .. note::
       This forms part of the old polynomial API. Since version 1.4, the
       new polynomial API defined in `numpy.polynomial` is preferred.
       A summary of the differences can be found in the
       :doc:`transition guide </reference/routines.polynomials>`.

    Returns the coefficients of the polynomial whose leading coefficient
    is one for the given sequence of zeros (multiple roots must be included
    in the sequence as many times as their multiplicity; see Examples).
    A square matrix (or array, which will be treated as a matrix) can also
    be given, in which case the coefficients of the characteristic polynomial
    of the matrix are returned.

    Parameters
    ----------
    seq_of_zeros : array_like, shape (N,) or (N, N)
        A sequence of polynomial roots, or a square array or matrix object.

    Returns
    -------
    c : ndarray
        1D array of polynomial coefficients from highest to lowest degree:

        ``c[0] * x**(N) + c[1] * x**(N-1) + ... + c[N-1] * x + c[N]``
        where c[0] always equals 1.

    Raises
    ------
    ValueError
        If input is the wrong shape (the input must be a 1-D or square
        2-D array).

    See Also
    --------
    polyval : Compute polynomial values.
    roots : Return the roots of a polynomial.
    polyfit : Least squares polynomial fit.
    poly1d : A one-dimensional polynomial class.

    Notes
    -----
    Specifying the roots of a polynomial still leaves one degree of
    freedom, typically represented by an undetermined leading
    coefficient. [1]_ In the case of this function, that coefficient -
    the first one in the returned array - is always taken as one. (If
    for some reason you have one other point, the only automatic way
    presently to leverage that information is to use ``polyfit``.)

    The characteristic polynomial, :math:`p_a(t)`, of an `n`-by-`n`
    matrix **A** is given by

    :math:`p_a(t) = \mathrm{det}(t\, \mathbf{I} - \mathbf{A})`,

    where **I** is the `n`-by-`n` identity matrix. [2]_

    References
    ----------
    .. [1] M. Sullivan and M. Sullivan, III, "Algebra and Trigonometry,
       Enhanced With Graphing Utilities," Prentice-Hall, pg. 318, 1996.

    .. [2] G. Strang, "Linear Algebra and Its Applications, 2nd Edition,"
       Academic Press, pg. 182, 1980.

    Examples
    --------
    Given a sequence of a polynomial's zeros:

    >>> import numpy as np

    >>> np.poly((0, 0, 0)) # Multiple root example
    array([1., 0., 0., 0.])

    The line above represents z**3 + 0*z**2 + 0*z + 0.

    >>> np.poly((-1./2, 0, 1./2))
    array([ 1.  ,  0.  , -0.25,  0.  ])

    The line above represents z**3 - z/4

    >>> np.poly((np.random.random(1)[0], 0, np.random.random(1)[0]))
    array([ 1.        , -0.77086955,  0.08618131,  0.        ]) # random

    Given a square array object:

    >>> P = np.array([[0, 1./3], [-1./2, 0]])
    >>> np.poly(P)
    array([1.        , 0.        , 0.16666667])

    Note how in all cases the leading coefficient is always 1.

Python Library Documentation: class poly1d in module numpy

class poly1d(builtins.object)
 |  poly1d(c_or_r, r=False, variable=None)
 |
 |  A one-dimensional polynomial class.
 |
 |  .. note::
 |     This forms part of the old polynomial API. Since version 1.4, the
 |     new polynomial API defined in `numpy.polynomial` is preferred.
 |     A summary of the differences can be found in the
 |     :doc:`transition guide </reference/routines.polynomials>`.
 |
 |  A convenience class, used to encapsulate "natural" operations on
 |  polynomials so that said operations may take on their customary
 |  form in code (see Examples).
 |
 |  Parameters
 |  ----------
 |  c_or_r : array_like
 |      The polynomial's coefficients, in decreasing powers, or if
 |      the value of the second parameter is True, the polynomial's
 |      roots (values where the polynomial evaluates to 0).  For example,
 |      ``poly1d([1, 2, 3])`` returns an object that represents
 |      :math:`x^2 + 2x + 3`, whereas ``poly1d([1, 2, 3], True)`` returns
 |      one that represents :math:`(x-1)(x-2)(x-3) = x^3 - 6x^2 + 11x -6`.
 |  r : bool, optional
 |      If True, `c_or_r` specifies the polynomial's roots; the default
 |      is False.
 |  variable : str, optional
 |      Changes the variable used when printing `p` from `x` to `variable`
 |      (see Examples).
 |
 |  Examples
 |  --------
 |  Construct the polynomial :math:`x^2 + 2x + 3`:
 |
 |  >>> import numpy as np
 |
 |  >>> p = np.poly1d([1, 2, 3])
 |  >>> print(np.poly1d(p))
 |     2
 |  1 x + 2 x + 3
 |
 |  Evaluate the polynomial at :math:`x = 0.5`:
 |
 |  >>> p(0.5)
 |  4.25
 |
 |  Find the roots:
 |
 |  >>> p.r
 |  array([-1.+1.41421356j, -1.-1.41421356j])
 |  >>> p(p.r)
 |  array([ -4.44089210e-16+0.j,  -4.44089210e-16+0.j]) # may vary
 |
 |  These numbers in the previous line represent (0, 0) to machine precision
 |
 |  Show the coefficients:
 |
 |  >>> p.c
 |  array([1, 2, 3])
 |
 |  Display the order (the leading zero-coefficients are removed):
 |
 |  >>> p.order
 |  2
 |
 |  Show the coefficient of the k-th power in the polynomial
 |  (which is equivalent to ``p.c[-(i+1)]``):
 |
 |  >>> p[1]
 |  2
 |
 |  Polynomials can be added, subtracted, multiplied, and divided
 |  (returns quotient and remainder):
 |
 |  >>> p * p
 |  poly1d([ 1,  4, 10, 12,  9])
 |
 |  >>> (p**3 + 4) / p
 |  (poly1d([ 1.,  4., 10., 12.,  9.]), poly1d([4.]))
 |
 |  ``asarray(p)`` gives the coefficient array, so polynomials can be
 |  used in all functions that accept arrays:
 |
 |  >>> p**2 # square of polynomial
 |  poly1d([ 1,  4, 10, 12,  9])
 |
 |  >>> np.square(p) # square of individual coefficients
 |  array([1, 4, 9])
 |
 |  The variable used in the string representation of `p` can be modified,
 |  using the `variable` parameter:
 |
 |  >>> p = np.poly1d([1,2,3], variable='z')
 |  >>> print(p)
 |     2
 |  1 z + 2 z + 3
 |
 |  Construct a polynomial from its roots:
 |
 |  >>> np.poly1d([1, 2], True)
 |  poly1d([ 1., -3.,  2.])
 |
 |  This is the same polynomial as obtained by:
 |
 |  >>> np.poly1d([1, -1]) * np.poly1d([1, -2])
 |  poly1d([ 1, -3,  2])
 |
 |  Methods defined here:
 |
 |  __add__(self, other) from numpy.lib._polynomial_impl.poly1d
 |
 |  __array__(self, t=None, copy=None) from numpy.lib._polynomial_impl.poly1d
 |
 |  __call__(self, val) from numpy.lib._polynomial_impl.poly1d
 |      Call self as a function.
 |
 |  __div__(self, other) from numpy.lib._polynomial_impl.poly1d
 |
 |  __eq__(self, other) from numpy.lib._polynomial_impl.poly1d
 |      Return self==value.
 |
 |  __getitem__(self, val) from numpy.lib._polynomial_impl.poly1d
 |
 |  __init__(self, c_or_r, r=False, variable=None) from numpy.lib._polynomial_impl.poly1d
 |      Initialize self.  See help(type(self)) for accurate signature.
 |
 |  __iter__(self) from numpy.lib._polynomial_impl.poly1d
 |
 |  __len__(self) from numpy.lib._polynomial_impl.poly1d
 |
 |  __mul__(self, other) from numpy.lib._polynomial_impl.poly1d
 |
 |  __ne__(self, other) from numpy.lib._polynomial_impl.poly1d
 |      Return self!=value.
 |
 |  __neg__(self) from numpy.lib._polynomial_impl.poly1d
 |
 |  __pos__(self) from numpy.lib._polynomial_impl.poly1d
 |
 |  __pow__(self, val) from numpy.lib._polynomial_impl.poly1d
 |
 |  __radd__(self, other) from numpy.lib._polynomial_impl.poly1d
 |
 |  __rdiv__(self, other) from numpy.lib._polynomial_impl.poly1d
 |
 |  __repr__(self) from numpy.lib._polynomial_impl.poly1d
 |      Return repr(self).
 |
 |  __rmul__(self, other) from numpy.lib._polynomial_impl.poly1d
 |
 |  __rsub__(self, other) from numpy.lib._polynomial_impl.poly1d
 |
 |  __rtruediv__ = __rdiv__(self, other)
 |
 |  __setitem__(self, key, val) from numpy.lib._polynomial_impl.poly1d
 |
 |  __str__(self) from numpy.lib._polynomial_impl.poly1d
 |      Return str(self).
 |
 |  __sub__(self, other) from numpy.lib._polynomial_impl.poly1d
 |
 |  __truediv__ = __div__(self, other)
 |
 |  deriv(self, m=1) from numpy.lib._polynomial_impl.poly1d
 |      Return a derivative of this polynomial.
 |
 |      Refer to `polyder` for full documentation.
 |
 |      See Also
 |      --------
 |      polyder : equivalent function
 |
 |  integ(self, m=1, k=0) from numpy.lib._polynomial_impl.poly1d
 |      Return an antiderivative (indefinite integral) of this polynomial.
 |
 |      Refer to `polyint` for full documentation.
 |
 |      See Also
 |      --------
 |      polyint : equivalent function
 |
 |  ----------------------------------------------------------------------
 |  Readonly properties defined here:
 |
 |  o
 |      The order or degree of the polynomial
 |
 |  order
 |      The order or degree of the polynomial
 |
 |  r
 |      The roots of the polynomial, where self(x) == 0
 |
 |  roots
 |      The roots of the polynomial, where self(x) == 0
 |
 |  variable
 |      The name of the polynomial variable
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object
 |
 |  c
 |      The polynomial coefficients
 |
 |  coef
 |      The polynomial coefficients
 |
 |  coefficients
 |      The polynomial coefficients
 |
 |  coeffs
 |      The polynomial coefficients
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes defined here:
 |
 |  __hash__ = None

Python Library Documentation: function polyadd in module autograd.tracer

polyadd(*args, called_by_autograd_dispatcher=False, **kwargs)
    Find the sum of two polynomials.

    .. note::
       This forms part of the old polynomial API. Since version 1.4, the
       new polynomial API defined in `numpy.polynomial` is preferred.
       A summary of the differences can be found in the
       :doc:`transition guide </reference/routines.polynomials>`.

    Returns the polynomial resulting from the sum of two input polynomials.
    Each input must be either a poly1d object or a 1D sequence of polynomial
    coefficients, from highest to lowest degree.

    Parameters
    ----------
    a1, a2 : array_like or poly1d object
        Input polynomials.

    Returns
    -------
    out : ndarray or poly1d object
        The sum of the inputs. If either input is a poly1d object, then the
        output is also a poly1d object. Otherwise, it is a 1D array of
        polynomial coefficients from highest to lowest degree.

    See Also
    --------
    poly1d : A one-dimensional polynomial class.
    poly, polyadd, polyder, polydiv, polyfit, polyint, polysub, polyval

    Examples
    --------
    >>> import numpy as np
    >>> np.polyadd([1, 2], [9, 5, 4])
    array([9, 6, 6])

    Using poly1d objects:

    >>> p1 = np.poly1d([1, 2])
    >>> p2 = np.poly1d([9, 5, 4])
    >>> print(p1)
    1 x + 2
    >>> print(p2)
       2
    9 x + 5 x + 4
    >>> print(np.polyadd(p1, p2))
       2
    9 x + 6 x + 6

Python Library Documentation: function polyder in module autograd.tracer

polyder(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the derivative of the specified order of a polynomial.

    .. note::
       This forms part of the old polynomial API. Since version 1.4, the
       new polynomial API defined in `numpy.polynomial` is preferred.
       A summary of the differences can be found in the
       :doc:`transition guide </reference/routines.polynomials>`.

    Parameters
    ----------
    p : poly1d or sequence
        Polynomial to differentiate.
        A sequence is interpreted as polynomial coefficients, see `poly1d`.
    m : int, optional
        Order of differentiation (default: 1)

    Returns
    -------
    der : poly1d
        A new polynomial representing the derivative.

    See Also
    --------
    polyint : Anti-derivative of a polynomial.
    poly1d : Class for one-dimensional polynomials.

    Examples
    --------
    The derivative of the polynomial :math:`x^3 + x^2 + x^1 + 1` is:

    >>> import numpy as np

    >>> p = np.poly1d([1,1,1,1])
    >>> p2 = np.polyder(p)
    >>> p2
    poly1d([3, 2, 1])

    which evaluates to:

    >>> p2(2.)
    17.0

    We can verify this, approximating the derivative with
    ``(f(x + h) - f(x))/h``:

    >>> (p(2. + 0.001) - p(2.)) / 0.001
    17.007000999997857

    The fourth-order derivative of a 3rd-order polynomial is zero:

    >>> np.polyder(p, 2)
    poly1d([6, 2])
    >>> np.polyder(p, 3)
    poly1d([6])
    >>> np.polyder(p, 4)
    poly1d([0])

Python Library Documentation: function polydiv in module autograd.tracer

polydiv(*args, called_by_autograd_dispatcher=False, **kwargs)
    Returns the quotient and remainder of polynomial division.

    .. note::
       This forms part of the old polynomial API. Since version 1.4, the
       new polynomial API defined in `numpy.polynomial` is preferred.
       A summary of the differences can be found in the
       :doc:`transition guide </reference/routines.polynomials>`.

    The input arrays are the coefficients (including any coefficients
    equal to zero) of the "numerator" (dividend) and "denominator"
    (divisor) polynomials, respectively.

    Parameters
    ----------
    u : array_like or poly1d
        Dividend polynomial's coefficients.

    v : array_like or poly1d
        Divisor polynomial's coefficients.

    Returns
    -------
    q : ndarray
        Coefficients, including those equal to zero, of the quotient.
    r : ndarray
        Coefficients, including those equal to zero, of the remainder.

    See Also
    --------
    poly, polyadd, polyder, polydiv, polyfit, polyint, polymul, polysub
    polyval

    Notes
    -----
    Both `u` and `v` must be 0-d or 1-d (ndim = 0 or 1), but `u.ndim` need
    not equal `v.ndim`. In other words, all four possible combinations -
    ``u.ndim = v.ndim = 0``, ``u.ndim = v.ndim = 1``,
    ``u.ndim = 1, v.ndim = 0``, and ``u.ndim = 0, v.ndim = 1`` - work.

    Examples
    --------
    .. math:: \frac{3x^2 + 5x + 2}{2x + 1} = 1.5x + 1.75, remainder 0.25

    >>> import numpy as np
    >>> x = np.array([3.0, 5.0, 2.0])
    >>> y = np.array([2.0, 1.0])
    >>> np.polydiv(x, y)
    (array([1.5 , 1.75]), array([0.25]))

Python Library Documentation: function polyfit in module autograd.tracer

polyfit(*args, called_by_autograd_dispatcher=False, **kwargs)
    Least squares polynomial fit.

    .. note::
       This forms part of the old polynomial API. Since version 1.4, the
       new polynomial API defined in `numpy.polynomial` is preferred.
       A summary of the differences can be found in the
       :doc:`transition guide </reference/routines.polynomials>`.

    Fit a polynomial ``p(x) = p[0] * x**deg + ... + p[deg]`` of degree `deg`
    to points `(x, y)`. Returns a vector of coefficients `p` that minimises
    the squared error in the order `deg`, `deg-1`, ... `0`.

    The `Polynomial.fit <numpy.polynomial.polynomial.Polynomial.fit>` class
    method is recommended for new code as it is more stable numerically. See
    the documentation of the method for more information.

    Parameters
    ----------
    x : array_like, shape (M,)
        x-coordinates of the M sample points ``(x[i], y[i])``.
    y : array_like, shape (M,) or (M, K)
        y-coordinates of the sample points. Several data sets of sample
        points sharing the same x-coordinates can be fitted at once by
        passing in a 2D-array that contains one dataset per column.
    deg : int
        Degree of the fitting polynomial
    rcond : float, optional
        Relative condition number of the fit. Singular values smaller than
        this relative to the largest singular value will be ignored. The
        default value is len(x)*eps, where eps is the relative precision of
        the float type, about 2e-16 in most cases.
    full : bool, optional
        Switch determining nature of return value. When it is False (the
        default) just the coefficients are returned, when True diagnostic
        information from the singular value decomposition is also returned.
    w : array_like, shape (M,), optional
        Weights. If not None, the weight ``w[i]`` applies to the unsquared
        residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are
        chosen so that the errors of the products ``w[i]*y[i]`` all have the
        same variance.  When using inverse-variance weighting, use
        ``w[i] = 1/sigma(y[i])``.  The default value is None.
    cov : bool or str, optional
        If given and not `False`, return not just the estimate but also its
        covariance matrix. By default, the covariance are scaled by
        chi2/dof, where dof = M - (deg + 1), i.e., the weights are presumed
        to be unreliable except in a relative sense and everything is scaled
        such that the reduced chi2 is unity. This scaling is omitted if
        ``cov='unscaled'``, as is relevant for the case that the weights are
        w = 1/sigma, with sigma known to be a reliable estimate of the
        uncertainty.

    Returns
    -------
    p : ndarray, shape (deg + 1,) or (deg + 1, K)
        Polynomial coefficients, highest power first.  If `y` was 2-D, the
        coefficients for `k`-th data set are in ``p[:,k]``.

    residuals, rank, singular_values, rcond
        These values are only returned if ``full == True``

        - residuals -- sum of squared residuals of the least squares fit
        - rank -- the effective rank of the scaled Vandermonde
           coefficient matrix
        - singular_values -- singular values of the scaled Vandermonde
           coefficient matrix
        - rcond -- value of `rcond`.

        For more details, see `numpy.linalg.lstsq`.

    V : ndarray, shape (deg + 1, deg + 1) or (deg + 1, deg + 1, K)
        Present only if ``full == False`` and ``cov == True``.  The covariance
        matrix of the polynomial coefficient estimates.  The diagonal of
        this matrix are the variance estimates for each coefficient.  If y
        is a 2-D array, then the covariance matrix for the `k`-th data set
        are in ``V[:,:,k]``


    Warns
    -----
    RankWarning
        The rank of the coefficient matrix in the least-squares fit is
        deficient. The warning is only raised if ``full == False``.

        The warnings can be turned off by

        >>> import warnings
        >>> warnings.simplefilter('ignore', np.exceptions.RankWarning)

    See Also
    --------
    polyval : Compute polynomial values.
    linalg.lstsq : Computes a least-squares fit.
    scipy.interpolate.UnivariateSpline : Computes spline fits.

    Notes
    -----
    The solution minimizes the squared error

    .. math::
        E = \sum_{j=0}^k |p(x_j) - y_j|^2

    in the equations::

        x[0]**n * p[0] + ... + x[0] * p[n-1] + p[n] = y[0]
        x[1]**n * p[0] + ... + x[1] * p[n-1] + p[n] = y[1]
        ...
        x[k]**n * p[0] + ... + x[k] * p[n-1] + p[n] = y[k]

    The coefficient matrix of the coefficients `p` is a Vandermonde matrix.

    `polyfit` issues a `~exceptions.RankWarning` when the least-squares fit is
    badly conditioned. This implies that the best fit is not well-defined due
    to numerical error. The results may be improved by lowering the polynomial
    degree or by replacing `x` by `x` - `x`.mean(). The `rcond` parameter
    can also be set to a value smaller than its default, but the resulting
    fit may be spurious: including contributions from the small singular
    values can add numerical noise to the result.

    Note that fitting polynomial coefficients is inherently badly conditioned
    when the degree of the polynomial is large or the interval of sample points
    is badly centered. The quality of the fit should always be checked in these
    cases. When polynomial fits are not satisfactory, splines may be a good
    alternative.

    References
    ----------
    .. [1] Wikipedia, "Curve fitting",
           https://en.wikipedia.org/wiki/Curve_fitting
    .. [2] Wikipedia, "Polynomial interpolation",
           https://en.wikipedia.org/wiki/Polynomial_interpolation

    Examples
    --------
    >>> import numpy as np
    >>> import warnings
    >>> x = np.array([0.0, 1.0, 2.0, 3.0,  4.0,  5.0])
    >>> y = np.array([0.0, 0.8, 0.9, 0.1, -0.8, -1.0])
    >>> z = np.polyfit(x, y, 3)
    >>> z
    array([ 0.08703704, -0.81349206,  1.69312169, -0.03968254]) # may vary

    It is convenient to use `poly1d` objects for dealing with polynomials:

    >>> p = np.poly1d(z)
    >>> p(0.5)
    0.6143849206349179 # may vary
    >>> p(3.5)
    -0.34732142857143039 # may vary
    >>> p(10)
    22.579365079365115 # may vary

    High-order polynomials may oscillate wildly:

    >>> with warnings.catch_warnings():
    ...     warnings.simplefilter('ignore', np.exceptions.RankWarning)
    ...     p30 = np.poly1d(np.polyfit(x, y, 30))
    ...
    >>> p30(4)
    -0.80000000000000204 # may vary
    >>> p30(5)
    -0.99999999999999445 # may vary
    >>> p30(4.5)
    -0.10547061179440398 # may vary

    Illustration:

    >>> import matplotlib.pyplot as plt
    >>> xp = np.linspace(-2, 6, 100)
    >>> _ = plt.plot(x, y, '.', xp, p(xp), '-', xp, p30(xp), '--')
    >>> plt.ylim(-2,2)
    (-2, 2)
    >>> plt.show()

Python Library Documentation: function polyint in module autograd.tracer

polyint(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return an antiderivative (indefinite integral) of a polynomial.

    .. note::
       This forms part of the old polynomial API. Since version 1.4, the
       new polynomial API defined in `numpy.polynomial` is preferred.
       A summary of the differences can be found in the
       :doc:`transition guide </reference/routines.polynomials>`.

    The returned order `m` antiderivative `P` of polynomial `p` satisfies
    :math:`\frac{d^m}{dx^m}P(x) = p(x)` and is defined up to `m - 1`
    integration constants `k`. The constants determine the low-order
    polynomial part

    .. math:: \frac{k_{m-1}}{0!} x^0 + \ldots + \frac{k_0}{(m-1)!}x^{m-1}

    of `P` so that :math:`P^{(j)}(0) = k_{m-j-1}`.

    Parameters
    ----------
    p : array_like or poly1d
        Polynomial to integrate.
        A sequence is interpreted as polynomial coefficients, see `poly1d`.
    m : int, optional
        Order of the antiderivative. (Default: 1)
    k : list of `m` scalars or scalar, optional
        Integration constants. They are given in the order of integration:
        those corresponding to highest-order terms come first.

        If ``None`` (default), all constants are assumed to be zero.
        If `m = 1`, a single scalar can be given instead of a list.

    See Also
    --------
    polyder : derivative of a polynomial
    poly1d.integ : equivalent method

    Examples
    --------
    The defining property of the antiderivative:

    >>> import numpy as np

    >>> p = np.poly1d([1,1,1])
    >>> P = np.polyint(p)
    >>> P
     poly1d([ 0.33333333,  0.5       ,  1.        ,  0.        ]) # may vary
    >>> np.polyder(P) == p
    True

    The integration constants default to zero, but can be specified:

    >>> P = np.polyint(p, 3)
    >>> P(0)
    0.0
    >>> np.polyder(P)(0)
    0.0
    >>> np.polyder(P, 2)(0)
    0.0
    >>> P = np.polyint(p, 3, k=[6,5,3])
    >>> P
    poly1d([ 0.01666667,  0.04166667,  0.16666667,  3. ,  5. ,  3. ]) # may vary

    Note that 3 = 6 / 2!, and that the constants are given in the order of
    integrations. Constant of the highest-order polynomial term comes first:

    >>> np.polyder(P, 2)(0)
    6.0
    >>> np.polyder(P, 1)(0)
    5.0
    >>> P(0)
    3.0

Python Library Documentation: function polymul in module autograd.tracer

polymul(*args, called_by_autograd_dispatcher=False, **kwargs)
    Find the product of two polynomials.

    .. note::
       This forms part of the old polynomial API. Since version 1.4, the
       new polynomial API defined in `numpy.polynomial` is preferred.
       A summary of the differences can be found in the
       :doc:`transition guide </reference/routines.polynomials>`.

    Finds the polynomial resulting from the multiplication of the two input
    polynomials. Each input must be either a poly1d object or a 1D sequence
    of polynomial coefficients, from highest to lowest degree.

    Parameters
    ----------
    a1, a2 : array_like or poly1d object
        Input polynomials.

    Returns
    -------
    out : ndarray or poly1d object
        The polynomial resulting from the multiplication of the inputs. If
        either inputs is a poly1d object, then the output is also a poly1d
        object. Otherwise, it is a 1D array of polynomial coefficients from
        highest to lowest degree.

    See Also
    --------
    poly1d : A one-dimensional polynomial class.
    poly, polyadd, polyder, polydiv, polyfit, polyint, polysub, polyval
    convolve : Array convolution. Same output as polymul, but has parameter
               for overlap mode.

    Examples
    --------
    >>> import numpy as np
    >>> np.polymul([1, 2, 3], [9, 5, 1])
    array([ 9, 23, 38, 17,  3])

    Using poly1d objects:

    >>> p1 = np.poly1d([1, 2, 3])
    >>> p2 = np.poly1d([9, 5, 1])
    >>> print(p1)
       2
    1 x + 2 x + 3
    >>> print(p2)
       2
    9 x + 5 x + 1
    >>> print(np.polymul(p1, p2))
       4      3      2
    9 x + 23 x + 38 x + 17 x + 3

Python Library Documentation: function polysub in module autograd.tracer

polysub(*args, called_by_autograd_dispatcher=False, **kwargs)
    Difference (subtraction) of two polynomials.

    .. note::
       This forms part of the old polynomial API. Since version 1.4, the
       new polynomial API defined in `numpy.polynomial` is preferred.
       A summary of the differences can be found in the
       :doc:`transition guide </reference/routines.polynomials>`.

    Given two polynomials `a1` and `a2`, returns ``a1 - a2``.
    `a1` and `a2` can be either array_like sequences of the polynomials'
    coefficients (including coefficients equal to zero), or `poly1d` objects.

    Parameters
    ----------
    a1, a2 : array_like or poly1d
        Minuend and subtrahend polynomials, respectively.

    Returns
    -------
    out : ndarray or poly1d
        Array or `poly1d` object of the difference polynomial's coefficients.

    See Also
    --------
    polyval, polydiv, polymul, polyadd

    Examples
    --------
    .. math:: (2 x^2 + 10 x - 2) - (3 x^2 + 10 x -4) = (-x^2 + 2)

    >>> import numpy as np

    >>> np.polysub([2, 10, -2], [3, 10, -4])
    array([-1,  0,  2])

Python Library Documentation: function polyval in module autograd.tracer

polyval(*args, called_by_autograd_dispatcher=False, **kwargs)
    Evaluate a polynomial at specific values.

    .. note::
       This forms part of the old polynomial API. Since version 1.4, the
       new polynomial API defined in `numpy.polynomial` is preferred.
       A summary of the differences can be found in the
       :doc:`transition guide </reference/routines.polynomials>`.

    If `p` is of length N, this function returns the value::

        p[0]*x**(N-1) + p[1]*x**(N-2) + ... + p[N-2]*x + p[N-1]

    If `x` is a sequence, then ``p(x)`` is returned for each element of ``x``.
    If `x` is another polynomial then the composite polynomial ``p(x(t))``
    is returned.

    Parameters
    ----------
    p : array_like or poly1d object
       1D array of polynomial coefficients (including coefficients equal
       to zero) from highest degree to the constant term, or an
       instance of poly1d.
    x : array_like or poly1d object
       A number, an array of numbers, or an instance of poly1d, at
       which to evaluate `p`.

    Returns
    -------
    values : ndarray or poly1d
       If `x` is a poly1d instance, the result is the composition of the two
       polynomials, i.e., `x` is "substituted" in `p` and the simplified
       result is returned. In addition, the type of `x` - array_like or
       poly1d - governs the type of the output: `x` array_like => `values`
       array_like, `x` a poly1d object => `values` is also.

    See Also
    --------
    poly1d: A polynomial class.

    Notes
    -----
    Horner's scheme [1]_ is used to evaluate the polynomial. Even so,
    for polynomials of high degree the values may be inaccurate due to
    rounding errors. Use carefully.

    If `x` is a subtype of `ndarray` the return value will be of the same type.

    References
    ----------
    .. [1] I. N. Bronshtein, K. A. Semendyayev, and K. A. Hirsch (Eng.
       trans. Ed.), *Handbook of Mathematics*, New York, Van Nostrand
       Reinhold Co., 1985, pg. 720.

    Examples
    --------
    >>> import numpy as np
    >>> np.polyval([3,0,1], 5)  # 3 * 5**2 + 0 * 5**1 + 1
    76
    >>> np.polyval([3,0,1], np.poly1d(5))
    poly1d([76])
    >>> np.polyval(np.poly1d([3,0,1]), 5)
    76
    >>> np.polyval(np.poly1d([3,0,1]), np.poly1d(5))
    poly1d([76])

Python Library Documentation: function positive in module autograd.tracer

positive(*args, called_by_autograd_dispatcher=False, **kwargs)
    positive(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Numerical positive, element-wise.

    .. versionadded:: 1.13.0

    Parameters
    ----------
    x : array_like or scalar
        Input array.

    Returns
    -------
    y : ndarray or scalar
        Returned array or scalar: `y = +x`.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    Equivalent to `x.copy()`, but only defined for types that support
    arithmetic.

    Examples
    --------
    >>> import numpy as np

    >>> x1 = np.array(([1., -1.]))
    >>> np.positive(x1)
    array([ 1., -1.])

    The unary ``+`` operator can be used as a shorthand for ``np.positive`` on
    ndarrays.

    >>> x1 = np.array(([1., -1.]))
    >>> +x1
    array([ 1., -1.])

Python Library Documentation: function power in module autograd.tracer

power(*args, called_by_autograd_dispatcher=False, **kwargs)
    power(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    First array elements raised to powers from second array, element-wise.

    Raise each base in `x1` to the positionally-corresponding power in
    `x2`.  `x1` and `x2` must be broadcastable to the same shape.

    An integer type raised to a negative integer power will raise a
    ``ValueError``.

    Negative values raised to a non-integral value will return ``nan``.
    To get complex results, cast the input to complex, or specify the
    ``dtype`` to be ``complex`` (see the example below).

    Parameters
    ----------
    x1 : array_like
        The bases.
    x2 : array_like
        The exponents.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The bases in `x1` raised to the exponents in `x2`.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    float_power : power function that promotes integers to float

    Examples
    --------
    >>> import numpy as np

    Cube each element in an array.

    >>> x1 = np.arange(6)
    >>> x1
    [0, 1, 2, 3, 4, 5]
    >>> np.power(x1, 3)
    array([  0,   1,   8,  27,  64, 125])

    Raise the bases to different exponents.

    >>> x2 = [1.0, 2.0, 3.0, 3.0, 2.0, 1.0]
    >>> np.power(x1, x2)
    array([  0.,   1.,   8.,  27.,  16.,   5.])

    The effect of broadcasting.

    >>> x2 = np.array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]])
    >>> x2
    array([[1, 2, 3, 3, 2, 1],
           [1, 2, 3, 3, 2, 1]])
    >>> np.power(x1, x2)
    array([[ 0,  1,  8, 27, 16,  5],
           [ 0,  1,  8, 27, 16,  5]])

    The ``**`` operator can be used as a shorthand for ``np.power`` on
    ndarrays.

    >>> x2 = np.array([1, 2, 3, 3, 2, 1])
    >>> x1 = np.arange(6)
    >>> x1 ** x2
    array([ 0,  1,  8, 27, 16,  5])

    Negative values raised to a non-integral value will result in ``nan``
    (and a warning will be generated).

    >>> x3 = np.array([-1.0, -4.0])
    >>> with np.errstate(invalid='ignore'):
    ...     p = np.power(x3, 1.5)
    ...
    >>> p
    array([nan, nan])

    To get complex results, give the argument ``dtype=complex``.

    >>> np.power(x3, 1.5, dtype=complex)
    array([-1.83697020e-16-1.j, -1.46957616e-15-8.j])

Python Library Documentation: function power in module autograd.tracer

power(*args, called_by_autograd_dispatcher=False, **kwargs)
    power(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    First array elements raised to powers from second array, element-wise.

    Raise each base in `x1` to the positionally-corresponding power in
    `x2`.  `x1` and `x2` must be broadcastable to the same shape.

    An integer type raised to a negative integer power will raise a
    ``ValueError``.

    Negative values raised to a non-integral value will return ``nan``.
    To get complex results, cast the input to complex, or specify the
    ``dtype`` to be ``complex`` (see the example below).

    Parameters
    ----------
    x1 : array_like
        The bases.
    x2 : array_like
        The exponents.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The bases in `x1` raised to the exponents in `x2`.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    float_power : power function that promotes integers to float

    Examples
    --------
    >>> import numpy as np

    Cube each element in an array.

    >>> x1 = np.arange(6)
    >>> x1
    [0, 1, 2, 3, 4, 5]
    >>> np.power(x1, 3)
    array([  0,   1,   8,  27,  64, 125])

    Raise the bases to different exponents.

    >>> x2 = [1.0, 2.0, 3.0, 3.0, 2.0, 1.0]
    >>> np.power(x1, x2)
    array([  0.,   1.,   8.,  27.,  16.,   5.])

    The effect of broadcasting.

    >>> x2 = np.array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]])
    >>> x2
    array([[1, 2, 3, 3, 2, 1],
           [1, 2, 3, 3, 2, 1]])
    >>> np.power(x1, x2)
    array([[ 0,  1,  8, 27, 16,  5],
           [ 0,  1,  8, 27, 16,  5]])

    The ``**`` operator can be used as a shorthand for ``np.power`` on
    ndarrays.

    >>> x2 = np.array([1, 2, 3, 3, 2, 1])
    >>> x1 = np.arange(6)
    >>> x1 ** x2
    array([ 0,  1,  8, 27, 16,  5])

    Negative values raised to a non-integral value will result in ``nan``
    (and a warning will be generated).

    >>> x3 = np.array([-1.0, -4.0])
    >>> with np.errstate(invalid='ignore'):
    ...     p = np.power(x3, 1.5)
    ...
    >>> p
    array([nan, nan])

    To get complex results, give the argument ``dtype=complex``.

    >>> np.power(x3, 1.5, dtype=complex)
    array([-1.83697020e-16-1.j, -1.46957616e-15-8.j])

Python Library Documentation: function primitive in module autograd.tracer

primitive(f_raw)
    Wraps a function so that its gradient can be specified and its invocation
    can be recorded. For examples, see the docs.

Python Library Documentation: function printoptions in module autograd.tracer

printoptions(*args, called_by_autograd_dispatcher=False, **kwargs)
    Context manager for setting print options.

    Set print options for the scope of the `with` block, and restore the old
    options at the end. See `set_printoptions` for the full description of
    available options.

    Examples
    --------
    >>> import numpy as np

    >>> from numpy.testing import assert_equal
    >>> with np.printoptions(precision=2):
    ...     np.array([2.0]) / 3
    array([0.67])

    The `as`-clause of the `with`-statement gives the current print options:

    >>> with np.printoptions(precision=2) as opts:
    ...      assert_equal(opts, np.get_printoptions())

    See Also
    --------
    set_printoptions, get_printoptions

Python Library Documentation: function prod in module autograd.tracer

prod(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the product of array elements over a given axis.

    Parameters
    ----------
    a : array_like
        Input data.
    axis : None or int or tuple of ints, optional
        Axis or axes along which a product is performed.  The default,
        axis=None, will calculate the product of all the elements in the
        input array. If axis is negative it counts from the last to the
        first axis.

        .. versionadded:: 1.7.0

        If axis is a tuple of ints, a product is performed on all of the
        axes specified in the tuple instead of a single axis or all the
        axes as before.
    dtype : dtype, optional
        The type of the returned array, as well as of the accumulator in
        which the elements are multiplied.  The dtype of `a` is used by
        default unless `a` has an integer dtype of less precision than the
        default platform integer.  In that case, if `a` is signed then the
        platform integer is used while if `a` is unsigned then an unsigned
        integer of the same precision as the platform integer is used.
    out : ndarray, optional
        Alternative output array in which to place the result. It must have
        the same shape as the expected output, but the type of the output
        values will be cast if necessary.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left in the
        result as dimensions with size one. With this option, the result
        will broadcast correctly against the input array.

        If the default value is passed, then `keepdims` will not be
        passed through to the `prod` method of sub-classes of
        `ndarray`, however any non-default value will be.  If the
        sub-class' method does not implement `keepdims` any
        exceptions will be raised.
    initial : scalar, optional
        The starting value for this product. See `~numpy.ufunc.reduce`
        for details.

        .. versionadded:: 1.15.0

    where : array_like of bool, optional
        Elements to include in the product. See `~numpy.ufunc.reduce`
        for details.

        .. versionadded:: 1.17.0

    Returns
    -------
    product_along_axis : ndarray, see `dtype` parameter above.
        An array shaped as `a` but with the specified axis removed.
        Returns a reference to `out` if specified.

    See Also
    --------
    ndarray.prod : equivalent method
    :ref:`ufuncs-output-type`

    Notes
    -----
    Arithmetic is modular when using integer types, and no error is
    raised on overflow.  That means that, on a 32-bit platform:

    >>> x = np.array([536870910, 536870910, 536870910, 536870910])
    >>> np.prod(x)
    16 # may vary

    The product of an empty array is the neutral element 1:

    >>> np.prod([])
    1.0

    Examples
    --------
    By default, calculate the product of all elements:

    >>> import numpy as np
    >>> np.prod([1.,2.])
    2.0

    Even when the input array is two-dimensional:

    >>> a = np.array([[1., 2.], [3., 4.]])
    >>> np.prod(a)
    24.0

    But we can also specify the axis over which to multiply:

    >>> np.prod(a, axis=1)
    array([  2.,  12.])
    >>> np.prod(a, axis=0)
    array([3., 8.])

    Or select specific elements to include:

    >>> np.prod([1., np.nan, 3.], where=[True, False, True])
    3.0

    If the type of `x` is unsigned, then the output type is
    the unsigned platform integer:

    >>> x = np.array([1, 2, 3], dtype=np.uint8)
    >>> np.prod(x).dtype == np.uint
    True

    If `x` is of a signed integer type, then the output type
    is the default platform integer:

    >>> x = np.array([1, 2, 3], dtype=np.int8)
    >>> np.prod(x).dtype == int
    True

    You can also start the product with a value other than one:

    >>> np.prod([1, 2], initial=5)
    10

Python Library Documentation: function promote_types in module autograd.tracer

promote_types(*args, called_by_autograd_dispatcher=False, **kwargs)
    promote_types(type1, type2)

    Returns the data type with the smallest size and smallest scalar
    kind to which both ``type1`` and ``type2`` may be safely cast.
    The returned data type is always considered "canonical", this mainly
    means that the promoted dtype will always be in native byte order.

    This function is symmetric, but rarely associative.

    Parameters
    ----------
    type1 : dtype or dtype specifier
        First data type.
    type2 : dtype or dtype specifier
        Second data type.

    Returns
    -------
    out : dtype
        The promoted data type.

    Notes
    -----
    Please see `numpy.result_type` for additional information about promotion.

    .. versionadded:: 1.6.0

    Starting in NumPy 1.9, promote_types function now returns a valid string
    length when given an integer or float dtype as one argument and a string
    dtype as another argument. Previously it always returned the input string
    dtype, even if it wasn't long enough to store the max integer/float value
    converted to a string.

    .. versionchanged:: 1.23.0

    NumPy now supports promotion for more structured dtypes.  It will now
    remove unnecessary padding from a structure dtype and promote included
    fields individually.

    See Also
    --------
    result_type, dtype, can_cast

    Examples
    --------
    >>> import numpy as np
    >>> np.promote_types('f4', 'f8')
    dtype('float64')

    >>> np.promote_types('i8', 'f4')
    dtype('float64')

    >>> np.promote_types('>i8', '<c8')
    dtype('complex128')

    >>> np.promote_types('i4', 'S8')
    dtype('S11')

    An example of a non-associative case:

    >>> p = np.promote_types
    >>> p('S', p('i1', 'u1'))
    dtype('S6')
    >>> p(p('S', 'i1'), 'u1')
    dtype('S4')

Python Library Documentation: function ptp in module autograd.tracer

ptp(*args, called_by_autograd_dispatcher=False, **kwargs)
    Range of values (maximum - minimum) along an axis.

    The name of the function comes from the acronym for 'peak to peak'.

    .. warning::
        `ptp` preserves the data type of the array. This means the
        return value for an input of signed integers with n bits
        (e.g. `numpy.int8`, `numpy.int16`, etc) is also a signed integer
        with n bits.  In that case, peak-to-peak values greater than
        ``2**(n-1)-1`` will be returned as negative values. An example
        with a work-around is shown below.

    Parameters
    ----------
    a : array_like
        Input values.
    axis : None or int or tuple of ints, optional
        Axis along which to find the peaks.  By default, flatten the
        array.  `axis` may be negative, in
        which case it counts from the last to the first axis.

        .. versionadded:: 1.15.0

        If this is a tuple of ints, a reduction is performed on multiple
        axes, instead of a single axis or all the axes as before.
    out : array_like
        Alternative output array in which to place the result. It must
        have the same shape and buffer length as the expected output,
        but the type of the output values will be cast if necessary.

    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the input array.

        If the default value is passed, then `keepdims` will not be
        passed through to the `ptp` method of sub-classes of
        `ndarray`, however any non-default value will be.  If the
        sub-class' method does not implement `keepdims` any
        exceptions will be raised.

    Returns
    -------
    ptp : ndarray or scalar
        The range of a given array - `scalar` if array is one-dimensional
        or a new array holding the result along the given axis

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([[4, 9, 2, 10],
    ...               [6, 9, 7, 12]])

    >>> np.ptp(x, axis=1)
    array([8, 6])

    >>> np.ptp(x, axis=0)
    array([2, 0, 5, 2])

    >>> np.ptp(x)
    10

    This example shows that a negative value can be returned when
    the input is an array of signed integers.

    >>> y = np.array([[1, 127],
    ...               [0, 127],
    ...               [-1, 127],
    ...               [-2, 127]], dtype=np.int8)
    >>> np.ptp(y, axis=1)
    array([ 126,  127, -128, -127], dtype=int8)

    A work-around is to use the `view()` method to view the result as
    unsigned integers with the same bit width:

    >>> np.ptp(y, axis=1).view(np.uint8)
    array([126, 127, 128, 129], dtype=uint8)

Python Library Documentation: function put in module autograd.tracer

put(*args, called_by_autograd_dispatcher=False, **kwargs)
    Replaces specified elements of an array with given values.

    The indexing works on the flattened target array. `put` is roughly
    equivalent to:

    ::

        a.flat[ind] = v

    Parameters
    ----------
    a : ndarray
        Target array.
    ind : array_like
        Target indices, interpreted as integers.
    v : array_like
        Values to place in `a` at target indices. If `v` is shorter than
        `ind` it will be repeated as necessary.
    mode : {'raise', 'wrap', 'clip'}, optional
        Specifies how out-of-bounds indices will behave.

        * 'raise' -- raise an error (default)
        * 'wrap' -- wrap around
        * 'clip' -- clip to the range

        'clip' mode means that all indices that are too large are replaced
        by the index that addresses the last element along that axis. Note
        that this disables indexing with negative numbers. In 'raise' mode,
        if an exception occurs the target array may still be modified.

    See Also
    --------
    putmask, place
    put_along_axis : Put elements by matching the array and the index arrays

    Examples
    --------
    >>> import numpy as np
    >>> a = np.arange(5)
    >>> np.put(a, [0, 2], [-44, -55])
    >>> a
    array([-44,   1, -55,   3,   4])

    >>> a = np.arange(5)
    >>> np.put(a, 22, -5, mode='clip')
    >>> a
    array([ 0,  1,  2,  3, -5])

Python Library Documentation: function put_along_axis in module autograd.tracer

put_along_axis(*args, called_by_autograd_dispatcher=False, **kwargs)
    Put values into the destination array by matching 1d index and data slices.

    This iterates over matching 1d slices oriented along the specified axis in
    the index and data arrays, and uses the former to place values into the
    latter. These slices can be different lengths.

    Functions returning an index along an axis, like `argsort` and
    `argpartition`, produce suitable indices for this function.

    .. versionadded:: 1.15.0

    Parameters
    ----------
    arr : ndarray (Ni..., M, Nk...)
        Destination array.
    indices : ndarray (Ni..., J, Nk...)
        Indices to change along each 1d slice of `arr`. This must match the
        dimension of arr, but dimensions in Ni and Nj may be 1 to broadcast
        against `arr`.
    values : array_like (Ni..., J, Nk...)
        values to insert at those indices. Its shape and dimension are
        broadcast to match that of `indices`.
    axis : int
        The axis to take 1d slices along. If axis is None, the destination
        array is treated as if a flattened 1d view had been created of it.

    Notes
    -----
    This is equivalent to (but faster than) the following use of `ndindex` and
    `s_`, which sets each of ``ii`` and ``kk`` to a tuple of indices::

        Ni, M, Nk = a.shape[:axis], a.shape[axis], a.shape[axis+1:]
        J = indices.shape[axis]  # Need not equal M

        for ii in ndindex(Ni):
            for kk in ndindex(Nk):
                a_1d       = a      [ii + s_[:,] + kk]
                indices_1d = indices[ii + s_[:,] + kk]
                values_1d  = values [ii + s_[:,] + kk]
                for j in range(J):
                    a_1d[indices_1d[j]] = values_1d[j]

    Equivalently, eliminating the inner loop, the last two lines would be::

                a_1d[indices_1d] = values_1d

    See Also
    --------
    take_along_axis :
        Take values from the input array by matching 1d index and data slices

    Examples
    --------
    >>> import numpy as np

    For this sample array

    >>> a = np.array([[10, 30, 20], [60, 40, 50]])

    We can replace the maximum values with:

    >>> ai = np.argmax(a, axis=1, keepdims=True)
    >>> ai
    array([[1],
           [0]])
    >>> np.put_along_axis(a, ai, 99, axis=1)
    >>> a
    array([[10, 99, 20],
           [99, 40, 50]])

Python Library Documentation: function putmask in module autograd.tracer

putmask(*args, called_by_autograd_dispatcher=False, **kwargs)
    putmask(a, mask, values)

    Changes elements of an array based on conditional and input values.

    Sets ``a.flat[n] = values[n]`` for each n where ``mask.flat[n]==True``.

    If `values` is not the same size as `a` and `mask` then it will repeat.
    This gives behavior different from ``a[mask] = values``.

    Parameters
    ----------
    a : ndarray
        Target array.
    mask : array_like
        Boolean mask array. It has to be the same shape as `a`.
    values : array_like
        Values to put into `a` where `mask` is True. If `values` is smaller
        than `a` it will be repeated.

    See Also
    --------
    place, put, take, copyto

    Examples
    --------
    >>> import numpy as np
    >>> x = np.arange(6).reshape(2, 3)
    >>> np.putmask(x, x>2, x**2)
    >>> x
    array([[ 0,  1,  2],
           [ 9, 16, 25]])

    If `values` is smaller than `a` it is repeated:

    >>> x = np.arange(5)
    >>> np.putmask(x, x>1, [-33, -44])
    >>> x
    array([  0,   1, -33, -44, -33])

Python Library Documentation: function quantile in module autograd.tracer

quantile(*args, called_by_autograd_dispatcher=False, **kwargs)
    Compute the q-th quantile of the data along the specified axis.

    .. versionadded:: 1.15.0

    Parameters
    ----------
    a : array_like of real numbers
        Input array or object that can be converted to an array.
    q : array_like of float
        Probability or sequence of probabilities of the quantiles to compute.
        Values must be between 0 and 1 inclusive.
    axis : {int, tuple of int, None}, optional
        Axis or axes along which the quantiles are computed. The default is
        to compute the quantile(s) along a flattened version of the array.
    out : ndarray, optional
        Alternative output array in which to place the result. It must have
        the same shape and buffer length as the expected output, but the
        type (of the output) will be cast if necessary.
    overwrite_input : bool, optional
        If True, then allow the input array `a` to be modified by
        intermediate calculations, to save memory. In this case, the
        contents of the input `a` after this function completes is
        undefined.
    method : str, optional
        This parameter specifies the method to use for estimating the
        quantile.  There are many different methods, some unique to NumPy.
        The recommended options, numbered as they appear in [1]_, are:

        1. 'inverted_cdf'
        2. 'averaged_inverted_cdf'
        3. 'closest_observation'
        4. 'interpolated_inverted_cdf'
        5. 'hazen'
        6. 'weibull'
        7. 'linear'  (default)
        8. 'median_unbiased'
        9. 'normal_unbiased'

        The first three methods are discontinuous. For backward compatibility
        with previous versions of NumPy, the following discontinuous variations
        of the default 'linear' (7.) option are available:

        * 'lower'
        * 'higher',
        * 'midpoint'
        * 'nearest'

        See Notes for details.

        .. versionchanged:: 1.22.0
            This argument was previously called "interpolation" and only
            offered the "linear" default and last four options.

    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left in
        the result as dimensions with size one. With this option, the
        result will broadcast correctly against the original array `a`.

    weights : array_like, optional
        An array of weights associated with the values in `a`. Each value in
        `a` contributes to the quantile according to its associated weight.
        The weights array can either be 1-D (in which case its length must be
        the size of `a` along the given axis) or of the same shape as `a`.
        If `weights=None`, then all data in `a` are assumed to have a
        weight equal to one.
        Only `method="inverted_cdf"` supports weights.
        See the notes for more details.

        .. versionadded:: 2.0.0

    interpolation : str, optional
        Deprecated name for the method keyword argument.

        .. deprecated:: 1.22.0

    Returns
    -------
    quantile : scalar or ndarray
        If `q` is a single probability and `axis=None`, then the result
        is a scalar. If multiple probability levels are given, first axis
        of the result corresponds to the quantiles. The other axes are
        the axes that remain after the reduction of `a`. If the input
        contains integers or floats smaller than ``float64``, the output
        data-type is ``float64``. Otherwise, the output data-type is the
        same as that of the input. If `out` is specified, that array is
        returned instead.

    See Also
    --------
    mean
    percentile : equivalent to quantile, but with q in the range [0, 100].
    median : equivalent to ``quantile(..., 0.5)``
    nanquantile

    Notes
    -----
    Given a sample `a` from an underlying distribution, `quantile` provides a
    nonparametric estimate of the inverse cumulative distribution function.

    By default, this is done by interpolating between adjacent elements in
    ``y``, a sorted copy of `a`::

        (1-g)*y[j] + g*y[j+1]

    where the index ``j`` and coefficient ``g`` are the integral and
    fractional components of ``q * (n-1)``, and ``n`` is the number of
    elements in the sample.

    This is a special case of Equation 1 of H&F [1]_. More generally,

    - ``j = (q*n + m - 1) // 1``, and
    - ``g = (q*n + m - 1) % 1``,

    where ``m`` may be defined according to several different conventions.
    The preferred convention may be selected using the ``method`` parameter:

    =============================== =============== ===============
    ``method``                      number in H&F   ``m``
    =============================== =============== ===============
    ``interpolated_inverted_cdf``   4               ``0``
    ``hazen``                       5               ``1/2``
    ``weibull``                     6               ``q``
    ``linear`` (default)            7               ``1 - q``
    ``median_unbiased``             8               ``q/3 + 1/3``
    ``normal_unbiased``             9               ``q/4 + 3/8``
    =============================== =============== ===============

    Note that indices ``j`` and ``j + 1`` are clipped to the range ``0`` to
    ``n - 1`` when the results of the formula would be outside the allowed
    range of non-negative indices. The ``- 1`` in the formulas for ``j`` and
    ``g`` accounts for Python's 0-based indexing.

    The table above includes only the estimators from H&F that are continuous
    functions of probability `q` (estimators 4-9). NumPy also provides the
    three discontinuous estimators from H&F (estimators 1-3), where ``j`` is
    defined as above, ``m`` is defined as follows, and ``g`` is a function
    of the real-valued ``index = q*n + m - 1`` and ``j``.

    1. ``inverted_cdf``: ``m = 0`` and ``g = int(index - j > 0)``
    2. ``averaged_inverted_cdf``: ``m = 0`` and
       ``g = (1 + int(index - j > 0)) / 2``
    3. ``closest_observation``: ``m = -1/2`` and
       ``g = 1 - int((index == j) & (j%2 == 1))``

    For backward compatibility with previous versions of NumPy, `quantile`
    provides four additional discontinuous estimators. Like
    ``method='linear'``, all have ``m = 1 - q`` so that ``j = q*(n-1) // 1``,
    but ``g`` is defined as follows.

    - ``lower``: ``g = 0``
    - ``midpoint``: ``g = 0.5``
    - ``higher``: ``g = 1``
    - ``nearest``: ``g = (q*(n-1) % 1) > 0.5``

    **Weighted quantiles:**
    More formally, the quantile at probability level :math:`q` of a cumulative
    distribution function :math:`F(y)=P(Y \leq y)` with probability measure
    :math:`P` is defined as any number :math:`x` that fulfills the
    *coverage conditions*

    .. math:: P(Y < x) \leq q \quad\text{and}\quad P(Y \leq x) \geq q

    with random variable :math:`Y\sim P`.
    Sample quantiles, the result of `quantile`, provide nonparametric
    estimation of the underlying population counterparts, represented by the
    unknown :math:`F`, given a data vector `a` of length ``n``.

    Some of the estimators above arise when one considers :math:`F` as the
    empirical distribution function of the data, i.e.
    :math:`F(y) = \frac{1}{n} \sum_i 1_{a_i \leq y}`.
    Then, different methods correspond to different choices of :math:`x` that
    fulfill the above coverage conditions. Methods that follow this approach
    are ``inverted_cdf`` and ``averaged_inverted_cdf``.

    For weighted quantiles, the coverage conditions still hold. The
    empirical cumulative distribution is simply replaced by its weighted
    version, i.e.
    :math:`P(Y \leq t) = \frac{1}{\sum_i w_i} \sum_i w_i 1_{x_i \leq t}`.
    Only ``method="inverted_cdf"`` supports weights.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[10, 7, 4], [3, 2, 1]])
    >>> a
    array([[10,  7,  4],
           [ 3,  2,  1]])
    >>> np.quantile(a, 0.5)
    3.5
    >>> np.quantile(a, 0.5, axis=0)
    array([6.5, 4.5, 2.5])
    >>> np.quantile(a, 0.5, axis=1)
    array([7.,  2.])
    >>> np.quantile(a, 0.5, axis=1, keepdims=True)
    array([[7.],
           [2.]])
    >>> m = np.quantile(a, 0.5, axis=0)
    >>> out = np.zeros_like(m)
    >>> np.quantile(a, 0.5, axis=0, out=out)
    array([6.5, 4.5, 2.5])
    >>> m
    array([6.5, 4.5, 2.5])
    >>> b = a.copy()
    >>> np.quantile(b, 0.5, axis=1, overwrite_input=True)
    array([7.,  2.])
    >>> assert not np.all(a == b)

    See also `numpy.percentile` for a visualization of most methods.

    References
    ----------
    .. [1] R. J. Hyndman and Y. Fan,
       "Sample quantiles in statistical packages,"
       The American Statistician, 50(4), pp. 361-365, 1996

Python Library Documentation: r_class in module autograd.numpy.numpy_wrapper object

class r_class(builtins.object)
 |  Methods defined here:
 |
 |  __getitem__(self, args)
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object

Python Library Documentation: class r_class in module autograd.numpy.numpy_wrapper

class r_class(builtins.object)
 |  Methods defined here:
 |
 |  __getitem__(self, args)
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object

Python Library Documentation: function rad2deg in module autograd.tracer

rad2deg(*args, called_by_autograd_dispatcher=False, **kwargs)
    rad2deg(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Convert angles from radians to degrees.

    Parameters
    ----------
    x : array_like
        Angle in radians.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The corresponding angle in degrees.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    deg2rad : Convert angles from degrees to radians.
    unwrap : Remove large jumps in angle by wrapping.

    Notes
    -----
    .. versionadded:: 1.3.0

    rad2deg(x) is ``180 * x / pi``.

    Examples
    --------
    >>> import numpy as np
    >>> np.rad2deg(np.pi/2)
    90.0

Python Library Documentation: function radians in module autograd.tracer

radians(*args, called_by_autograd_dispatcher=False, **kwargs)
    radians(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Convert angles from degrees to radians.

    Parameters
    ----------
    x : array_like
        Input array in degrees.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The corresponding radian values.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    deg2rad : equivalent function

    Examples
    --------
    >>> import numpy as np

    Convert a degree array to radians

    >>> deg = np.arange(12.) * 30.
    >>> np.radians(deg)
    array([ 0.        ,  0.52359878,  1.04719755,  1.57079633,  2.0943951 ,
            2.61799388,  3.14159265,  3.66519143,  4.1887902 ,  4.71238898,
            5.23598776,  5.75958653])

    >>> out = np.zeros((deg.shape))
    >>> ret = np.radians(deg, out)
    >>> ret is out
    True

Python Library Documentation: function ravel in module autograd.tracer

ravel(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return a contiguous flattened array.

    A 1-D array, containing the elements of the input, is returned.  A copy is
    made only if needed.

    As of NumPy 1.10, the returned array will have the same type as the input
    array. (for example, a masked array will be returned for a masked array
    input)

    Parameters
    ----------
    a : array_like
        Input array.  The elements in `a` are read in the order specified by
        `order`, and packed as a 1-D array.
    order : {'C','F', 'A', 'K'}, optional

        The elements of `a` are read using this index order. 'C' means
        to index the elements in row-major, C-style order,
        with the last axis index changing fastest, back to the first
        axis index changing slowest.  'F' means to index the elements
        in column-major, Fortran-style order, with the
        first index changing fastest, and the last index changing
        slowest. Note that the 'C' and 'F' options take no account of
        the memory layout of the underlying array, and only refer to
        the order of axis indexing.  'A' means to read the elements in
        Fortran-like index order if `a` is Fortran *contiguous* in
        memory, C-like order otherwise.  'K' means to read the
        elements in the order they occur in memory, except for
        reversing the data when strides are negative.  By default, 'C'
        index order is used.

    Returns
    -------
    y : array_like
        y is a contiguous 1-D array of the same subtype as `a`,
        with shape ``(a.size,)``.
        Note that matrices are special cased for backward compatibility,
        if `a` is a matrix, then y is a 1-D ndarray.

    See Also
    --------
    ndarray.flat : 1-D iterator over an array.
    ndarray.flatten : 1-D array copy of the elements of an array
                      in row-major order.
    ndarray.reshape : Change the shape of an array without changing its data.

    Notes
    -----
    In row-major, C-style order, in two dimensions, the row index
    varies the slowest, and the column index the quickest.  This can
    be generalized to multiple dimensions, where row-major order
    implies that the index along the first axis varies slowest, and
    the index along the last quickest.  The opposite holds for
    column-major, Fortran-style index ordering.

    When a view is desired in as many cases as possible, ``arr.reshape(-1)``
    may be preferable. However, ``ravel`` supports ``K`` in the optional
    ``order`` argument while ``reshape`` does not.

    Examples
    --------
    It is equivalent to ``reshape(-1, order=order)``.

    >>> import numpy as np
    >>> x = np.array([[1, 2, 3], [4, 5, 6]])
    >>> np.ravel(x)
    array([1, 2, 3, 4, 5, 6])

    >>> x.reshape(-1)
    array([1, 2, 3, 4, 5, 6])

    >>> np.ravel(x, order='F')
    array([1, 4, 2, 5, 3, 6])

    When ``order`` is 'A', it will preserve the array's 'C' or 'F' ordering:

    >>> np.ravel(x.T)
    array([1, 4, 2, 5, 3, 6])
    >>> np.ravel(x.T, order='A')
    array([1, 2, 3, 4, 5, 6])

    When ``order`` is 'K', it will preserve orderings that are neither 'C'
    nor 'F', but won't reverse axes:

    >>> a = np.arange(3)[::-1]; a
    array([2, 1, 0])
    >>> a.ravel(order='C')
    array([2, 1, 0])
    >>> a.ravel(order='K')
    array([2, 1, 0])

    >>> a = np.arange(12).reshape(2,3,2).swapaxes(1,2); a
    array([[[ 0,  2,  4],
            [ 1,  3,  5]],
           [[ 6,  8, 10],
            [ 7,  9, 11]]])
    >>> a.ravel(order='C')
    array([ 0,  2,  4,  1,  3,  5,  6,  8, 10,  7,  9, 11])
    >>> a.ravel(order='K')
    array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11])

Python Library Documentation: function ravel_multi_index in module autograd.tracer

ravel_multi_index(*args, called_by_autograd_dispatcher=False, **kwargs)
    ravel_multi_index(multi_index, dims, mode='raise', order='C')

    Converts a tuple of index arrays into an array of flat
    indices, applying boundary modes to the multi-index.

    Parameters
    ----------
    multi_index : tuple of array_like
        A tuple of integer arrays, one array for each dimension.
    dims : tuple of ints
        The shape of array into which the indices from ``multi_index`` apply.
    mode : {'raise', 'wrap', 'clip'}, optional
        Specifies how out-of-bounds indices are handled.  Can specify
        either one mode or a tuple of modes, one mode per index.

        * 'raise' -- raise an error (default)
        * 'wrap' -- wrap around
        * 'clip' -- clip to the range

        In 'clip' mode, a negative index which would normally
        wrap will clip to 0 instead.
    order : {'C', 'F'}, optional
        Determines whether the multi-index should be viewed as
        indexing in row-major (C-style) or column-major
        (Fortran-style) order.

    Returns
    -------
    raveled_indices : ndarray
        An array of indices into the flattened version of an array
        of dimensions ``dims``.

    See Also
    --------
    unravel_index

    Notes
    -----
    .. versionadded:: 1.6.0

    Examples
    --------
    >>> import numpy as np
    >>> arr = np.array([[3,6,6],[4,5,1]])
    >>> np.ravel_multi_index(arr, (7,6))
    array([22, 41, 37])
    >>> np.ravel_multi_index(arr, (7,6), order='F')
    array([31, 41, 13])
    >>> np.ravel_multi_index(arr, (4,6), mode='clip')
    array([22, 23, 19])
    >>> np.ravel_multi_index(arr, (4,4), mode=('clip','wrap'))
    array([12, 13, 13])

    >>> np.ravel_multi_index((3,1,4,1), (6,7,8,9))
    1621

Python Library Documentation: function real in module autograd.tracer

real(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the real part of the complex argument.

    Parameters
    ----------
    val : array_like
        Input array.

    Returns
    -------
    out : ndarray or scalar
        The real component of the complex argument. If `val` is real, the type
        of `val` is used for the output.  If `val` has complex elements, the
        returned type is float.

    See Also
    --------
    real_if_close, imag, angle

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([1+2j, 3+4j, 5+6j])
    >>> a.real
    array([1.,  3.,  5.])
    >>> a.real = 9
    >>> a
    array([9.+2.j,  9.+4.j,  9.+6.j])
    >>> a.real = np.array([9, 8, 7])
    >>> a
    array([9.+2.j,  8.+4.j,  7.+6.j])
    >>> np.real(1 + 1j)
    1.0

Python Library Documentation: function real_if_close in module autograd.tracer

real_if_close(*args, called_by_autograd_dispatcher=False, **kwargs)
    If input is complex with all imaginary parts close to zero, return
    real parts.

    "Close to zero" is defined as `tol` * (machine epsilon of the type for
    `a`).

    Parameters
    ----------
    a : array_like
        Input array.
    tol : float
        Tolerance in machine epsilons for the complex part of the elements
        in the array. If the tolerance is <=1, then the absolute tolerance
        is used.

    Returns
    -------
    out : ndarray
        If `a` is real, the type of `a` is used for the output.  If `a`
        has complex elements, the returned type is float.

    See Also
    --------
    real, imag, angle

    Notes
    -----
    Machine epsilon varies from machine to machine and between data types
    but Python floats on most platforms have a machine epsilon equal to
    2.2204460492503131e-16.  You can use 'np.finfo(float).eps' to print
    out the machine epsilon for floats.

    Examples
    --------
    >>> import numpy as np
    >>> np.finfo(float).eps
    2.2204460492503131e-16 # may vary

    >>> np.real_if_close([2.1 + 4e-14j, 5.2 + 3e-15j], tol=1000)
    array([2.1, 5.2])
    >>> np.real_if_close([2.1 + 4e-13j, 5.2 + 3e-15j], tol=1000)
    array([2.1+4.e-13j, 5.2 + 3e-15j])

Python Library Documentation: class recarray in module numpy.rec

class recarray(numpy.ndarray)
 |  recarray(shape, dtype=None, buf=None, offset=0, strides=None, formats=None, names=None, titles=None, byteorder=None, aligned=False, order='C')
 |
 |  Construct an ndarray that allows field access using attributes.
 |
 |  Arrays may have a data-types containing fields, analogous
 |  to columns in a spread sheet.  An example is ``[(x, int), (y, float)]``,
 |  where each entry in the array is a pair of ``(int, float)``.  Normally,
 |  these attributes are accessed using dictionary lookups such as ``arr['x']``
 |  and ``arr['y']``.  Record arrays allow the fields to be accessed as members
 |  of the array, using ``arr.x`` and ``arr.y``.
 |
 |  Parameters
 |  ----------
 |  shape : tuple
 |      Shape of output array.
 |  dtype : data-type, optional
 |      The desired data-type.  By default, the data-type is determined
 |      from `formats`, `names`, `titles`, `aligned` and `byteorder`.
 |  formats : list of data-types, optional
 |      A list containing the data-types for the different columns, e.g.
 |      ``['i4', 'f8', 'i4']``.  `formats` does *not* support the new
 |      convention of using types directly, i.e. ``(int, float, int)``.
 |      Note that `formats` must be a list, not a tuple.
 |      Given that `formats` is somewhat limited, we recommend specifying
 |      `dtype` instead.
 |  names : tuple of str, optional
 |      The name of each column, e.g. ``('x', 'y', 'z')``.
 |  buf : buffer, optional
 |      By default, a new array is created of the given shape and data-type.
 |      If `buf` is specified and is an object exposing the buffer interface,
 |      the array will use the memory from the existing buffer.  In this case,
 |      the `offset` and `strides` keywords are available.
 |
 |  Other Parameters
 |  ----------------
 |  titles : tuple of str, optional
 |      Aliases for column names.  For example, if `names` were
 |      ``('x', 'y', 'z')`` and `titles` is
 |      ``('x_coordinate', 'y_coordinate', 'z_coordinate')``, then
 |      ``arr['x']`` is equivalent to both ``arr.x`` and ``arr.x_coordinate``.
 |  byteorder : {'<', '>', '='}, optional
 |      Byte-order for all fields.
 |  aligned : bool, optional
 |      Align the fields in memory as the C-compiler would.
 |  strides : tuple of ints, optional
 |      Buffer (`buf`) is interpreted according to these strides (strides
 |      define how many bytes each array element, row, column, etc.
 |      occupy in memory).
 |  offset : int, optional
 |      Start reading buffer (`buf`) from this offset onwards.
 |  order : {'C', 'F'}, optional
 |      Row-major (C-style) or column-major (Fortran-style) order.
 |
 |  Returns
 |  -------
 |  rec : recarray
 |      Empty array of the given shape and type.
 |
 |  See Also
 |  --------
 |  numpy.rec.fromrecords : Construct a record array from data.
 |  numpy.record : fundamental data-type for `recarray`.
 |  numpy.rec.format_parser : determine data-type from formats, names, titles.
 |
 |  Notes
 |  -----
 |  This constructor can be compared to ``empty``: it creates a new record
 |  array but does not fill it with data.  To create a record array from data,
 |  use one of the following methods:
 |
 |  1. Create a standard ndarray and convert it to a record array,
 |     using ``arr.view(np.recarray)``
 |  2. Use the `buf` keyword.
 |  3. Use `np.rec.fromrecords`.
 |
 |  Examples
 |  --------
 |  Create an array with two fields, ``x`` and ``y``:
 |
 |  >>> import numpy as np
 |  >>> x = np.array([(1.0, 2), (3.0, 4)], dtype=[('x', '<f8'), ('y', '<i8')])
 |  >>> x
 |  array([(1., 2), (3., 4)], dtype=[('x', '<f8'), ('y', '<i8')])
 |
 |  >>> x['x']
 |  array([1., 3.])
 |
 |  View the array as a record array:
 |
 |  >>> x = x.view(np.recarray)
 |
 |  >>> x.x
 |  array([1., 3.])
 |
 |  >>> x.y
 |  array([2, 4])
 |
 |  Create a new, empty record array:
 |
 |  >>> np.recarray((2,),
 |  ... dtype=[('x', int), ('y', float), ('z', int)]) #doctest: +SKIP
 |  rec.array([(-1073741821, 1.2249118382103472e-301, 24547520),
 |         (3471280, 1.2134086255804012e-316, 0)],
 |        dtype=[('x', '<i4'), ('y', '<f8'), ('z', '<i4')])
 |
 |  Method resolution order:
 |      recarray
 |      numpy.ndarray
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __array_finalize__(self, obj) from numpy._core.records.recarray
 |      a.__array_finalize__(obj, /)
 |
 |      Present so subclasses can call super. Does nothing.
 |
 |  __getattribute__(self, attr) from numpy._core.records.recarray
 |      Return getattr(self, name).
 |
 |  __getitem__(self, indx) from numpy._core.records.recarray
 |      Return self[key].
 |
 |  __repr__(self) from numpy._core.records.recarray
 |      Return repr(self).
 |
 |  __setattr__(self, attr, val) from numpy._core.records.recarray
 |      Implement setattr(self, name, value).
 |
 |  field(self, attr, val=None) from numpy._core.records.recarray
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(subtype, shape, dtype=None, buf=None, offset=0, strides=None, formats=None, names=None, titles=None, byteorder=None, aligned=False, order='C') from numpy._core.records.recarray
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.ndarray:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      a.__array__([dtype], *, copy=None)
 |
 |      For ``dtype`` parameter it returns a new reference to self if
 |      ``dtype`` is not given or it matches array's data type.
 |      A new array of provided data type is returned if ``dtype``
 |      is different from the current data type of the array.
 |      For ``copy`` parameter it returns a new reference to self if
 |      ``copy=False`` or ``copy=None`` and copying isn't enforced by ``dtype``
 |      parameter. The method returns a new array for ``copy=True``, regardless of
 |      ``dtype`` parameter.
 |
 |      A more detailed explanation of the ``__array__`` interface
 |      can be found in :ref:`dunder_array.interface`.
 |
 |  __array_function__(...)
 |
 |  __array_namespace__(...)
 |
 |  __array_ufunc__(...)
 |
 |  __array_wrap__(...)
 |      a.__array_wrap__(array[, context], /)
 |
 |      Returns a view of `array` with the same type as self.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __complex__(...)
 |
 |  __contains__(self, key, /)
 |      Return bool(key in self).
 |
 |  __copy__(...)
 |      a.__copy__()
 |
 |      Used if :func:`copy.copy` is called on an array. Returns a copy of the array.
 |
 |      Equivalent to ``a.copy(order='K')``.
 |
 |  __deepcopy__(...)
 |      a.__deepcopy__(memo, /)
 |
 |      Used if :func:`copy.deepcopy` is called on an array.
 |
 |  __delitem__(self, key, /)
 |      Delete self[key].
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __dlpack__(...)
 |      a.__dlpack__(*, stream=None, max_version=None, dl_device=None, copy=None)
 |
 |      DLPack Protocol: Part of the Array API.
 |
 |  __dlpack_device__(...)
 |      a.__dlpack_device__()
 |
 |      DLPack Protocol: Part of the Array API.
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      Default object formatter.
 |
 |      Return str(self) if format_spec is empty. Raise TypeError otherwise.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __iadd__(self, value, /)
 |      Return self+=value.
 |
 |  __iand__(self, value, /)
 |      Return self&=value.
 |
 |  __ifloordiv__(self, value, /)
 |      Return self//=value.
 |
 |  __ilshift__(self, value, /)
 |      Return self<<=value.
 |
 |  __imatmul__(self, value, /)
 |      Return self@=value.
 |
 |  __imod__(self, value, /)
 |      Return self%=value.
 |
 |  __imul__(self, value, /)
 |      Return self*=value.
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __ior__(self, value, /)
 |      Return self|=value.
 |
 |  __ipow__(self, value, /)
 |      Return self**=value.
 |
 |  __irshift__(self, value, /)
 |      Return self>>=value.
 |
 |  __isub__(self, value, /)
 |      Return self-=value.
 |
 |  __iter__(self, /)
 |      Implement iter(self).
 |
 |  __itruediv__(self, value, /)
 |      Return self/=value.
 |
 |  __ixor__(self, value, /)
 |      Return self^=value.
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __matmul__(self, value, /)
 |      Return self@value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      a.__reduce__()
 |
 |      For pickling.
 |
 |  __reduce_ex__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmatmul__(self, value, /)
 |      Return value@self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setitem__(self, key, value, /)
 |      Set self[key] to value.
 |
 |  __setstate__(...)
 |      a.__setstate__(state, /)
 |
 |      For unpickling.
 |
 |      The `state` argument must be a sequence that contains the following
 |      elements:
 |
 |      Parameters
 |      ----------
 |      version : int
 |          optional pickle version. If omitted defaults to 0.
 |      shape : tuple
 |      dtype : data-type
 |      isFortran : bool
 |      rawdata : string or list
 |          a binary string with the data (or a list if 'a' is an object array)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      a.all(axis=None, out=None, keepdims=False, *, where=True)
 |
 |      Returns True if all elements evaluate to True.
 |
 |      Refer to `numpy.all` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.all : equivalent function
 |
 |  any(...)
 |      a.any(axis=None, out=None, keepdims=False, *, where=True)
 |
 |      Returns True if any of the elements of `a` evaluate to True.
 |
 |      Refer to `numpy.any` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.any : equivalent function
 |
 |  argmax(...)
 |      a.argmax(axis=None, out=None, *, keepdims=False)
 |
 |      Return indices of the maximum values along the given axis.
 |
 |      Refer to `numpy.argmax` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.argmax : equivalent function
 |
 |  argmin(...)
 |      a.argmin(axis=None, out=None, *, keepdims=False)
 |
 |      Return indices of the minimum values along the given axis.
 |
 |      Refer to `numpy.argmin` for detailed documentation.
 |
 |      See Also
 |      --------
 |      numpy.argmin : equivalent function
 |
 |  argpartition(...)
 |      a.argpartition(kth, axis=-1, kind='introselect', order=None)
 |
 |      Returns the indices that would partition this array.
 |
 |      Refer to `numpy.argpartition` for full documentation.
 |
 |      .. versionadded:: 1.8.0
 |
 |      See Also
 |      --------
 |      numpy.argpartition : equivalent function
 |
 |  argsort(...)
 |      a.argsort(axis=-1, kind=None, order=None)
 |
 |      Returns the indices that would sort this array.
 |
 |      Refer to `numpy.argsort` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.argsort : equivalent function
 |
 |  astype(...)
 |      a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True)
 |
 |      Copy of the array, cast to a specified type.
 |
 |      Parameters
 |      ----------
 |      dtype : str or dtype
 |          Typecode or data-type to which the array is cast.
 |      order : {'C', 'F', 'A', 'K'}, optional
 |          Controls the memory layout order of the result.
 |          'C' means C order, 'F' means Fortran order, 'A'
 |          means 'F' order if all the arrays are Fortran contiguous,
 |          'C' order otherwise, and 'K' means as close to the
 |          order the array elements appear in memory as possible.
 |          Default is 'K'.
 |      casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
 |          Controls what kind of data casting may occur. Defaults to 'unsafe'
 |          for backwards compatibility.
 |
 |          * 'no' means the data types should not be cast at all.
 |          * 'equiv' means only byte-order changes are allowed.
 |          * 'safe' means only casts which can preserve values are allowed.
 |          * 'same_kind' means only safe casts or casts within a kind,
 |            like float64 to float32, are allowed.
 |          * 'unsafe' means any data conversions may be done.
 |      subok : bool, optional
 |          If True, then sub-classes will be passed-through (default), otherwise
 |          the returned array will be forced to be a base-class array.
 |      copy : bool, optional
 |          By default, astype always returns a newly allocated array. If this
 |          is set to false, and the `dtype`, `order`, and `subok`
 |          requirements are satisfied, the input array is returned instead
 |          of a copy.
 |
 |      Returns
 |      -------
 |      arr_t : ndarray
 |          Unless `copy` is False and the other conditions for returning the input
 |          array are satisfied (see description for `copy` input parameter), `arr_t`
 |          is a new array of the same shape as the input array, with dtype, order
 |          given by `dtype`, `order`.
 |
 |      Notes
 |      -----
 |      .. versionchanged:: 1.17.0
 |         Casting between a simple data type and a structured one is possible only
 |         for "unsafe" casting.  Casting to multiple fields is allowed, but
 |         casting from multiple fields is not.
 |
 |      .. versionchanged:: 1.9.0
 |         Casting from numeric to string types in 'safe' casting mode requires
 |         that the string dtype length is long enough to store the max
 |         integer/float value converted.
 |
 |      Raises
 |      ------
 |      ComplexWarning
 |          When casting from complex to float or int. To avoid this,
 |          one should use ``a.real.astype(t)``.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 2.5])
 |      >>> x
 |      array([1. ,  2. ,  2.5])
 |
 |      >>> x.astype(int)
 |      array([1, 2, 2])
 |
 |  byteswap(...)
 |      a.byteswap(inplace=False)
 |
 |      Swap the bytes of the array elements
 |
 |      Toggle between low-endian and big-endian data representation by
 |      returning a byteswapped array, optionally swapped in-place.
 |      Arrays of byte-strings are not swapped. The real and imaginary
 |      parts of a complex number are swapped individually.
 |
 |      Parameters
 |      ----------
 |      inplace : bool, optional
 |          If ``True``, swap bytes in-place, default is ``False``.
 |
 |      Returns
 |      -------
 |      out : ndarray
 |          The byteswapped array. If `inplace` is ``True``, this is
 |          a view to self.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> A = np.array([1, 256, 8755], dtype=np.int16)
 |      >>> list(map(hex, A))
 |      ['0x1', '0x100', '0x2233']
 |      >>> A.byteswap(inplace=True)
 |      array([  256,     1, 13090], dtype=int16)
 |      >>> list(map(hex, A))
 |      ['0x100', '0x1', '0x3322']
 |
 |      Arrays of byte-strings are not swapped
 |
 |      >>> A = np.array([b'ceg', b'fac'])
 |      >>> A.byteswap()
 |      array([b'ceg', b'fac'], dtype='|S3')
 |
 |      ``A.view(A.dtype.newbyteorder()).byteswap()`` produces an array with
 |      the same values but different representation in memory
 |
 |      >>> A = np.array([1, 2, 3])
 |      >>> A.view(np.uint8)
 |      array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,
 |             0, 0], dtype=uint8)
 |      >>> A.view(A.dtype.newbyteorder()).byteswap(inplace=True)
 |      array([1, 2, 3])
 |      >>> A.view(np.uint8)
 |      array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0,
 |             0, 3], dtype=uint8)
 |
 |  choose(...)
 |      a.choose(choices, out=None, mode='raise')
 |
 |      Use an index array to construct a new array from a set of choices.
 |
 |      Refer to `numpy.choose` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.choose : equivalent function
 |
 |  clip(...)
 |      a.clip(min=None, max=None, out=None, **kwargs)
 |
 |      Return an array whose values are limited to ``[min, max]``.
 |      One of max or min must be given.
 |
 |      Refer to `numpy.clip` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.clip : equivalent function
 |
 |  compress(...)
 |      a.compress(condition, axis=None, out=None)
 |
 |      Return selected slices of this array along given axis.
 |
 |      Refer to `numpy.compress` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.compress : equivalent function
 |
 |  conj(...)
 |      a.conj()
 |
 |      Complex-conjugate all elements.
 |
 |      Refer to `numpy.conjugate` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.conjugate : equivalent function
 |
 |  conjugate(...)
 |      a.conjugate()
 |
 |      Return the complex conjugate, element-wise.
 |
 |      Refer to `numpy.conjugate` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.conjugate : equivalent function
 |
 |  copy(...)
 |      a.copy(order='C')
 |
 |      Return a copy of the array.
 |
 |      Parameters
 |      ----------
 |      order : {'C', 'F', 'A', 'K'}, optional
 |          Controls the memory layout of the copy. 'C' means C-order,
 |          'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
 |          'C' otherwise. 'K' means match the layout of `a` as closely
 |          as possible. (Note that this function and :func:`numpy.copy` are very
 |          similar but have different default values for their order=
 |          arguments, and this function always passes sub-classes through.)
 |
 |      See also
 |      --------
 |      numpy.copy : Similar function with different default behavior
 |      numpy.copyto
 |
 |      Notes
 |      -----
 |      This function is the preferred method for creating an array copy.  The
 |      function :func:`numpy.copy` is similar, but it defaults to using order 'K',
 |      and will not pass sub-classes through by default.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([[1,2,3],[4,5,6]], order='F')
 |
 |      >>> y = x.copy()
 |
 |      >>> x.fill(0)
 |
 |      >>> x
 |      array([[0, 0, 0],
 |             [0, 0, 0]])
 |
 |      >>> y
 |      array([[1, 2, 3],
 |             [4, 5, 6]])
 |
 |      >>> y.flags['C_CONTIGUOUS']
 |      True
 |
 |      For arrays containing Python objects (e.g. dtype=object),
 |      the copy is a shallow one. The new array will contain the
 |      same object which may lead to surprises if that object can
 |      be modified (is mutable):
 |
 |      >>> a = np.array([1, 'm', [2, 3, 4]], dtype=object)
 |      >>> b = a.copy()
 |      >>> b[2][0] = 10
 |      >>> a
 |      array([1, 'm', list([10, 3, 4])], dtype=object)
 |
 |      To ensure all elements within an ``object`` array are copied,
 |      use `copy.deepcopy`:
 |
 |      >>> import copy
 |      >>> a = np.array([1, 'm', [2, 3, 4]], dtype=object)
 |      >>> c = copy.deepcopy(a)
 |      >>> c[2][0] = 10
 |      >>> c
 |      array([1, 'm', list([10, 3, 4])], dtype=object)
 |      >>> a
 |      array([1, 'm', list([2, 3, 4])], dtype=object)
 |
 |  cumprod(...)
 |      a.cumprod(axis=None, dtype=None, out=None)
 |
 |      Return the cumulative product of the elements along the given axis.
 |
 |      Refer to `numpy.cumprod` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.cumprod : equivalent function
 |
 |  cumsum(...)
 |      a.cumsum(axis=None, dtype=None, out=None)
 |
 |      Return the cumulative sum of the elements along the given axis.
 |
 |      Refer to `numpy.cumsum` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.cumsum : equivalent function
 |
 |  diagonal(...)
 |      a.diagonal(offset=0, axis1=0, axis2=1)
 |
 |      Return specified diagonals. In NumPy 1.9 the returned array is a
 |      read-only view instead of a copy as in previous NumPy versions.  In
 |      a future version the read-only restriction will be removed.
 |
 |      Refer to :func:`numpy.diagonal` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.diagonal : equivalent function
 |
 |  dot(...)
 |
 |  dump(...)
 |      a.dump(file)
 |
 |      Dump a pickle of the array to the specified file.
 |      The array can be read back with pickle.load or numpy.load.
 |
 |      Parameters
 |      ----------
 |      file : str or Path
 |          A string naming the dump file.
 |
 |          .. versionchanged:: 1.17.0
 |              `pathlib.Path` objects are now accepted.
 |
 |  dumps(...)
 |      a.dumps()
 |
 |      Returns the pickle of the array as a string.
 |      pickle.loads will convert the string back to an array.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |  fill(...)
 |      a.fill(value)
 |
 |      Fill the array with a scalar value.
 |
 |      Parameters
 |      ----------
 |      value : scalar
 |          All elements of `a` will be assigned this value.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([1, 2])
 |      >>> a.fill(0)
 |      >>> a
 |      array([0, 0])
 |      >>> a = np.empty(2)
 |      >>> a.fill(1)
 |      >>> a
 |      array([1.,  1.])
 |
 |      Fill expects a scalar value and always behaves the same as assigning
 |      to a single array element.  The following is a rare example where this
 |      distinction is important:
 |
 |      >>> a = np.array([None, None], dtype=object)
 |      >>> a[0] = np.array(3)
 |      >>> a
 |      array([array(3), None], dtype=object)
 |      >>> a.fill(np.array(3))
 |      >>> a
 |      array([array(3), array(3)], dtype=object)
 |
 |      Where other forms of assignments will unpack the array being assigned:
 |
 |      >>> a[...] = np.array(3)
 |      >>> a
 |      array([3, 3], dtype=object)
 |
 |  flatten(...)
 |      a.flatten(order='C')
 |
 |      Return a copy of the array collapsed into one dimension.
 |
 |      Parameters
 |      ----------
 |      order : {'C', 'F', 'A', 'K'}, optional
 |          'C' means to flatten in row-major (C-style) order.
 |          'F' means to flatten in column-major (Fortran-
 |          style) order. 'A' means to flatten in column-major
 |          order if `a` is Fortran *contiguous* in memory,
 |          row-major order otherwise. 'K' means to flatten
 |          `a` in the order the elements occur in memory.
 |          The default is 'C'.
 |
 |      Returns
 |      -------
 |      y : ndarray
 |          A copy of the input array, flattened to one dimension.
 |
 |      See Also
 |      --------
 |      ravel : Return a flattened array.
 |      flat : A 1-D flat iterator over the array.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1,2], [3,4]])
 |      >>> a.flatten()
 |      array([1, 2, 3, 4])
 |      >>> a.flatten('F')
 |      array([1, 3, 2, 4])
 |
 |  getfield(...)
 |      a.getfield(dtype, offset=0)
 |
 |      Returns a field of the given array as a certain type.
 |
 |      A field is a view of the array data with a given data-type. The values in
 |      the view are determined by the given type and the offset into the current
 |      array in bytes. The offset needs to be such that the view dtype fits in the
 |      array dtype; for example an array of dtype complex128 has 16-byte elements.
 |      If taking a view with a 32-bit integer (4 bytes), the offset needs to be
 |      between 0 and 12 bytes.
 |
 |      Parameters
 |      ----------
 |      dtype : str or dtype
 |          The data type of the view. The dtype size of the view can not be larger
 |          than that of the array itself.
 |      offset : int
 |          Number of bytes to skip before beginning the element view.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.diag([1.+1.j]*2)
 |      >>> x[1, 1] = 2 + 4.j
 |      >>> x
 |      array([[1.+1.j,  0.+0.j],
 |             [0.+0.j,  2.+4.j]])
 |      >>> x.getfield(np.float64)
 |      array([[1.,  0.],
 |             [0.,  2.]])
 |
 |      By choosing an offset of 8 bytes we can select the complex part of the
 |      array for our view:
 |
 |      >>> x.getfield(np.float64, offset=8)
 |      array([[1.,  0.],
 |             [0.,  4.]])
 |
 |  item(...)
 |      a.item(*args)
 |
 |      Copy an element of an array to a standard Python scalar and return it.
 |
 |      Parameters
 |      ----------
 |      \*args : Arguments (variable number and type)
 |
 |          * none: in this case, the method only works for arrays
 |            with one element (`a.size == 1`), which element is
 |            copied into a standard Python scalar object and returned.
 |
 |          * int_type: this argument is interpreted as a flat index into
 |            the array, specifying which element to copy and return.
 |
 |          * tuple of int_types: functions as does a single int_type argument,
 |            except that the argument is interpreted as an nd-index into the
 |            array.
 |
 |      Returns
 |      -------
 |      z : Standard Python scalar object
 |          A copy of the specified element of the array as a suitable
 |          Python scalar
 |
 |      Notes
 |      -----
 |      When the data type of `a` is longdouble or clongdouble, item() returns
 |      a scalar array object because there is no available Python scalar that
 |      would not lose information. Void arrays return a buffer object for item(),
 |      unless fields are defined, in which case a tuple is returned.
 |
 |      `item` is very similar to a[args], except, instead of an array scalar,
 |      a standard Python scalar is returned. This can be useful for speeding up
 |      access to elements of the array and doing arithmetic on elements of the
 |      array using Python's optimized math.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.random.seed(123)
 |      >>> x = np.random.randint(9, size=(3, 3))
 |      >>> x
 |      array([[2, 2, 6],
 |             [1, 3, 6],
 |             [1, 0, 1]])
 |      >>> x.item(3)
 |      1
 |      >>> x.item(7)
 |      0
 |      >>> x.item((0, 1))
 |      2
 |      >>> x.item((2, 2))
 |      1
 |
 |      For an array with object dtype, elements are returned as-is.
 |
 |      >>> a = np.array([np.int64(1)], dtype=object)
 |      >>> a.item() #return np.int64
 |      np.int64(1)
 |
 |  max(...)
 |      a.max(axis=None, out=None, keepdims=False, initial=<no value>, where=True)
 |
 |      Return the maximum along a given axis.
 |
 |      Refer to `numpy.amax` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.amax : equivalent function
 |
 |  mean(...)
 |      a.mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True)
 |
 |      Returns the average of the array elements along given axis.
 |
 |      Refer to `numpy.mean` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.mean : equivalent function
 |
 |  min(...)
 |      a.min(axis=None, out=None, keepdims=False, initial=<no value>, where=True)
 |
 |      Return the minimum along a given axis.
 |
 |      Refer to `numpy.amin` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.amin : equivalent function
 |
 |  nonzero(...)
 |      a.nonzero()
 |
 |      Return the indices of the elements that are non-zero.
 |
 |      Refer to `numpy.nonzero` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.nonzero : equivalent function
 |
 |  partition(...)
 |      a.partition(kth, axis=-1, kind='introselect', order=None)
 |
 |      Partially sorts the elements in the array in such a way that the value of
 |      the element in k-th position is in the position it would be in a sorted
 |      array. In the output array, all elements smaller than the k-th element
 |      are located to the left of this element and all equal or greater are
 |      located to its right. The ordering of the elements in the two partitions
 |      on the either side of the k-th element in the output array is undefined.
 |
 |      .. versionadded:: 1.8.0
 |
 |      Parameters
 |      ----------
 |      kth : int or sequence of ints
 |          Element index to partition by. The kth element value will be in its
 |          final sorted position and all smaller elements will be moved before it
 |          and all equal or greater elements behind it.
 |          The order of all elements in the partitions is undefined.
 |          If provided with a sequence of kth it will partition all elements
 |          indexed by kth of them into their sorted position at once.
 |
 |          .. deprecated:: 1.22.0
 |              Passing booleans as index is deprecated.
 |      axis : int, optional
 |          Axis along which to sort. Default is -1, which means sort along the
 |          last axis.
 |      kind : {'introselect'}, optional
 |          Selection algorithm. Default is 'introselect'.
 |      order : str or list of str, optional
 |          When `a` is an array with fields defined, this argument specifies
 |          which fields to compare first, second, etc. A single field can
 |          be specified as a string, and not all fields need to be specified,
 |          but unspecified fields will still be used, in the order in which
 |          they come up in the dtype, to break ties.
 |
 |      See Also
 |      --------
 |      numpy.partition : Return a partitioned copy of an array.
 |      argpartition : Indirect partition.
 |      sort : Full sort.
 |
 |      Notes
 |      -----
 |      See ``np.partition`` for notes on the different algorithms.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([3, 4, 2, 1])
 |      >>> a.partition(3)
 |      >>> a
 |      array([2, 1, 3, 4]) # may vary
 |
 |      >>> a.partition((1, 3))
 |      >>> a
 |      array([1, 2, 3, 4])
 |
 |  prod(...)
 |      a.prod(axis=None, dtype=None, out=None, keepdims=False,
 |          initial=1, where=True)
 |
 |      Return the product of the array elements over the given axis
 |
 |      Refer to `numpy.prod` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.prod : equivalent function
 |
 |  put(...)
 |      a.put(indices, values, mode='raise')
 |
 |      Set ``a.flat[n] = values[n]`` for all `n` in indices.
 |
 |      Refer to `numpy.put` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.put : equivalent function
 |
 |  ravel(...)
 |      a.ravel([order])
 |
 |      Return a flattened array.
 |
 |      Refer to `numpy.ravel` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.ravel : equivalent function
 |
 |      ndarray.flat : a flat iterator on the array.
 |
 |  repeat(...)
 |      a.repeat(repeats, axis=None)
 |
 |      Repeat elements of an array.
 |
 |      Refer to `numpy.repeat` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.repeat : equivalent function
 |
 |  reshape(...)
 |      a.reshape(shape, /, *, order='C', copy=None)
 |
 |      Returns an array containing the same data with a new shape.
 |
 |      Refer to `numpy.reshape` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.reshape : equivalent function
 |
 |      Notes
 |      -----
 |      Unlike the free function `numpy.reshape`, this method on `ndarray` allows
 |      the elements of the shape parameter to be passed in as separate arguments.
 |      For example, ``a.reshape(10, 11)`` is equivalent to
 |      ``a.reshape((10, 11))``.
 |
 |  resize(...)
 |      a.resize(new_shape, refcheck=True)
 |
 |      Change shape and size of array in-place.
 |
 |      Parameters
 |      ----------
 |      new_shape : tuple of ints, or `n` ints
 |          Shape of resized array.
 |      refcheck : bool, optional
 |          If False, reference count will not be checked. Default is True.
 |
 |      Returns
 |      -------
 |      None
 |
 |      Raises
 |      ------
 |      ValueError
 |          If `a` does not own its own data or references or views to it exist,
 |          and the data memory must be changed.
 |          PyPy only: will always raise if the data memory must be changed, since
 |          there is no reliable way to determine if references or views to it
 |          exist.
 |
 |      SystemError
 |          If the `order` keyword argument is specified. This behaviour is a
 |          bug in NumPy.
 |
 |      See Also
 |      --------
 |      resize : Return a new array with the specified shape.
 |
 |      Notes
 |      -----
 |      This reallocates space for the data area if necessary.
 |
 |      Only contiguous arrays (data elements consecutive in memory) can be
 |      resized.
 |
 |      The purpose of the reference count check is to make sure you
 |      do not use this array as a buffer for another Python object and then
 |      reallocate the memory. However, reference counts can increase in
 |      other ways so if you are sure that you have not shared the memory
 |      for this array with another Python object, then you may safely set
 |      `refcheck` to False.
 |
 |      Examples
 |      --------
 |      Shrinking an array: array is flattened (in the order that the data are
 |      stored in memory), resized, and reshaped:
 |
 |      >>> import numpy as np
 |
 |      >>> a = np.array([[0, 1], [2, 3]], order='C')
 |      >>> a.resize((2, 1))
 |      >>> a
 |      array([[0],
 |             [1]])
 |
 |      >>> a = np.array([[0, 1], [2, 3]], order='F')
 |      >>> a.resize((2, 1))
 |      >>> a
 |      array([[0],
 |             [2]])
 |
 |      Enlarging an array: as above, but missing entries are filled with zeros:
 |
 |      >>> b = np.array([[0, 1], [2, 3]])
 |      >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple
 |      >>> b
 |      array([[0, 1, 2],
 |             [3, 0, 0]])
 |
 |      Referencing an array prevents resizing...
 |
 |      >>> c = a
 |      >>> a.resize((1, 1))
 |      Traceback (most recent call last):
 |      ...
 |      ValueError: cannot resize an array that references or is referenced ...
 |
 |      Unless `refcheck` is False:
 |
 |      >>> a.resize((1, 1), refcheck=False)
 |      >>> a
 |      array([[0]])
 |      >>> c
 |      array([[0]])
 |
 |  round(...)
 |      a.round(decimals=0, out=None)
 |
 |      Return `a` with each element rounded to the given number of decimals.
 |
 |      Refer to `numpy.around` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.around : equivalent function
 |
 |  searchsorted(...)
 |      a.searchsorted(v, side='left', sorter=None)
 |
 |      Find indices where elements of v should be inserted in a to maintain order.
 |
 |      For full documentation, see `numpy.searchsorted`
 |
 |      See Also
 |      --------
 |      numpy.searchsorted : equivalent function
 |
 |  setfield(...)
 |      a.setfield(val, dtype, offset=0)
 |
 |      Put a value into a specified place in a field defined by a data-type.
 |
 |      Place `val` into `a`'s field defined by `dtype` and beginning `offset`
 |      bytes into the field.
 |
 |      Parameters
 |      ----------
 |      val : object
 |          Value to be placed in field.
 |      dtype : dtype object
 |          Data-type of the field in which to place `val`.
 |      offset : int, optional
 |          The number of bytes into the field at which to place `val`.
 |
 |      Returns
 |      -------
 |      None
 |
 |      See Also
 |      --------
 |      getfield
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.eye(3)
 |      >>> x.getfield(np.float64)
 |      array([[1.,  0.,  0.],
 |             [0.,  1.,  0.],
 |             [0.,  0.,  1.]])
 |      >>> x.setfield(3, np.int32)
 |      >>> x.getfield(np.int32)
 |      array([[3, 3, 3],
 |             [3, 3, 3],
 |             [3, 3, 3]], dtype=int32)
 |      >>> x
 |      array([[1.0e+000, 1.5e-323, 1.5e-323],
 |             [1.5e-323, 1.0e+000, 1.5e-323],
 |             [1.5e-323, 1.5e-323, 1.0e+000]])
 |      >>> x.setfield(np.eye(3), np.int32)
 |      >>> x
 |      array([[1.,  0.,  0.],
 |             [0.,  1.,  0.],
 |             [0.,  0.,  1.]])
 |
 |  setflags(...)
 |      a.setflags(write=None, align=None, uic=None)
 |
 |      Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY,
 |      respectively.
 |
 |      These Boolean-valued flags affect how numpy interprets the memory
 |      area used by `a` (see Notes below). The ALIGNED flag can only
 |      be set to True if the data is actually aligned according to the type.
 |      The WRITEBACKIFCOPY flag can never be set
 |      to True. The flag WRITEABLE can only be set to True if the array owns its
 |      own memory, or the ultimate owner of the memory exposes a writeable buffer
 |      interface, or is a string. (The exception for string is made so that
 |      unpickling can be done without copying memory.)
 |
 |      Parameters
 |      ----------
 |      write : bool, optional
 |          Describes whether or not `a` can be written to.
 |      align : bool, optional
 |          Describes whether or not `a` is aligned properly for its type.
 |      uic : bool, optional
 |          Describes whether or not `a` is a copy of another "base" array.
 |
 |      Notes
 |      -----
 |      Array flags provide information about how the memory area used
 |      for the array is to be interpreted. There are 7 Boolean flags
 |      in use, only three of which can be changed by the user:
 |      WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.
 |
 |      WRITEABLE (W) the data area can be written to;
 |
 |      ALIGNED (A) the data and strides are aligned appropriately for the hardware
 |      (as determined by the compiler);
 |
 |      WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced
 |      by .base). When the C-API function PyArray_ResolveWritebackIfCopy is
 |      called, the base array will be updated with the contents of this array.
 |
 |      All flags can be accessed using the single (upper case) letter as well
 |      as the full name.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> y = np.array([[3, 1, 7],
 |      ...               [2, 0, 0],
 |      ...               [8, 5, 9]])
 |      >>> y
 |      array([[3, 1, 7],
 |             [2, 0, 0],
 |             [8, 5, 9]])
 |      >>> y.flags
 |        C_CONTIGUOUS : True
 |        F_CONTIGUOUS : False
 |        OWNDATA : True
 |        WRITEABLE : True
 |        ALIGNED : True
 |        WRITEBACKIFCOPY : False
 |      >>> y.setflags(write=0, align=0)
 |      >>> y.flags
 |        C_CONTIGUOUS : True
 |        F_CONTIGUOUS : False
 |        OWNDATA : True
 |        WRITEABLE : False
 |        ALIGNED : False
 |        WRITEBACKIFCOPY : False
 |      >>> y.setflags(uic=1)
 |      Traceback (most recent call last):
 |        File "<stdin>", line 1, in <module>
 |      ValueError: cannot set WRITEBACKIFCOPY flag to True
 |
 |  sort(...)
 |      a.sort(axis=-1, kind=None, order=None)
 |
 |      Sort an array in-place. Refer to `numpy.sort` for full documentation.
 |
 |      Parameters
 |      ----------
 |      axis : int, optional
 |          Axis along which to sort. Default is -1, which means sort along the
 |          last axis.
 |      kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
 |          Sorting algorithm. The default is 'quicksort'. Note that both 'stable'
 |          and 'mergesort' use timsort under the covers and, in general, the
 |          actual implementation will vary with datatype. The 'mergesort' option
 |          is retained for backwards compatibility.
 |
 |          .. versionchanged:: 1.15.0
 |             The 'stable' option was added.
 |
 |      order : str or list of str, optional
 |          When `a` is an array with fields defined, this argument specifies
 |          which fields to compare first, second, etc.  A single field can
 |          be specified as a string, and not all fields need be specified,
 |          but unspecified fields will still be used, in the order in which
 |          they come up in the dtype, to break ties.
 |
 |      See Also
 |      --------
 |      numpy.sort : Return a sorted copy of an array.
 |      numpy.argsort : Indirect sort.
 |      numpy.lexsort : Indirect stable sort on multiple keys.
 |      numpy.searchsorted : Find elements in sorted array.
 |      numpy.partition: Partial sort.
 |
 |      Notes
 |      -----
 |      See `numpy.sort` for notes on the different sorting algorithms.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1,4], [3,1]])
 |      >>> a.sort(axis=1)
 |      >>> a
 |      array([[1, 4],
 |             [1, 3]])
 |      >>> a.sort(axis=0)
 |      >>> a
 |      array([[1, 3],
 |             [1, 4]])
 |
 |      Use the `order` keyword to specify a field to use when sorting a
 |      structured array:
 |
 |      >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])
 |      >>> a.sort(order='y')
 |      >>> a
 |      array([(b'c', 1), (b'a', 2)],
 |            dtype=[('x', 'S1'), ('y', '<i8')])
 |
 |  squeeze(...)
 |      a.squeeze(axis=None)
 |
 |      Remove axes of length one from `a`.
 |
 |      Refer to `numpy.squeeze` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.squeeze : equivalent function
 |
 |  std(...)
 |      a.std(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)
 |
 |      Returns the standard deviation of the array elements along given axis.
 |
 |      Refer to `numpy.std` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.std : equivalent function
 |
 |  sum(...)
 |      a.sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)
 |
 |      Return the sum of the array elements over the given axis.
 |
 |      Refer to `numpy.sum` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.sum : equivalent function
 |
 |  swapaxes(...)
 |      a.swapaxes(axis1, axis2)
 |
 |      Return a view of the array with `axis1` and `axis2` interchanged.
 |
 |      Refer to `numpy.swapaxes` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.swapaxes : equivalent function
 |
 |  take(...)
 |      a.take(indices, axis=None, out=None, mode='raise')
 |
 |      Return an array formed from the elements of `a` at the given indices.
 |
 |      Refer to `numpy.take` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.take : equivalent function
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |      a.tobytes(order='C')
 |
 |      Construct Python bytes containing the raw data bytes in the array.
 |
 |      Constructs Python bytes showing a copy of the raw contents of
 |      data memory. The bytes object is produced in C-order by default.
 |      This behavior is controlled by the ``order`` parameter.
 |
 |      .. versionadded:: 1.9.0
 |
 |      Parameters
 |      ----------
 |      order : {'C', 'F', 'A'}, optional
 |          Controls the memory layout of the bytes object. 'C' means C-order,
 |          'F' means F-order, 'A' (short for *Any*) means 'F' if `a` is
 |          Fortran contiguous, 'C' otherwise. Default is 'C'.
 |
 |      Returns
 |      -------
 |      s : bytes
 |          Python bytes exhibiting a copy of `a`'s raw data.
 |
 |      See also
 |      --------
 |      frombuffer
 |          Inverse of this operation, construct a 1-dimensional array from Python
 |          bytes.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([[0, 1], [2, 3]], dtype='<u2')
 |      >>> x.tobytes()
 |      b'\x00\x00\x01\x00\x02\x00\x03\x00'
 |      >>> x.tobytes('C') == x.tobytes()
 |      True
 |      >>> x.tobytes('F')
 |      b'\x00\x00\x02\x00\x01\x00\x03\x00'
 |
 |  tofile(...)
 |      a.tofile(fid, sep="", format="%s")
 |
 |      Write array to a file as text or binary (default).
 |
 |      Data is always written in 'C' order, independent of the order of `a`.
 |      The data produced by this method can be recovered using the function
 |      fromfile().
 |
 |      Parameters
 |      ----------
 |      fid : file or str or Path
 |          An open file object, or a string containing a filename.
 |
 |          .. versionchanged:: 1.17.0
 |              `pathlib.Path` objects are now accepted.
 |
 |      sep : str
 |          Separator between array items for text output.
 |          If "" (empty), a binary file is written, equivalent to
 |          ``file.write(a.tobytes())``.
 |      format : str
 |          Format string for text file output.
 |          Each entry in the array is formatted to text by first converting
 |          it to the closest Python type, and then using "format" % item.
 |
 |      Notes
 |      -----
 |      This is a convenience function for quick storage of array data.
 |      Information on endianness and precision is lost, so this method is not a
 |      good choice for files intended to archive data or transport data between
 |      machines with different endianness. Some of these problems can be overcome
 |      by outputting the data as text files, at the expense of speed and file
 |      size.
 |
 |      When fid is a file object, array contents are directly written to the
 |      file, bypassing the file object's ``write`` method. As a result, tofile
 |      cannot be used with files objects supporting compression (e.g., GzipFile)
 |      or file-like objects that do not support ``fileno()`` (e.g., BytesIO).
 |
 |  tolist(...)
 |      a.tolist()
 |
 |      Return the array as an ``a.ndim``-levels deep nested list of Python scalars.
 |
 |      Return a copy of the array data as a (nested) Python list.
 |      Data items are converted to the nearest compatible builtin Python type, via
 |      the `~numpy.ndarray.item` function.
 |
 |      If ``a.ndim`` is 0, then since the depth of the nested list is 0, it will
 |      not be a list at all, but a simple Python scalar.
 |
 |      Parameters
 |      ----------
 |      none
 |
 |      Returns
 |      -------
 |      y : object, or list of object, or list of list of object, or ...
 |          The possibly nested list of array elements.
 |
 |      Notes
 |      -----
 |      The array may be recreated via ``a = np.array(a.tolist())``, although this
 |      may sometimes lose precision.
 |
 |      Examples
 |      --------
 |      For a 1D array, ``a.tolist()`` is almost the same as ``list(a)``,
 |      except that ``tolist`` changes numpy scalars to Python scalars:
 |
 |      >>> import numpy as np
 |      >>> a = np.uint32([1, 2])
 |      >>> a_list = list(a)
 |      >>> a_list
 |      [1, 2]
 |      >>> type(a_list[0])
 |      <class 'numpy.uint32'>
 |      >>> a_tolist = a.tolist()
 |      >>> a_tolist
 |      [1, 2]
 |      >>> type(a_tolist[0])
 |      <class 'int'>
 |
 |      Additionally, for a 2D array, ``tolist`` applies recursively:
 |
 |      >>> a = np.array([[1, 2], [3, 4]])
 |      >>> list(a)
 |      [array([1, 2]), array([3, 4])]
 |      >>> a.tolist()
 |      [[1, 2], [3, 4]]
 |
 |      The base case for this recursion is a 0D array:
 |
 |      >>> a = np.array(1)
 |      >>> list(a)
 |      Traceback (most recent call last):
 |        ...
 |      TypeError: iteration over a 0-d array
 |      >>> a.tolist()
 |      1
 |
 |  tostring(...)
 |      a.tostring(order='C')
 |
 |      A compatibility alias for `~ndarray.tobytes`, with exactly the same
 |      behavior.
 |
 |      Despite its name, it returns :class:`bytes` not :class:`str`\ s.
 |
 |      .. deprecated:: 1.19.0
 |
 |  trace(...)
 |      a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)
 |
 |      Return the sum along diagonals of the array.
 |
 |      Refer to `numpy.trace` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.trace : equivalent function
 |
 |  transpose(...)
 |      a.transpose(*axes)
 |
 |      Returns a view of the array with axes transposed.
 |
 |      Refer to `numpy.transpose` for full documentation.
 |
 |      Parameters
 |      ----------
 |      axes : None, tuple of ints, or `n` ints
 |
 |       * None or no argument: reverses the order of the axes.
 |
 |       * tuple of ints: `i` in the `j`-th place in the tuple means that the
 |         array's `i`-th axis becomes the transposed array's `j`-th axis.
 |
 |       * `n` ints: same as an n-tuple of the same ints (this form is
 |         intended simply as a "convenience" alternative to the tuple form).
 |
 |      Returns
 |      -------
 |      p : ndarray
 |          View of the array with its axes suitably permuted.
 |
 |      See Also
 |      --------
 |      transpose : Equivalent function.
 |      ndarray.T : Array property returning the array transposed.
 |      ndarray.reshape : Give a new shape to an array without changing its data.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1, 2], [3, 4]])
 |      >>> a
 |      array([[1, 2],
 |             [3, 4]])
 |      >>> a.transpose()
 |      array([[1, 3],
 |             [2, 4]])
 |      >>> a.transpose((1, 0))
 |      array([[1, 3],
 |             [2, 4]])
 |      >>> a.transpose(1, 0)
 |      array([[1, 3],
 |             [2, 4]])
 |
 |      >>> a = np.array([1, 2, 3, 4])
 |      >>> a
 |      array([1, 2, 3, 4])
 |      >>> a.transpose()
 |      array([1, 2, 3, 4])
 |
 |  var(...)
 |      a.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)
 |
 |      Returns the variance of the array elements, along given axis.
 |
 |      Refer to `numpy.var` for full documentation.
 |
 |      See Also
 |      --------
 |      numpy.var : equivalent function
 |
 |  view(...)
 |      a.view([dtype][, type])
 |
 |      New view of array with the same data.
 |
 |      .. note::
 |          Passing None for ``dtype`` is different from omitting the parameter,
 |          since the former invokes ``dtype(None)`` which is an alias for
 |          ``dtype('float64')``.
 |
 |      Parameters
 |      ----------
 |      dtype : data-type or ndarray sub-class, optional
 |          Data-type descriptor of the returned view, e.g., float32 or int16.
 |          Omitting it results in the view having the same data-type as `a`.
 |          This argument can also be specified as an ndarray sub-class, which
 |          then specifies the type of the returned object (this is equivalent to
 |          setting the ``type`` parameter).
 |      type : Python type, optional
 |          Type of the returned view, e.g., ndarray or matrix.  Again, omission
 |          of the parameter results in type preservation.
 |
 |      Notes
 |      -----
 |      ``a.view()`` is used two different ways:
 |
 |      ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view
 |      of the array's memory with a different data-type.  This can cause a
 |      reinterpretation of the bytes of memory.
 |
 |      ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just
 |      returns an instance of `ndarray_subclass` that looks at the same array
 |      (same shape, dtype, etc.)  This does not cause a reinterpretation of the
 |      memory.
 |
 |      For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of
 |      bytes per entry than the previous dtype (for example, converting a regular
 |      array to a structured array), then the last axis of ``a`` must be
 |      contiguous. This axis will be resized in the result.
 |
 |      .. versionchanged:: 1.23.0
 |         Only the last axis needs to be contiguous. Previously, the entire array
 |         had to be C-contiguous.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([(-1, 2)], dtype=[('a', np.int8), ('b', np.int8)])
 |
 |      Viewing array data using a different type and dtype:
 |
 |      >>> nonneg = np.dtype([("a", np.uint8), ("b", np.uint8)])
 |      >>> y = x.view(dtype=nonneg, type=np.recarray)
 |      >>> x["a"]
 |      array([-1], dtype=int8)
 |      >>> y.a
 |      array([255], dtype=uint8)
 |
 |      Creating a view on a structured array so it can be used in calculations
 |
 |      >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])
 |      >>> xv = x.view(dtype=np.int8).reshape(-1,2)
 |      >>> xv
 |      array([[1, 2],
 |             [3, 4]], dtype=int8)
 |      >>> xv.mean(0)
 |      array([2.,  3.])
 |
 |      Making changes to the view changes the underlying array
 |
 |      >>> xv[0,1] = 20
 |      >>> x
 |      array([(1, 20), (3,  4)], dtype=[('a', 'i1'), ('b', 'i1')])
 |
 |      Using a view to convert an array to a recarray:
 |
 |      >>> z = x.view(np.recarray)
 |      >>> z.a
 |      array([1, 3], dtype=int8)
 |
 |      Views share data:
 |
 |      >>> x[0] = (9, 10)
 |      >>> z[0]
 |      np.record((9, 10), dtype=[('a', 'i1'), ('b', 'i1')])
 |
 |      Views that change the dtype size (bytes per entry) should normally be
 |      avoided on arrays defined by slices, transposes, fortran-ordering, etc.:
 |
 |      >>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16)
 |      >>> y = x[:, ::2]
 |      >>> y
 |      array([[1, 3],
 |             [4, 6]], dtype=int16)
 |      >>> y.view(dtype=[('width', np.int16), ('length', np.int16)])
 |      Traceback (most recent call last):
 |          ...
 |      ValueError: To change to a dtype of a different size, the last axis must be contiguous
 |      >>> z = y.copy()
 |      >>> z.view(dtype=[('width', np.int16), ('length', np.int16)])
 |      array([[(1, 3)],
 |             [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])
 |
 |      However, views that change dtype are totally fine for arrays with a
 |      contiguous last axis, even if the rest of the axes are not C-contiguous:
 |
 |      >>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4)
 |      >>> x.transpose(1, 0, 2).view(np.int16)
 |      array([[[ 256,  770],
 |              [3340, 3854]],
 |      <BLANKLINE>
 |             [[1284, 1798],
 |              [4368, 4882]],
 |      <BLANKLINE>
 |             [[2312, 2826],
 |              [5396, 5910]]], dtype=int16)
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from numpy.ndarray:
 |
 |  __class_getitem__(...)
 |      a.__class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.ndarray` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.ndarray` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.ndarray[Any, np.dtype[Any]]
 |      numpy.ndarray[typing.Any, numpy.dtype[typing.Any]]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |      numpy.typing.NDArray : An ndarray alias :term:`generic <generic type>`
 |                          w.r.t. its `dtype.type <numpy.dtype.type>`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.ndarray:
 |
 |  T
 |      View of the transposed array.
 |
 |      Same as ``self.transpose()``.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1, 2], [3, 4]])
 |      >>> a
 |      array([[1, 2],
 |             [3, 4]])
 |      >>> a.T
 |      array([[1, 3],
 |             [2, 4]])
 |
 |      >>> a = np.array([1, 2, 3, 4])
 |      >>> a
 |      array([1, 2, 3, 4])
 |      >>> a.T
 |      array([1, 2, 3, 4])
 |
 |      See Also
 |      --------
 |      transpose
 |
 |  __array_interface__
 |      Array protocol: Python side.
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: C-struct side.
 |
 |  base
 |      Base object if memory is from some other object.
 |
 |      Examples
 |      --------
 |      The base of an array that owns its memory is None:
 |
 |      >>> import numpy as np
 |      >>> x = np.array([1,2,3,4])
 |      >>> x.base is None
 |      True
 |
 |      Slicing creates a view, whose memory is shared with x:
 |
 |      >>> y = x[2:]
 |      >>> y.base is x
 |      True
 |
 |  ctypes
 |      An object to simplify the interaction of the array with the ctypes
 |      module.
 |
 |      This attribute creates an object that makes it easier to use arrays
 |      when calling shared libraries with the ctypes module. The returned
 |      object has, among others, data, shape, and strides attributes (see
 |      Notes below) which themselves return ctypes objects that can be used
 |      as arguments to a shared library.
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      c : Python object
 |          Possessing attributes data, shape, strides, etc.
 |
 |      See Also
 |      --------
 |      numpy.ctypeslib
 |
 |      Notes
 |      -----
 |      Below are the public attributes of this object which were documented
 |      in "Guide to NumPy" (we have omitted undocumented public attributes,
 |      as well as documented private attributes):
 |
 |      .. autoattribute:: numpy._core._internal._ctypes.data
 |          :noindex:
 |
 |      .. autoattribute:: numpy._core._internal._ctypes.shape
 |          :noindex:
 |
 |      .. autoattribute:: numpy._core._internal._ctypes.strides
 |          :noindex:
 |
 |      .. automethod:: numpy._core._internal._ctypes.data_as
 |          :noindex:
 |
 |      .. automethod:: numpy._core._internal._ctypes.shape_as
 |          :noindex:
 |
 |      .. automethod:: numpy._core._internal._ctypes.strides_as
 |          :noindex:
 |
 |      If the ctypes module is not available, then the ctypes attribute
 |      of array objects still returns something useful, but ctypes objects
 |      are not returned and errors may be raised instead. In particular,
 |      the object will still have the ``as_parameter`` attribute which will
 |      return an integer equal to the data attribute.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> import ctypes
 |      >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)
 |      >>> x
 |      array([[0, 1],
 |             [2, 3]], dtype=int32)
 |      >>> x.ctypes.data
 |      31962608 # may vary
 |      >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))
 |      <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary
 |      >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents
 |      c_uint(0)
 |      >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents
 |      c_ulong(4294967296)
 |      >>> x.ctypes.shape
 |      <numpy._core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary
 |      >>> x.ctypes.strides
 |      <numpy._core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary
 |
 |  data
 |      Python buffer object pointing to the start of the array's data.
 |
 |  device
 |
 |  dtype
 |      Data-type of the array's elements.
 |
 |      .. warning::
 |
 |          Setting ``arr.dtype`` is discouraged and may be deprecated in the
 |          future.  Setting will replace the ``dtype`` without modifying the
 |          memory (see also `ndarray.view` and `ndarray.astype`).
 |
 |      Parameters
 |      ----------
 |      None
 |
 |      Returns
 |      -------
 |      d : numpy dtype object
 |
 |      See Also
 |      --------
 |      ndarray.astype : Cast the values contained in the array to a new data-type.
 |      ndarray.view : Create a view of the same data but a different data-type.
 |      numpy.dtype
 |
 |      Examples
 |      --------
 |      >>> x
 |      array([[0, 1],
 |             [2, 3]])
 |      >>> x.dtype
 |      dtype('int32')
 |      >>> type(x.dtype)
 |      <type 'numpy.dtype'>
 |
 |  flags
 |      Information about the memory layout of the array.
 |
 |      Attributes
 |      ----------
 |      C_CONTIGUOUS (C)
 |          The data is in a single, C-style contiguous segment.
 |      F_CONTIGUOUS (F)
 |          The data is in a single, Fortran-style contiguous segment.
 |      OWNDATA (O)
 |          The array owns the memory it uses or borrows it from another object.
 |      WRITEABLE (W)
 |          The data area can be written to.  Setting this to False locks
 |          the data, making it read-only.  A view (slice, etc.) inherits WRITEABLE
 |          from its base array at creation time, but a view of a writeable
 |          array may be subsequently locked while the base array remains writeable.
 |          (The opposite is not true, in that a view of a locked array may not
 |          be made writeable.  However, currently, locking a base object does not
 |          lock any views that already reference it, so under that circumstance it
 |          is possible to alter the contents of a locked array via a previously
 |          created writeable view onto it.)  Attempting to change a non-writeable
 |          array raises a RuntimeError exception.
 |      ALIGNED (A)
 |          The data and all elements are aligned appropriately for the hardware.
 |      WRITEBACKIFCOPY (X)
 |          This array is a copy of some other array. The C-API function
 |          PyArray_ResolveWritebackIfCopy must be called before deallocating
 |          to the base array will be updated with the contents of this array.
 |      FNC
 |          F_CONTIGUOUS and not C_CONTIGUOUS.
 |      FORC
 |          F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).
 |      BEHAVED (B)
 |          ALIGNED and WRITEABLE.
 |      CARRAY (CA)
 |          BEHAVED and C_CONTIGUOUS.
 |      FARRAY (FA)
 |          BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.
 |
 |      Notes
 |      -----
 |      The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``),
 |      or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag
 |      names are only supported in dictionary access.
 |
 |      Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be
 |      changed by the user, via direct assignment to the attribute or dictionary
 |      entry, or by calling `ndarray.setflags`.
 |
 |      The array flags cannot be set arbitrarily:
 |
 |      - WRITEBACKIFCOPY can only be set ``False``.
 |      - ALIGNED can only be set ``True`` if the data is truly aligned.
 |      - WRITEABLE can only be set ``True`` if the array owns its own memory
 |        or the ultimate owner of the memory exposes a writeable buffer
 |        interface or is a string.
 |
 |      Arrays can be both C-style and Fortran-style contiguous simultaneously.
 |      This is clear for 1-dimensional arrays, but can also be true for higher
 |      dimensional arrays.
 |
 |      Even for contiguous arrays a stride for a given dimension
 |      ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1``
 |      or the array has no elements.
 |      It does *not* generally hold that ``self.strides[-1] == self.itemsize``
 |      for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for
 |      Fortran-style contiguous arrays is true.
 |
 |  flat
 |      A 1-D iterator over the array.
 |
 |      This is a `numpy.flatiter` instance, which acts similarly to, but is not
 |      a subclass of, Python's built-in iterator object.
 |
 |      See Also
 |      --------
 |      flatten : Return a copy of the array collapsed into one dimension.
 |
 |      flatiter
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.arange(1, 7).reshape(2, 3)
 |      >>> x
 |      array([[1, 2, 3],
 |             [4, 5, 6]])
 |      >>> x.flat[3]
 |      4
 |      >>> x.T
 |      array([[1, 4],
 |             [2, 5],
 |             [3, 6]])
 |      >>> x.T.flat[3]
 |      5
 |      >>> type(x.flat)
 |      <class 'numpy.flatiter'>
 |
 |      An assignment example:
 |
 |      >>> x.flat = 3; x
 |      array([[3, 3, 3],
 |             [3, 3, 3]])
 |      >>> x.flat[[1,4]] = 1; x
 |      array([[3, 1, 3],
 |             [3, 1, 3]])
 |
 |  imag
 |      The imaginary part of the array.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.sqrt([1+0j, 0+1j])
 |      >>> x.imag
 |      array([ 0.        ,  0.70710678])
 |      >>> x.imag.dtype
 |      dtype('float64')
 |
 |  itemset
 |
 |  itemsize
 |      Length of one array element in bytes.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1,2,3], dtype=np.float64)
 |      >>> x.itemsize
 |      8
 |      >>> x = np.array([1,2,3], dtype=np.complex128)
 |      >>> x.itemsize
 |      16
 |
 |  mT
 |      View of the matrix transposed array.
 |
 |      The matrix transpose is the transpose of the last two dimensions, even
 |      if the array is of higher dimension.
 |
 |      .. versionadded:: 2.0
 |
 |      Raises
 |      ------
 |      ValueError
 |          If the array is of dimension less than 2.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> a = np.array([[1, 2], [3, 4]])
 |      >>> a
 |      array([[1, 2],
 |             [3, 4]])
 |      >>> a.mT
 |      array([[1, 3],
 |             [2, 4]])
 |
 |      >>> a = np.arange(8).reshape((2, 2, 2))
 |      >>> a
 |      array([[[0, 1],
 |              [2, 3]],
 |      <BLANKLINE>
 |             [[4, 5],
 |              [6, 7]]])
 |      >>> a.mT
 |      array([[[0, 2],
 |              [1, 3]],
 |      <BLANKLINE>
 |             [[4, 6],
 |              [5, 7]]])
 |
 |  nbytes
 |      Total bytes consumed by the elements of the array.
 |
 |      Notes
 |      -----
 |      Does not include memory consumed by non-element attributes of the
 |      array object.
 |
 |      See Also
 |      --------
 |      sys.getsizeof
 |          Memory consumed by the object itself without parents in case view.
 |          This does include memory consumed by non-element attributes.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.zeros((3,5,2), dtype=np.complex128)
 |      >>> x.nbytes
 |      480
 |      >>> np.prod(x.shape) * x.itemsize
 |      480
 |
 |  ndim
 |      Number of array dimensions.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 3])
 |      >>> x.ndim
 |      1
 |      >>> y = np.zeros((2, 3, 4))
 |      >>> y.ndim
 |      3
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the array.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.sqrt([1+0j, 0+1j])
 |      >>> x.real
 |      array([ 1.        ,  0.70710678])
 |      >>> x.real.dtype
 |      dtype('float64')
 |
 |      See Also
 |      --------
 |      numpy.real : equivalent function
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |      The shape property is usually used to get the current shape of an array,
 |      but may also be used to reshape the array in-place by assigning a tuple of
 |      array dimensions to it.  As with `numpy.reshape`, one of the new shape
 |      dimensions can be -1, in which case its value is inferred from the size of
 |      the array and the remaining dimensions. Reshaping an array in-place will
 |      fail if a copy is required.
 |
 |      .. warning::
 |
 |          Setting ``arr.shape`` is discouraged and may be deprecated in the
 |          future.  Using `ndarray.reshape` is the preferred approach.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.array([1, 2, 3, 4])
 |      >>> x.shape
 |      (4,)
 |      >>> y = np.zeros((2, 3, 4))
 |      >>> y.shape
 |      (2, 3, 4)
 |      >>> y.shape = (3, 8)
 |      >>> y
 |      array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
 |             [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
 |             [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])
 |      >>> y.shape = (3, 6)
 |      Traceback (most recent call last):
 |        File "<stdin>", line 1, in <module>
 |      ValueError: total size of new array must be unchanged
 |      >>> np.zeros((4,2))[::2].shape = (-1,)
 |      Traceback (most recent call last):
 |        File "<stdin>", line 1, in <module>
 |      AttributeError: Incompatible shape for in-place modification. Use
 |      `.reshape()` to make a copy with the desired shape.
 |
 |      See Also
 |      --------
 |      numpy.shape : Equivalent getter function.
 |      numpy.reshape : Function similar to setting ``shape``.
 |      ndarray.reshape : Method similar to setting ``shape``.
 |
 |  size
 |      Number of elements in the array.
 |
 |      Equal to ``np.prod(a.shape)``, i.e., the product of the array's
 |      dimensions.
 |
 |      Notes
 |      -----
 |      `a.size` returns a standard arbitrary precision Python integer. This
 |      may not be the case with other methods of obtaining the same value
 |      (like the suggested ``np.prod(a.shape)``, which returns an instance
 |      of ``np.int_``), and may be relevant if the value is used further in
 |      calculations that may overflow a fixed size integer type.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> x = np.zeros((3, 5, 2), dtype=np.complex128)
 |      >>> x.size
 |      30
 |      >>> np.prod(x.shape)
 |      30
 |
 |  strides
 |      Tuple of bytes to step in each dimension when traversing an array.
 |
 |      The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a`
 |      is::
 |
 |          offset = sum(np.array(i) * a.strides)
 |
 |      A more detailed explanation of strides can be found in
 |      :ref:`arrays.ndarray`.
 |
 |      .. warning::
 |
 |          Setting ``arr.strides`` is discouraged and may be deprecated in the
 |          future.  `numpy.lib.stride_tricks.as_strided` should be preferred
 |          to create a new view of the same data in a safer way.
 |
 |      Notes
 |      -----
 |      Imagine an array of 32-bit integers (each 4 bytes)::
 |
 |        x = np.array([[0, 1, 2, 3, 4],
 |                      [5, 6, 7, 8, 9]], dtype=np.int32)
 |
 |      This array is stored in memory as 40 bytes, one after the other
 |      (known as a contiguous block of memory).  The strides of an array tell
 |      us how many bytes we have to skip in memory to move to the next position
 |      along a certain axis.  For example, we have to skip 4 bytes (1 value) to
 |      move to the next column, but 20 bytes (5 values) to get to the same
 |      position in the next row.  As such, the strides for the array `x` will be
 |      ``(20, 4)``.
 |
 |      See Also
 |      --------
 |      numpy.lib.stride_tricks.as_strided
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> y = np.reshape(np.arange(2*3*4), (2,3,4))
 |      >>> y
 |      array([[[ 0,  1,  2,  3],
 |              [ 4,  5,  6,  7],
 |              [ 8,  9, 10, 11]],
 |             [[12, 13, 14, 15],
 |              [16, 17, 18, 19],
 |              [20, 21, 22, 23]]])
 |      >>> y.strides
 |      (48, 16, 4)
 |      >>> y[1,1,1]
 |      17
 |      >>> offset=sum(y.strides * np.array((1,1,1)))
 |      >>> offset/y.itemsize
 |      17
 |
 |      >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)
 |      >>> x.strides
 |      (32, 4, 224, 1344)
 |      >>> i = np.array([3,5,2,2])
 |      >>> offset = sum(i * x.strides)
 |      >>> x[3,5,2,2]
 |      813
 |      >>> offset / x.itemsize
 |      813
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes inherited from numpy.ndarray:
 |
 |  __hash__ = None

Python Library Documentation: function reciprocal in module autograd.tracer

reciprocal(*args, called_by_autograd_dispatcher=False, **kwargs)
    reciprocal(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the reciprocal of the argument, element-wise.

    Calculates ``1/x``.

    Parameters
    ----------
    x : array_like
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        Return array.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    .. note::
        This function is not designed to work with integers.

    For integer arguments with absolute value larger than 1 the result is
    always zero because of the way Python handles integer division.  For
    integer zero the result is an overflow.

    Examples
    --------
    >>> import numpy as np
    >>> np.reciprocal(2.)
    0.5
    >>> np.reciprocal([1, 2., 3.33])
    array([ 1.       ,  0.5      ,  0.3003003])

Python Library Documentation: class record in module numpy

class record(void)
 |  A data-type scalar that allows field access as attribute lookup.
 |
 |  Method resolution order:
 |      record
 |      void
 |      flexible
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __getattribute__(self, attr) from numpy._core.records.record
 |      Return getattr(self, name).
 |
 |  __getitem__(self, indx) from numpy._core.records.record
 |      Return self[key].
 |
 |  __repr__(self) from numpy._core.records.record
 |      Return repr(self).
 |
 |  __setattr__(self, attr, val) from numpy._core.records.record
 |      Implement setattr(self, name, value).
 |
 |  __str__(self) from numpy._core.records.record
 |      Return str(self).
 |
 |  pprint(self) from numpy._core.records.record
 |      Pretty-print all fields.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from void:
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __delitem__(self, key, /)
 |      Delete self[key].
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __setitem__(self, key, value, /)
 |      Set self[key] to value.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  ----------------------------------------------------------------------
 |  Static methods inherited from void:
 |
 |  __new__(*args, **kwargs) class method of numpy.void
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from void:
 |
 |  base
 |      base object
 |
 |  dtype
 |      dtype object
 |
 |  flags
 |      integer value of flags
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: function remainder in module autograd.tracer

remainder(*args, called_by_autograd_dispatcher=False, **kwargs)
    remainder(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Returns the element-wise remainder of division.

    Computes the remainder complementary to the `floor_divide` function.  It is
    equivalent to the Python modulus operator ``x1 % x2`` and has the same sign
    as the divisor `x2`. The MATLAB function equivalent to ``np.remainder``
    is ``mod``.

    .. warning::

        This should not be confused with:

        * Python 3.7's `math.remainder` and C's ``remainder``, which
          computes the IEEE remainder, which are the complement to
          ``round(x1 / x2)``.
        * The MATLAB ``rem`` function and or the C ``%`` operator which is the
          complement to ``int(x1 / x2)``.

    Parameters
    ----------
    x1 : array_like
        Dividend array.
    x2 : array_like
        Divisor array.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The element-wise remainder of the quotient ``floor_divide(x1, x2)``.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    floor_divide : Equivalent of Python ``//`` operator.
    divmod : Simultaneous floor division and remainder.
    fmod : Equivalent of the MATLAB ``rem`` function.
    divide, floor

    Notes
    -----
    Returns 0 when `x2` is 0 and both `x1` and `x2` are (arrays of)
    integers.
    ``mod`` is an alias of ``remainder``.

    Examples
    --------
    >>> import numpy as np
    >>> np.remainder([4, 7], [2, 3])
    array([0, 1])
    >>> np.remainder(np.arange(7), 5)
    array([0, 1, 2, 3, 4, 0, 1])

    The ``%`` operator can be used as a shorthand for ``np.remainder`` on
    ndarrays.

    >>> x1 = np.arange(7)
    >>> x1 % 5
    array([0, 1, 2, 3, 4, 0, 1])

Python Library Documentation: function repeat in module autograd.tracer

repeat(*args, called_by_autograd_dispatcher=False, **kwargs)
    Repeat each element of an array after themselves

    Parameters
    ----------
    a : array_like
        Input array.
    repeats : int or array of ints
        The number of repetitions for each element.  `repeats` is broadcasted
        to fit the shape of the given axis.
    axis : int, optional
        The axis along which to repeat values.  By default, use the
        flattened input array, and return a flat output array.

    Returns
    -------
    repeated_array : ndarray
        Output array which has the same shape as `a`, except along
        the given axis.

    See Also
    --------
    tile : Tile an array.
    unique : Find the unique elements of an array.

    Examples
    --------
    >>> import numpy as np
    >>> np.repeat(3, 4)
    array([3, 3, 3, 3])
    >>> x = np.array([[1,2],[3,4]])
    >>> np.repeat(x, 2)
    array([1, 1, 2, 2, 3, 3, 4, 4])
    >>> np.repeat(x, 3, axis=1)
    array([[1, 1, 1, 2, 2, 2],
           [3, 3, 3, 4, 4, 4]])
    >>> np.repeat(x, [1, 2], axis=0)
    array([[1, 2],
           [3, 4],
           [3, 4]])

Python Library Documentation: function require in module autograd.tracer

require(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return an ndarray of the provided type that satisfies requirements.

    This function is useful to be sure that an array with the correct flags
    is returned for passing to compiled code (perhaps through ctypes).

    Parameters
    ----------
    a : array_like
       The object to be converted to a type-and-requirement-satisfying array.
    dtype : data-type
       The required data-type. If None preserve the current dtype. If your
       application requires the data to be in native byteorder, include
       a byteorder specification as a part of the dtype specification.
    requirements : str or sequence of str
       The requirements list can be any of the following

       * 'F_CONTIGUOUS' ('F') - ensure a Fortran-contiguous array
       * 'C_CONTIGUOUS' ('C') - ensure a C-contiguous array
       * 'ALIGNED' ('A')      - ensure a data-type aligned array
       * 'WRITEABLE' ('W')    - ensure a writable array
       * 'OWNDATA' ('O')      - ensure an array that owns its own data
       * 'ENSUREARRAY', ('E') - ensure a base array, instead of a subclass
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    out : ndarray
        Array with specified requirements and type if given.

    See Also
    --------
    asarray : Convert input to an ndarray.
    asanyarray : Convert to an ndarray, but pass through ndarray subclasses.
    ascontiguousarray : Convert input to a contiguous array.
    asfortranarray : Convert input to an ndarray with column-major
                     memory order.
    ndarray.flags : Information about the memory layout of the array.

    Notes
    -----
    The returned array will be guaranteed to have the listed requirements
    by making a copy if needed.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.arange(6).reshape(2,3)
    >>> x.flags
      C_CONTIGUOUS : True
      F_CONTIGUOUS : False
      OWNDATA : False
      WRITEABLE : True
      ALIGNED : True
      WRITEBACKIFCOPY : False

    >>> y = np.require(x, dtype=np.float32, requirements=['A', 'O', 'W', 'F'])
    >>> y.flags
      C_CONTIGUOUS : False
      F_CONTIGUOUS : True
      OWNDATA : True
      WRITEABLE : True
      ALIGNED : True
      WRITEBACKIFCOPY : False

Python Library Documentation: function reshape in module autograd.tracer

reshape(*args, called_by_autograd_dispatcher=False, **kwargs)
    Gives a new shape to an array without changing its data.

    Parameters
    ----------
    a : array_like
        Array to be reshaped.
    shape : int or tuple of ints
        The new shape should be compatible with the original shape. If
        an integer, then the result will be a 1-D array of that length.
        One shape dimension can be -1. In this case, the value is
        inferred from the length of the array and remaining dimensions.
    order : {'C', 'F', 'A'}, optional
        Read the elements of ``a`` using this index order, and place the
        elements into the reshaped array using this index order. 'C'
        means to read / write the elements using C-like index order,
        with the last axis index changing fastest, back to the first
        axis index changing slowest. 'F' means to read / write the
        elements using Fortran-like index order, with the first index
        changing fastest, and the last index changing slowest. Note that
        the 'C' and 'F' options take no account of the memory layout of
        the underlying array, and only refer to the order of indexing.
        'A' means to read / write the elements in Fortran-like index
        order if ``a`` is Fortran *contiguous* in memory, C-like order
        otherwise.
    newshape : int or tuple of ints
        .. deprecated:: 2.1
            Replaced by ``shape`` argument. Retained for backward
            compatibility.
    copy : bool, optional
        If ``True``, then the array data is copied. If ``None``, a copy will
        only be made if it's required by ``order``. For ``False`` it raises
        a ``ValueError`` if a copy cannot be avoided. Default: ``None``.

    Returns
    -------
    reshaped_array : ndarray
        This will be a new view object if possible; otherwise, it will
        be a copy.  Note there is no guarantee of the *memory layout* (C- or
        Fortran- contiguous) of the returned array.

    See Also
    --------
    ndarray.reshape : Equivalent method.

    Notes
    -----
    It is not always possible to change the shape of an array without copying
    the data.

    The ``order`` keyword gives the index ordering both for *fetching*
    the values from ``a``, and then *placing* the values into the output
    array. For example, let's say you have an array:

    >>> a = np.arange(6).reshape((3, 2))
    >>> a
    array([[0, 1],
           [2, 3],
           [4, 5]])

    You can think of reshaping as first raveling the array (using the given
    index order), then inserting the elements from the raveled array into the
    new array using the same kind of index ordering as was used for the
    raveling.

    >>> np.reshape(a, (2, 3)) # C-like index ordering
    array([[0, 1, 2],
           [3, 4, 5]])
    >>> np.reshape(np.ravel(a), (2, 3)) # equivalent to C ravel then C reshape
    array([[0, 1, 2],
           [3, 4, 5]])
    >>> np.reshape(a, (2, 3), order='F') # Fortran-like index ordering
    array([[0, 4, 3],
           [2, 1, 5]])
    >>> np.reshape(np.ravel(a, order='F'), (2, 3), order='F')
    array([[0, 4, 3],
           [2, 1, 5]])

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[1,2,3], [4,5,6]])
    >>> np.reshape(a, 6)
    array([1, 2, 3, 4, 5, 6])
    >>> np.reshape(a, 6, order='F')
    array([1, 4, 2, 5, 3, 6])

    >>> np.reshape(a, (3,-1))       # the unspecified value is inferred to be 2
    array([[1, 2],
           [3, 4],
           [5, 6]])

Python Library Documentation: function resize in module autograd.tracer

resize(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return a new array with the specified shape.

    If the new array is larger than the original array, then the new
    array is filled with repeated copies of `a`.  Note that this behavior
    is different from a.resize(new_shape) which fills with zeros instead
    of repeated copies of `a`.

    Parameters
    ----------
    a : array_like
        Array to be resized.

    new_shape : int or tuple of int
        Shape of resized array.

    Returns
    -------
    reshaped_array : ndarray
        The new array is formed from the data in the old array, repeated
        if necessary to fill out the required number of elements.  The
        data are repeated iterating over the array in C-order.

    See Also
    --------
    numpy.reshape : Reshape an array without changing the total size.
    numpy.pad : Enlarge and pad an array.
    numpy.repeat : Repeat elements of an array.
    ndarray.resize : resize an array in-place.

    Notes
    -----
    When the total size of the array does not change `~numpy.reshape` should
    be used.  In most other cases either indexing (to reduce the size)
    or padding (to increase the size) may be a more appropriate solution.

    Warning: This functionality does **not** consider axes separately,
    i.e. it does not apply interpolation/extrapolation.
    It fills the return array with the required number of elements, iterating
    over `a` in C-order, disregarding axes (and cycling back from the start if
    the new shape is larger).  This functionality is therefore not suitable to
    resize images, or data where each axis represents a separate and distinct
    entity.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[0,1],[2,3]])
    >>> np.resize(a,(2,3))
    array([[0, 1, 2],
           [3, 0, 1]])
    >>> np.resize(a,(1,4))
    array([[0, 1, 2, 3]])
    >>> np.resize(a,(2,4))
    array([[0, 1, 2, 3],
           [0, 1, 2, 3]])

Python Library Documentation: function result_type in module autograd.tracer

result_type(*args, **kwargs)
    result_type(*arrays_and_dtypes)

    Returns the type that results from applying the NumPy
    type promotion rules to the arguments.

    Type promotion in NumPy works similarly to the rules in languages
    like C++, with some slight differences.  When both scalars and
    arrays are used, the array's type takes precedence and the actual value
    of the scalar is taken into account.

    For example, calculating 3*a, where a is an array of 32-bit floats,
    intuitively should result in a 32-bit float output.  If the 3 is a
    32-bit integer, the NumPy rules indicate it can't convert losslessly
    into a 32-bit float, so a 64-bit float should be the result type.
    By examining the value of the constant, '3', we see that it fits in
    an 8-bit integer, which can be cast losslessly into the 32-bit float.

    Parameters
    ----------
    arrays_and_dtypes : list of arrays and dtypes
        The operands of some operation whose result type is needed.

    Returns
    -------
    out : dtype
        The result type.

    See also
    --------
    dtype, promote_types, min_scalar_type, can_cast

    Notes
    -----
    .. versionadded:: 1.6.0

    The specific algorithm used is as follows.

    Categories are determined by first checking which of boolean,
    integer (int/uint), or floating point (float/complex) the maximum
    kind of all the arrays and the scalars are.

    If there are only scalars or the maximum category of the scalars
    is higher than the maximum category of the arrays,
    the data types are combined with :func:`promote_types`
    to produce the return value.

    Otherwise, `min_scalar_type` is called on each scalar, and
    the resulting data types are all combined with :func:`promote_types`
    to produce the return value.

    The set of int values is not a subset of the uint values for types
    with the same number of bits, something not reflected in
    :func:`min_scalar_type`, but handled as a special case in `result_type`.

    Examples
    --------
    >>> import numpy as np
    >>> np.result_type(3, np.arange(7, dtype='i1'))
    dtype('int8')

    >>> np.result_type('i4', 'c8')
    dtype('complex128')

    >>> np.result_type(3.0, -2)
    dtype('float64')

Python Library Documentation: function right_shift in module autograd.tracer

right_shift(*args, called_by_autograd_dispatcher=False, **kwargs)
    right_shift(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Shift the bits of an integer to the right.

    Bits are shifted to the right `x2`.  Because the internal
    representation of numbers is in binary format, this operation is
    equivalent to dividing `x1` by ``2**x2``.

    Parameters
    ----------
    x1 : array_like, int
        Input values.
    x2 : array_like, int
        Number of bits to remove at the right of `x1`.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray, int
        Return `x1` with bits shifted `x2` times to the right.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    left_shift : Shift the bits of an integer to the left.
    binary_repr : Return the binary representation of the input number
        as a string.

    Examples
    --------
    >>> import numpy as np
    >>> np.binary_repr(10)
    '1010'
    >>> np.right_shift(10, 1)
    5
    >>> np.binary_repr(5)
    '101'

    >>> np.right_shift(10, [1,2,3])
    array([5, 2, 1])

    The ``>>`` operator can be used as a shorthand for ``np.right_shift`` on
    ndarrays.

    >>> x1 = 10
    >>> x2 = np.array([1,2,3])
    >>> x1 >> x2
    array([5, 2, 1])

Python Library Documentation: function rint in module autograd.tracer

rint(*args, called_by_autograd_dispatcher=False, **kwargs)
    rint(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Round elements of the array to the nearest integer.

    Parameters
    ----------
    x : array_like
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Output array is same shape and type as `x`.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    fix, ceil, floor, trunc

    Notes
    -----
    For values exactly halfway between rounded decimal values, NumPy
    rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0,
    -0.5 and 0.5 round to 0.0, etc.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
    >>> np.rint(a)
    array([-2., -2., -0.,  0.,  2.,  2.,  2.])

Python Library Documentation: function roll in module autograd.tracer

roll(*args, called_by_autograd_dispatcher=False, **kwargs)
    Roll array elements along a given axis.

    Elements that roll beyond the last position are re-introduced at
    the first.

    Parameters
    ----------
    a : array_like
        Input array.
    shift : int or tuple of ints
        The number of places by which elements are shifted.  If a tuple,
        then `axis` must be a tuple of the same size, and each of the
        given axes is shifted by the corresponding number.  If an int
        while `axis` is a tuple of ints, then the same value is used for
        all given axes.
    axis : int or tuple of ints, optional
        Axis or axes along which elements are shifted.  By default, the
        array is flattened before shifting, after which the original
        shape is restored.

    Returns
    -------
    res : ndarray
        Output array, with the same shape as `a`.

    See Also
    --------
    rollaxis : Roll the specified axis backwards, until it lies in a
               given position.

    Notes
    -----
    .. versionadded:: 1.12.0

    Supports rolling over multiple dimensions simultaneously.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.arange(10)
    >>> np.roll(x, 2)
    array([8, 9, 0, 1, 2, 3, 4, 5, 6, 7])
    >>> np.roll(x, -2)
    array([2, 3, 4, 5, 6, 7, 8, 9, 0, 1])

    >>> x2 = np.reshape(x, (2, 5))
    >>> x2
    array([[0, 1, 2, 3, 4],
           [5, 6, 7, 8, 9]])
    >>> np.roll(x2, 1)
    array([[9, 0, 1, 2, 3],
           [4, 5, 6, 7, 8]])
    >>> np.roll(x2, -1)
    array([[1, 2, 3, 4, 5],
           [6, 7, 8, 9, 0]])
    >>> np.roll(x2, 1, axis=0)
    array([[5, 6, 7, 8, 9],
           [0, 1, 2, 3, 4]])
    >>> np.roll(x2, -1, axis=0)
    array([[5, 6, 7, 8, 9],
           [0, 1, 2, 3, 4]])
    >>> np.roll(x2, 1, axis=1)
    array([[4, 0, 1, 2, 3],
           [9, 5, 6, 7, 8]])
    >>> np.roll(x2, -1, axis=1)
    array([[1, 2, 3, 4, 0],
           [6, 7, 8, 9, 5]])
    >>> np.roll(x2, (1, 1), axis=(1, 0))
    array([[9, 5, 6, 7, 8],
           [4, 0, 1, 2, 3]])
    >>> np.roll(x2, (2, 1), axis=(1, 0))
    array([[8, 9, 5, 6, 7],
           [3, 4, 0, 1, 2]])

Python Library Documentation: function rollaxis in module autograd.tracer

rollaxis(*args, called_by_autograd_dispatcher=False, **kwargs)
    Roll the specified axis backwards, until it lies in a given position.

    This function continues to be supported for backward compatibility, but you
    should prefer `moveaxis`. The `moveaxis` function was added in NumPy
    1.11.

    Parameters
    ----------
    a : ndarray
        Input array.
    axis : int
        The axis to be rolled. The positions of the other axes do not
        change relative to one another.
    start : int, optional
        When ``start <= axis``, the axis is rolled back until it lies in
        this position. When ``start > axis``, the axis is rolled until it
        lies before this position. The default, 0, results in a "complete"
        roll. The following table describes how negative values of ``start``
        are interpreted:

        .. table::
           :align: left

           +-------------------+----------------------+
           |     ``start``     | Normalized ``start`` |
           +===================+======================+
           | ``-(arr.ndim+1)`` | raise ``AxisError``  |
           +-------------------+----------------------+
           | ``-arr.ndim``     | 0                    |
           +-------------------+----------------------+
           | |vdots|           | |vdots|              |
           +-------------------+----------------------+
           | ``-1``            | ``arr.ndim-1``       |
           +-------------------+----------------------+
           | ``0``             | ``0``                |
           +-------------------+----------------------+
           | |vdots|           | |vdots|              |
           +-------------------+----------------------+
           | ``arr.ndim``      | ``arr.ndim``         |
           +-------------------+----------------------+
           | ``arr.ndim + 1``  | raise ``AxisError``  |
           +-------------------+----------------------+

        .. |vdots|   unicode:: U+22EE .. Vertical Ellipsis

    Returns
    -------
    res : ndarray
        For NumPy >= 1.10.0 a view of `a` is always returned. For earlier
        NumPy versions a view of `a` is returned only if the order of the
        axes is changed, otherwise the input array is returned.

    See Also
    --------
    moveaxis : Move array axes to new positions.
    roll : Roll the elements of an array by a number of positions along a
        given axis.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.ones((3,4,5,6))
    >>> np.rollaxis(a, 3, 1).shape
    (3, 6, 4, 5)
    >>> np.rollaxis(a, 2).shape
    (5, 3, 4, 6)
    >>> np.rollaxis(a, 1, 4).shape
    (3, 5, 6, 4)

Python Library Documentation: function roots in module autograd.tracer

roots(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the roots of a polynomial with coefficients given in p.

    .. note::
       This forms part of the old polynomial API. Since version 1.4, the
       new polynomial API defined in `numpy.polynomial` is preferred.
       A summary of the differences can be found in the
       :doc:`transition guide </reference/routines.polynomials>`.

    The values in the rank-1 array `p` are coefficients of a polynomial.
    If the length of `p` is n+1 then the polynomial is described by::

      p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]

    Parameters
    ----------
    p : array_like
        Rank-1 array of polynomial coefficients.

    Returns
    -------
    out : ndarray
        An array containing the roots of the polynomial.

    Raises
    ------
    ValueError
        When `p` cannot be converted to a rank-1 array.

    See also
    --------
    poly : Find the coefficients of a polynomial with a given sequence
           of roots.
    polyval : Compute polynomial values.
    polyfit : Least squares polynomial fit.
    poly1d : A one-dimensional polynomial class.

    Notes
    -----
    The algorithm relies on computing the eigenvalues of the
    companion matrix [1]_.

    References
    ----------
    .. [1] R. A. Horn & C. R. Johnson, *Matrix Analysis*.  Cambridge, UK:
        Cambridge University Press, 1999, pp. 146-7.

    Examples
    --------
    >>> import numpy as np
    >>> coeff = [3.2, 2, 1]
    >>> np.roots(coeff)
    array([-0.3125+0.46351241j, -0.3125-0.46351241j])

Python Library Documentation: function rot90 in module autograd.tracer

rot90(*args, called_by_autograd_dispatcher=False, **kwargs)
    Rotate an array by 90 degrees in the plane specified by axes.

    Rotation direction is from the first towards the second axis.
    This means for a 2D array with the default `k` and `axes`, the
    rotation will be counterclockwise.

    Parameters
    ----------
    m : array_like
        Array of two or more dimensions.
    k : integer
        Number of times the array is rotated by 90 degrees.
    axes : (2,) array_like
        The array is rotated in the plane defined by the axes.
        Axes must be different.

        .. versionadded:: 1.12.0

    Returns
    -------
    y : ndarray
        A rotated view of `m`.

    See Also
    --------
    flip : Reverse the order of elements in an array along the given axis.
    fliplr : Flip an array horizontally.
    flipud : Flip an array vertically.

    Notes
    -----
    ``rot90(m, k=1, axes=(1,0))``  is the reverse of
    ``rot90(m, k=1, axes=(0,1))``

    ``rot90(m, k=1, axes=(1,0))`` is equivalent to
    ``rot90(m, k=-1, axes=(0,1))``

    Examples
    --------
    >>> import numpy as np
    >>> m = np.array([[1,2],[3,4]], int)
    >>> m
    array([[1, 2],
           [3, 4]])
    >>> np.rot90(m)
    array([[2, 4],
           [1, 3]])
    >>> np.rot90(m, 2)
    array([[4, 3],
           [2, 1]])
    >>> m = np.arange(8).reshape((2,2,2))
    >>> np.rot90(m, 1, (1,2))
    array([[[1, 3],
            [0, 2]],
           [[5, 7],
            [4, 6]]])

Python Library Documentation: function round in module autograd.tracer

round(*args, called_by_autograd_dispatcher=False, **kwargs)
    Evenly round to the given number of decimals.

    Parameters
    ----------
    a : array_like
        Input data.
    decimals : int, optional
        Number of decimal places to round to (default: 0).  If
        decimals is negative, it specifies the number of positions to
        the left of the decimal point.
    out : ndarray, optional
        Alternative output array in which to place the result. It must have
        the same shape as the expected output, but the type of the output
        values will be cast if necessary. See :ref:`ufuncs-output-type`
        for more details.

    Returns
    -------
    rounded_array : ndarray
        An array of the same type as `a`, containing the rounded values.
        Unless `out` was specified, a new array is created.  A reference to
        the result is returned.

        The real and imaginary parts of complex numbers are rounded
        separately.  The result of rounding a float is a float.

    See Also
    --------
    ndarray.round : equivalent method
    around : an alias for this function
    ceil, fix, floor, rint, trunc


    Notes
    -----
    For values exactly halfway between rounded decimal values, NumPy
    rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0,
    -0.5 and 0.5 round to 0.0, etc.

    ``np.round`` uses a fast but sometimes inexact algorithm to round
    floating-point datatypes. For positive `decimals` it is equivalent to
    ``np.true_divide(np.rint(a * 10**decimals), 10**decimals)``, which has
    error due to the inexact representation of decimal fractions in the IEEE
    floating point standard [1]_ and errors introduced when scaling by powers
    of ten. For instance, note the extra "1" in the following:

        >>> np.round(56294995342131.5, 3)
        56294995342131.51

    If your goal is to print such values with a fixed number of decimals, it is
    preferable to use numpy's float printing routines to limit the number of
    printed decimals:

        >>> np.format_float_positional(56294995342131.5, precision=3)
        '56294995342131.5'

    The float printing routines use an accurate but much more computationally
    demanding algorithm to compute the number of digits after the decimal
    point.

    Alternatively, Python's builtin `round` function uses a more accurate
    but slower algorithm for 64-bit floating point values:

        >>> round(56294995342131.5, 3)
        56294995342131.5
        >>> np.round(16.055, 2), round(16.055, 2)  # equals 16.0549999999999997
        (16.06, 16.05)


    References
    ----------
    .. [1] "Lecture Notes on the Status of IEEE 754", William Kahan,
           https://people.eecs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF

    Examples
    --------
    >>> import numpy as np
    >>> np.round([0.37, 1.64])
    array([0., 2.])
    >>> np.round([0.37, 1.64], decimals=1)
    array([0.4, 1.6])
    >>> np.round([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value
    array([0., 2., 2., 4., 4.])
    >>> np.round([1,2,3,11], decimals=1) # ndarray of ints is returned
    array([ 1,  2,  3, 11])
    >>> np.round([1,2,3,11], decimals=-1)
    array([ 0,  0,  0, 10])

Python Library Documentation: function <lambda> in module autograd.numpy.numpy_wrapper

<lambda> lambda tup

Python Library Documentation: function save in module autograd.tracer

save(*args, called_by_autograd_dispatcher=False, **kwargs)
    Save an array to a binary file in NumPy ``.npy`` format.

    Parameters
    ----------
    file : file, str, or pathlib.Path
        File or filename to which the data is saved. If file is a file-object,
        then the filename is unchanged.  If file is a string or Path,
        a ``.npy`` extension will be appended to the filename if it does not
        already have one.
    arr : array_like
        Array data to be saved.
    allow_pickle : bool, optional
        Allow saving object arrays using Python pickles. Reasons for
        disallowing pickles include security (loading pickled data can execute
        arbitrary code) and portability (pickled objects may not be loadable
        on different Python installations, for example if the stored objects
        require libraries that are not available, and not all pickled data is
        compatible between different versions of Python).
        Default: True
    fix_imports : bool, optional
        The `fix_imports` flag is deprecated and has no effect.

        .. deprecated:: 2.1
            This flag is ignored since NumPy 1.17 and was only needed to
            support loading some files in Python 2 written in Python 3.

    See Also
    --------
    savez : Save several arrays into a ``.npz`` archive
    savetxt, load

    Notes
    -----
    For a description of the ``.npy`` format, see :py:mod:`numpy.lib.format`.

    Any data saved to the file is appended to the end of the file.

    Examples
    --------
    >>> import numpy as np

    >>> from tempfile import TemporaryFile
    >>> outfile = TemporaryFile()

    >>> x = np.arange(10)
    >>> np.save(outfile, x)

    >>> _ = outfile.seek(0) # Only needed to simulate closing & reopening file
    >>> np.load(outfile)
    array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])


    >>> with open('test.npy', 'wb') as f:
    ...     np.save(f, np.array([1, 2]))
    ...     np.save(f, np.array([1, 3]))
    >>> with open('test.npy', 'rb') as f:
    ...     a = np.load(f)
    ...     b = np.load(f)
    >>> print(a, b)
    # [1 2] [1 3]

Python Library Documentation: function savetxt in module autograd.tracer

savetxt(*args, called_by_autograd_dispatcher=False, **kwargs)
    Save an array to a text file.

    Parameters
    ----------
    fname : filename, file handle or pathlib.Path
        If the filename ends in ``.gz``, the file is automatically saved in
        compressed gzip format.  `loadtxt` understands gzipped files
        transparently.
    X : 1D or 2D array_like
        Data to be saved to a text file.
    fmt : str or sequence of strs, optional
        A single format (%10.5f), a sequence of formats, or a
        multi-format string, e.g. 'Iteration %d -- %10.5f', in which
        case `delimiter` is ignored. For complex `X`, the legal options
        for `fmt` are:

        * a single specifier, ``fmt='%.4e'``, resulting in numbers formatted
          like ``' (%s+%sj)' % (fmt, fmt)``
        * a full string specifying every real and imaginary part, e.g.
          ``' %.4e %+.4ej %.4e %+.4ej %.4e %+.4ej'`` for 3 columns
        * a list of specifiers, one per column - in this case, the real
          and imaginary part must have separate specifiers,
          e.g. ``['%.3e + %.3ej', '(%.15e%+.15ej)']`` for 2 columns
    delimiter : str, optional
        String or character separating columns.
    newline : str, optional
        String or character separating lines.

        .. versionadded:: 1.5.0
    header : str, optional
        String that will be written at the beginning of the file.

        .. versionadded:: 1.7.0
    footer : str, optional
        String that will be written at the end of the file.

        .. versionadded:: 1.7.0
    comments : str, optional
        String that will be prepended to the ``header`` and ``footer`` strings,
        to mark them as comments. Default: '# ',  as expected by e.g.
        ``numpy.loadtxt``.

        .. versionadded:: 1.7.0
    encoding : {None, str}, optional
        Encoding used to encode the outputfile. Does not apply to output
        streams. If the encoding is something other than 'bytes' or 'latin1'
        you will not be able to load the file in NumPy versions < 1.14. Default
        is 'latin1'.

        .. versionadded:: 1.14.0


    See Also
    --------
    save : Save an array to a binary file in NumPy ``.npy`` format
    savez : Save several arrays into an uncompressed ``.npz`` archive
    savez_compressed : Save several arrays into a compressed ``.npz`` archive

    Notes
    -----
    Further explanation of the `fmt` parameter
    (``%[flag]width[.precision]specifier``):

    flags:
        ``-`` : left justify

        ``+`` : Forces to precede result with + or -.

        ``0`` : Left pad the number with zeros instead of space (see width).

    width:
        Minimum number of characters to be printed. The value is not truncated
        if it has more characters.

    precision:
        - For integer specifiers (eg. ``d,i,o,x``), the minimum number of
          digits.
        - For ``e, E`` and ``f`` specifiers, the number of digits to print
          after the decimal point.
        - For ``g`` and ``G``, the maximum number of significant digits.
        - For ``s``, the maximum number of characters.

    specifiers:
        ``c`` : character

        ``d`` or ``i`` : signed decimal integer

        ``e`` or ``E`` : scientific notation with ``e`` or ``E``.

        ``f`` : decimal floating point

        ``g,G`` : use the shorter of ``e,E`` or ``f``

        ``o`` : signed octal

        ``s`` : string of characters

        ``u`` : unsigned decimal integer

        ``x,X`` : unsigned hexadecimal integer

    This explanation of ``fmt`` is not complete, for an exhaustive
    specification see [1]_.

    References
    ----------
    .. [1] `Format Specification Mini-Language
           <https://docs.python.org/library/string.html#format-specification-mini-language>`_,
           Python Documentation.

    Examples
    --------
    >>> import numpy as np
    >>> x = y = z = np.arange(0.0,5.0,1.0)
    >>> np.savetxt('test.out', x, delimiter=',')   # X is an array
    >>> np.savetxt('test.out', (x,y,z))   # x,y,z equal sized 1D arrays
    >>> np.savetxt('test.out', x, fmt='%1.4e')   # use exponential notation

Python Library Documentation: function savez in module autograd.tracer

savez(*args, called_by_autograd_dispatcher=False, **kwargs)
    Save several arrays into a single file in uncompressed ``.npz`` format.

    Provide arrays as keyword arguments to store them under the
    corresponding name in the output file: ``savez(fn, x=x, y=y)``.

    If arrays are specified as positional arguments, i.e., ``savez(fn,
    x, y)``, their names will be `arr_0`, `arr_1`, etc.

    Parameters
    ----------
    file : file, str, or pathlib.Path
        Either the filename (string) or an open file (file-like object)
        where the data will be saved. If file is a string or a Path, the
        ``.npz`` extension will be appended to the filename if it is not
        already there.
    args : Arguments, optional
        Arrays to save to the file. Please use keyword arguments (see
        `kwds` below) to assign names to arrays.  Arrays specified as
        args will be named "arr_0", "arr_1", and so on.
    kwds : Keyword arguments, optional
        Arrays to save to the file. Each array will be saved to the
        output file with its corresponding keyword name.

    Returns
    -------
    None

    See Also
    --------
    save : Save a single array to a binary file in NumPy format.
    savetxt : Save an array to a file as plain text.
    savez_compressed : Save several arrays into a compressed ``.npz`` archive

    Notes
    -----
    The ``.npz`` file format is a zipped archive of files named after the
    variables they contain.  The archive is not compressed and each file
    in the archive contains one variable in ``.npy`` format. For a
    description of the ``.npy`` format, see :py:mod:`numpy.lib.format`.

    When opening the saved ``.npz`` file with `load` a `~lib.npyio.NpzFile`
    object is returned. This is a dictionary-like object which can be queried
    for its list of arrays (with the ``.files`` attribute), and for the arrays
    themselves.

    Keys passed in `kwds` are used as filenames inside the ZIP archive.
    Therefore, keys should be valid filenames; e.g., avoid keys that begin with
    ``/`` or contain ``.``.

    When naming variables with keyword arguments, it is not possible to name a
    variable ``file``, as this would cause the ``file`` argument to be defined
    twice in the call to ``savez``.

    Examples
    --------
    >>> import numpy as np
    >>> from tempfile import TemporaryFile
    >>> outfile = TemporaryFile()
    >>> x = np.arange(10)
    >>> y = np.sin(x)

    Using `savez` with \*args, the arrays are saved with default names.

    >>> np.savez(outfile, x, y)
    >>> _ = outfile.seek(0) # Only needed to simulate closing & reopening file
    >>> npzfile = np.load(outfile)
    >>> npzfile.files
    ['arr_0', 'arr_1']
    >>> npzfile['arr_0']
    array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

    Using `savez` with \**kwds, the arrays are saved with the keyword names.

    >>> outfile = TemporaryFile()
    >>> np.savez(outfile, x=x, y=y)
    >>> _ = outfile.seek(0)
    >>> npzfile = np.load(outfile)
    >>> sorted(npzfile.files)
    ['x', 'y']
    >>> npzfile['x']
    array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

Python Library Documentation: function savez_compressed in module autograd.tracer

savez_compressed(*args, called_by_autograd_dispatcher=False, **kwargs)
    Save several arrays into a single file in compressed ``.npz`` format.

    Provide arrays as keyword arguments to store them under the
    corresponding name in the output file: ``savez_compressed(fn, x=x, y=y)``.

    If arrays are specified as positional arguments, i.e.,
    ``savez_compressed(fn, x, y)``, their names will be `arr_0`, `arr_1`, etc.

    Parameters
    ----------
    file : file, str, or pathlib.Path
        Either the filename (string) or an open file (file-like object)
        where the data will be saved. If file is a string or a Path, the
        ``.npz`` extension will be appended to the filename if it is not
        already there.
    args : Arguments, optional
        Arrays to save to the file. Please use keyword arguments (see
        `kwds` below) to assign names to arrays.  Arrays specified as
        args will be named "arr_0", "arr_1", and so on.
    kwds : Keyword arguments, optional
        Arrays to save to the file. Each array will be saved to the
        output file with its corresponding keyword name.

    Returns
    -------
    None

    See Also
    --------
    numpy.save : Save a single array to a binary file in NumPy format.
    numpy.savetxt : Save an array to a file as plain text.
    numpy.savez : Save several arrays into an uncompressed ``.npz`` file format
    numpy.load : Load the files created by savez_compressed.

    Notes
    -----
    The ``.npz`` file format is a zipped archive of files named after the
    variables they contain.  The archive is compressed with
    ``zipfile.ZIP_DEFLATED`` and each file in the archive contains one variable
    in ``.npy`` format. For a description of the ``.npy`` format, see
    :py:mod:`numpy.lib.format`.


    When opening the saved ``.npz`` file with `load` a `~lib.npyio.NpzFile`
    object is returned. This is a dictionary-like object which can be queried
    for its list of arrays (with the ``.files`` attribute), and for the arrays
    themselves.

    Examples
    --------
    >>> import numpy as np
    >>> test_array = np.random.rand(3, 2)
    >>> test_vector = np.random.rand(4)
    >>> np.savez_compressed('/tmp/123', a=test_array, b=test_vector)
    >>> loaded = np.load('/tmp/123.npz')
    >>> print(np.array_equal(test_array, loaded['a']))
    True
    >>> print(np.array_equal(test_vector, loaded['b']))
    True

Python Library Documentation: function searchsorted in module autograd.tracer

searchsorted(*args, called_by_autograd_dispatcher=False, **kwargs)
    Find indices where elements should be inserted to maintain order.

    Find the indices into a sorted array `a` such that, if the
    corresponding elements in `v` were inserted before the indices, the
    order of `a` would be preserved.

    Assuming that `a` is sorted:

    ======  ============================
    `side`  returned index `i` satisfies
    ======  ============================
    left    ``a[i-1] < v <= a[i]``
    right   ``a[i-1] <= v < a[i]``
    ======  ============================

    Parameters
    ----------
    a : 1-D array_like
        Input array. If `sorter` is None, then it must be sorted in
        ascending order, otherwise `sorter` must be an array of indices
        that sort it.
    v : array_like
        Values to insert into `a`.
    side : {'left', 'right'}, optional
        If 'left', the index of the first suitable location found is given.
        If 'right', return the last such index.  If there is no suitable
        index, return either 0 or N (where N is the length of `a`).
    sorter : 1-D array_like, optional
        Optional array of integer indices that sort array a into ascending
        order. They are typically the result of argsort.

        .. versionadded:: 1.7.0

    Returns
    -------
    indices : int or array of ints
        Array of insertion points with the same shape as `v`,
        or an integer if `v` is a scalar.

    See Also
    --------
    sort : Return a sorted copy of an array.
    histogram : Produce histogram from 1-D data.

    Notes
    -----
    Binary search is used to find the required insertion points.

    As of NumPy 1.4.0 `searchsorted` works with real/complex arrays containing
    `nan` values. The enhanced sort order is documented in `sort`.

    This function uses the same algorithm as the builtin python
    `bisect.bisect_left` (``side='left'``) and `bisect.bisect_right`
    (``side='right'``) functions, which is also vectorized
    in the `v` argument.

    Examples
    --------
    >>> import numpy as np
    >>> np.searchsorted([11,12,13,14,15], 13)
    2
    >>> np.searchsorted([11,12,13,14,15], 13, side='right')
    3
    >>> np.searchsorted([11,12,13,14,15], [-10, 20, 12, 13])
    array([0, 5, 1, 2])

Python Library Documentation: function select in module autograd.numpy.numpy_wrapper

select(condlist, choicelist, default=0)

Python Library Documentation: function set_printoptions in module autograd.tracer

set_printoptions(*args, called_by_autograd_dispatcher=False, **kwargs)
    Set printing options.

    These options determine the way floating point numbers, arrays and
    other NumPy objects are displayed.

    Parameters
    ----------
    precision : int or None, optional
        Number of digits of precision for floating point output (default 8).
        May be None if `floatmode` is not `fixed`, to print as many digits as
        necessary to uniquely specify the value.
    threshold : int, optional
        Total number of array elements which trigger summarization
        rather than full repr (default 1000).
        To always use the full repr without summarization, pass `sys.maxsize`.
    edgeitems : int, optional
        Number of array items in summary at beginning and end of
        each dimension (default 3).
    linewidth : int, optional
        The number of characters per line for the purpose of inserting
        line breaks (default 75).
    suppress : bool, optional
        If True, always print floating point numbers using fixed point
        notation, in which case numbers equal to zero in the current precision
        will print as zero.  If False, then scientific notation is used when
        absolute value of the smallest number is < 1e-4 or the ratio of the
        maximum absolute value to the minimum is > 1e3. The default is False.
    nanstr : str, optional
        String representation of floating point not-a-number (default nan).
    infstr : str, optional
        String representation of floating point infinity (default inf).
    sign : string, either '-', '+', or ' ', optional
        Controls printing of the sign of floating-point types. If '+', always
        print the sign of positive values. If ' ', always prints a space
        (whitespace character) in the sign position of positive values.  If
        '-', omit the sign character of positive values. (default '-')

        .. versionchanged:: 2.0
             The sign parameter can now be an integer type, previously
             types were floating-point types.

    formatter : dict of callables, optional
        If not None, the keys should indicate the type(s) that the respective
        formatting function applies to.  Callables should return a string.
        Types that are not specified (by their corresponding keys) are handled
        by the default formatters.  Individual types for which a formatter
        can be set are:

        - 'bool'
        - 'int'
        - 'timedelta' : a `numpy.timedelta64`
        - 'datetime' : a `numpy.datetime64`
        - 'float'
        - 'longfloat' : 128-bit floats
        - 'complexfloat'
        - 'longcomplexfloat' : composed of two 128-bit floats
        - 'numpystr' : types `numpy.bytes_` and `numpy.str_`
        - 'object' : `np.object_` arrays

        Other keys that can be used to set a group of types at once are:

        - 'all' : sets all types
        - 'int_kind' : sets 'int'
        - 'float_kind' : sets 'float' and 'longfloat'
        - 'complex_kind' : sets 'complexfloat' and 'longcomplexfloat'
        - 'str_kind' : sets 'numpystr'
    floatmode : str, optional
        Controls the interpretation of the `precision` option for
        floating-point types. Can take the following values
        (default maxprec_equal):

        * 'fixed': Always print exactly `precision` fractional digits,
                even if this would print more or fewer digits than
                necessary to specify the value uniquely.
        * 'unique': Print the minimum number of fractional digits necessary
                to represent each value uniquely. Different elements may
                have a different number of digits. The value of the
                `precision` option is ignored.
        * 'maxprec': Print at most `precision` fractional digits, but if
                an element can be uniquely represented with fewer digits
                only print it with that many.
        * 'maxprec_equal': Print at most `precision` fractional digits,
                but if every element in the array can be uniquely
                represented with an equal number of fewer digits, use that
                many digits for all elements.
    legacy : string or `False`, optional
        If set to the string ``'1.13'`` enables 1.13 legacy printing mode. This
        approximates numpy 1.13 print output by including a space in the sign
        position of floats and different behavior for 0d arrays. This also
        enables 1.21 legacy printing mode (described below).

        If set to the string ``'1.21'`` enables 1.21 legacy printing mode. This
        approximates numpy 1.21 print output of complex structured dtypes
        by not inserting spaces after commas that separate fields and after
        colons.

        If set to ``'1.25'`` approximates printing of 1.25 which mainly means
        that numeric scalars are printed without their type information, e.g.
        as ``3.0`` rather than ``np.float64(3.0)``.

        If set to `False`, disables legacy mode.

        Unrecognized strings will be ignored with a warning for forward
        compatibility.

        .. versionadded:: 1.14.0
        .. versionchanged:: 1.22.0
        .. versionchanged:: 2.0

    override_repr: callable, optional
        If set a passed function will be used for generating arrays' repr.
        Other options will be ignored.

    See Also
    --------
    get_printoptions, printoptions, array2string

    Notes
    -----
    `formatter` is always reset with a call to `set_printoptions`.

    Use `printoptions` as a context manager to set the values temporarily.

    Examples
    --------
    Floating point precision can be set:

    >>> import numpy as np
    >>> np.set_printoptions(precision=4)
    >>> np.array([1.123456789])
    [1.1235]

    Long arrays can be summarised:

    >>> np.set_printoptions(threshold=5)
    >>> np.arange(10)
    array([0, 1, 2, ..., 7, 8, 9])

    Small results can be suppressed:

    >>> eps = np.finfo(float).eps
    >>> x = np.arange(4.)
    >>> x**2 - (x + eps)**2
    array([-4.9304e-32, -4.4409e-16,  0.0000e+00,  0.0000e+00])
    >>> np.set_printoptions(suppress=True)
    >>> x**2 - (x + eps)**2
    array([-0., -0.,  0.,  0.])

    A custom formatter can be used to display array elements as desired:

    >>> np.set_printoptions(formatter={'all':lambda x: 'int: '+str(-x)})
    >>> x = np.arange(3)
    >>> x
    array([int: 0, int: -1, int: -2])
    >>> np.set_printoptions()  # formatter gets reset
    >>> x
    array([0, 1, 2])

    To put back the default options, you can use:

    >>> np.set_printoptions(edgeitems=3, infstr='inf',
    ... linewidth=75, nanstr='nan', precision=8,
    ... suppress=False, threshold=1000, formatter=None)

    Also to temporarily override options, use `printoptions`
    as a context manager:

    >>> with np.printoptions(precision=2, suppress=True, threshold=5):
    ...     np.linspace(0, 10, 10)
    array([ 0.  ,  1.11,  2.22, ...,  7.78,  8.89, 10.  ])

Python Library Documentation: function setbufsize in module autograd.tracer

setbufsize(*args, called_by_autograd_dispatcher=False, **kwargs)
    Set the size of the buffer used in ufuncs.

    .. versionchanged:: 2.0
        The scope of setting the buffer is tied to the `numpy.errstate`
        context.  Exiting a ``with errstate():`` will also restore the bufsize.

    Parameters
    ----------
    size : int
        Size of buffer.

    Returns
    -------
    bufsize : int
        Previous size of ufunc buffer in bytes.

    Examples
    --------
    When exiting a `numpy.errstate` context manager the bufsize is restored:

    >>> import numpy as np
    >>> with np.errstate():
    ...     np.setbufsize(4096)
    ...     print(np.getbufsize())
    ...
    8192
    4096
    >>> np.getbufsize()
    8192

Python Library Documentation: function setdiff1d in module autograd.tracer

setdiff1d(*args, called_by_autograd_dispatcher=False, **kwargs)
    Find the set difference of two arrays.

    Return the unique values in `ar1` that are not in `ar2`.

    Parameters
    ----------
    ar1 : array_like
        Input array.
    ar2 : array_like
        Input comparison array.
    assume_unique : bool
        If True, the input arrays are both assumed to be unique, which
        can speed up the calculation.  Default is False.

    Returns
    -------
    setdiff1d : ndarray
        1D array of values in `ar1` that are not in `ar2`. The result
        is sorted when `assume_unique=False`, but otherwise only sorted
        if the input is sorted.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([1, 2, 3, 2, 4, 1])
    >>> b = np.array([3, 4, 5, 6])
    >>> np.setdiff1d(a, b)
    array([1, 2])

Python Library Documentation: function seterr in module autograd.tracer

seterr(*args, called_by_autograd_dispatcher=False, **kwargs)
    Set how floating-point errors are handled.

    Note that operations on integer scalar types (such as `int16`) are
    handled like floating point, and are affected by these settings.

    Parameters
    ----------
    all : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
        Set treatment for all types of floating-point errors at once:

        - ignore: Take no action when the exception occurs.
        - warn: Print a :exc:`RuntimeWarning` (via the Python `warnings`
          module).
        - raise: Raise a :exc:`FloatingPointError`.
        - call: Call a function specified using the `seterrcall` function.
        - print: Print a warning directly to ``stdout``.
        - log: Record error in a Log object specified by `seterrcall`.

        The default is not to change the current behavior.
    divide : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
        Treatment for division by zero.
    over : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
        Treatment for floating-point overflow.
    under : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
        Treatment for floating-point underflow.
    invalid : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
        Treatment for invalid floating-point operation.

    Returns
    -------
    old_settings : dict
        Dictionary containing the old settings.

    See also
    --------
    seterrcall : Set a callback function for the 'call' mode.
    geterr, geterrcall, errstate

    Notes
    -----
    The floating-point exceptions are defined in the IEEE 754 standard [1]_:

    - Division by zero: infinite result obtained from finite numbers.
    - Overflow: result too large to be expressed.
    - Underflow: result so close to zero that some precision
      was lost.
    - Invalid operation: result is not an expressible number, typically
      indicates that a NaN was produced.

    .. [1] https://en.wikipedia.org/wiki/IEEE_754

    Examples
    --------
    >>> import numpy as np
    >>> orig_settings = np.seterr(all='ignore')  # seterr to known value
    >>> np.int16(32000) * np.int16(3)
    30464
    >>> np.seterr(over='raise')
    {'divide': 'ignore', 'over': 'ignore', 'under': 'ignore', 'invalid': 'ignore'}
    >>> old_settings = np.seterr(all='warn', over='raise')
    >>> np.int16(32000) * np.int16(3)
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    FloatingPointError: overflow encountered in scalar multiply

    >>> old_settings = np.seterr(all='print')
    >>> np.geterr()
    {'divide': 'print', 'over': 'print', 'under': 'print', 'invalid': 'print'}
    >>> np.int16(32000) * np.int16(3)
    30464
    >>> np.seterr(**orig_settings)  # restore original
    {'divide': 'print', 'over': 'print', 'under': 'print', 'invalid': 'print'}

Python Library Documentation: function seterrcall in module autograd.tracer

seterrcall(*args, called_by_autograd_dispatcher=False, **kwargs)
    Set the floating-point error callback function or log object.

    There are two ways to capture floating-point error messages.  The first
    is to set the error-handler to 'call', using `seterr`.  Then, set
    the function to call using this function.

    The second is to set the error-handler to 'log', using `seterr`.
    Floating-point errors then trigger a call to the 'write' method of
    the provided object.

    Parameters
    ----------
    func : callable f(err, flag) or object with write method
        Function to call upon floating-point errors ('call'-mode) or
        object whose 'write' method is used to log such message ('log'-mode).

        The call function takes two arguments. The first is a string describing
        the type of error (such as "divide by zero", "overflow", "underflow",
        or "invalid value"), and the second is the status flag.  The flag is a
        byte, whose four least-significant bits indicate the type of error, one
        of "divide", "over", "under", "invalid"::

          [0 0 0 0 divide over under invalid]

        In other words, ``flags = divide + 2*over + 4*under + 8*invalid``.

        If an object is provided, its write method should take one argument,
        a string.

    Returns
    -------
    h : callable, log instance or None
        The old error handler.

    See Also
    --------
    seterr, geterr, geterrcall

    Examples
    --------
    Callback upon error:

    >>> def err_handler(type, flag):
    ...     print("Floating point error (%s), with flag %s" % (type, flag))
    ...

    >>> import numpy as np

    >>> orig_handler = np.seterrcall(err_handler)
    >>> orig_err = np.seterr(all='call')

    >>> np.array([1, 2, 3]) / 0.0
    Floating point error (divide by zero), with flag 1
    array([inf, inf, inf])

    >>> np.seterrcall(orig_handler)
    <function err_handler at 0x...>
    >>> np.seterr(**orig_err)
    {'divide': 'call', 'over': 'call', 'under': 'call', 'invalid': 'call'}

    Log error message:

    >>> class Log:
    ...     def write(self, msg):
    ...         print("LOG: %s" % msg)
    ...

    >>> log = Log()
    >>> saved_handler = np.seterrcall(log)
    >>> save_err = np.seterr(all='log')

    >>> np.array([1, 2, 3]) / 0.0
    LOG: Warning: divide by zero encountered in divide
    array([inf, inf, inf])

    >>> np.seterrcall(orig_handler)
    <numpy.Log object at 0x...>
    >>> np.seterr(**orig_err)
    {'divide': 'log', 'over': 'log', 'under': 'log', 'invalid': 'log'}

Python Library Documentation: function setxor1d in module autograd.tracer

setxor1d(*args, called_by_autograd_dispatcher=False, **kwargs)
    Find the set exclusive-or of two arrays.

    Return the sorted, unique values that are in only one (not both) of the
    input arrays.

    Parameters
    ----------
    ar1, ar2 : array_like
        Input arrays.
    assume_unique : bool
        If True, the input arrays are both assumed to be unique, which
        can speed up the calculation. Default is False.

    Returns
    -------
    setxor1d : ndarray
        Sorted 1D array of unique values that are in only one of the input
        arrays.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([1, 2, 3, 2, 4])
    >>> b = np.array([2, 3, 5, 7, 5])
    >>> np.setxor1d(a,b)
    array([1, 4, 5, 7])

Python Library Documentation: function shape in module autograd.tracer

shape(*args, **kwargs)
    Return the shape of an array.

    Parameters
    ----------
    a : array_like
        Input array.

    Returns
    -------
    shape : tuple of ints
        The elements of the shape tuple give the lengths of the
        corresponding array dimensions.

    See Also
    --------
    len : ``len(a)`` is equivalent to ``np.shape(a)[0]`` for N-D arrays with
          ``N>=1``.
    ndarray.shape : Equivalent array method.

    Examples
    --------
    >>> import numpy as np
    >>> np.shape(np.eye(3))
    (3, 3)
    >>> np.shape([[1, 3]])
    (1, 2)
    >>> np.shape([0])
    (1,)
    >>> np.shape(0)
    ()

    >>> a = np.array([(1, 2), (3, 4), (5, 6)],
    ...              dtype=[('x', 'i4'), ('y', 'i4')])
    >>> np.shape(a)
    (3,)
    >>> a.shape
    (3,)

Python Library Documentation: function shares_memory in module autograd.tracer

shares_memory(*args, called_by_autograd_dispatcher=False, **kwargs)
    shares_memory(a, b, /, max_work=None)

    Determine if two arrays share memory.

    .. warning::

       This function can be exponentially slow for some inputs, unless
       `max_work` is set to zero or a positive integer.
       If in doubt, use `numpy.may_share_memory` instead.

    Parameters
    ----------
    a, b : ndarray
        Input arrays
    max_work : int, optional
        Effort to spend on solving the overlap problem (maximum number
        of candidate solutions to consider). The following special
        values are recognized:

        max_work=-1 (default)
            The problem is solved exactly. In this case, the function returns
            True only if there is an element shared between the arrays. Finding
            the exact solution may take extremely long in some cases.
        max_work=0
            Only the memory bounds of a and b are checked.
            This is equivalent to using ``may_share_memory()``.

    Raises
    ------
    numpy.exceptions.TooHardError
        Exceeded max_work.

    Returns
    -------
    out : bool

    See Also
    --------
    may_share_memory

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([1, 2, 3, 4])
    >>> np.shares_memory(x, np.array([5, 6, 7]))
    False
    >>> np.shares_memory(x[::2], x)
    True
    >>> np.shares_memory(x[::2], x[1::2])
    False

    Checking whether two arrays share memory is NP-complete, and
    runtime may increase exponentially in the number of
    dimensions. Hence, `max_work` should generally be set to a finite
    number, as it is possible to construct examples that take
    extremely long to run:

    >>> from numpy.lib.stride_tricks import as_strided
    >>> x = np.zeros([192163377], dtype=np.int8)
    >>> x1 = as_strided(
    ...     x, strides=(36674, 61119, 85569), shape=(1049, 1049, 1049))
    >>> x2 = as_strided(
    ...     x[64023025:], strides=(12223, 12224, 1), shape=(1049, 1049, 1))
    >>> np.shares_memory(x1, x2, max_work=1000)
    Traceback (most recent call last):
    ...
    numpy.exceptions.TooHardError: Exceeded max_work

    Running ``np.shares_memory(x1, x2)`` without `max_work` set takes
    around 1 minute for this case. It is possible to find problems
    that take still significantly longer.

Python Library Documentation: class IntdtypeSubclass in module autograd.numpy.numpy_wrapper

class IntdtypeSubclass(numpy.int16)
 |  IntdtypeSubclass(*args, **kwargs)
 |
 |  Method resolution order:
 |      IntdtypeSubclass
 |      numpy.int16
 |      numpy.signedinteger
 |      numpy.integer
 |      numpy.number
 |      numpy.generic
 |      builtins.object
 |
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs) from autograd.tracer.notrace_primitive.<locals>
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.int16:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      int16.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.int16(127).bit_count()
 |      7
 |      >>> np.int16(-127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from numpy.int16:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from numpy.generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from numpy.generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: function show in module autograd.tracer

show(*args, called_by_autograd_dispatcher=False, **kwargs)
    Show libraries and system information on which NumPy was built
    and is being used

    Parameters
    ----------
    mode : {`'stdout'`, `'dicts'`}, optional.
        Indicates how to display the config information.
        `'stdout'` prints to console, `'dicts'` returns a dictionary
        of the configuration.

    Returns
    -------
    out : {`dict`, `None`}
        If mode is `'dicts'`, a dict is returned, else None

    See Also
    --------
    get_include : Returns the directory containing NumPy C
                  header files.

    Notes
    -----
    1. The `'stdout'` mode will give more readable
       output if ``pyyaml`` is installed

Python Library Documentation: function show_runtime in module autograd.tracer

show_runtime(*args, called_by_autograd_dispatcher=False, **kwargs)
    Print information about various resources in the system
    including available intrinsic support and BLAS/LAPACK library
    in use

    .. versionadded:: 1.24.0

    See Also
    --------
    show_config : Show libraries in the system on which NumPy was built.

    Notes
    -----
    1. Information is derived with the help of `threadpoolctl <https://pypi.org/project/threadpoolctl/>`_
       library if available.
    2. SIMD related information is derived from ``__cpu_features__``,
       ``__cpu_baseline__`` and ``__cpu_dispatch__``

Python Library Documentation: function sign in module autograd.tracer

sign(*args, called_by_autograd_dispatcher=False, **kwargs)
    sign(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Returns an element-wise indication of the sign of a number.

    The `sign` function returns ``-1 if x < 0, 0 if x==0, 1 if x > 0``.  nan
    is returned for nan inputs.

    For complex inputs, the `sign` function returns ``x / abs(x)``, the
    generalization of the above (and ``0 if x==0``).

    .. versionchanged:: 2.0.0
        Definition of complex sign changed to follow the Array API standard.

    Parameters
    ----------
    x : array_like
        Input values.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The sign of `x`.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    There is more than one definition of sign in common use for complex
    numbers.  The definition used here, :math:`x/|x|`, is the more common
    and useful one, but is different from the one used in numpy prior to
    version 2.0, :math:`x/\sqrt{x*x}`, which is equivalent to
    ``sign(x.real) + 0j if x.real != 0 else sign(x.imag) + 0j``.

    Examples
    --------
    >>> import numpy as np
    >>> np.sign([-5., 4.5])
    array([-1.,  1.])
    >>> np.sign(0)
    0
    >>> np.sign([3-4j, 8j])
    array([0.6-0.8j, 0. +1.j ])

Python Library Documentation: function signbit in module autograd.tracer

signbit(*args, called_by_autograd_dispatcher=False, **kwargs)
    signbit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Returns element-wise True where signbit is set (less than zero).

    Parameters
    ----------
    x : array_like
        The input value(s).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    result : ndarray of bool
        Output array, or reference to `out` if that was supplied.
        This is a scalar if `x` is a scalar.

    Examples
    --------
    >>> import numpy as np
    >>> np.signbit(-1.2)
    True
    >>> np.signbit(np.array([1, -2.3, 2.1]))
    array([False,  True, False])

Python Library Documentation: class signedinteger in module numpy

class signedinteger(integer)
 |  Abstract base class of all signed integer scalar types.
 |
 |  Method resolution order:
 |      signedinteger
 |      integer
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods inherited from integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from number:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes inherited from generic:
 |
 |  __hash__ = None

Python Library Documentation: function sin in module autograd.tracer

sin(*args, called_by_autograd_dispatcher=False, **kwargs)
    sin(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Trigonometric sine, element-wise.

    Parameters
    ----------
    x : array_like
        Angle, in radians (:math:`2 \pi` rad equals 360 degrees).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : array_like
        The sine of each element of x.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    arcsin, sinh, cos

    Notes
    -----
    The sine is one of the fundamental functions of trigonometry (the
    mathematical study of triangles).  Consider a circle of radius 1
    centered on the origin.  A ray comes in from the :math:`+x` axis, makes
    an angle at the origin (measured counter-clockwise from that axis), and
    departs from the origin.  The :math:`y` coordinate of the outgoing
    ray's intersection with the unit circle is the sine of that angle.  It
    ranges from -1 for :math:`x=3\pi / 2` to +1 for :math:`\pi / 2.`  The
    function has zeroes where the angle is a multiple of :math:`\pi`.
    Sines of angles between :math:`\pi` and :math:`2\pi` are negative.
    The numerous properties of the sine and related functions are included
    in any standard trigonometry text.

    Examples
    --------
    >>> import numpy as np

    Print sine of one angle:

    >>> np.sin(np.pi/2.)
    1.0

    Print sines of an array of angles given in degrees:

    >>> np.sin(np.array((0., 30., 45., 60., 90.)) * np.pi / 180. )
    array([ 0.        ,  0.5       ,  0.70710678,  0.8660254 ,  1.        ])

    Plot the sine function:

    >>> import matplotlib.pylab as plt
    >>> x = np.linspace(-np.pi, np.pi, 201)
    >>> plt.plot(x, np.sin(x))
    >>> plt.xlabel('Angle [rad]')
    >>> plt.ylabel('sin(x)')
    >>> plt.axis('tight')
    >>> plt.show()

Python Library Documentation: function sinc in module autograd.tracer

sinc(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the normalized sinc function.

    The sinc function is equal to :math:`\sin(\pi x)/(\pi x)` for any argument
    :math:`x\ne 0`. ``sinc(0)`` takes the limit value 1, making ``sinc`` not
    only everywhere continuous but also infinitely differentiable.

    .. note::

        Note the normalization factor of ``pi`` used in the definition.
        This is the most commonly used definition in signal processing.
        Use ``sinc(x / np.pi)`` to obtain the unnormalized sinc function
        :math:`\sin(x)/x` that is more common in mathematics.

    Parameters
    ----------
    x : ndarray
        Array (possibly multi-dimensional) of values for which to calculate
        ``sinc(x)``.

    Returns
    -------
    out : ndarray
        ``sinc(x)``, which has the same shape as the input.

    Notes
    -----
    The name sinc is short for "sine cardinal" or "sinus cardinalis".

    The sinc function is used in various signal processing applications,
    including in anti-aliasing, in the construction of a Lanczos resampling
    filter, and in interpolation.

    For bandlimited interpolation of discrete-time signals, the ideal
    interpolation kernel is proportional to the sinc function.

    References
    ----------
    .. [1] Weisstein, Eric W. "Sinc Function." From MathWorld--A Wolfram Web
           Resource. https://mathworld.wolfram.com/SincFunction.html
    .. [2] Wikipedia, "Sinc function",
           https://en.wikipedia.org/wiki/Sinc_function

    Examples
    --------
    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> x = np.linspace(-4, 4, 41)
    >>> np.sinc(x)
     array([-3.89804309e-17,  -4.92362781e-02,  -8.40918587e-02, # may vary
            -8.90384387e-02,  -5.84680802e-02,   3.89804309e-17,
            6.68206631e-02,   1.16434881e-01,   1.26137788e-01,
            8.50444803e-02,  -3.89804309e-17,  -1.03943254e-01,
            -1.89206682e-01,  -2.16236208e-01,  -1.55914881e-01,
            3.89804309e-17,   2.33872321e-01,   5.04551152e-01,
            7.56826729e-01,   9.35489284e-01,   1.00000000e+00,
            9.35489284e-01,   7.56826729e-01,   5.04551152e-01,
            2.33872321e-01,   3.89804309e-17,  -1.55914881e-01,
           -2.16236208e-01,  -1.89206682e-01,  -1.03943254e-01,
           -3.89804309e-17,   8.50444803e-02,   1.26137788e-01,
            1.16434881e-01,   6.68206631e-02,   3.89804309e-17,
            -5.84680802e-02,  -8.90384387e-02,  -8.40918587e-02,
            -4.92362781e-02,  -3.89804309e-17])

    >>> plt.plot(x, np.sinc(x))
    [<matplotlib.lines.Line2D object at 0x...>]
    >>> plt.title("Sinc Function")
    Text(0.5, 1.0, 'Sinc Function')
    >>> plt.ylabel("Amplitude")
    Text(0, 0.5, 'Amplitude')
    >>> plt.xlabel("X")
    Text(0.5, 0, 'X')
    >>> plt.show()

Python Library Documentation: class float32 in module numpy

class float32(floating)
 |  Single-precision floating-point number type, compatible with C ``float``.
 |
 |  :Character code: ``'f'``
 |  :Canonical name: `numpy.single`
 |  :Alias on this platform (win32 AMD64): `numpy.float32`: 32-bit-precision floating-point number type: sign bit, 8 bits exponent, 23 bits mantissa.
 |
 |  Method resolution order:
 |      float32
 |      floating
 |      inexact
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  as_integer_ratio(...)
 |      single.as_integer_ratio() -> (int, int)
 |
 |      Return a pair of integers, whose ratio is exactly equal to the original
 |      floating point number, and with a positive denominator.
 |      Raise `OverflowError` on infinities and a `ValueError` on NaNs.
 |
 |      >>> np.single(10.0).as_integer_ratio()
 |      (10, 1)
 |      >>> np.single(0.0).as_integer_ratio()
 |      (0, 1)
 |      >>> np.single(-.25).as_integer_ratio()
 |      (-1, 4)
 |
 |  is_integer(...)
 |      single.is_integer() -> bool
 |
 |      Return ``True`` if the floating point number is finite with integral
 |      value, and ``False`` otherwise.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> np.single(-2.0).is_integer()
 |      True
 |      >>> np.single(3.2).is_integer()
 |      False
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from floating:
 |
 |  __round__(...)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: function sinh in module autograd.tracer

sinh(*args, called_by_autograd_dispatcher=False, **kwargs)
    sinh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Hyperbolic sine, element-wise.

    Equivalent to ``1/2 * (np.exp(x) - np.exp(-x))`` or
    ``-1j * np.sin(1j*x)``.

    Parameters
    ----------
    x : array_like
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The corresponding hyperbolic sine values.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    If `out` is provided, the function writes the result into it,
    and returns a reference to `out`.  (See Examples)

    References
    ----------
    M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions.
    New York, NY: Dover, 1972, pg. 83.

    Examples
    --------
    >>> import numpy as np
    >>> np.sinh(0)
    0.0
    >>> np.sinh(np.pi*1j/2)
    1j
    >>> np.sinh(np.pi*1j) # (exact value is 0)
    1.2246063538223773e-016j
    >>> # Discrepancy due to vagaries of floating point arithmetic.

    >>> # Example of providing the optional output parameter
    >>> out1 = np.array([0], dtype='d')
    >>> out2 = np.sinh([0.1], out1)
    >>> out2 is out1
    True

    >>> # Example of ValueError due to provision of shape mis-matched `out`
    >>> np.sinh(np.zeros((3,3)),np.zeros((2,2)))
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ValueError: operands could not be broadcast together with shapes (3,3) (2,2)

Python Library Documentation: function size in module autograd.tracer

size(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the number of elements along a given axis.

    Parameters
    ----------
    a : array_like
        Input data.
    axis : int, optional
        Axis along which the elements are counted.  By default, give
        the total number of elements.

    Returns
    -------
    element_count : int
        Number of elements along the specified axis.

    See Also
    --------
    shape : dimensions of array
    ndarray.shape : dimensions of array
    ndarray.size : number of elements in array

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[1,2,3],[4,5,6]])
    >>> np.size(a)
    6
    >>> np.size(a,1)
    3
    >>> np.size(a,0)
    2

Python Library Documentation: function sort in module autograd.tracer

sort(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return a sorted copy of an array.

    Parameters
    ----------
    a : array_like
        Array to be sorted.
    axis : int or None, optional
        Axis along which to sort. If None, the array is flattened before
        sorting. The default is -1, which sorts along the last axis.
    kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
        Sorting algorithm. The default is 'quicksort'. Note that both 'stable'
        and 'mergesort' use timsort or radix sort under the covers and,
        in general, the actual implementation will vary with data type.
        The 'mergesort' option is retained for backwards compatibility.

        .. versionchanged:: 1.15.0.
           The 'stable' option was added.

    order : str or list of str, optional
        When `a` is an array with fields defined, this argument specifies
        which fields to compare first, second, etc.  A single field can
        be specified as a string, and not all fields need be specified,
        but unspecified fields will still be used, in the order in which
        they come up in the dtype, to break ties.
    stable : bool, optional
        Sort stability. If ``True``, the returned array will maintain
        the relative order of ``a`` values which compare as equal.
        If ``False`` or ``None``, this is not guaranteed. Internally,
        this option selects ``kind='stable'``. Default: ``None``.

        .. versionadded:: 2.0.0

    Returns
    -------
    sorted_array : ndarray
        Array of the same type and shape as `a`.

    See Also
    --------
    ndarray.sort : Method to sort an array in-place.
    argsort : Indirect sort.
    lexsort : Indirect stable sort on multiple keys.
    searchsorted : Find elements in a sorted array.
    partition : Partial sort.

    Notes
    -----
    The various sorting algorithms are characterized by their average speed,
    worst case performance, work space size, and whether they are stable. A
    stable sort keeps items with the same key in the same relative
    order. The four algorithms implemented in NumPy have the following
    properties:

    =========== ======= ============= ============ ========
       kind      speed   worst case    work space   stable
    =========== ======= ============= ============ ========
    'quicksort'    1     O(n^2)            0          no
    'heapsort'     3     O(n*log(n))       0          no
    'mergesort'    2     O(n*log(n))      ~n/2        yes
    'timsort'      2     O(n*log(n))      ~n/2        yes
    =========== ======= ============= ============ ========

    .. note:: The datatype determines which of 'mergesort' or 'timsort'
       is actually used, even if 'mergesort' is specified. User selection
       at a finer scale is not currently available.

    For performance, ``sort`` makes a temporary copy if needed to make the data
    `contiguous <https://numpy.org/doc/stable/glossary.html#term-contiguous>`_
    in memory along the sort axis. For even better performance and reduced
    memory consumption, ensure that the array is already contiguous along the
    sort axis.

    The sort order for complex numbers is lexicographic. If both the real
    and imaginary parts are non-nan then the order is determined by the
    real parts except when they are equal, in which case the order is
    determined by the imaginary parts.

    Previous to numpy 1.4.0 sorting real and complex arrays containing nan
    values led to undefined behaviour. In numpy versions >= 1.4.0 nan
    values are sorted to the end. The extended sort order is:

      * Real: [R, nan]
      * Complex: [R + Rj, R + nanj, nan + Rj, nan + nanj]

    where R is a non-nan real value. Complex values with the same nan
    placements are sorted according to the non-nan part if it exists.
    Non-nan values are sorted as before.

    .. versionadded:: 1.12.0

    quicksort has been changed to:
    `introsort <https://en.wikipedia.org/wiki/Introsort>`_.
    When sorting does not make enough progress it switches to
    `heapsort <https://en.wikipedia.org/wiki/Heapsort>`_.
    This implementation makes quicksort O(n*log(n)) in the worst case.

    'stable' automatically chooses the best stable sorting algorithm
    for the data type being sorted.
    It, along with 'mergesort' is currently mapped to
    `timsort <https://en.wikipedia.org/wiki/Timsort>`_
    or `radix sort <https://en.wikipedia.org/wiki/Radix_sort>`_
    depending on the data type.
    API forward compatibility currently limits the
    ability to select the implementation and it is hardwired for the different
    data types.

    .. versionadded:: 1.17.0

    Timsort is added for better performance on already or nearly
    sorted data. On random data timsort is almost identical to
    mergesort. It is now used for stable sort while quicksort is still the
    default sort if none is chosen. For timsort details, refer to
    `CPython listsort.txt
    <https://github.com/python/cpython/blob/3.7/Objects/listsort.txt>`_
    'mergesort' and 'stable' are mapped to radix sort for integer data types.
    Radix sort is an O(n) sort instead of O(n log n).

    .. versionchanged:: 1.18.0

    NaT now sorts to the end of arrays for consistency with NaN.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[1,4],[3,1]])
    >>> np.sort(a)                # sort along the last axis
    array([[1, 4],
           [1, 3]])
    >>> np.sort(a, axis=None)     # sort the flattened array
    array([1, 1, 3, 4])
    >>> np.sort(a, axis=0)        # sort along the first axis
    array([[1, 1],
           [3, 4]])

    Use the `order` keyword to specify a field to use when sorting a
    structured array:

    >>> dtype = [('name', 'S10'), ('height', float), ('age', int)]
    >>> values = [('Arthur', 1.8, 41), ('Lancelot', 1.9, 38),
    ...           ('Galahad', 1.7, 38)]
    >>> a = np.array(values, dtype=dtype)       # create a structured array
    >>> np.sort(a, order='height')                        # doctest: +SKIP
    array([('Galahad', 1.7, 38), ('Arthur', 1.8, 41),
           ('Lancelot', 1.8999999999999999, 38)],
          dtype=[('name', '|S10'), ('height', '<f8'), ('age', '<i4')])

    Sort by age, then height if ages are equal:

    >>> np.sort(a, order=['age', 'height'])               # doctest: +SKIP
    array([('Galahad', 1.7, 38), ('Lancelot', 1.8999999999999999, 38),
           ('Arthur', 1.8, 41)],
          dtype=[('name', '|S10'), ('height', '<f8'), ('age', '<i4')])

Python Library Documentation: function sort_complex in module autograd.tracer

sort_complex(*args, called_by_autograd_dispatcher=False, **kwargs)
    Sort a complex array using the real part first, then the imaginary part.

    Parameters
    ----------
    a : array_like
        Input array

    Returns
    -------
    out : complex ndarray
        Always returns a sorted complex array.

    Examples
    --------
    >>> import numpy as np
    >>> np.sort_complex([5, 3, 6, 2, 1])
    array([1.+0.j, 2.+0.j, 3.+0.j, 5.+0.j, 6.+0.j])

    >>> np.sort_complex([1 + 2j, 2 - 1j, 3 - 2j, 3 - 3j, 3 + 5j])
    array([1.+2.j,  2.-1.j,  3.-3.j,  3.-2.j,  3.+5.j])

Python Library Documentation: function spacing in module autograd.tracer

spacing(*args, called_by_autograd_dispatcher=False, **kwargs)
    spacing(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the distance between x and the nearest adjacent number.

    Parameters
    ----------
    x : array_like
        Values to find the spacing of.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        The spacing of values of `x`.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    It can be considered as a generalization of EPS:
    ``spacing(np.float64(1)) == np.finfo(np.float64).eps``, and there
    should not be any representable number between ``x + spacing(x)`` and
    x for any finite x.

    Spacing of +- inf and NaN is NaN.

    Examples
    --------
    >>> import numpy as np
    >>> np.spacing(1) == np.finfo(np.float64).eps
    True

Python Library Documentation: function split in module autograd.tracer

split(*args, called_by_autograd_dispatcher=False, **kwargs)
    Split an array into multiple sub-arrays as views into `ary`.

    Parameters
    ----------
    ary : ndarray
        Array to be divided into sub-arrays.
    indices_or_sections : int or 1-D array
        If `indices_or_sections` is an integer, N, the array will be divided
        into N equal arrays along `axis`.  If such a split is not possible,
        an error is raised.

        If `indices_or_sections` is a 1-D array of sorted integers, the entries
        indicate where along `axis` the array is split.  For example,
        ``[2, 3]`` would, for ``axis=0``, result in

        - ary[:2]
        - ary[2:3]
        - ary[3:]

        If an index exceeds the dimension of the array along `axis`,
        an empty sub-array is returned correspondingly.
    axis : int, optional
        The axis along which to split, default is 0.

    Returns
    -------
    sub-arrays : list of ndarrays
        A list of sub-arrays as views into `ary`.

    Raises
    ------
    ValueError
        If `indices_or_sections` is given as an integer, but
        a split does not result in equal division.

    See Also
    --------
    array_split : Split an array into multiple sub-arrays of equal or
                  near-equal size.  Does not raise an exception if
                  an equal division cannot be made.
    hsplit : Split array into multiple sub-arrays horizontally (column-wise).
    vsplit : Split array into multiple sub-arrays vertically (row wise).
    dsplit : Split array into multiple sub-arrays along the 3rd axis (depth).
    concatenate : Join a sequence of arrays along an existing axis.
    stack : Join a sequence of arrays along a new axis.
    hstack : Stack arrays in sequence horizontally (column wise).
    vstack : Stack arrays in sequence vertically (row wise).
    dstack : Stack arrays in sequence depth wise (along third dimension).

    Examples
    --------
    >>> import numpy as np
    >>> x = np.arange(9.0)
    >>> np.split(x, 3)
    [array([0.,  1.,  2.]), array([3.,  4.,  5.]), array([6.,  7.,  8.])]

    >>> x = np.arange(8.0)
    >>> np.split(x, [3, 5, 6, 10])
    [array([0.,  1.,  2.]),
     array([3.,  4.]),
     array([5.]),
     array([6.,  7.]),
     array([], dtype=float64)]

Python Library Documentation: function sqrt in module autograd.tracer

sqrt(*args, called_by_autograd_dispatcher=False, **kwargs)
    sqrt(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the non-negative square-root of an array, element-wise.

    Parameters
    ----------
    x : array_like
        The values whose square-roots are required.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        An array of the same shape as `x`, containing the positive
        square-root of each element in `x`.  If any element in `x` is
        complex, a complex array is returned (and the square-roots of
        negative reals are calculated).  If all of the elements in `x`
        are real, so is `y`, with negative elements returning ``nan``.
        If `out` was provided, `y` is a reference to it.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    emath.sqrt
        A version which returns complex numbers when given negative reals.
        Note that 0.0 and -0.0 are handled differently for complex inputs.

    Notes
    -----
    *sqrt* has--consistent with common convention--as its branch cut the
    real "interval" [`-inf`, 0), and is continuous from above on it.
    A branch cut is a curve in the complex plane across which a given
    complex function fails to be continuous.

    Examples
    --------
    >>> import numpy as np
    >>> np.sqrt([1,4,9])
    array([ 1.,  2.,  3.])

    >>> np.sqrt([4, -1, -3+4J])
    array([ 2.+0.j,  0.+1.j,  1.+2.j])

    >>> np.sqrt([4, -1, np.inf])
    array([ 2., nan, inf])

Python Library Documentation: function square in module autograd.tracer

square(*args, called_by_autograd_dispatcher=False, **kwargs)
    square(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the element-wise square of the input.

    Parameters
    ----------
    x : array_like
        Input data.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    out : ndarray or scalar
        Element-wise `x*x`, of the same shape and dtype as `x`.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    numpy.linalg.matrix_power
    sqrt
    power

    Examples
    --------
    >>> import numpy as np
    >>> np.square([-1j, 1])
    array([-1.-0.j,  1.+0.j])

Python Library Documentation: function squeeze in module autograd.tracer

squeeze(*args, called_by_autograd_dispatcher=False, **kwargs)
    Remove axes of length one from `a`.

    Parameters
    ----------
    a : array_like
        Input data.
    axis : None or int or tuple of ints, optional
        .. versionadded:: 1.7.0

        Selects a subset of the entries of length one in the
        shape. If an axis is selected with shape entry greater than
        one, an error is raised.

    Returns
    -------
    squeezed : ndarray
        The input array, but with all or a subset of the
        dimensions of length 1 removed. This is always `a` itself
        or a view into `a`. Note that if all axes are squeezed,
        the result is a 0d array and not a scalar.

    Raises
    ------
    ValueError
        If `axis` is not None, and an axis being squeezed is not of length 1

    See Also
    --------
    expand_dims : The inverse operation, adding entries of length one
    reshape : Insert, remove, and combine dimensions, and resize existing ones

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([[[0], [1], [2]]])
    >>> x.shape
    (1, 3, 1)
    >>> np.squeeze(x).shape
    (3,)
    >>> np.squeeze(x, axis=0).shape
    (3, 1)
    >>> np.squeeze(x, axis=1).shape
    Traceback (most recent call last):
    ...
    ValueError: cannot select an axis to squeeze out which has size
    not equal to one
    >>> np.squeeze(x, axis=2).shape
    (1, 3)
    >>> x = np.array([[1234]])
    >>> x.shape
    (1, 1)
    >>> np.squeeze(x)
    array(1234)  # 0d array
    >>> np.squeeze(x).shape
    ()
    >>> np.squeeze(x)[()]
    1234

Python Library Documentation: function stack in module autograd.numpy.numpy_wrapper

stack(arrays, axis=0)

Python Library Documentation: function std in module autograd.numpy.numpy_wrapper

std(a, *args, **kwargs)

Python Library Documentation: class str_ in module numpy

class str_(builtins.str, character)
 |  A unicode string.
 |
 |  This type strips trailing null codepoints.
 |
 |  >>> s = np.str_("abc\x00")
 |  >>> s
 |  'abc'
 |
 |  Unlike the builtin :class:`str`, this supports the
 |  :ref:`python:bufferobjects`, exposing its contents as UCS4:
 |
 |  >>> m = memoryview(np.str_("abc"))
 |  >>> m.format
 |  '3w'
 |  >>> m.tobytes()
 |  b'a\x00\x00\x00b\x00\x00\x00c\x00\x00\x00'
 |
 |  :Character code: ``'U'``
 |
 |  Method resolution order:
 |      str_
 |      builtins.str
 |      character
 |      flexible
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from builtins.str:
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __contains__(self, key, /)
 |      Return bool(key in self).
 |
 |  __format__(self, format_spec, /)
 |      Return a formatted version of the string as described by format_spec.
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __getnewargs__(...)
 |
 |  __iter__(self, /)
 |      Implement iter(self).
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __sizeof__(self, /)
 |      Return the size of the string in memory, in bytes.
 |
 |  capitalize(self, /)
 |      Return a capitalized version of the string.
 |
 |      More specifically, make the first character have upper case and the rest lower
 |      case.
 |
 |  casefold(self, /)
 |      Return a version of the string suitable for caseless comparisons.
 |
 |  center(self, width, fillchar=' ', /)
 |      Return a centered string of length width.
 |
 |      Padding is done using the specified fill character (default is a space).
 |
 |  count(...)
 |      S.count(sub[, start[, end]]) -> int
 |
 |      Return the number of non-overlapping occurrences of substring sub in
 |      string S[start:end].  Optional arguments start and end are
 |      interpreted as in slice notation.
 |
 |  encode(self, /, encoding='utf-8', errors='strict')
 |      Encode the string using the codec registered for encoding.
 |
 |      encoding
 |        The encoding in which to encode the string.
 |      errors
 |        The error handling scheme to use for encoding errors.
 |        The default is 'strict' meaning that encoding errors raise a
 |        UnicodeEncodeError.  Other possible values are 'ignore', 'replace' and
 |        'xmlcharrefreplace' as well as any other name registered with
 |        codecs.register_error that can handle UnicodeEncodeErrors.
 |
 |  endswith(...)
 |      S.endswith(suffix[, start[, end]]) -> bool
 |
 |      Return True if S ends with the specified suffix, False otherwise.
 |      With optional start, test S beginning at that position.
 |      With optional end, stop comparing S at that position.
 |      suffix can also be a tuple of strings to try.
 |
 |  expandtabs(self, /, tabsize=8)
 |      Return a copy where all tab characters are expanded using spaces.
 |
 |      If tabsize is not given, a tab size of 8 characters is assumed.
 |
 |  find(...)
 |      S.find(sub[, start[, end]]) -> int
 |
 |      Return the lowest index in S where substring sub is found,
 |      such that sub is contained within S[start:end].  Optional
 |      arguments start and end are interpreted as in slice notation.
 |
 |      Return -1 on failure.
 |
 |  format(...)
 |      S.format(*args, **kwargs) -> str
 |
 |      Return a formatted version of S, using substitutions from args and kwargs.
 |      The substitutions are identified by braces ('{' and '}').
 |
 |  format_map(...)
 |      S.format_map(mapping) -> str
 |
 |      Return a formatted version of S, using substitutions from mapping.
 |      The substitutions are identified by braces ('{' and '}').
 |
 |  index(...)
 |      S.index(sub[, start[, end]]) -> int
 |
 |      Return the lowest index in S where substring sub is found,
 |      such that sub is contained within S[start:end].  Optional
 |      arguments start and end are interpreted as in slice notation.
 |
 |      Raises ValueError when the substring is not found.
 |
 |  isalnum(self, /)
 |      Return True if the string is an alpha-numeric string, False otherwise.
 |
 |      A string is alpha-numeric if all characters in the string are alpha-numeric and
 |      there is at least one character in the string.
 |
 |  isalpha(self, /)
 |      Return True if the string is an alphabetic string, False otherwise.
 |
 |      A string is alphabetic if all characters in the string are alphabetic and there
 |      is at least one character in the string.
 |
 |  isascii(self, /)
 |      Return True if all characters in the string are ASCII, False otherwise.
 |
 |      ASCII characters have code points in the range U+0000-U+007F.
 |      Empty string is ASCII too.
 |
 |  isdecimal(self, /)
 |      Return True if the string is a decimal string, False otherwise.
 |
 |      A string is a decimal string if all characters in the string are decimal and
 |      there is at least one character in the string.
 |
 |  isdigit(self, /)
 |      Return True if the string is a digit string, False otherwise.
 |
 |      A string is a digit string if all characters in the string are digits and there
 |      is at least one character in the string.
 |
 |  isidentifier(self, /)
 |      Return True if the string is a valid Python identifier, False otherwise.
 |
 |      Call keyword.iskeyword(s) to test whether string s is a reserved identifier,
 |      such as "def" or "class".
 |
 |  islower(self, /)
 |      Return True if the string is a lowercase string, False otherwise.
 |
 |      A string is lowercase if all cased characters in the string are lowercase and
 |      there is at least one cased character in the string.
 |
 |  isnumeric(self, /)
 |      Return True if the string is a numeric string, False otherwise.
 |
 |      A string is numeric if all characters in the string are numeric and there is at
 |      least one character in the string.
 |
 |  isprintable(self, /)
 |      Return True if the string is printable, False otherwise.
 |
 |      A string is printable if all of its characters are considered printable in
 |      repr() or if it is empty.
 |
 |  isspace(self, /)
 |      Return True if the string is a whitespace string, False otherwise.
 |
 |      A string is whitespace if all characters in the string are whitespace and there
 |      is at least one character in the string.
 |
 |  istitle(self, /)
 |      Return True if the string is a title-cased string, False otherwise.
 |
 |      In a title-cased string, upper- and title-case characters may only
 |      follow uncased characters and lowercase characters only cased ones.
 |
 |  isupper(self, /)
 |      Return True if the string is an uppercase string, False otherwise.
 |
 |      A string is uppercase if all cased characters in the string are uppercase and
 |      there is at least one cased character in the string.
 |
 |  join(self, iterable, /)
 |      Concatenate any number of strings.
 |
 |      The string whose method is called is inserted in between each given string.
 |      The result is returned as a new string.
 |
 |      Example: '.'.join(['ab', 'pq', 'rs']) -> 'ab.pq.rs'
 |
 |  ljust(self, width, fillchar=' ', /)
 |      Return a left-justified string of length width.
 |
 |      Padding is done using the specified fill character (default is a space).
 |
 |  lower(self, /)
 |      Return a copy of the string converted to lowercase.
 |
 |  lstrip(self, chars=None, /)
 |      Return a copy of the string with leading whitespace removed.
 |
 |      If chars is given and not None, remove characters in chars instead.
 |
 |  partition(self, sep, /)
 |      Partition the string into three parts using the given separator.
 |
 |      This will search for the separator in the string.  If the separator is found,
 |      returns a 3-tuple containing the part before the separator, the separator
 |      itself, and the part after it.
 |
 |      If the separator is not found, returns a 3-tuple containing the original string
 |      and two empty strings.
 |
 |  removeprefix(self, prefix, /)
 |      Return a str with the given prefix string removed if present.
 |
 |      If the string starts with the prefix string, return string[len(prefix):].
 |      Otherwise, return a copy of the original string.
 |
 |  removesuffix(self, suffix, /)
 |      Return a str with the given suffix string removed if present.
 |
 |      If the string ends with the suffix string and that suffix is not empty,
 |      return string[:-len(suffix)]. Otherwise, return a copy of the original
 |      string.
 |
 |  replace(self, old, new, count=-1, /)
 |      Return a copy with all occurrences of substring old replaced by new.
 |
 |        count
 |          Maximum number of occurrences to replace.
 |          -1 (the default value) means replace all occurrences.
 |
 |      If the optional argument count is given, only the first count occurrences are
 |      replaced.
 |
 |  rfind(...)
 |      S.rfind(sub[, start[, end]]) -> int
 |
 |      Return the highest index in S where substring sub is found,
 |      such that sub is contained within S[start:end].  Optional
 |      arguments start and end are interpreted as in slice notation.
 |
 |      Return -1 on failure.
 |
 |  rindex(...)
 |      S.rindex(sub[, start[, end]]) -> int
 |
 |      Return the highest index in S where substring sub is found,
 |      such that sub is contained within S[start:end].  Optional
 |      arguments start and end are interpreted as in slice notation.
 |
 |      Raises ValueError when the substring is not found.
 |
 |  rjust(self, width, fillchar=' ', /)
 |      Return a right-justified string of length width.
 |
 |      Padding is done using the specified fill character (default is a space).
 |
 |  rpartition(self, sep, /)
 |      Partition the string into three parts using the given separator.
 |
 |      This will search for the separator in the string, starting at the end. If
 |      the separator is found, returns a 3-tuple containing the part before the
 |      separator, the separator itself, and the part after it.
 |
 |      If the separator is not found, returns a 3-tuple containing two empty strings
 |      and the original string.
 |
 |  rsplit(self, /, sep=None, maxsplit=-1)
 |      Return a list of the substrings in the string, using sep as the separator string.
 |
 |        sep
 |          The separator used to split the string.
 |
 |          When set to None (the default value), will split on any whitespace
 |          character (including \n \r \t \f and spaces) and will discard
 |          empty strings from the result.
 |        maxsplit
 |          Maximum number of splits.
 |          -1 (the default value) means no limit.
 |
 |      Splitting starts at the end of the string and works to the front.
 |
 |  rstrip(self, chars=None, /)
 |      Return a copy of the string with trailing whitespace removed.
 |
 |      If chars is given and not None, remove characters in chars instead.
 |
 |  split(self, /, sep=None, maxsplit=-1)
 |      Return a list of the substrings in the string, using sep as the separator string.
 |
 |        sep
 |          The separator used to split the string.
 |
 |          When set to None (the default value), will split on any whitespace
 |          character (including \n \r \t \f and spaces) and will discard
 |          empty strings from the result.
 |        maxsplit
 |          Maximum number of splits.
 |          -1 (the default value) means no limit.
 |
 |      Splitting starts at the front of the string and works to the end.
 |
 |      Note, str.split() is mainly useful for data that has been intentionally
 |      delimited.  With natural text that includes punctuation, consider using
 |      the regular expression module.
 |
 |  splitlines(self, /, keepends=False)
 |      Return a list of the lines in the string, breaking at line boundaries.
 |
 |      Line breaks are not included in the resulting list unless keepends is given and
 |      true.
 |
 |  startswith(...)
 |      S.startswith(prefix[, start[, end]]) -> bool
 |
 |      Return True if S starts with the specified prefix, False otherwise.
 |      With optional start, test S beginning at that position.
 |      With optional end, stop comparing S at that position.
 |      prefix can also be a tuple of strings to try.
 |
 |  strip(self, chars=None, /)
 |      Return a copy of the string with leading and trailing whitespace removed.
 |
 |      If chars is given and not None, remove characters in chars instead.
 |
 |  swapcase(self, /)
 |      Convert uppercase characters to lowercase and lowercase characters to uppercase.
 |
 |  title(self, /)
 |      Return a version of the string where each word is titlecased.
 |
 |      More specifically, words start with uppercased characters and all remaining
 |      cased characters have lower case.
 |
 |  translate(self, table, /)
 |      Replace each character in the string using the given translation table.
 |
 |        table
 |          Translation table, which must be a mapping of Unicode ordinals to
 |          Unicode ordinals, strings, or None.
 |
 |      The table must implement lookup/indexing via __getitem__, for instance a
 |      dictionary or list.  If this operation raises LookupError, the character is
 |      left untouched.  Characters mapped to None are deleted.
 |
 |  upper(self, /)
 |      Return a copy of the string converted to uppercase.
 |
 |  zfill(self, width, /)
 |      Pad a numeric string with zeros on the left, to fill a field of the given width.
 |
 |      The string is never truncated.
 |
 |  ----------------------------------------------------------------------
 |  Static methods inherited from builtins.str:
 |
 |  maketrans(...)
 |      Return a translation table usable for str.translate().
 |
 |      If there is only one argument, it must be a dictionary mapping Unicode
 |      ordinals (integers) or characters to Unicode ordinals, strings or None.
 |      Character keys will be then converted to ordinals.
 |      If there are two arguments, they must be strings of equal length, and
 |      in the resulting dictionary, each character in x will be mapped to the
 |      character at the same position in y. If there is a third argument, it
 |      must be a string, whose characters will be mapped to None in the result.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: function subtract in module autograd.tracer

subtract(*args, called_by_autograd_dispatcher=False, **kwargs)
    subtract(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Subtract arguments, element-wise.

    Parameters
    ----------
    x1, x2 : array_like
        The arrays to be subtracted from each other.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The difference of `x1` and `x2`, element-wise.
        This is a scalar if both `x1` and `x2` are scalars.

    Notes
    -----
    Equivalent to ``x1 - x2`` in terms of array broadcasting.

    Examples
    --------
    >>> import numpy as np
    >>> np.subtract(1.0, 4.0)
    -3.0

    >>> x1 = np.arange(9.0).reshape((3, 3))
    >>> x2 = np.arange(3.0)
    >>> np.subtract(x1, x2)
    array([[ 0.,  0.,  0.],
           [ 3.,  3.,  3.],
           [ 6.,  6.,  6.]])

    The ``-`` operator can be used as a shorthand for ``np.subtract`` on
    ndarrays.

    >>> x1 = np.arange(9.0).reshape((3, 3))
    >>> x2 = np.arange(3.0)
    >>> x1 - x2
    array([[0., 0., 0.],
           [3., 3., 3.],
           [6., 6., 6.]])

Python Library Documentation: function sum in module autograd.tracer

sum(*args, called_by_autograd_dispatcher=False, **kwargs)
    Sum of array elements over a given axis.

    Parameters
    ----------
    a : array_like
        Elements to sum.
    axis : None or int or tuple of ints, optional
        Axis or axes along which a sum is performed.  The default,
        axis=None, will sum all of the elements of the input array.  If
        axis is negative it counts from the last to the first axis.

        .. versionadded:: 1.7.0

        If axis is a tuple of ints, a sum is performed on all of the axes
        specified in the tuple instead of a single axis or all the axes as
        before.
    dtype : dtype, optional
        The type of the returned array and of the accumulator in which the
        elements are summed.  The dtype of `a` is used by default unless `a`
        has an integer dtype of less precision than the default platform
        integer.  In that case, if `a` is signed then the platform integer
        is used while if `a` is unsigned then an unsigned integer of the
        same precision as the platform integer is used.
    out : ndarray, optional
        Alternative output array in which to place the result. It must have
        the same shape as the expected output, but the type of the output
        values will be cast if necessary.
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the input array.

        If the default value is passed, then `keepdims` will not be
        passed through to the `sum` method of sub-classes of
        `ndarray`, however any non-default value will be.  If the
        sub-class' method does not implement `keepdims` any
        exceptions will be raised.
    initial : scalar, optional
        Starting value for the sum. See `~numpy.ufunc.reduce` for details.

        .. versionadded:: 1.15.0

    where : array_like of bool, optional
        Elements to include in the sum. See `~numpy.ufunc.reduce` for details.

        .. versionadded:: 1.17.0

    Returns
    -------
    sum_along_axis : ndarray
        An array with the same shape as `a`, with the specified
        axis removed.   If `a` is a 0-d array, or if `axis` is None, a scalar
        is returned.  If an output array is specified, a reference to
        `out` is returned.

    See Also
    --------
    ndarray.sum : Equivalent method.
    add: ``numpy.add.reduce`` equivalent function.
    cumsum : Cumulative sum of array elements.
    trapezoid : Integration of array values using composite trapezoidal rule.

    mean, average

    Notes
    -----
    Arithmetic is modular when using integer types, and no error is
    raised on overflow.

    The sum of an empty array is the neutral element 0:

    >>> np.sum([])
    0.0

    For floating point numbers the numerical precision of sum (and
    ``np.add.reduce``) is in general limited by directly adding each number
    individually to the result causing rounding errors in every step.
    However, often numpy will use a  numerically better approach (partial
    pairwise summation) leading to improved precision in many use-cases.
    This improved precision is always provided when no ``axis`` is given.
    When ``axis`` is given, it will depend on which axis is summed.
    Technically, to provide the best speed possible, the improved precision
    is only used when the summation is along the fast axis in memory.
    Note that the exact precision may vary depending on other parameters.
    In contrast to NumPy, Python's ``math.fsum`` function uses a slower but
    more precise approach to summation.
    Especially when summing a large number of lower precision floating point
    numbers, such as ``float32``, numerical errors can become significant.
    In such cases it can be advisable to use `dtype="float64"` to use a higher
    precision for the output.

    Examples
    --------
    >>> import numpy as np
    >>> np.sum([0.5, 1.5])
    2.0
    >>> np.sum([0.5, 0.7, 0.2, 1.5], dtype=np.int32)
    1
    >>> np.sum([[0, 1], [0, 5]])
    6
    >>> np.sum([[0, 1], [0, 5]], axis=0)
    array([0, 6])
    >>> np.sum([[0, 1], [0, 5]], axis=1)
    array([1, 5])
    >>> np.sum([[0, 1], [np.nan, 5]], where=[False, True], axis=1)
    array([1., 5.])

    If the accumulator is too small, overflow occurs:

    >>> np.ones(128, dtype=np.int8).sum(dtype=np.int8)
    -128

    You can also start the sum with a value other than zero:

    >>> np.sum([10], initial=5)
    15

Python Library Documentation: function swapaxes in module autograd.tracer

swapaxes(*args, called_by_autograd_dispatcher=False, **kwargs)
    Interchange two axes of an array.

    Parameters
    ----------
    a : array_like
        Input array.
    axis1 : int
        First axis.
    axis2 : int
        Second axis.

    Returns
    -------
    a_swapped : ndarray
        For NumPy >= 1.10.0, if `a` is an ndarray, then a view of `a` is
        returned; otherwise a new array is created. For earlier NumPy
        versions a view of `a` is returned only if the order of the
        axes is changed, otherwise the input array is returned.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([[1,2,3]])
    >>> np.swapaxes(x,0,1)
    array([[1],
           [2],
           [3]])

    >>> x = np.array([[[0,1],[2,3]],[[4,5],[6,7]]])
    >>> x
    array([[[0, 1],
            [2, 3]],
           [[4, 5],
            [6, 7]]])

    >>> np.swapaxes(x,0,2)
    array([[[0, 4],
            [2, 6]],
           [[1, 5],
            [3, 7]]])

Python Library Documentation: function take in module autograd.tracer

take(*args, called_by_autograd_dispatcher=False, **kwargs)
    Take elements from an array along an axis.

    When axis is not None, this function does the same thing as "fancy"
    indexing (indexing arrays using arrays); however, it can be easier to use
    if you need elements along a given axis. A call such as
    ``np.take(arr, indices, axis=3)`` is equivalent to
    ``arr[:,:,:,indices,...]``.

    Explained without fancy indexing, this is equivalent to the following use
    of `ndindex`, which sets each of ``ii``, ``jj``, and ``kk`` to a tuple of
    indices::

        Ni, Nk = a.shape[:axis], a.shape[axis+1:]
        Nj = indices.shape
        for ii in ndindex(Ni):
            for jj in ndindex(Nj):
                for kk in ndindex(Nk):
                    out[ii + jj + kk] = a[ii + (indices[jj],) + kk]

    Parameters
    ----------
    a : array_like (Ni..., M, Nk...)
        The source array.
    indices : array_like (Nj...)
        The indices of the values to extract.

        .. versionadded:: 1.8.0

        Also allow scalars for indices.
    axis : int, optional
        The axis over which to select values. By default, the flattened
        input array is used.
    out : ndarray, optional (Ni..., Nj..., Nk...)
        If provided, the result will be placed in this array. It should
        be of the appropriate shape and dtype. Note that `out` is always
        buffered if `mode='raise'`; use other modes for better performance.
    mode : {'raise', 'wrap', 'clip'}, optional
        Specifies how out-of-bounds indices will behave.

        * 'raise' -- raise an error (default)
        * 'wrap' -- wrap around
        * 'clip' -- clip to the range

        'clip' mode means that all indices that are too large are replaced
        by the index that addresses the last element along that axis. Note
        that this disables indexing with negative numbers.

    Returns
    -------
    out : ndarray (Ni..., Nj..., Nk...)
        The returned array has the same type as `a`.

    See Also
    --------
    compress : Take elements using a boolean mask
    ndarray.take : equivalent method
    take_along_axis : Take elements by matching the array and the index arrays

    Notes
    -----

    By eliminating the inner loop in the description above, and using `s_` to
    build simple slice objects, `take` can be expressed  in terms of applying
    fancy indexing to each 1-d slice::

        Ni, Nk = a.shape[:axis], a.shape[axis+1:]
        for ii in ndindex(Ni):
            for kk in ndindex(Nj):
                out[ii + s_[...,] + kk] = a[ii + s_[:,] + kk][indices]

    For this reason, it is equivalent to (but faster than) the following use
    of `apply_along_axis`::

        out = np.apply_along_axis(lambda a_1d: a_1d[indices], axis, a)

    Examples
    --------
    >>> import numpy as np
    >>> a = [4, 3, 5, 7, 6, 8]
    >>> indices = [0, 1, 4]
    >>> np.take(a, indices)
    array([4, 3, 6])

    In this example if `a` is an ndarray, "fancy" indexing can be used.

    >>> a = np.array(a)
    >>> a[indices]
    array([4, 3, 6])

    If `indices` is not one dimensional, the output also has these dimensions.

    >>> np.take(a, [[0, 1], [2, 3]])
    array([[4, 3],
           [5, 7]])

Python Library Documentation: function take_along_axis in module autograd.tracer

take_along_axis(*args, called_by_autograd_dispatcher=False, **kwargs)
    Take values from the input array by matching 1d index and data slices.

    This iterates over matching 1d slices oriented along the specified axis in
    the index and data arrays, and uses the former to look up values in the
    latter. These slices can be different lengths.

    Functions returning an index along an axis, like `argsort` and
    `argpartition`, produce suitable indices for this function.

    .. versionadded:: 1.15.0

    Parameters
    ----------
    arr : ndarray (Ni..., M, Nk...)
        Source array
    indices : ndarray (Ni..., J, Nk...)
        Indices to take along each 1d slice of `arr`. This must match the
        dimension of arr, but dimensions Ni and Nj only need to broadcast
        against `arr`.
    axis : int
        The axis to take 1d slices along. If axis is None, the input array is
        treated as if it had first been flattened to 1d, for consistency with
        `sort` and `argsort`.

    Returns
    -------
    out: ndarray (Ni..., J, Nk...)
        The indexed result.

    Notes
    -----
    This is equivalent to (but faster than) the following use of `ndindex` and
    `s_`, which sets each of ``ii`` and ``kk`` to a tuple of indices::

        Ni, M, Nk = a.shape[:axis], a.shape[axis], a.shape[axis+1:]
        J = indices.shape[axis]  # Need not equal M
        out = np.empty(Ni + (J,) + Nk)

        for ii in ndindex(Ni):
            for kk in ndindex(Nk):
                a_1d       = a      [ii + s_[:,] + kk]
                indices_1d = indices[ii + s_[:,] + kk]
                out_1d     = out    [ii + s_[:,] + kk]
                for j in range(J):
                    out_1d[j] = a_1d[indices_1d[j]]

    Equivalently, eliminating the inner loop, the last two lines would be::

                out_1d[:] = a_1d[indices_1d]

    See Also
    --------
    take : Take along an axis, using the same indices for every 1d slice
    put_along_axis :
        Put values into the destination array by matching 1d index and data slices

    Examples
    --------
    >>> import numpy as np

    For this sample array

    >>> a = np.array([[10, 30, 20], [60, 40, 50]])

    We can sort either by using sort directly, or argsort and this function

    >>> np.sort(a, axis=1)
    array([[10, 20, 30],
           [40, 50, 60]])
    >>> ai = np.argsort(a, axis=1)
    >>> ai
    array([[0, 2, 1],
           [1, 2, 0]])
    >>> np.take_along_axis(a, ai, axis=1)
    array([[10, 20, 30],
           [40, 50, 60]])

    The same works for max and min, if you maintain the trivial dimension
    with ``keepdims``:

    >>> np.max(a, axis=1, keepdims=True)
    array([[30],
           [60]])
    >>> ai = np.argmax(a, axis=1, keepdims=True)
    >>> ai
    array([[1],
           [0]])
    >>> np.take_along_axis(a, ai, axis=1)
    array([[30],
           [60]])

    If we want to get the max and min at the same time, we can stack the
    indices first

    >>> ai_min = np.argmin(a, axis=1, keepdims=True)
    >>> ai_max = np.argmax(a, axis=1, keepdims=True)
    >>> ai = np.concatenate([ai_min, ai_max], axis=1)
    >>> ai
    array([[0, 1],
           [1, 0]])
    >>> np.take_along_axis(a, ai, axis=1)
    array([[10, 30],
           [40, 60]])

Python Library Documentation: function tan in module autograd.tracer

tan(*args, called_by_autograd_dispatcher=False, **kwargs)
    tan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Compute tangent element-wise.

    Equivalent to ``np.sin(x)/np.cos(x)`` element-wise.

    Parameters
    ----------
    x : array_like
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The corresponding tangent values.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    If `out` is provided, the function writes the result into it,
    and returns a reference to `out`.  (See Examples)

    References
    ----------
    M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions.
    New York, NY: Dover, 1972.

    Examples
    --------
    >>> import numpy as np
    >>> from math import pi
    >>> np.tan(np.array([-pi,pi/2,pi]))
    array([  1.22460635e-16,   1.63317787e+16,  -1.22460635e-16])
    >>>
    >>> # Example of providing the optional output parameter illustrating
    >>> # that what is returned is a reference to said parameter
    >>> out1 = np.array([0], dtype='d')
    >>> out2 = np.cos([0.1], out1)
    >>> out2 is out1
    True
    >>>
    >>> # Example of ValueError due to provision of shape mis-matched `out`
    >>> np.cos(np.zeros((3,3)),np.zeros((2,2)))
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ValueError: operands could not be broadcast together with shapes (3,3) (2,2)

Python Library Documentation: function tanh in module autograd.tracer

tanh(*args, called_by_autograd_dispatcher=False, **kwargs)
    tanh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Compute hyperbolic tangent element-wise.

    Equivalent to ``np.sinh(x)/np.cosh(x)`` or ``-1j * np.tan(1j*x)``.

    Parameters
    ----------
    x : array_like
        Input array.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The corresponding hyperbolic tangent values.
        This is a scalar if `x` is a scalar.

    Notes
    -----
    If `out` is provided, the function writes the result into it,
    and returns a reference to `out`.  (See Examples)

    References
    ----------
    .. [1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions.
           New York, NY: Dover, 1972, pg. 83.
           https://personal.math.ubc.ca/~cbm/aands/page_83.htm

    .. [2] Wikipedia, "Hyperbolic function",
           https://en.wikipedia.org/wiki/Hyperbolic_function

    Examples
    --------
    >>> import numpy as np
    >>> np.tanh((0, np.pi*1j, np.pi*1j/2))
    array([ 0. +0.00000000e+00j,  0. -1.22460635e-16j,  0. +1.63317787e+16j])

    >>> # Example of providing the optional output parameter illustrating
    >>> # that what is returned is a reference to said parameter
    >>> out1 = np.array([0], dtype='d')
    >>> out2 = np.tanh([0.1], out1)
    >>> out2 is out1
    True

    >>> # Example of ValueError due to provision of shape mis-matched `out`
    >>> np.tanh(np.zeros((3,3)),np.zeros((2,2)))
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ValueError: operands could not be broadcast together with shapes (3,3) (2,2)

Python Library Documentation: function tensordot in module autograd.tracer

tensordot(*args, called_by_autograd_dispatcher=False, **kwargs)
    Compute tensor dot product along specified axes.

    Given two tensors, `a` and `b`, and an array_like object containing
    two array_like objects, ``(a_axes, b_axes)``, sum the products of
    `a`'s and `b`'s elements (components) over the axes specified by
    ``a_axes`` and ``b_axes``. The third argument can be a single non-negative
    integer_like scalar, ``N``; if it is such, then the last ``N`` dimensions
    of `a` and the first ``N`` dimensions of `b` are summed over.

    Parameters
    ----------
    a, b : array_like
        Tensors to "dot".

    axes : int or (2,) array_like
        * integer_like
          If an int N, sum over the last N axes of `a` and the first N axes
          of `b` in order. The sizes of the corresponding axes must match.
        * (2,) array_like
          Or, a list of axes to be summed over, first sequence applying to `a`,
          second to `b`. Both elements array_like must be of the same length.

    Returns
    -------
    output : ndarray
        The tensor dot product of the input.

    See Also
    --------
    dot, einsum

    Notes
    -----
    Three common use cases are:

    * ``axes = 0`` : tensor product :math:`a\otimes b`
    * ``axes = 1`` : tensor dot product :math:`a\cdot b`
    * ``axes = 2`` : (default) tensor double contraction :math:`a:b`

    When `axes` is a positive integer ``N``, the operation starts with
    axis ``-N`` of `a` and axis ``0`` of `b`, and it continues through
    axis ``-1`` of `a` and axis ``N-1`` of `b` (inclusive).

    When there is more than one axis to sum over - and they are not the last
    (first) axes of `a` (`b`) - the argument `axes` should consist of
    two sequences of the same length, with the first axis to sum over given
    first in both sequences, the second axis second, and so forth.

    The shape of the result consists of the non-contracted axes of the
    first tensor, followed by the non-contracted axes of the second.

    Examples
    --------
    A "traditional" example:

    >>> import numpy as np
    >>> a = np.arange(60.).reshape(3,4,5)
    >>> b = np.arange(24.).reshape(4,3,2)
    >>> c = np.tensordot(a,b, axes=([1,0],[0,1]))
    >>> c.shape
    (5, 2)
    >>> c
    array([[4400., 4730.],
           [4532., 4874.],
           [4664., 5018.],
           [4796., 5162.],
           [4928., 5306.]])
    >>> # A slower but equivalent way of computing the same...
    >>> d = np.zeros((5,2))
    >>> for i in range(5):
    ...   for j in range(2):
    ...     for k in range(3):
    ...       for n in range(4):
    ...         d[i,j] += a[k,n,i] * b[n,k,j]
    >>> c == d
    array([[ True,  True],
           [ True,  True],
           [ True,  True],
           [ True,  True],
           [ True,  True]])

    An extended example taking advantage of the overloading of + and \*:

    >>> a = np.array(range(1, 9))
    >>> a.shape = (2, 2, 2)
    >>> A = np.array(('a', 'b', 'c', 'd'), dtype=object)
    >>> A.shape = (2, 2)
    >>> a; A
    array([[[1, 2],
            [3, 4]],
           [[5, 6],
            [7, 8]]])
    array([['a', 'b'],
           ['c', 'd']], dtype=object)

    >>> np.tensordot(a, A) # third argument default is 2 for double-contraction
    array(['abbcccdddd', 'aaaaabbbbbbcccccccdddddddd'], dtype=object)

    >>> np.tensordot(a, A, 1)
    array([[['acc', 'bdd'],
            ['aaacccc', 'bbbdddd']],
           [['aaaaacccccc', 'bbbbbdddddd'],
            ['aaaaaaacccccccc', 'bbbbbbbdddddddd']]], dtype=object)

    >>> np.tensordot(a, A, 0) # tensor product (result too long to incl.)
    array([[[[['a', 'b'],
              ['c', 'd']],
              ...

    >>> np.tensordot(a, A, (0, 1))
    array([[['abbbbb', 'cddddd'],
            ['aabbbbbb', 'ccdddddd']],
           [['aaabbbbbbb', 'cccddddddd'],
            ['aaaabbbbbbbb', 'ccccdddddddd']]], dtype=object)

    >>> np.tensordot(a, A, (2, 1))
    array([[['abb', 'cdd'],
            ['aaabbbb', 'cccdddd']],
           [['aaaaabbbbbb', 'cccccdddddd'],
            ['aaaaaaabbbbbbbb', 'cccccccdddddddd']]], dtype=object)

    >>> np.tensordot(a, A, ((0, 1), (0, 1)))
    array(['abbbcccccddddddd', 'aabbbbccccccdddddddd'], dtype=object)

    >>> np.tensordot(a, A, ((2, 1), (1, 0)))
    array(['acccbbdddd', 'aaaaacccccccbbbbbbdddddddd'], dtype=object)

Python Library Documentation: function [unknown name] in module autograd.tracer

[unknown name](*args, called_by_autograd_dispatcher=False, **kwargs)
    Pytest test runner.

    A test function is typically added to a package's __init__.py like so::

      from numpy._pytesttester import PytestTester
      test = PytestTester(__name__).test
      del PytestTester

    Calling this test function finds and runs all tests associated with the
    module and all its sub-modules.

    Attributes
    ----------
    module_name : str
        Full path to the package to test.

    Parameters
    ----------
    module_name : module name
        The name of the module to test.

    Notes
    -----
    Unlike the previous ``nose``-based implementation, this class is not
    publicly exposed as it performs some ``numpy``-specific warning
    suppression.

Python Library Documentation: function tile in module autograd.tracer

tile(*args, called_by_autograd_dispatcher=False, **kwargs)
    Construct an array by repeating A the number of times given by reps.

    If `reps` has length ``d``, the result will have dimension of
    ``max(d, A.ndim)``.

    If ``A.ndim < d``, `A` is promoted to be d-dimensional by prepending new
    axes. So a shape (3,) array is promoted to (1, 3) for 2-D replication,
    or shape (1, 1, 3) for 3-D replication. If this is not the desired
    behavior, promote `A` to d-dimensions manually before calling this
    function.

    If ``A.ndim > d``, `reps` is promoted to `A`.ndim by prepending 1's to it.
    Thus for an `A` of shape (2, 3, 4, 5), a `reps` of (2, 2) is treated as
    (1, 1, 2, 2).

    Note : Although tile may be used for broadcasting, it is strongly
    recommended to use numpy's broadcasting operations and functions.

    Parameters
    ----------
    A : array_like
        The input array.
    reps : array_like
        The number of repetitions of `A` along each axis.

    Returns
    -------
    c : ndarray
        The tiled output array.

    See Also
    --------
    repeat : Repeat elements of an array.
    broadcast_to : Broadcast an array to a new shape

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([0, 1, 2])
    >>> np.tile(a, 2)
    array([0, 1, 2, 0, 1, 2])
    >>> np.tile(a, (2, 2))
    array([[0, 1, 2, 0, 1, 2],
           [0, 1, 2, 0, 1, 2]])
    >>> np.tile(a, (2, 1, 2))
    array([[[0, 1, 2, 0, 1, 2]],
           [[0, 1, 2, 0, 1, 2]]])

    >>> b = np.array([[1, 2], [3, 4]])
    >>> np.tile(b, 2)
    array([[1, 2, 1, 2],
           [3, 4, 3, 4]])
    >>> np.tile(b, (2, 1))
    array([[1, 2],
           [3, 4],
           [1, 2],
           [3, 4]])

    >>> c = np.array([1,2,3,4])
    >>> np.tile(c,(4,1))
    array([[1, 2, 3, 4],
           [1, 2, 3, 4],
           [1, 2, 3, 4],
           [1, 2, 3, 4]])

Python Library Documentation: class timedelta64 in module numpy

class timedelta64(signedinteger)
 |  A timedelta stored as a 64-bit integer.
 |
 |  See :ref:`arrays.datetime` for more information.
 |
 |  :Character code: ``'m'``
 |
 |  Method resolution order:
 |      timedelta64
 |      signedinteger
 |      integer
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: function trace in module autograd.tracer

trace(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the sum along diagonals of the array.

    If `a` is 2-D, the sum along its diagonal with the given offset
    is returned, i.e., the sum of elements ``a[i,i+offset]`` for all i.

    If `a` has more than two dimensions, then the axes specified by axis1 and
    axis2 are used to determine the 2-D sub-arrays whose traces are returned.
    The shape of the resulting array is the same as that of `a` with `axis1`
    and `axis2` removed.

    Parameters
    ----------
    a : array_like
        Input array, from which the diagonals are taken.
    offset : int, optional
        Offset of the diagonal from the main diagonal. Can be both positive
        and negative. Defaults to 0.
    axis1, axis2 : int, optional
        Axes to be used as the first and second axis of the 2-D sub-arrays
        from which the diagonals should be taken. Defaults are the first two
        axes of `a`.
    dtype : dtype, optional
        Determines the data-type of the returned array and of the accumulator
        where the elements are summed. If dtype has the value None and `a` is
        of integer type of precision less than the default integer
        precision, then the default integer precision is used. Otherwise,
        the precision is the same as that of `a`.
    out : ndarray, optional
        Array into which the output is placed. Its type is preserved and
        it must be of the right shape to hold the output.

    Returns
    -------
    sum_along_diagonals : ndarray
        If `a` is 2-D, the sum along the diagonal is returned.  If `a` has
        larger dimensions, then an array of sums along diagonals is returned.

    See Also
    --------
    diag, diagonal, diagflat

    Examples
    --------
    >>> import numpy as np
    >>> np.trace(np.eye(3))
    3.0
    >>> a = np.arange(8).reshape((2,2,2))
    >>> np.trace(a)
    array([6, 8])

    >>> a = np.arange(24).reshape((2,2,2,3))
    >>> np.trace(a).shape
    (2, 3)

Python Library Documentation: function transpose in module autograd.tracer

transpose(*args, called_by_autograd_dispatcher=False, **kwargs)
    Returns an array with axes transposed.

    For a 1-D array, this returns an unchanged view of the original array, as a
    transposed vector is simply the same vector.
    To convert a 1-D array into a 2-D column vector, an additional dimension
    must be added, e.g., ``np.atleast_2d(a).T`` achieves this, as does
    ``a[:, np.newaxis]``.
    For a 2-D array, this is the standard matrix transpose.
    For an n-D array, if axes are given, their order indicates how the
    axes are permuted (see Examples). If axes are not provided, then
    ``transpose(a).shape == a.shape[::-1]``.

    Parameters
    ----------
    a : array_like
        Input array.
    axes : tuple or list of ints, optional
        If specified, it must be a tuple or list which contains a permutation
        of [0,1,...,N-1] where N is the number of axes of `a`. The `i`'th axis
        of the returned array will correspond to the axis numbered ``axes[i]``
        of the input. If not specified, defaults to ``range(a.ndim)[::-1]``,
        which reverses the order of the axes.

    Returns
    -------
    p : ndarray
        `a` with its axes permuted. A view is returned whenever possible.

    See Also
    --------
    ndarray.transpose : Equivalent method.
    moveaxis : Move axes of an array to new positions.
    argsort : Return the indices that would sort an array.

    Notes
    -----
    Use ``transpose(a, argsort(axes))`` to invert the transposition of tensors
    when using the `axes` keyword argument.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[1, 2], [3, 4]])
    >>> a
    array([[1, 2],
           [3, 4]])
    >>> np.transpose(a)
    array([[1, 3],
           [2, 4]])

    >>> a = np.array([1, 2, 3, 4])
    >>> a
    array([1, 2, 3, 4])
    >>> np.transpose(a)
    array([1, 2, 3, 4])

    >>> a = np.ones((1, 2, 3))
    >>> np.transpose(a, (1, 0, 2)).shape
    (2, 1, 3)

    >>> a = np.ones((2, 3, 4, 5))
    >>> np.transpose(a).shape
    (5, 4, 3, 2)

Python Library Documentation: function trapezoid in module autograd.tracer

trapezoid(*args, called_by_autograd_dispatcher=False, **kwargs)
    Integrate along the given axis using the composite trapezoidal rule.

    If `x` is provided, the integration happens in sequence along its
    elements - they are not sorted.

    Integrate `y` (`x`) along each 1d slice on the given axis, compute
    :math:`\int y(x) dx`.
    When `x` is specified, this integrates along the parametric curve,
    computing :math:`\int_t y(t) dt =
    \int_t y(t) \left.\frac{dx}{dt}\right|_{x=x(t)} dt`.

    .. versionadded:: 2.0.0

    Parameters
    ----------
    y : array_like
        Input array to integrate.
    x : array_like, optional
        The sample points corresponding to the `y` values. If `x` is None,
        the sample points are assumed to be evenly spaced `dx` apart. The
        default is None.
    dx : scalar, optional
        The spacing between sample points when `x` is None. The default is 1.
    axis : int, optional
        The axis along which to integrate.

    Returns
    -------
    trapezoid : float or ndarray
        Definite integral of `y` = n-dimensional array as approximated along
        a single axis by the trapezoidal rule. If `y` is a 1-dimensional array,
        then the result is a float. If `n` is greater than 1, then the result
        is an `n`-1 dimensional array.

    See Also
    --------
    sum, cumsum

    Notes
    -----
    Image [2]_ illustrates trapezoidal rule -- y-axis locations of points
    will be taken from `y` array, by default x-axis distances between
    points will be 1.0, alternatively they can be provided with `x` array
    or with `dx` scalar.  Return value will be equal to combined area under
    the red lines.


    References
    ----------
    .. [1] Wikipedia page: https://en.wikipedia.org/wiki/Trapezoidal_rule

    .. [2] Illustration image:
           https://en.wikipedia.org/wiki/File:Composite_trapezoidal_rule_illustration.png

    Examples
    --------
    >>> import numpy as np

    Use the trapezoidal rule on evenly spaced points:

    >>> np.trapezoid([1, 2, 3])
    4.0

    The spacing between sample points can be selected by either the
    ``x`` or ``dx`` arguments:

    >>> np.trapezoid([1, 2, 3], x=[4, 6, 8])
    8.0
    >>> np.trapezoid([1, 2, 3], dx=2)
    8.0

    Using a decreasing ``x`` corresponds to integrating in reverse:

    >>> np.trapezoid([1, 2, 3], x=[8, 6, 4])
    -8.0

    More generally ``x`` is used to integrate along a parametric curve. We can
    estimate the integral :math:`\int_0^1 x^2 = 1/3` using:

    >>> x = np.linspace(0, 1, num=50)
    >>> y = x**2
    >>> np.trapezoid(y, x)
    0.33340274885464394

    Or estimate the area of a circle, noting we repeat the sample which closes
    the curve:

    >>> theta = np.linspace(0, 2 * np.pi, num=1000, endpoint=True)
    >>> np.trapezoid(np.cos(theta), x=np.sin(theta))
    3.141571941375841

    ``np.trapezoid`` can be applied along a specified axis to do multiple
    computations in one call:

    >>> a = np.arange(6).reshape(2, 3)
    >>> a
    array([[0, 1, 2],
           [3, 4, 5]])
    >>> np.trapezoid(a, axis=0)
    array([1.5, 2.5, 3.5])
    >>> np.trapezoid(a, axis=1)
    array([2.,  8.])

Python Library Documentation: function trapz in module autograd.tracer

trapz(*args, called_by_autograd_dispatcher=False, **kwargs)
    `trapz` is deprecated in NumPy 2.0.

    Please use `trapezoid` instead, or one of the numerical integration
    functions in `scipy.integrate`.

Python Library Documentation: function tri in module autograd.tracer

tri(*args, called_by_autograd_dispatcher=False, **kwargs)
    An array with ones at and below the given diagonal and zeros elsewhere.

    Parameters
    ----------
    N : int
        Number of rows in the array.
    M : int, optional
        Number of columns in the array.
        By default, `M` is taken equal to `N`.
    k : int, optional
        The sub-diagonal at and below which the array is filled.
        `k` = 0 is the main diagonal, while `k` < 0 is below it,
        and `k` > 0 is above.  The default is 0.
    dtype : dtype, optional
        Data type of the returned array.  The default is float.
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    tri : ndarray of shape (N, M)
        Array with its lower triangle filled with ones and zero elsewhere;
        in other words ``T[i,j] == 1`` for ``j <= i + k``, 0 otherwise.

    Examples
    --------
    >>> import numpy as np
    >>> np.tri(3, 5, 2, dtype=int)
    array([[1, 1, 1, 0, 0],
           [1, 1, 1, 1, 0],
           [1, 1, 1, 1, 1]])

    >>> np.tri(3, 5, -1)
    array([[0.,  0.,  0.,  0.,  0.],
           [1.,  0.,  0.,  0.,  0.],
           [1.,  1.,  0.,  0.,  0.]])

Python Library Documentation: function tril in module autograd.tracer

tril(*args, called_by_autograd_dispatcher=False, **kwargs)
    Lower triangle of an array.

    Return a copy of an array with elements above the `k`-th diagonal zeroed.
    For arrays with ``ndim`` exceeding 2, `tril` will apply to the final two
    axes.

    Parameters
    ----------
    m : array_like, shape (..., M, N)
        Input array.
    k : int, optional
        Diagonal above which to zero elements.  `k = 0` (the default) is the
        main diagonal, `k < 0` is below it and `k > 0` is above.

    Returns
    -------
    tril : ndarray, shape (..., M, N)
        Lower triangle of `m`, of same shape and data-type as `m`.

    See Also
    --------
    triu : same thing, only for the upper triangle

    Examples
    --------
    >>> import numpy as np
    >>> np.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
    array([[ 0,  0,  0],
           [ 4,  0,  0],
           [ 7,  8,  0],
           [10, 11, 12]])

    >>> np.tril(np.arange(3*4*5).reshape(3, 4, 5))
    array([[[ 0,  0,  0,  0,  0],
            [ 5,  6,  0,  0,  0],
            [10, 11, 12,  0,  0],
            [15, 16, 17, 18,  0]],
           [[20,  0,  0,  0,  0],
            [25, 26,  0,  0,  0],
            [30, 31, 32,  0,  0],
            [35, 36, 37, 38,  0]],
           [[40,  0,  0,  0,  0],
            [45, 46,  0,  0,  0],
            [50, 51, 52,  0,  0],
            [55, 56, 57, 58,  0]]])

Python Library Documentation: function tril_indices in module autograd.tracer

tril_indices(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the indices for the lower-triangle of an (n, m) array.

    Parameters
    ----------
    n : int
        The row dimension of the arrays for which the returned
        indices will be valid.
    k : int, optional
        Diagonal offset (see `tril` for details).
    m : int, optional
        .. versionadded:: 1.9.0

        The column dimension of the arrays for which the returned
        arrays will be valid.
        By default `m` is taken equal to `n`.


    Returns
    -------
    inds : tuple of arrays
        The indices for the triangle. The returned tuple contains two arrays,
        each with the indices along one dimension of the array.

    See also
    --------
    triu_indices : similar function, for upper-triangular.
    mask_indices : generic function accepting an arbitrary mask function.
    tril, triu

    Notes
    -----
    .. versionadded:: 1.4.0

    Examples
    --------
    >>> import numpy as np

    Compute two different sets of indices to access 4x4 arrays, one for the
    lower triangular part starting at the main diagonal, and one starting two
    diagonals further right:

    >>> il1 = np.tril_indices(4)
    >>> il2 = np.tril_indices(4, 2)

    Here is how they can be used with a sample array:

    >>> a = np.arange(16).reshape(4, 4)
    >>> a
    array([[ 0,  1,  2,  3],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11],
           [12, 13, 14, 15]])

    Both for indexing:

    >>> a[il1]
    array([ 0,  4,  5, ..., 13, 14, 15])

    And for assigning values:

    >>> a[il1] = -1
    >>> a
    array([[-1,  1,  2,  3],
           [-1, -1,  6,  7],
           [-1, -1, -1, 11],
           [-1, -1, -1, -1]])

    These cover almost the whole array (two diagonals right of the main one):

    >>> a[il2] = -10
    >>> a
    array([[-10, -10, -10,   3],
           [-10, -10, -10, -10],
           [-10, -10, -10, -10],
           [-10, -10, -10, -10]])

Python Library Documentation: function tril_indices_from in module autograd.tracer

tril_indices_from(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the indices for the lower-triangle of arr.

    See `tril_indices` for full details.

    Parameters
    ----------
    arr : array_like
        The indices will be valid for square arrays whose dimensions are
        the same as arr.
    k : int, optional
        Diagonal offset (see `tril` for details).

    Examples
    --------
    >>> import numpy as np

    Create a 4 by 4 array

    >>> a = np.arange(16).reshape(4, 4)
    >>> a
    array([[ 0,  1,  2,  3],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11],
           [12, 13, 14, 15]])

    Pass the array to get the indices of the lower triangular elements.

    >>> trili = np.tril_indices_from(a)
    >>> trili
    (array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3]), array([0, 0, 1, 0, 1, 2, 0, 1, 2, 3]))

    >>> a[trili]
    array([ 0,  4,  5,  8,  9, 10, 12, 13, 14, 15])

    This is syntactic sugar for tril_indices().

    >>> np.tril_indices(a.shape[0])
    (array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3]), array([0, 0, 1, 0, 1, 2, 0, 1, 2, 3]))

    Use the `k` parameter to return the indices for the lower triangular array
    up to the k-th diagonal.

    >>> trili1 = np.tril_indices_from(a, k=1)
    >>> a[trili1]
    array([ 0,  1,  4,  5,  6,  8,  9, 10, 11, 12, 13, 14, 15])

    See Also
    --------
    tril_indices, tril, triu_indices_from

    Notes
    -----
    .. versionadded:: 1.4.0

Python Library Documentation: function trim_zeros in module autograd.tracer

trim_zeros(*args, called_by_autograd_dispatcher=False, **kwargs)
    Trim the leading and/or trailing zeros from a 1-D array or sequence.

    Parameters
    ----------
    filt : 1-D array or sequence
        Input array.
    trim : str, optional
        A string with 'f' representing trim from front and 'b' to trim from
        back. Default is 'fb', trim zeros from both front and back of the
        array.

    Returns
    -------
    trimmed : 1-D array or sequence
        The result of trimming the input. The input data type is preserved.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array((0, 0, 0, 1, 2, 3, 0, 2, 1, 0))
    >>> np.trim_zeros(a)
    array([1, 2, 3, 0, 2, 1])

    >>> np.trim_zeros(a, 'b')
    array([0, 0, 0, ..., 0, 2, 1])

    The input data type is preserved, list/tuple in means list/tuple out.

    >>> np.trim_zeros([0, 1, 2, 0])
    [1, 2]

Python Library Documentation: function triu in module autograd.tracer

triu(*args, called_by_autograd_dispatcher=False, **kwargs)
    Upper triangle of an array.

    Return a copy of an array with the elements below the `k`-th diagonal
    zeroed. For arrays with ``ndim`` exceeding 2, `triu` will apply to the
    final two axes.

    Please refer to the documentation for `tril` for further details.

    See Also
    --------
    tril : lower triangle of an array

    Examples
    --------
    >>> import numpy as np
    >>> np.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
    array([[ 1,  2,  3],
           [ 4,  5,  6],
           [ 0,  8,  9],
           [ 0,  0, 12]])

    >>> np.triu(np.arange(3*4*5).reshape(3, 4, 5))
    array([[[ 0,  1,  2,  3,  4],
            [ 0,  6,  7,  8,  9],
            [ 0,  0, 12, 13, 14],
            [ 0,  0,  0, 18, 19]],
           [[20, 21, 22, 23, 24],
            [ 0, 26, 27, 28, 29],
            [ 0,  0, 32, 33, 34],
            [ 0,  0,  0, 38, 39]],
           [[40, 41, 42, 43, 44],
            [ 0, 46, 47, 48, 49],
            [ 0,  0, 52, 53, 54],
            [ 0,  0,  0, 58, 59]]])

Python Library Documentation: function triu_indices in module autograd.tracer

triu_indices(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the indices for the upper-triangle of an (n, m) array.

    Parameters
    ----------
    n : int
        The size of the arrays for which the returned indices will
        be valid.
    k : int, optional
        Diagonal offset (see `triu` for details).
    m : int, optional
        .. versionadded:: 1.9.0

        The column dimension of the arrays for which the returned
        arrays will be valid.
        By default `m` is taken equal to `n`.


    Returns
    -------
    inds : tuple, shape(2) of ndarrays, shape(`n`)
        The indices for the triangle. The returned tuple contains two arrays,
        each with the indices along one dimension of the array.  Can be used
        to slice a ndarray of shape(`n`, `n`).

    See also
    --------
    tril_indices : similar function, for lower-triangular.
    mask_indices : generic function accepting an arbitrary mask function.
    triu, tril

    Notes
    -----
    .. versionadded:: 1.4.0

    Examples
    --------
    >>> import numpy as np

    Compute two different sets of indices to access 4x4 arrays, one for the
    upper triangular part starting at the main diagonal, and one starting two
    diagonals further right:

    >>> iu1 = np.triu_indices(4)
    >>> iu2 = np.triu_indices(4, 2)

    Here is how they can be used with a sample array:

    >>> a = np.arange(16).reshape(4, 4)
    >>> a
    array([[ 0,  1,  2,  3],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11],
           [12, 13, 14, 15]])

    Both for indexing:

    >>> a[iu1]
    array([ 0,  1,  2, ..., 10, 11, 15])

    And for assigning values:

    >>> a[iu1] = -1
    >>> a
    array([[-1, -1, -1, -1],
           [ 4, -1, -1, -1],
           [ 8,  9, -1, -1],
           [12, 13, 14, -1]])

    These cover only a small part of the whole array (two diagonals right
    of the main one):

    >>> a[iu2] = -10
    >>> a
    array([[ -1,  -1, -10, -10],
           [  4,  -1,  -1, -10],
           [  8,   9,  -1,  -1],
           [ 12,  13,  14,  -1]])

Python Library Documentation: function triu_indices_from in module autograd.tracer

triu_indices_from(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return the indices for the upper-triangle of arr.

    See `triu_indices` for full details.

    Parameters
    ----------
    arr : ndarray, shape(N, N)
        The indices will be valid for square arrays.
    k : int, optional
        Diagonal offset (see `triu` for details).

    Returns
    -------
    triu_indices_from : tuple, shape(2) of ndarray, shape(N)
        Indices for the upper-triangle of `arr`.

    Examples
    --------
    >>> import numpy as np

    Create a 4 by 4 array

    >>> a = np.arange(16).reshape(4, 4)
    >>> a
    array([[ 0,  1,  2,  3],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11],
           [12, 13, 14, 15]])

    Pass the array to get the indices of the upper triangular elements.

    >>> triui = np.triu_indices_from(a)
    >>> triui
    (array([0, 0, 0, 0, 1, 1, 1, 2, 2, 3]), array([0, 1, 2, 3, 1, 2, 3, 2, 3, 3]))

    >>> a[triui]
    array([ 0,  1,  2,  3,  5,  6,  7, 10, 11, 15])

    This is syntactic sugar for triu_indices().

    >>> np.triu_indices(a.shape[0])
    (array([0, 0, 0, 0, 1, 1, 1, 2, 2, 3]), array([0, 1, 2, 3, 1, 2, 3, 2, 3, 3]))

    Use the `k` parameter to return the indices for the upper triangular array
    from the k-th diagonal.

    >>> triuim1 = np.triu_indices_from(a, k=1)
    >>> a[triuim1]
    array([ 1,  2,  3,  6,  7, 11])


    See Also
    --------
    triu_indices, triu, tril_indices_from

    Notes
    -----
    .. versionadded:: 1.4.0

Python Library Documentation: function divide in module autograd.tracer

divide(*args, called_by_autograd_dispatcher=False, **kwargs)
    divide(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Divide arguments element-wise.

    Parameters
    ----------
    x1 : array_like
        Dividend array.
    x2 : array_like
        Divisor array.
        If ``x1.shape != x2.shape``, they must be broadcastable to a common
        shape (which becomes the shape of the output).
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray or scalar
        The quotient ``x1/x2``, element-wise.
        This is a scalar if both `x1` and `x2` are scalars.

    See Also
    --------
    seterr : Set whether to raise or warn on overflow, underflow and
             division by zero.

    Notes
    -----
    Equivalent to ``x1`` / ``x2`` in terms of array-broadcasting.

    The ``true_divide(x1, x2)`` function is an alias for
    ``divide(x1, x2)``.

    Examples
    --------
    >>> import numpy as np
    >>> np.divide(2.0, 4.0)
    0.5
    >>> x1 = np.arange(9.0).reshape((3, 3))
    >>> x2 = np.arange(3.0)
    >>> np.divide(x1, x2)
    array([[nan, 1. , 1. ],
           [inf, 4. , 2.5],
           [inf, 7. , 4. ]])

    The ``/`` operator can be used as a shorthand for ``np.divide`` on
    ndarrays.

    >>> x1 = np.arange(9.0).reshape((3, 3))
    >>> x2 = 2 * np.ones(3)
    >>> x1 / x2
    array([[0. , 0.5, 1. ],
           [1.5, 2. , 2.5],
           [3. , 3.5, 4. ]])

Python Library Documentation: function trunc in module autograd.tracer

trunc(*args, called_by_autograd_dispatcher=False, **kwargs)
    trunc(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

    Return the truncated value of the input, element-wise.

    The truncated value of the scalar `x` is the nearest integer `i` which
    is closer to zero than `x` is. In short, the fractional part of the
    signed number `x` is discarded.

    Parameters
    ----------
    x : array_like
        Input data.
    out : ndarray, None, or tuple of ndarray and None, optional
        A location into which the result is stored. If provided, it must have
        a shape that the inputs broadcast to. If not provided or None,
        a freshly-allocated array is returned. A tuple (possible only as a
        keyword argument) must have length equal to the number of outputs.
    where : array_like, optional
        This condition is broadcast over the input. At locations where the
        condition is True, the `out` array will be set to the ufunc result.
        Elsewhere, the `out` array will retain its original value.
        Note that if an uninitialized `out` array is created via the default
        ``out=None``, locations within it where the condition is False will
        remain uninitialized.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray or scalar
        The truncated value of each element in `x`.
        This is a scalar if `x` is a scalar.

    See Also
    --------
    ceil, floor, rint, fix

    Notes
    -----
    .. versionadded:: 1.3.0

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
    >>> np.trunc(a)
    array([-1., -1., -0.,  0.,  1.,  1.,  2.])

Python Library Documentation: function typename in module autograd.tracer

typename(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return a description for the given data type code.

    Parameters
    ----------
    char : str
        Data type code.

    Returns
    -------
    out : str
        Description of the input data type code.

    See Also
    --------
    dtype

    Examples
    --------
    >>> import numpy as np
    >>> typechars = ['S1', '?', 'B', 'D', 'G', 'F', 'I', 'H', 'L', 'O', 'Q',
    ...              'S', 'U', 'V', 'b', 'd', 'g', 'f', 'i', 'h', 'l', 'q']
    >>> for typechar in typechars:
    ...     print(typechar, ' : ', np.typename(typechar))
    ...
    S1  :  character
    ?  :  bool
    B  :  unsigned char
    D  :  complex double precision
    G  :  complex long double precision
    F  :  complex single precision
    I  :  unsigned integer
    H  :  unsigned short
    L  :  unsigned long integer
    O  :  object
    Q  :  unsigned long long integer
    S  :  string
    U  :  unicode
    V  :  void
    b  :  signed char
    d  :  double precision
    g  :  long precision
    f  :  single precision
    i  :  integer
    h  :  short
    l  :  long integer
    q  :  long long integer

Python Library Documentation: class uint8 in module numpy

class uint8(unsignedinteger)
 |  Unsigned integer type, compatible with C ``unsigned char``.
 |
 |  :Character code: ``'B'``
 |  :Canonical name: `numpy.ubyte`
 |  :Alias on this platform (win32 AMD64): `numpy.uint8`: 8-bit unsigned integer (``0`` to ``255``).
 |
 |  Method resolution order:
 |      uint8
 |      unsignedinteger
 |      integer
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      uint8.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.uint8(127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class ufunc in module numpy

class ufunc(builtins.object)
 |  Functions that operate element by element on whole arrays.
 |
 |  To see the documentation for a specific ufunc, use `info`.  For
 |  example, ``np.info(np.sin)``.  Because ufuncs are written in C
 |  (for speed) and linked into Python with NumPy's ufunc facility,
 |  Python's help() function finds this page whenever help() is called
 |  on a ufunc.
 |
 |  A detailed explanation of ufuncs can be found in the docs for :ref:`ufuncs`.
 |
 |  **Calling ufuncs:** ``op(*x[, out], where=True, **kwargs)``
 |
 |  Apply `op` to the arguments `*x` elementwise, broadcasting the arguments.
 |
 |  The broadcasting rules are:
 |
 |  * Dimensions of length 1 may be prepended to either array.
 |  * Arrays may be repeated along dimensions of length 1.
 |
 |  Parameters
 |  ----------
 |  *x : array_like
 |      Input arrays.
 |  out : ndarray, None, or tuple of ndarray and None, optional
 |      Alternate array object(s) in which to put the result; if provided, it
 |      must have a shape that the inputs broadcast to. A tuple of arrays
 |      (possible only as a keyword argument) must have length equal to the
 |      number of outputs; use None for uninitialized outputs to be
 |      allocated by the ufunc.
 |  where : array_like, optional
 |      This condition is broadcast over the input. At locations where the
 |      condition is True, the `out` array will be set to the ufunc result.
 |      Elsewhere, the `out` array will retain its original value.
 |      Note that if an uninitialized `out` array is created via the default
 |      ``out=None``, locations within it where the condition is False will
 |      remain uninitialized.
 |  **kwargs
 |      For other keyword-only arguments, see the :ref:`ufunc docs <ufuncs.kwargs>`.
 |
 |  Returns
 |  -------
 |  r : ndarray or tuple of ndarray
 |      `r` will have the shape that the arrays in `x` broadcast to; if `out` is
 |      provided, it will be returned. If not, `r` will be allocated and
 |      may contain uninitialized values. If the function has more than one
 |      output, then the result will be a tuple of arrays.
 |
 |  Methods defined here:
 |
 |  __call__(self, /, *args, **kwargs)
 |      Call self as a function.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  accumulate(...)
 |      accumulate(array, axis=0, dtype=None, out=None)
 |
 |      Accumulate the result of applying the operator to all elements.
 |
 |      For a one-dimensional array, accumulate produces results equivalent to::
 |
 |        r = np.empty(len(A))
 |        t = op.identity        # op = the ufunc being applied to A's  elements
 |        for i in range(len(A)):
 |            t = op(t, A[i])
 |            r[i] = t
 |        return r
 |
 |      For example, add.accumulate() is equivalent to np.cumsum().
 |
 |      For a multi-dimensional array, accumulate is applied along only one
 |      axis (axis zero by default; see Examples below) so repeated use is
 |      necessary if one wants to accumulate over multiple axes.
 |
 |      Parameters
 |      ----------
 |      array : array_like
 |          The array to act on.
 |      axis : int, optional
 |          The axis along which to apply the accumulation; default is zero.
 |      dtype : data-type code, optional
 |          The data-type used to represent the intermediate results. Defaults
 |          to the data-type of the output array if such is provided, or the
 |          data-type of the input array if no output array is provided.
 |      out : ndarray, None, or tuple of ndarray and None, optional
 |          A location into which the result is stored. If not provided or None,
 |          a freshly-allocated array is returned. For consistency with
 |          ``ufunc.__call__``, if given as a keyword, this may be wrapped in a
 |          1-element tuple.
 |
 |          .. versionchanged:: 1.13.0
 |             Tuples are allowed for keyword argument.
 |
 |      Returns
 |      -------
 |      r : ndarray
 |          The accumulated values. If `out` was supplied, `r` is a reference to
 |          `out`.
 |
 |      Examples
 |      --------
 |      1-D array examples:
 |
 |      >>> import numpy as np
 |      >>> np.add.accumulate([2, 3, 5])
 |      array([ 2,  5, 10])
 |      >>> np.multiply.accumulate([2, 3, 5])
 |      array([ 2,  6, 30])
 |
 |      2-D array examples:
 |
 |      >>> I = np.eye(2)
 |      >>> I
 |      array([[1.,  0.],
 |             [0.,  1.]])
 |
 |      Accumulate along axis 0 (rows), down columns:
 |
 |      >>> np.add.accumulate(I, 0)
 |      array([[1.,  0.],
 |             [1.,  1.]])
 |      >>> np.add.accumulate(I) # no axis specified = axis zero
 |      array([[1.,  0.],
 |             [1.,  1.]])
 |
 |      Accumulate along axis 1 (columns), through rows:
 |
 |      >>> np.add.accumulate(I, 1)
 |      array([[1.,  1.],
 |             [0.,  1.]])
 |
 |  at(...)
 |      at(a, indices, b=None, /)
 |
 |      Performs unbuffered in place operation on operand 'a' for elements
 |      specified by 'indices'. For addition ufunc, this method is equivalent to
 |      ``a[indices] += b``, except that results are accumulated for elements that
 |      are indexed more than once. For example, ``a[[0,0]] += 1`` will only
 |      increment the first element once because of buffering, whereas
 |      ``add.at(a, [0,0], 1)`` will increment the first element twice.
 |
 |      .. versionadded:: 1.8.0
 |
 |      Parameters
 |      ----------
 |      a : array_like
 |          The array to perform in place operation on.
 |      indices : array_like or tuple
 |          Array like index object or slice object for indexing into first
 |          operand. If first operand has multiple dimensions, indices can be a
 |          tuple of array like index objects or slice objects.
 |      b : array_like
 |          Second operand for ufuncs requiring two operands. Operand must be
 |          broadcastable over first operand after indexing or slicing.
 |
 |      Examples
 |      --------
 |      Set items 0 and 1 to their negative values:
 |
 |      >>> import numpy as np
 |      >>> a = np.array([1, 2, 3, 4])
 |      >>> np.negative.at(a, [0, 1])
 |      >>> a
 |      array([-1, -2,  3,  4])
 |
 |      Increment items 0 and 1, and increment item 2 twice:
 |
 |      >>> a = np.array([1, 2, 3, 4])
 |      >>> np.add.at(a, [0, 1, 2, 2], 1)
 |      >>> a
 |      array([2, 3, 5, 4])
 |
 |      Add items 0 and 1 in first array to second array,
 |      and store results in first array:
 |
 |      >>> a = np.array([1, 2, 3, 4])
 |      >>> b = np.array([1, 2])
 |      >>> np.add.at(a, [0, 1], b)
 |      >>> a
 |      array([2, 4, 3, 4])
 |
 |  outer(...)
 |      outer(A, B, /, **kwargs)
 |
 |      Apply the ufunc `op` to all pairs (a, b) with a in `A` and b in `B`.
 |
 |      Let ``M = A.ndim``, ``N = B.ndim``. Then the result, `C`, of
 |      ``op.outer(A, B)`` is an array of dimension M + N such that:
 |
 |      .. math:: C[i_0, ..., i_{M-1}, j_0, ..., j_{N-1}] =
 |         op(A[i_0, ..., i_{M-1}], B[j_0, ..., j_{N-1}])
 |
 |      For `A` and `B` one-dimensional, this is equivalent to::
 |
 |        r = empty(len(A),len(B))
 |        for i in range(len(A)):
 |            for j in range(len(B)):
 |                r[i,j] = op(A[i], B[j])  # op = ufunc in question
 |
 |      Parameters
 |      ----------
 |      A : array_like
 |          First array
 |      B : array_like
 |          Second array
 |      kwargs : any
 |          Arguments to pass on to the ufunc. Typically `dtype` or `out`.
 |          See `ufunc` for a comprehensive overview of all available arguments.
 |
 |      Returns
 |      -------
 |      r : ndarray
 |          Output array
 |
 |      See Also
 |      --------
 |      numpy.outer : A less powerful version of ``np.multiply.outer``
 |                    that `ravel`\ s all inputs to 1D. This exists
 |                    primarily for compatibility with old code.
 |
 |      tensordot : ``np.tensordot(a, b, axes=((), ()))`` and
 |                  ``np.multiply.outer(a, b)`` behave same for all
 |                  dimensions of a and b.
 |
 |      Examples
 |      --------
 |      >>> np.multiply.outer([1, 2, 3], [4, 5, 6])
 |      array([[ 4,  5,  6],
 |             [ 8, 10, 12],
 |             [12, 15, 18]])
 |
 |      A multi-dimensional example:
 |
 |      >>> A = np.array([[1, 2, 3], [4, 5, 6]])
 |      >>> A.shape
 |      (2, 3)
 |      >>> B = np.array([[1, 2, 3, 4]])
 |      >>> B.shape
 |      (1, 4)
 |      >>> C = np.multiply.outer(A, B)
 |      >>> C.shape; C
 |      (2, 3, 1, 4)
 |      array([[[[ 1,  2,  3,  4]],
 |              [[ 2,  4,  6,  8]],
 |              [[ 3,  6,  9, 12]]],
 |             [[[ 4,  8, 12, 16]],
 |              [[ 5, 10, 15, 20]],
 |              [[ 6, 12, 18, 24]]]])
 |
 |  reduce(...)
 |      reduce(array, axis=0, dtype=None, out=None, keepdims=False, initial=<no value>, where=True)
 |
 |      Reduces `array`'s dimension by one, by applying ufunc along one axis.
 |
 |      Let :math:`array.shape = (N_0, ..., N_i, ..., N_{M-1})`.  Then
 |      :math:`ufunc.reduce(array, axis=i)[k_0, ..,k_{i-1}, k_{i+1}, .., k_{M-1}]` =
 |      the result of iterating `j` over :math:`range(N_i)`, cumulatively applying
 |      ufunc to each :math:`array[k_0, ..,k_{i-1}, j, k_{i+1}, .., k_{M-1}]`.
 |      For a one-dimensional array, reduce produces results equivalent to:
 |      ::
 |
 |       r = op.identity # op = ufunc
 |       for i in range(len(A)):
 |         r = op(r, A[i])
 |       return r
 |
 |      For example, add.reduce() is equivalent to sum().
 |
 |      Parameters
 |      ----------
 |      array : array_like
 |          The array to act on.
 |      axis : None or int or tuple of ints, optional
 |          Axis or axes along which a reduction is performed.
 |          The default (`axis` = 0) is perform a reduction over the first
 |          dimension of the input array. `axis` may be negative, in
 |          which case it counts from the last to the first axis.
 |
 |          .. versionadded:: 1.7.0
 |
 |          If this is None, a reduction is performed over all the axes.
 |          If this is a tuple of ints, a reduction is performed on multiple
 |          axes, instead of a single axis or all the axes as before.
 |
 |          For operations which are either not commutative or not associative,
 |          doing a reduction over multiple axes is not well-defined. The
 |          ufuncs do not currently raise an exception in this case, but will
 |          likely do so in the future.
 |      dtype : data-type code, optional
 |          The data type used to perform the operation. Defaults to that of
 |          ``out`` if given, and the data type of ``array`` otherwise (though
 |          upcast to conserve precision for some cases, such as
 |          ``numpy.add.reduce`` for integer or boolean input).
 |      out : ndarray, None, or tuple of ndarray and None, optional
 |          A location into which the result is stored. If not provided or None,
 |          a freshly-allocated array is returned. For consistency with
 |          ``ufunc.__call__``, if given as a keyword, this may be wrapped in a
 |          1-element tuple.
 |
 |          .. versionchanged:: 1.13.0
 |             Tuples are allowed for keyword argument.
 |      keepdims : bool, optional
 |          If this is set to True, the axes which are reduced are left
 |          in the result as dimensions with size one. With this option,
 |          the result will broadcast correctly against the original `array`.
 |
 |          .. versionadded:: 1.7.0
 |      initial : scalar, optional
 |          The value with which to start the reduction.
 |          If the ufunc has no identity or the dtype is object, this defaults
 |          to None - otherwise it defaults to ufunc.identity.
 |          If ``None`` is given, the first element of the reduction is used,
 |          and an error is thrown if the reduction is empty.
 |
 |          .. versionadded:: 1.15.0
 |
 |      where : array_like of bool, optional
 |          A boolean array which is broadcasted to match the dimensions
 |          of `array`, and selects elements to include in the reduction. Note
 |          that for ufuncs like ``minimum`` that do not have an identity
 |          defined, one has to pass in also ``initial``.
 |
 |          .. versionadded:: 1.17.0
 |
 |      Returns
 |      -------
 |      r : ndarray
 |          The reduced array. If `out` was supplied, `r` is a reference to it.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.multiply.reduce([2,3,5])
 |      30
 |
 |      A multi-dimensional array example:
 |
 |      >>> X = np.arange(8).reshape((2,2,2))
 |      >>> X
 |      array([[[0, 1],
 |              [2, 3]],
 |             [[4, 5],
 |              [6, 7]]])
 |      >>> np.add.reduce(X, 0)
 |      array([[ 4,  6],
 |             [ 8, 10]])
 |      >>> np.add.reduce(X) # confirm: default axis value is 0
 |      array([[ 4,  6],
 |             [ 8, 10]])
 |      >>> np.add.reduce(X, 1)
 |      array([[ 2,  4],
 |             [10, 12]])
 |      >>> np.add.reduce(X, 2)
 |      array([[ 1,  5],
 |             [ 9, 13]])
 |
 |      You can use the ``initial`` keyword argument to initialize the reduction
 |      with a different value, and ``where`` to select specific elements to include:
 |
 |      >>> np.add.reduce([10], initial=5)
 |      15
 |      >>> np.add.reduce(np.ones((2, 2, 2)), axis=(0, 2), initial=10)
 |      array([14., 14.])
 |      >>> a = np.array([10., np.nan, 10])
 |      >>> np.add.reduce(a, where=~np.isnan(a))
 |      20.0
 |
 |      Allows reductions of empty arrays where they would normally fail, i.e.
 |      for ufuncs without an identity.
 |
 |      >>> np.minimum.reduce([], initial=np.inf)
 |      inf
 |      >>> np.minimum.reduce([[1., 2.], [3., 4.]], initial=10., where=[True, False])
 |      array([ 1., 10.])
 |      >>> np.minimum.reduce([])
 |      Traceback (most recent call last):
 |          ...
 |      ValueError: zero-size array to reduction operation minimum which has no identity
 |
 |  reduceat(...)
 |      reduceat(array, indices, axis=0, dtype=None, out=None)
 |
 |      Performs a (local) reduce with specified slices over a single axis.
 |
 |      For i in ``range(len(indices))``, `reduceat` computes
 |      ``ufunc.reduce(array[indices[i]:indices[i+1]])``, which becomes the i-th
 |      generalized "row" parallel to `axis` in the final result (i.e., in a
 |      2-D array, for example, if `axis = 0`, it becomes the i-th row, but if
 |      `axis = 1`, it becomes the i-th column).  There are three exceptions to this:
 |
 |      * when ``i = len(indices) - 1`` (so for the last index),
 |        ``indices[i+1] = array.shape[axis]``.
 |      * if ``indices[i] >= indices[i + 1]``, the i-th generalized "row" is
 |        simply ``array[indices[i]]``.
 |      * if ``indices[i] >= len(array)`` or ``indices[i] < 0``, an error is raised.
 |
 |      The shape of the output depends on the size of `indices`, and may be
 |      larger than `array` (this happens if ``len(indices) > array.shape[axis]``).
 |
 |      Parameters
 |      ----------
 |      array : array_like
 |          The array to act on.
 |      indices : array_like
 |          Paired indices, comma separated (not colon), specifying slices to
 |          reduce.
 |      axis : int, optional
 |          The axis along which to apply the reduceat.
 |      dtype : data-type code, optional
 |          The data type used to perform the operation. Defaults to that of
 |          ``out`` if given, and the data type of ``array`` otherwise (though
 |          upcast to conserve precision for some cases, such as
 |          ``numpy.add.reduce`` for integer or boolean input).
 |      out : ndarray, None, or tuple of ndarray and None, optional
 |          A location into which the result is stored. If not provided or None,
 |          a freshly-allocated array is returned. For consistency with
 |          ``ufunc.__call__``, if given as a keyword, this may be wrapped in a
 |          1-element tuple.
 |
 |          .. versionchanged:: 1.13.0
 |             Tuples are allowed for keyword argument.
 |
 |      Returns
 |      -------
 |      r : ndarray
 |          The reduced values. If `out` was supplied, `r` is a reference to
 |          `out`.
 |
 |      Notes
 |      -----
 |      A descriptive example:
 |
 |      If `array` is 1-D, the function `ufunc.accumulate(array)` is the same as
 |      ``ufunc.reduceat(array, indices)[::2]`` where `indices` is
 |      ``range(len(array) - 1)`` with a zero placed
 |      in every other element:
 |      ``indices = zeros(2 * len(array) - 1)``,
 |      ``indices[1::2] = range(1, len(array))``.
 |
 |      Don't be fooled by this attribute's name: `reduceat(array)` is not
 |      necessarily smaller than `array`.
 |
 |      Examples
 |      --------
 |      To take the running sum of four successive values:
 |
 |      >>> import numpy as np
 |      >>> np.add.reduceat(np.arange(8),[0,4, 1,5, 2,6, 3,7])[::2]
 |      array([ 6, 10, 14, 18])
 |
 |      A 2-D example:
 |
 |      >>> x = np.linspace(0, 15, 16).reshape(4,4)
 |      >>> x
 |      array([[ 0.,   1.,   2.,   3.],
 |             [ 4.,   5.,   6.,   7.],
 |             [ 8.,   9.,  10.,  11.],
 |             [12.,  13.,  14.,  15.]])
 |
 |      ::
 |
 |       # reduce such that the result has the following five rows:
 |       # [row1 + row2 + row3]
 |       # [row4]
 |       # [row2]
 |       # [row3]
 |       # [row1 + row2 + row3 + row4]
 |
 |      >>> np.add.reduceat(x, [0, 3, 1, 2, 0])
 |      array([[12.,  15.,  18.,  21.],
 |             [12.,  13.,  14.,  15.],
 |             [ 4.,   5.,   6.,   7.],
 |             [ 8.,   9.,  10.,  11.],
 |             [24.,  28.,  32.,  36.]])
 |
 |      ::
 |
 |       # reduce such that result has the following two columns:
 |       # [col1 * col2 * col3, col4]
 |
 |      >>> np.multiply.reduceat(x, [0, 3], 1)
 |      array([[   0.,     3.],
 |             [ 120.,     7.],
 |             [ 720.,    11.],
 |             [2184.,    15.]])
 |
 |  resolve_dtypes(...)
 |      resolve_dtypes(dtypes, *, signature=None, casting=None, reduction=False)
 |
 |      Find the dtypes NumPy will use for the operation.  Both input and
 |      output dtypes are returned and may differ from those provided.
 |
 |      .. note::
 |
 |          This function always applies NEP 50 rules since it is not provided
 |          any actual values.  The Python types ``int``, ``float``, and
 |          ``complex`` thus behave weak and should be passed for "untyped"
 |          Python input.
 |
 |      Parameters
 |      ----------
 |      dtypes : tuple of dtypes, None, or literal int, float, complex
 |          The input dtypes for each operand.  Output operands can be
 |          None, indicating that the dtype must be found.
 |      signature : tuple of DTypes or None, optional
 |          If given, enforces exact DType (classes) of the specific operand.
 |          The ufunc ``dtype`` argument is equivalent to passing a tuple with
 |          only output dtypes set.
 |      casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
 |          The casting mode when casting is necessary.  This is identical to
 |          the ufunc call casting modes.
 |      reduction : boolean
 |          If given, the resolution assumes a reduce operation is happening
 |          which slightly changes the promotion and type resolution rules.
 |          `dtypes` is usually something like ``(None, np.dtype("i2"), None)``
 |          for reductions (first input is also the output).
 |
 |          .. note::
 |
 |              The default casting mode is "same_kind", however, as of
 |              NumPy 1.24, NumPy uses "unsafe" for reductions.
 |
 |      Returns
 |      -------
 |      dtypes : tuple of dtypes
 |          The dtypes which NumPy would use for the calculation.  Note that
 |          dtypes may not match the passed in ones (casting is necessary).
 |
 |
 |      Examples
 |      --------
 |      This API requires passing dtypes, define them for convenience:
 |
 |      >>> import numpy as np
 |      >>> int32 = np.dtype("int32")
 |      >>> float32 = np.dtype("float32")
 |
 |      The typical ufunc call does not pass an output dtype.  `numpy.add` has two
 |      inputs and one output, so leave the output as ``None`` (not provided):
 |
 |      >>> np.add.resolve_dtypes((int32, float32, None))
 |      (dtype('float64'), dtype('float64'), dtype('float64'))
 |
 |      The loop found uses "float64" for all operands (including the output), the
 |      first input would be cast.
 |
 |      ``resolve_dtypes`` supports "weak" handling for Python scalars by passing
 |      ``int``, ``float``, or ``complex``:
 |
 |      >>> np.add.resolve_dtypes((float32, float, None))
 |      (dtype('float32'), dtype('float32'), dtype('float32'))
 |
 |      Where the Python ``float`` behaves samilar to a Python value ``0.0``
 |      in a ufunc call.  (See :ref:`NEP 50 <NEP50>` for details.)
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  identity
 |      The identity value.
 |
 |      Data attribute containing the identity element for the ufunc,
 |      if it has one. If it does not, the attribute value is None.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.add.identity
 |      0
 |      >>> np.multiply.identity
 |      1
 |      >>> np.power.identity
 |      1
 |      >>> print(np.exp.identity)
 |      None
 |
 |  nargs
 |      The number of arguments.
 |
 |      Data attribute containing the number of arguments the ufunc takes, including
 |      optional ones.
 |
 |      Notes
 |      -----
 |      Typically this value will be one more than what you might expect
 |      because all ufuncs take  the optional "out" argument.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.add.nargs
 |      3
 |      >>> np.multiply.nargs
 |      3
 |      >>> np.power.nargs
 |      3
 |      >>> np.exp.nargs
 |      2
 |
 |  nin
 |      The number of inputs.
 |
 |      Data attribute containing the number of arguments the ufunc treats as input.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.add.nin
 |      2
 |      >>> np.multiply.nin
 |      2
 |      >>> np.power.nin
 |      2
 |      >>> np.exp.nin
 |      1
 |
 |  nout
 |      The number of outputs.
 |
 |      Data attribute containing the number of arguments the ufunc treats as output.
 |
 |      Notes
 |      -----
 |      Since all ufuncs can take output arguments, this will always be at least 1.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.add.nout
 |      1
 |      >>> np.multiply.nout
 |      1
 |      >>> np.power.nout
 |      1
 |      >>> np.exp.nout
 |      1
 |
 |  ntypes
 |      The number of types.
 |
 |      The number of numerical NumPy types - of which there are 18 total - on which
 |      the ufunc can operate.
 |
 |      See Also
 |      --------
 |      numpy.ufunc.types
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.add.ntypes
 |      18
 |      >>> np.multiply.ntypes
 |      18
 |      >>> np.power.ntypes
 |      17
 |      >>> np.exp.ntypes
 |      7
 |      >>> np.remainder.ntypes
 |      14
 |
 |  signature
 |      Definition of the core elements a generalized ufunc operates on.
 |
 |      The signature determines how the dimensions of each input/output array
 |      are split into core and loop dimensions:
 |
 |      1. Each dimension in the signature is matched to a dimension of the
 |         corresponding passed-in array, starting from the end of the shape tuple.
 |      2. Core dimensions assigned to the same label in the signature must have
 |         exactly matching sizes, no broadcasting is performed.
 |      3. The core dimensions are removed from all inputs and the remaining
 |         dimensions are broadcast together, defining the loop dimensions.
 |
 |      Notes
 |      -----
 |      Generalized ufuncs are used internally in many linalg functions, and in
 |      the testing suite; the examples below are taken from these.
 |      For ufuncs that operate on scalars, the signature is None, which is
 |      equivalent to '()' for every argument.
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.linalg._umath_linalg.det.signature
 |      '(m,m)->()'
 |      >>> np.matmul.signature
 |      '(n?,k),(k,m?)->(n?,m?)'
 |      >>> np.add.signature is None
 |      True  # equivalent to '(),()->()'
 |
 |  types
 |      Returns a list with types grouped input->output.
 |
 |      Data attribute listing the data-type "Domain-Range" groupings the ufunc can
 |      deliver. The data-types are given using the character codes.
 |
 |      See Also
 |      --------
 |      numpy.ufunc.ntypes
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.add.types
 |      ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l',
 |      'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D',
 |      'GG->G', 'OO->O']
 |
 |      >>> np.multiply.types
 |      ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l',
 |      'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D',
 |      'GG->G', 'OO->O']
 |
 |      >>> np.power.types
 |      ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L',
 |      'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D', 'GG->G',
 |      'OO->O']
 |
 |      >>> np.exp.types
 |      ['f->f', 'd->d', 'g->g', 'F->F', 'D->D', 'G->G', 'O->O']
 |
 |      >>> np.remainder.types
 |      ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L',
 |      'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'OO->O']

Python Library Documentation: class uint64 in module numpy

class uint64(unsignedinteger)
 |  Unsigned signed integer type, 64bit on 64bit systems and 32bit on 32bit
 |  systems.
 |
 |  :Character code: ``'Q'``
 |  :Canonical name: `numpy.uint`
 |  :Alias on this platform (win32 AMD64): `numpy.uint64`: 64-bit unsigned integer (``0`` to ``18_446_744_073_709_551_615``).
 |  :Alias on this platform (win32 AMD64): `numpy.uintp`: Unsigned integer large enough to fit pointer, compatible with C ``uintptr_t``.
 |
 |  Method resolution order:
 |      uint64
 |      unsignedinteger
 |      integer
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      uint64.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.uint64(127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class uint16 in module numpy

class uint16(unsignedinteger)
 |  Unsigned integer type, compatible with C ``unsigned short``.
 |
 |  :Character code: ``'H'``
 |  :Canonical name: `numpy.ushort`
 |  :Alias on this platform (win32 AMD64): `numpy.uint16`: 16-bit unsigned integer (``0`` to ``65_535``).
 |
 |  Method resolution order:
 |      uint16
 |      unsignedinteger
 |      integer
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      uint16.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.uint16(127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class uint32 in module numpy

class uint32(unsignedinteger)
 |  Method resolution order:
 |      uint32
 |      unsignedinteger
 |      integer
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      uint32.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.uint32(127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class uint64 in module numpy

class uint64(unsignedinteger)
 |  Unsigned signed integer type, 64bit on 64bit systems and 32bit on 32bit
 |  systems.
 |
 |  :Character code: ``'Q'``
 |  :Canonical name: `numpy.uint`
 |  :Alias on this platform (win32 AMD64): `numpy.uint64`: 64-bit unsigned integer (``0`` to ``18_446_744_073_709_551_615``).
 |  :Alias on this platform (win32 AMD64): `numpy.uintp`: Unsigned integer large enough to fit pointer, compatible with C ``uintptr_t``.
 |
 |  Method resolution order:
 |      uint64
 |      unsignedinteger
 |      integer
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      uint64.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.uint64(127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class uint8 in module numpy

class uint8(unsignedinteger)
 |  Unsigned integer type, compatible with C ``unsigned char``.
 |
 |  :Character code: ``'B'``
 |  :Canonical name: `numpy.ubyte`
 |  :Alias on this platform (win32 AMD64): `numpy.uint8`: 8-bit unsigned integer (``0`` to ``255``).
 |
 |  Method resolution order:
 |      uint8
 |      unsignedinteger
 |      integer
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      uint8.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.uint8(127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class uintc in module numpy

class uintc(unsignedinteger)
 |  Unsigned integer type, compatible with C ``unsigned int``.
 |
 |  :Character code: ``'I'``
 |
 |  Method resolution order:
 |      uintc
 |      unsignedinteger
 |      integer
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class uint64 in module numpy

class uint64(unsignedinteger)
 |  Unsigned signed integer type, 64bit on 64bit systems and 32bit on 32bit
 |  systems.
 |
 |  :Character code: ``'Q'``
 |  :Canonical name: `numpy.uint`
 |  :Alias on this platform (win32 AMD64): `numpy.uint64`: 64-bit unsigned integer (``0`` to ``18_446_744_073_709_551_615``).
 |  :Alias on this platform (win32 AMD64): `numpy.uintp`: Unsigned integer large enough to fit pointer, compatible with C ``uintptr_t``.
 |
 |  Method resolution order:
 |      uint64
 |      unsignedinteger
 |      integer
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      uint64.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.uint64(127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class uint32 in module numpy

class uint32(unsignedinteger)
 |  Method resolution order:
 |      uint32
 |      unsignedinteger
 |      integer
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      uint32.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.uint32(127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: class uint64 in module numpy

class uint64(unsignedinteger)
 |  Unsigned signed integer type, 64bit on 64bit systems and 32bit on 32bit
 |  systems.
 |
 |  :Character code: ``'Q'``
 |  :Canonical name: `numpy.uint`
 |  :Alias on this platform (win32 AMD64): `numpy.uint64`: 64-bit unsigned integer (``0`` to ``18_446_744_073_709_551_615``).
 |  :Alias on this platform (win32 AMD64): `numpy.uintp`: Unsigned integer large enough to fit pointer, compatible with C ``uintptr_t``.
 |
 |  Method resolution order:
 |      uint64
 |      unsignedinteger
 |      integer
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      uint64.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.uint64(127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: function union1d in module autograd.tracer

union1d(*args, called_by_autograd_dispatcher=False, **kwargs)
    Find the union of two arrays.

    Return the unique, sorted array of values that are in either of the two
    input arrays.

    Parameters
    ----------
    ar1, ar2 : array_like
        Input arrays. They are flattened if they are not already 1D.

    Returns
    -------
    union1d : ndarray
        Unique, sorted union of the input arrays.

    Examples
    --------
    >>> import numpy as np
    >>> np.union1d([-1, 0, 1], [-2, 0, 2])
    array([-2, -1,  0,  1,  2])

    To find the union of more than two arrays, use functools.reduce:

    >>> from functools import reduce
    >>> reduce(np.union1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2]))
    array([1, 2, 3, 4, 6])

Python Library Documentation: function unique in module autograd.tracer

unique(*args, called_by_autograd_dispatcher=False, **kwargs)
    Find the unique elements of an array.

    Returns the sorted unique elements of an array. There are three optional
    outputs in addition to the unique elements:

    * the indices of the input array that give the unique values
    * the indices of the unique array that reconstruct the input array
    * the number of times each unique value comes up in the input array

    Parameters
    ----------
    ar : array_like
        Input array. Unless `axis` is specified, this will be flattened if it
        is not already 1-D.
    return_index : bool, optional
        If True, also return the indices of `ar` (along the specified axis,
        if provided, or in the flattened array) that result in the unique array.
    return_inverse : bool, optional
        If True, also return the indices of the unique array (for the specified
        axis, if provided) that can be used to reconstruct `ar`.
    return_counts : bool, optional
        If True, also return the number of times each unique item appears
        in `ar`.
    axis : int or None, optional
        The axis to operate on. If None, `ar` will be flattened. If an integer,
        the subarrays indexed by the given axis will be flattened and treated
        as the elements of a 1-D array with the dimension of the given axis,
        see the notes for more details.  Object arrays or structured arrays
        that contain objects are not supported if the `axis` kwarg is used. The
        default is None.

        .. versionadded:: 1.13.0

    equal_nan : bool, optional
        If True, collapses multiple NaN values in the return array into one.

        .. versionadded:: 1.24

    Returns
    -------
    unique : ndarray
        The sorted unique values.
    unique_indices : ndarray, optional
        The indices of the first occurrences of the unique values in the
        original array. Only provided if `return_index` is True.
    unique_inverse : ndarray, optional
        The indices to reconstruct the original array from the
        unique array. Only provided if `return_inverse` is True.
    unique_counts : ndarray, optional
        The number of times each of the unique values comes up in the
        original array. Only provided if `return_counts` is True.

        .. versionadded:: 1.9.0

    See Also
    --------
    repeat : Repeat elements of an array.

    Notes
    -----
    When an axis is specified the subarrays indexed by the axis are sorted.
    This is done by making the specified axis the first dimension of the array
    (move the axis to the first dimension to keep the order of the other axes)
    and then flattening the subarrays in C order. The flattened subarrays are
    then viewed as a structured type with each element given a label, with the
    effect that we end up with a 1-D array of structured types that can be
    treated in the same way as any other 1-D array. The result is that the
    flattened subarrays are sorted in lexicographic order starting with the
    first element.

    .. versionchanged: 1.21
        If nan values are in the input array, a single nan is put
        to the end of the sorted unique values.

        Also for complex arrays all NaN values are considered equivalent
        (no matter whether the NaN is in the real or imaginary part).
        As the representant for the returned array the smallest one in the
        lexicographical order is chosen - see np.sort for how the lexicographical
        order is defined for complex arrays.

    .. versionchanged: 2.0
        For multi-dimensional inputs, ``unique_inverse`` is reshaped
        such that the input can be reconstructed using
        ``np.take(unique, unique_inverse, axis=axis)``. The result is
        now not 1-dimensional when ``axis=None``.

        Note that in NumPy 2.0.0 a higher dimensional array was returned also
        when ``axis`` was not ``None``.  This was reverted, but
        ``inverse.reshape(-1)`` can be used to ensure compatibility with both
        versions.

    Examples
    --------
    >>> import numpy as np
    >>> np.unique([1, 1, 2, 2, 3, 3])
    array([1, 2, 3])
    >>> a = np.array([[1, 1], [2, 3]])
    >>> np.unique(a)
    array([1, 2, 3])

    Return the unique rows of a 2D array

    >>> a = np.array([[1, 0, 0], [1, 0, 0], [2, 3, 4]])
    >>> np.unique(a, axis=0)
    array([[1, 0, 0], [2, 3, 4]])

    Return the indices of the original array that give the unique values:

    >>> a = np.array(['a', 'b', 'b', 'c', 'a'])
    >>> u, indices = np.unique(a, return_index=True)
    >>> u
    array(['a', 'b', 'c'], dtype='<U1')
    >>> indices
    array([0, 1, 3])
    >>> a[indices]
    array(['a', 'b', 'c'], dtype='<U1')

    Reconstruct the input array from the unique values and inverse:

    >>> a = np.array([1, 2, 6, 4, 2, 3, 2])
    >>> u, indices = np.unique(a, return_inverse=True)
    >>> u
    array([1, 2, 3, 4, 6])
    >>> indices
    array([0, 1, 4, 3, 1, 2, 1])
    >>> u[indices]
    array([1, 2, 6, 4, 2, 3, 2])

    Reconstruct the input values from the unique values and counts:

    >>> a = np.array([1, 2, 6, 4, 2, 3, 2])
    >>> values, counts = np.unique(a, return_counts=True)
    >>> values
    array([1, 2, 3, 4, 6])
    >>> counts
    array([1, 3, 1, 1, 1])
    >>> np.repeat(values, counts)
    array([1, 2, 2, 2, 3, 4, 6])    # original order not preserved

Python Library Documentation: function unique_all in module autograd.tracer

unique_all(*args, called_by_autograd_dispatcher=False, **kwargs)
    Find the unique elements of an array, and counts, inverse and indices.

    This function is an Array API compatible alternative to:

    >>> x = np.array([1, 1, 2])
    >>> np.unique(x, return_index=True, return_inverse=True,
    ...           return_counts=True, equal_nan=False)
    (array([1, 2]), array([0, 2]), array([0, 0, 1]), array([2, 1]))

    Parameters
    ----------
    x : array_like
        Input array. It will be flattened if it is not already 1-D.

    Returns
    -------
    out : namedtuple
        The result containing:

        * values - The unique elements of an input array.
        * indices - The first occurring indices for each unique element.
        * inverse_indices - The indices from the set of unique elements
          that reconstruct `x`.
        * counts - The corresponding counts for each unique element.

    See Also
    --------
    unique : Find the unique elements of an array.

    Examples
    --------
    >>> import numpy as np
    >>> np.unique_all([1, 1, 2])
    UniqueAllResult(values=array([1, 2]),
                    indices=array([0, 2]),
                    inverse_indices=array([0, 0, 1]),
                    counts=array([2, 1]))

Python Library Documentation: function unique_counts in module autograd.tracer

unique_counts(*args, called_by_autograd_dispatcher=False, **kwargs)
    Find the unique elements and counts of an input array `x`.

    This function is an Array API compatible alternative to:

    >>> x = np.array([1, 1, 2])
    >>> np.unique(x, return_counts=True, equal_nan=False)
    (array([1, 2]), array([2, 1]))

    Parameters
    ----------
    x : array_like
        Input array. It will be flattened if it is not already 1-D.

    Returns
    -------
    out : namedtuple
        The result containing:

        * values - The unique elements of an input array.
        * counts - The corresponding counts for each unique element.

    See Also
    --------
    unique : Find the unique elements of an array.

    Examples
    --------
    >>> import numpy as np
    >>> np.unique_counts([1, 1, 2])
    UniqueCountsResult(values=array([1, 2]), counts=array([2, 1]))

Python Library Documentation: function unique_inverse in module autograd.tracer

unique_inverse(*args, called_by_autograd_dispatcher=False, **kwargs)
    Find the unique elements of `x` and indices to reconstruct `x`.

    This function is Array API compatible alternative to:

    >>> x = np.array([1, 1, 2])
    >>> np.unique(x, return_inverse=True, equal_nan=False)
    (array([1, 2]), array([0, 0, 1]))

    Parameters
    ----------
    x : array_like
        Input array. It will be flattened if it is not already 1-D.

    Returns
    -------
    out : namedtuple
        The result containing:

        * values - The unique elements of an input array.
        * inverse_indices - The indices from the set of unique elements
          that reconstruct `x`.

    See Also
    --------
    unique : Find the unique elements of an array.

    Examples
    --------
    >>> import numpy as np
    >>> np.unique_inverse([1, 1, 2])
    UniqueInverseResult(values=array([1, 2]), inverse_indices=array([0, 0, 1]))

Python Library Documentation: function unique_values in module autograd.tracer

unique_values(*args, called_by_autograd_dispatcher=False, **kwargs)
    Returns the unique elements of an input array `x`.

    This function is Array API compatible alternative to:

    >>> x = np.array([1, 1, 2])
    >>> np.unique(x, equal_nan=False)
    array([1, 2])

    Parameters
    ----------
    x : array_like
        Input array. It will be flattened if it is not already 1-D.

    Returns
    -------
    out : ndarray
        The unique elements of an input array.

    See Also
    --------
    unique : Find the unique elements of an array.

    Examples
    --------
    >>> import numpy as np
    >>> np.unique_values([1, 1, 2])
    array([1, 2])

Python Library Documentation: function unpackbits in module autograd.tracer

unpackbits(*args, called_by_autograd_dispatcher=False, **kwargs)
    unpackbits(a, /, axis=None, count=None, bitorder='big')

    Unpacks elements of a uint8 array into a binary-valued output array.

    Each element of `a` represents a bit-field that should be unpacked
    into a binary-valued output array. The shape of the output array is
    either 1-D (if `axis` is ``None``) or the same shape as the input
    array with unpacking done along the axis specified.

    Parameters
    ----------
    a : ndarray, uint8 type
       Input array.
    axis : int, optional
        The dimension over which bit-unpacking is done.
        ``None`` implies unpacking the flattened array.
    count : int or None, optional
        The number of elements to unpack along `axis`, provided as a way
        of undoing the effect of packing a size that is not a multiple
        of eight. A non-negative number means to only unpack `count`
        bits. A negative number means to trim off that many bits from
        the end. ``None`` means to unpack the entire array (the
        default). Counts larger than the available number of bits will
        add zero padding to the output. Negative counts must not
        exceed the available number of bits.

        .. versionadded:: 1.17.0

    bitorder : {'big', 'little'}, optional
        The order of the returned bits. 'big' will mimic bin(val),
        ``3 = 0b00000011 => [0, 0, 0, 0, 0, 0, 1, 1]``, 'little' will reverse
        the order to ``[1, 1, 0, 0, 0, 0, 0, 0]``.
        Defaults to 'big'.

        .. versionadded:: 1.17.0

    Returns
    -------
    unpacked : ndarray, uint8 type
       The elements are binary-valued (0 or 1).

    See Also
    --------
    packbits : Packs the elements of a binary-valued array into bits in
               a uint8 array.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([[2], [7], [23]], dtype=np.uint8)
    >>> a
    array([[ 2],
           [ 7],
           [23]], dtype=uint8)
    >>> b = np.unpackbits(a, axis=1)
    >>> b
    array([[0, 0, 0, 0, 0, 0, 1, 0],
           [0, 0, 0, 0, 0, 1, 1, 1],
           [0, 0, 0, 1, 0, 1, 1, 1]], dtype=uint8)
    >>> c = np.unpackbits(a, axis=1, count=-3)
    >>> c
    array([[0, 0, 0, 0, 0],
           [0, 0, 0, 0, 0],
           [0, 0, 0, 1, 0]], dtype=uint8)

    >>> p = np.packbits(b, axis=0)
    >>> np.unpackbits(p, axis=0)
    array([[0, 0, 0, 0, 0, 0, 1, 0],
           [0, 0, 0, 0, 0, 1, 1, 1],
           [0, 0, 0, 1, 0, 1, 1, 1],
           [0, 0, 0, 0, 0, 0, 0, 0],
           [0, 0, 0, 0, 0, 0, 0, 0],
           [0, 0, 0, 0, 0, 0, 0, 0],
           [0, 0, 0, 0, 0, 0, 0, 0],
           [0, 0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
    >>> np.array_equal(b, np.unpackbits(p, axis=0, count=b.shape[0]))
    True

Python Library Documentation: function unravel_index in module autograd.tracer

unravel_index(*args, called_by_autograd_dispatcher=False, **kwargs)
    unravel_index(indices, shape, order='C')

    Converts a flat index or array of flat indices into a tuple
    of coordinate arrays.

    Parameters
    ----------
    indices : array_like
        An integer array whose elements are indices into the flattened
        version of an array of dimensions ``shape``. Before version 1.6.0,
        this function accepted just one index value.
    shape : tuple of ints
        The shape of the array to use for unraveling ``indices``.

        .. versionchanged:: 1.16.0
            Renamed from ``dims`` to ``shape``.

    order : {'C', 'F'}, optional
        Determines whether the indices should be viewed as indexing in
        row-major (C-style) or column-major (Fortran-style) order.

        .. versionadded:: 1.6.0

    Returns
    -------
    unraveled_coords : tuple of ndarray
        Each array in the tuple has the same shape as the ``indices``
        array.

    See Also
    --------
    ravel_multi_index

    Examples
    --------
    >>> import numpy as np
    >>> np.unravel_index([22, 41, 37], (7,6))
    (array([3, 6, 6]), array([4, 5, 1]))
    >>> np.unravel_index([31, 41, 13], (7,6), order='F')
    (array([3, 6, 6]), array([4, 5, 1]))

    >>> np.unravel_index(1621, (6,7,8,9))
    (3, 1, 4, 1)

Python Library Documentation: class unsignedinteger in module numpy

class unsignedinteger(integer)
 |  Abstract base class of all unsigned integer scalar types.
 |
 |  Method resolution order:
 |      unsignedinteger
 |      integer
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods inherited from integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from number:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes inherited from generic:
 |
 |  __hash__ = None

Python Library Documentation: function unstack in module autograd.tracer

unstack(*args, called_by_autograd_dispatcher=False, **kwargs)
    Split an array into a sequence of arrays along the given axis.

    The ``axis`` parameter specifies the dimension along which the array will
    be split. For example, if ``axis=0`` (the default) it will be the first
    dimension and if ``axis=-1`` it will be the last dimension.

    The result is a tuple of arrays split along ``axis``.

    .. versionadded:: 2.1.0

    Parameters
    ----------
    x : ndarray
        The array to be unstacked.
    axis : int, optional
        Axis along which the array will be split. Default: ``0``.

    Returns
    -------
    unstacked : tuple of ndarrays
        The unstacked arrays.

    See Also
    --------
    stack : Join a sequence of arrays along a new axis.
    concatenate : Join a sequence of arrays along an existing axis.
    block : Assemble an nd-array from nested lists of blocks.
    split : Split array into a list of multiple sub-arrays of equal size.

    Notes
    -----
    ``unstack`` serves as the reverse operation of :py:func:`stack`, i.e.,
    ``stack(unstack(x, axis=axis), axis=axis) == x``.

    This function is equivalent to ``tuple(np.moveaxis(x, axis, 0))``, since
    iterating on an array iterates along the first axis.

    Examples
    --------
    >>> arr = np.arange(24).reshape((2, 3, 4))
    >>> np.unstack(arr)
    (array([[ 0,  1,  2,  3],
            [ 4,  5,  6,  7],
            [ 8,  9, 10, 11]]),
     array([[12, 13, 14, 15],
            [16, 17, 18, 19],
            [20, 21, 22, 23]]))
    >>> np.unstack(arr, axis=1)
    (array([[ 0,  1,  2,  3],
            [12, 13, 14, 15]]),
     array([[ 4,  5,  6,  7],
            [16, 17, 18, 19]]),
     array([[ 8,  9, 10, 11],
            [20, 21, 22, 23]]))
    >>> arr2 = np.stack(np.unstack(arr, axis=1), axis=1)
    >>> arr2.shape
    (2, 3, 4)
    >>> np.all(arr == arr2)
    np.True_

Python Library Documentation: function unwrap in module autograd.tracer

unwrap(*args, called_by_autograd_dispatcher=False, **kwargs)
    Unwrap by taking the complement of large deltas with respect to the period.

    This unwraps a signal `p` by changing elements which have an absolute
    difference from their predecessor of more than ``max(discont, period/2)``
    to their `period`-complementary values.

    For the default case where `period` is :math:`2\pi` and `discont` is
    :math:`\pi`, this unwraps a radian phase `p` such that adjacent differences
    are never greater than :math:`\pi` by adding :math:`2k\pi` for some
    integer :math:`k`.

    Parameters
    ----------
    p : array_like
        Input array.
    discont : float, optional
        Maximum discontinuity between values, default is ``period/2``.
        Values below ``period/2`` are treated as if they were ``period/2``.
        To have an effect different from the default, `discont` should be
        larger than ``period/2``.
    axis : int, optional
        Axis along which unwrap will operate, default is the last axis.
    period : float, optional
        Size of the range over which the input wraps. By default, it is
        ``2 pi``.

        .. versionadded:: 1.21.0

    Returns
    -------
    out : ndarray
        Output array.

    See Also
    --------
    rad2deg, deg2rad

    Notes
    -----
    If the discontinuity in `p` is smaller than ``period/2``,
    but larger than `discont`, no unwrapping is done because taking
    the complement would only make the discontinuity larger.

    Examples
    --------
    >>> import numpy as np
    >>> phase = np.linspace(0, np.pi, num=5)
    >>> phase[3:] += np.pi
    >>> phase
    array([ 0.        ,  0.78539816,  1.57079633,  5.49778714,  6.28318531]) # may vary
    >>> np.unwrap(phase)
    array([ 0.        ,  0.78539816,  1.57079633, -0.78539816,  0.        ]) # may vary
    >>> np.unwrap([0, 1, 2, -1, 0], period=4)
    array([0, 1, 2, 3, 4])
    >>> np.unwrap([ 1, 2, 3, 4, 5, 6, 1, 2, 3], period=6)
    array([1, 2, 3, 4, 5, 6, 7, 8, 9])
    >>> np.unwrap([2, 3, 4, 5, 2, 3, 4, 5], period=4)
    array([2, 3, 4, 5, 6, 7, 8, 9])
    >>> phase_deg = np.mod(np.linspace(0 ,720, 19), 360) - 180
    >>> np.unwrap(phase_deg, period=360)
    array([-180., -140., -100.,  -60.,  -20.,   20.,   60.,  100.,  140.,
            180.,  220.,  260.,  300.,  340.,  380.,  420.,  460.,  500.,
            540.])

Python Library Documentation: class uint16 in module numpy

class uint16(unsignedinteger)
 |  Unsigned integer type, compatible with C ``unsigned short``.
 |
 |  :Character code: ``'H'``
 |  :Canonical name: `numpy.ushort`
 |  :Alias on this platform (win32 AMD64): `numpy.uint16`: 16-bit unsigned integer (``0`` to ``65_535``).
 |
 |  Method resolution order:
 |      uint16
 |      unsignedinteger
 |      integer
 |      number
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __index__(self, /)
 |      Return self converted to an integer, if self is suitable for use as an index into a list.
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  bit_count(...)
 |      uint16.bit_count() -> int
 |
 |      Computes the number of 1-bits in the absolute value of the input.
 |      Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
 |
 |      Examples
 |      --------
 |      >>> np.uint16(127).bit_count()
 |      7
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  __class_getitem__(...)
 |      __class_getitem__(item, /)
 |
 |      Return a parametrized wrapper around the `~numpy.number` type.
 |
 |      .. versionadded:: 1.22
 |
 |      Returns
 |      -------
 |      alias : types.GenericAlias
 |          A parametrized `~numpy.number` type.
 |
 |      Examples
 |      --------
 |      >>> from typing import Any
 |      >>> import numpy as np
 |
 |      >>> np.signedinteger[Any]
 |      numpy.signedinteger[typing.Any]
 |
 |      See Also
 |      --------
 |      :pep:`585` : Type hinting generics in standard collections.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from integer:
 |
 |  __round__(...)
 |
 |  is_integer(...)
 |      integer.is_integer() -> bool
 |
 |      Return ``True`` if the number is finite with integral value.
 |
 |      .. versionadded:: 1.22
 |
 |      Examples
 |      --------
 |      >>> import numpy as np
 |      >>> np.int64(-2).is_integer()
 |      True
 |      >>> np.uint32(5).is_integer()
 |      True
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from integer:
 |
 |  denominator
 |      denominator of value (1)
 |
 |  numerator
 |      numerator of value (the value itself)
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  base
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.base`.
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  dtype
 |      Get array data-descriptor.
 |
 |  flags
 |      The integer value of flags.
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: function vander in module autograd.tracer

vander(*args, called_by_autograd_dispatcher=False, **kwargs)
    Generate a Vandermonde matrix.

    The columns of the output matrix are powers of the input vector. The
    order of the powers is determined by the `increasing` boolean argument.
    Specifically, when `increasing` is False, the `i`-th output column is
    the input vector raised element-wise to the power of ``N - i - 1``. Such
    a matrix with a geometric progression in each row is named for Alexandre-
    Theophile Vandermonde.

    Parameters
    ----------
    x : array_like
        1-D input array.
    N : int, optional
        Number of columns in the output.  If `N` is not specified, a square
        array is returned (``N = len(x)``).
    increasing : bool, optional
        Order of the powers of the columns.  If True, the powers increase
        from left to right, if False (the default) they are reversed.

        .. versionadded:: 1.9.0

    Returns
    -------
    out : ndarray
        Vandermonde matrix.  If `increasing` is False, the first column is
        ``x^(N-1)``, the second ``x^(N-2)`` and so forth. If `increasing` is
        True, the columns are ``x^0, x^1, ..., x^(N-1)``.

    See Also
    --------
    polynomial.polynomial.polyvander

    Examples
    --------
    >>> import numpy as np
    >>> x = np.array([1, 2, 3, 5])
    >>> N = 3
    >>> np.vander(x, N)
    array([[ 1,  1,  1],
           [ 4,  2,  1],
           [ 9,  3,  1],
           [25,  5,  1]])

    >>> np.column_stack([x**(N-1-i) for i in range(N)])
    array([[ 1,  1,  1],
           [ 4,  2,  1],
           [ 9,  3,  1],
           [25,  5,  1]])

    >>> x = np.array([1, 2, 3, 5])
    >>> np.vander(x)
    array([[  1,   1,   1,   1],
           [  8,   4,   2,   1],
           [ 27,   9,   3,   1],
           [125,  25,   5,   1]])
    >>> np.vander(x, increasing=True)
    array([[  1,   1,   1,   1],
           [  1,   2,   4,   8],
           [  1,   3,   9,  27],
           [  1,   5,  25, 125]])

    The determinant of a square Vandermonde matrix is the product
    of the differences between the values of the input vector:

    >>> np.linalg.det(np.vander(x))
    48.000000000000043 # may vary
    >>> (5-3)*(5-2)*(5-1)*(3-2)*(3-1)*(2-1)
    48

Python Library Documentation: function var in module autograd.numpy.numpy_wrapper

var(a, *args, **kwargs)

Python Library Documentation: function vdot in module autograd.tracer

vdot(*args, called_by_autograd_dispatcher=False, **kwargs)
    vdot(a, b, /)

    Return the dot product of two vectors.

    The vdot(`a`, `b`) function handles complex numbers differently than
    dot(`a`, `b`).  If the first argument is complex the complex conjugate
    of the first argument is used for the calculation of the dot product.

    Note that `vdot` handles multidimensional arrays differently than `dot`:
    it does *not* perform a matrix product, but flattens input arguments
    to 1-D vectors first. Consequently, it should only be used for vectors.

    Parameters
    ----------
    a : array_like
        If `a` is complex the complex conjugate is taken before calculation
        of the dot product.
    b : array_like
        Second argument to the dot product.

    Returns
    -------
    output : ndarray
        Dot product of `a` and `b`.  Can be an int, float, or
        complex depending on the types of `a` and `b`.

    See Also
    --------
    dot : Return the dot product without using the complex conjugate of the
          first argument.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([1+2j,3+4j])
    >>> b = np.array([5+6j,7+8j])
    >>> np.vdot(a, b)
    (70-8j)
    >>> np.vdot(b, a)
    (70+8j)

    Note that higher-dimensional arrays are flattened!

    >>> a = np.array([[1, 4], [5, 6]])
    >>> b = np.array([[4, 1], [2, 2]])
    >>> np.vdot(a, b)
    30
    >>> np.vdot(b, a)
    30
    >>> 1*4 + 4*1 + 5*2 + 6*2
    30

Python Library Documentation: function vecdot in module autograd.tracer

vecdot(*args, called_by_autograd_dispatcher=False, **kwargs)
    vecdot(x1, x2, /, out=None, *, casting='same_kind', order='K', dtype=None, subok=True[, signature, axes, axis])

    Vector dot product of two arrays.

    Let :math:`\mathbf{a}` be a vector in `x1` and :math:`\mathbf{b}` be
    a corresponding vector in `x2`. The dot product is defined as:

    .. math::
       \mathbf{a} \cdot \mathbf{b} = \sum_{i=0}^{n-1} \overline{a_i}b_i

    where the sum is over the last dimension (unless `axis` is specified) and
    where :math:`\overline{a_i}` denotes the complex conjugate if :math:`a_i`
    is complex and the identity otherwise.

    Parameters
    ----------
    x1, x2 : array_like
        Input arrays, scalars not allowed.
    out : ndarray, optional
        A location into which the result is stored. If provided, it must have
        a shape that the broadcasted shape of `x1` and `x2` with the last axis
        removed. If not provided or None, a freshly-allocated array is used.
    **kwargs
        For other keyword-only arguments, see the
        :ref:`ufunc docs <ufuncs.kwargs>`.

    Returns
    -------
    y : ndarray
        The vector dot product of the inputs.
        This is a scalar only when both x1, x2 are 1-d vectors.

    Raises
    ------
    ValueError
        If the last dimension of `x1` is not the same size as
        the last dimension of `x2`.

        If a scalar value is passed in.

    See Also
    --------
    vdot : same but flattens arguments first
    einsum : Einstein summation convention.

    Examples
    --------
    >>> import numpy as np

    Get the projected size along a given normal for an array of vectors.

    >>> v = np.array([[0., 5., 0.], [0., 0., 10.], [0., 6., 8.]])
    >>> n = np.array([0., 0.6, 0.8])
    >>> np.vecdot(v, n)
    array([ 3.,  8., 10.])

    .. versionadded:: 2.0.0

Python Library Documentation: class vectorize in module numpy

class vectorize(builtins.object)
 |  vectorize(pyfunc=<no value>, otypes=None, doc=None, excluded=None, cache=False, signature=None)
 |
 |  vectorize(pyfunc=np._NoValue, otypes=None, doc=None, excluded=None,
 |  cache=False, signature=None)
 |
 |  Returns an object that acts like pyfunc, but takes arrays as input.
 |
 |  Define a vectorized function which takes a nested sequence of objects or
 |  numpy arrays as inputs and returns a single numpy array or a tuple of numpy
 |  arrays. The vectorized function evaluates `pyfunc` over successive tuples
 |  of the input arrays like the python map function, except it uses the
 |  broadcasting rules of numpy.
 |
 |  The data type of the output of `vectorized` is determined by calling
 |  the function with the first element of the input.  This can be avoided
 |  by specifying the `otypes` argument.
 |
 |  Parameters
 |  ----------
 |  pyfunc : callable, optional
 |      A python function or method.
 |      Can be omitted to produce a decorator with keyword arguments.
 |  otypes : str or list of dtypes, optional
 |      The output data type. It must be specified as either a string of
 |      typecode characters or a list of data type specifiers. There should
 |      be one data type specifier for each output.
 |  doc : str, optional
 |      The docstring for the function. If None, the docstring will be the
 |      ``pyfunc.__doc__``.
 |  excluded : set, optional
 |      Set of strings or integers representing the positional or keyword
 |      arguments for which the function will not be vectorized.  These will be
 |      passed directly to `pyfunc` unmodified.
 |
 |      .. versionadded:: 1.7.0
 |
 |  cache : bool, optional
 |      If `True`, then cache the first function call that determines the number
 |      of outputs if `otypes` is not provided.
 |
 |      .. versionadded:: 1.7.0
 |
 |  signature : string, optional
 |      Generalized universal function signature, e.g., ``(m,n),(n)->(m)`` for
 |      vectorized matrix-vector multiplication. If provided, ``pyfunc`` will
 |      be called with (and expected to return) arrays with shapes given by the
 |      size of corresponding core dimensions. By default, ``pyfunc`` is
 |      assumed to take scalars as input and output.
 |
 |      .. versionadded:: 1.12.0
 |
 |  Returns
 |  -------
 |  out : callable
 |      A vectorized function if ``pyfunc`` was provided,
 |      a decorator otherwise.
 |
 |  See Also
 |  --------
 |  frompyfunc : Takes an arbitrary Python function and returns a ufunc
 |
 |  Notes
 |  -----
 |  The `vectorize` function is provided primarily for convenience, not for
 |  performance. The implementation is essentially a for loop.
 |
 |  If `otypes` is not specified, then a call to the function with the
 |  first argument will be used to determine the number of outputs.  The
 |  results of this call will be cached if `cache` is `True` to prevent
 |  calling the function twice.  However, to implement the cache, the
 |  original function must be wrapped which will slow down subsequent
 |  calls, so only do this if your function is expensive.
 |
 |  The new keyword argument interface and `excluded` argument support
 |  further degrades performance.
 |
 |  References
 |  ----------
 |  .. [1] :doc:`/reference/c-api/generalized-ufuncs`
 |
 |  Examples
 |  --------
 |  >>> import numpy as np
 |  >>> def myfunc(a, b):
 |  ...     "Return a-b if a>b, otherwise return a+b"
 |  ...     if a > b:
 |  ...         return a - b
 |  ...     else:
 |  ...         return a + b
 |
 |  >>> vfunc = np.vectorize(myfunc)
 |  >>> vfunc([1, 2, 3, 4], 2)
 |  array([3, 4, 1, 2])
 |
 |  The docstring is taken from the input function to `vectorize` unless it
 |  is specified:
 |
 |  >>> vfunc.__doc__
 |  'Return a-b if a>b, otherwise return a+b'
 |  >>> vfunc = np.vectorize(myfunc, doc='Vectorized `myfunc`')
 |  >>> vfunc.__doc__
 |  'Vectorized `myfunc`'
 |
 |  The output type is determined by evaluating the first element of the input,
 |  unless it is specified:
 |
 |  >>> out = vfunc([1, 2, 3, 4], 2)
 |  >>> type(out[0])
 |  <class 'numpy.int64'>
 |  >>> vfunc = np.vectorize(myfunc, otypes=[float])
 |  >>> out = vfunc([1, 2, 3, 4], 2)
 |  >>> type(out[0])
 |  <class 'numpy.float64'>
 |
 |  The `excluded` argument can be used to prevent vectorizing over certain
 |  arguments.  This can be useful for array-like arguments of a fixed length
 |  such as the coefficients for a polynomial as in `polyval`:
 |
 |  >>> def mypolyval(p, x):
 |  ...     _p = list(p)
 |  ...     res = _p.pop(0)
 |  ...     while _p:
 |  ...         res = res*x + _p.pop(0)
 |  ...     return res
 |  >>> vpolyval = np.vectorize(mypolyval, excluded=['p'])
 |  >>> vpolyval(p=[1, 2, 3], x=[0, 1])
 |  array([3, 6])
 |
 |  Positional arguments may also be excluded by specifying their position:
 |
 |  >>> vpolyval.excluded.add(0)
 |  >>> vpolyval([1, 2, 3], x=[0, 1])
 |  array([3, 6])
 |
 |  The `signature` argument allows for vectorizing functions that act on
 |  non-scalar arrays of fixed length. For example, you can use it for a
 |  vectorized calculation of Pearson correlation coefficient and its p-value:
 |
 |  >>> import scipy.stats
 |  >>> pearsonr = np.vectorize(scipy.stats.pearsonr,
 |  ...                 signature='(n),(n)->(),()')
 |  >>> pearsonr([[0, 1, 2, 3]], [[1, 2, 3, 4], [4, 3, 2, 1]])
 |  (array([ 1., -1.]), array([ 0.,  0.]))
 |
 |  Or for a vectorized convolution:
 |
 |  >>> convolve = np.vectorize(np.convolve, signature='(n),(m)->(k)')
 |  >>> convolve(np.eye(4), [1, 2, 1])
 |  array([[1., 2., 1., 0., 0., 0.],
 |         [0., 1., 2., 1., 0., 0.],
 |         [0., 0., 1., 2., 1., 0.],
 |         [0., 0., 0., 1., 2., 1.]])
 |
 |  Decorator syntax is supported.  The decorator can be called as
 |  a function to provide keyword arguments:
 |
 |  >>> @np.vectorize
 |  ... def identity(x):
 |  ...     return x
 |  ...
 |  >>> identity([0, 1, 2])
 |  array([0, 1, 2])
 |  >>> @np.vectorize(otypes=[float])
 |  ... def as_float(x):
 |  ...     return x
 |  ...
 |  >>> as_float([0, 1, 2])
 |  array([0., 1., 2.])
 |
 |  Methods defined here:
 |
 |  __call__(self, *args, **kwargs) from numpy.lib._function_base_impl.vectorize
 |      Call self as a function.
 |
 |  __init__(self, pyfunc=<no value>, otypes=None, doc=None, excluded=None, cache=False, signature=None) from numpy.lib._function_base_impl.vectorize
 |      Initialize self.  See help(type(self)) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  __weakref__
 |      list of weak references to the object

Python Library Documentation: class void in module numpy

class void(flexible)
 |  np.void(length_or_data, /, dtype=None)
 |
 |  Create a new structured or unstructured void scalar.
 |
 |  Parameters
 |  ----------
 |  length_or_data : int, array-like, bytes-like, object
 |     One of multiple meanings (see notes).  The length or
 |     bytes data of an unstructured void.  Or alternatively,
 |     the data to be stored in the new scalar when `dtype`
 |     is provided.
 |     This can be an array-like, in which case an array may
 |     be returned.
 |  dtype : dtype, optional
 |     If provided the dtype of the new scalar.  This dtype must
 |     be "void" dtype (i.e. a structured or unstructured void,
 |     see also :ref:`defining-structured-types`).
 |
 |     .. versionadded:: 1.24
 |
 |  Notes
 |  -----
 |  For historical reasons and because void scalars can represent both
 |  arbitrary byte data and structured dtypes, the void constructor
 |  has three calling conventions:
 |
 |  1. ``np.void(5)`` creates a ``dtype="V5"`` scalar filled with five
 |     ``\0`` bytes.  The 5 can be a Python or NumPy integer.
 |  2. ``np.void(b"bytes-like")`` creates a void scalar from the byte string.
 |     The dtype itemsize will match the byte string length, here ``"V10"``.
 |  3. When a ``dtype=`` is passed the call is roughly the same as an
 |     array creation.  However, a void scalar rather than array is returned.
 |
 |  Please see the examples which show all three different conventions.
 |
 |  Examples
 |  --------
 |  >>> np.void(5)
 |  np.void(b'\x00\x00\x00\x00\x00')
 |  >>> np.void(b'abcd')
 |  np.void(b'\x61\x62\x63\x64')
 |  >>> np.void((3.2, b'eggs'), dtype="d,S5")
 |  np.void((3.2, b'eggs'), dtype=[('f0', '<f8'), ('f1', 'S5')])
 |  >>> np.void(3, dtype=[('x', np.int8), ('y', np.int8)])
 |  np.void((3, 3), dtype=[('x', 'i1'), ('y', 'i1')])
 |
 |  :Character code: ``'V'``
 |
 |  Method resolution order:
 |      void
 |      flexible
 |      generic
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __buffer__(self, flags, /)
 |      Return a buffer object that exposes the underlying memory of the object.
 |
 |  __delitem__(self, key, /)
 |      Delete self[key].
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __setitem__(self, key, value, /)
 |      Set self[key] to value.
 |
 |  __str__(self, /)
 |      Return str(self).
 |
 |  getfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.getfield`.
 |
 |  setfield(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setfield`.
 |
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  base
 |      base object
 |
 |  dtype
 |      dtype object
 |
 |  flags
 |      integer value of flags
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from generic:
 |
 |  __abs__(self, /)
 |      abs(self)
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __and__(self, value, /)
 |      Return self&value.
 |
 |  __array__(...)
 |      sc.__array__(dtype) return 0-dim array from scalar with specified dtype
 |
 |  __array_namespace__(...)
 |
 |  __array_wrap__(...)
 |      sc.__array_wrap__(obj) return scalar from array
 |
 |  __bool__(self, /)
 |      True if self else False
 |
 |  __copy__(...)
 |
 |  __deepcopy__(...)
 |
 |  __divmod__(self, value, /)
 |      Return divmod(self, value).
 |
 |  __float__(self, /)
 |      float(self)
 |
 |  __floordiv__(self, value, /)
 |      Return self//value.
 |
 |  __format__(...)
 |      NumPy array scalar formatter
 |
 |  __int__(self, /)
 |      int(self)
 |
 |  __invert__(self, /)
 |      ~self
 |
 |  __lshift__(self, value, /)
 |      Return self<<value.
 |
 |  __mod__(self, value, /)
 |      Return self%value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __neg__(self, /)
 |      -self
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __pos__(self, /)
 |      +self
 |
 |  __pow__(self, value, mod=None, /)
 |      Return pow(self, value, mod).
 |
 |  __radd__(self, value, /)
 |      Return value+self.
 |
 |  __rand__(self, value, /)
 |      Return value&self.
 |
 |  __rdivmod__(self, value, /)
 |      Return divmod(value, self).
 |
 |  __reduce__(...)
 |      Helper for pickle.
 |
 |  __rfloordiv__(self, value, /)
 |      Return value//self.
 |
 |  __rlshift__(self, value, /)
 |      Return value<<self.
 |
 |  __rmod__(self, value, /)
 |      Return value%self.
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __rpow__(self, value, mod=None, /)
 |      Return pow(value, self, mod).
 |
 |  __rrshift__(self, value, /)
 |      Return value>>self.
 |
 |  __rshift__(self, value, /)
 |      Return self>>value.
 |
 |  __rsub__(self, value, /)
 |      Return value-self.
 |
 |  __rtruediv__(self, value, /)
 |      Return value/self.
 |
 |  __rxor__(self, value, /)
 |      Return value^self.
 |
 |  __setstate__(...)
 |
 |  __sizeof__(...)
 |      Size of object in memory, in bytes.
 |
 |  __sub__(self, value, /)
 |      Return self-value.
 |
 |  __truediv__(self, value, /)
 |      Return self/value.
 |
 |  __xor__(self, value, /)
 |      Return self^value.
 |
 |  all(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.all`.
 |
 |  any(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.any`.
 |
 |  argmax(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmax`.
 |
 |  argmin(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argmin`.
 |
 |  argsort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.argsort`.
 |
 |  astype(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.astype`.
 |
 |  byteswap(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.byteswap`.
 |
 |  choose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.choose`.
 |
 |  clip(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.clip`.
 |
 |  compress(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.compress`.
 |
 |  conj(...)
 |
 |  conjugate(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.conjugate`.
 |
 |  copy(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.copy`.
 |
 |  cumprod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumprod`.
 |
 |  cumsum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.cumsum`.
 |
 |  diagonal(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.diagonal`.
 |
 |  dump(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dump`.
 |
 |  dumps(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.dumps`.
 |
 |  fill(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.fill`.
 |
 |  flatten(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.flatten`.
 |
 |  item(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.item`.
 |
 |  max(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.max`.
 |
 |  mean(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.mean`.
 |
 |  min(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.min`.
 |
 |  nonzero(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.nonzero`.
 |
 |  prod(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.prod`.
 |
 |  put(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.put`.
 |
 |  ravel(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.ravel`.
 |
 |  repeat(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.repeat`.
 |
 |  reshape(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.reshape`.
 |
 |  resize(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.resize`.
 |
 |  round(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.round`.
 |
 |  searchsorted(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.searchsorted`.
 |
 |  setflags(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.setflags`.
 |
 |  sort(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sort`.
 |
 |  squeeze(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.squeeze`.
 |
 |  std(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.std`.
 |
 |  sum(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.sum`.
 |
 |  swapaxes(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.swapaxes`.
 |
 |  take(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.take`.
 |
 |  to_device(...)
 |
 |  tobytes(...)
 |
 |  tofile(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tofile`.
 |
 |  tolist(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tolist`.
 |
 |  tostring(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.tostring`.
 |
 |  trace(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.trace`.
 |
 |  transpose(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.transpose`.
 |
 |  var(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.var`.
 |
 |  view(...)
 |      Scalar method identical to the corresponding array attribute.
 |
 |      Please see `ndarray.view`.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from generic:
 |
 |  T
 |      Scalar attribute identical to the corresponding array attribute.
 |
 |      Please see `ndarray.T`.
 |
 |  __array_interface__
 |      Array protocol: Python side
 |
 |  __array_priority__
 |      Array priority.
 |
 |  __array_struct__
 |      Array protocol: struct
 |
 |  data
 |      Pointer to start of data.
 |
 |  device
 |
 |  flat
 |      A 1-D view of the scalar.
 |
 |  imag
 |      The imaginary part of the scalar.
 |
 |  itemset
 |
 |  itemsize
 |      The length of one element in bytes.
 |
 |  nbytes
 |
 |  ndim
 |      The number of array dimensions.
 |
 |  newbyteorder
 |
 |  ptp
 |
 |  real
 |      The real part of the scalar.
 |
 |  shape
 |      Tuple of array dimensions.
 |
 |  size
 |      The number of elements in the gentype.
 |
 |  strides
 |      Tuple of bytes steps in each dimension.

Python Library Documentation: function vsplit in module autograd.tracer

vsplit(*args, called_by_autograd_dispatcher=False, **kwargs)
    Split an array into multiple sub-arrays vertically (row-wise).

    Please refer to the ``split`` documentation.  ``vsplit`` is equivalent
    to ``split`` with `axis=0` (default), the array is always split along the
    first axis regardless of the array dimension.

    See Also
    --------
    split : Split an array into multiple sub-arrays of equal size.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.arange(16.0).reshape(4, 4)
    >>> x
    array([[ 0.,   1.,   2.,   3.],
           [ 4.,   5.,   6.,   7.],
           [ 8.,   9.,  10.,  11.],
           [12.,  13.,  14.,  15.]])
    >>> np.vsplit(x, 2)
    [array([[0., 1., 2., 3.],
            [4., 5., 6., 7.]]),
     array([[ 8.,  9., 10., 11.],
            [12., 13., 14., 15.]])]
    >>> np.vsplit(x, np.array([3, 6]))
    [array([[ 0.,  1.,  2.,  3.],
            [ 4.,  5.,  6.,  7.],
            [ 8.,  9., 10., 11.]]),
     array([[12., 13., 14., 15.]]),
     array([], shape=(0, 4), dtype=float64)]

    With a higher dimensional array the split is still along the first axis.

    >>> x = np.arange(8.0).reshape(2, 2, 2)
    >>> x
    array([[[0.,  1.],
            [2.,  3.]],
           [[4.,  5.],
            [6.,  7.]]])
    >>> np.vsplit(x, 2)
    [array([[[0., 1.],
             [2., 3.]]]),
     array([[[4., 5.],
             [6., 7.]]])]

Python Library Documentation: function <lambda> in module autograd.numpy.numpy_wrapper

<lambda> lambda tup

Python Library Documentation: function custom_where in module autograd.numpy

custom_where(condition, *args, **kwargs)

Python Library Documentation: function wrap_if_boxes_inside in module autograd.numpy.numpy_wrapper

wrap_if_boxes_inside(raw_array, slow_op_name=None)

Python Library Documentation: function wrap_intdtype in module autograd.numpy.numpy_wrapper

wrap_intdtype(cls)

Python Library Documentation: function wrap_namespace in module autograd.numpy.numpy_wrapper

wrap_namespace(old, new)

Python Library Documentation: function zeros in module autograd.tracer

zeros(*args, called_by_autograd_dispatcher=False, **kwargs)
    zeros(shape, dtype=float, order='C', *, like=None)

    Return a new array of given shape and type, filled with zeros.

    Parameters
    ----------
    shape : int or tuple of ints
        Shape of the new array, e.g., ``(2, 3)`` or ``2``.
    dtype : data-type, optional
        The desired data-type for the array, e.g., `numpy.int8`.  Default is
        `numpy.float64`.
    order : {'C', 'F'}, optional, default: 'C'
        Whether to store multi-dimensional data in row-major
        (C-style) or column-major (Fortran-style) order in
        memory.
    like : array_like, optional
        Reference object to allow the creation of arrays which are not
        NumPy arrays. If an array-like passed in as ``like`` supports
        the ``__array_function__`` protocol, the result will be defined
        by it. In this case, it ensures the creation of an array object
        compatible with that passed in via this argument.

        .. versionadded:: 1.20.0

    Returns
    -------
    out : ndarray
        Array of zeros with the given shape, dtype, and order.

    See Also
    --------
    zeros_like : Return an array of zeros with shape and type of input.
    empty : Return a new uninitialized array.
    ones : Return a new array setting values to one.
    full : Return a new array of given shape filled with value.

    Examples
    --------
    >>> import numpy as np
    >>> np.zeros(5)
    array([ 0.,  0.,  0.,  0.,  0.])

    >>> np.zeros((5,), dtype=int)
    array([0, 0, 0, 0, 0])

    >>> np.zeros((2, 1))
    array([[ 0.],
           [ 0.]])

    >>> s = (2,2)
    >>> np.zeros(s)
    array([[ 0.,  0.],
           [ 0.,  0.]])

    >>> np.zeros((2,), dtype=[('x', 'i4'), ('y', 'i4')]) # custom dtype
    array([(0, 0), (0, 0)],
          dtype=[('x', '<i4'), ('y', '<i4')])

Python Library Documentation: function zeros_like in module autograd.tracer

zeros_like(*args, called_by_autograd_dispatcher=False, **kwargs)
    Return an array of zeros with the same shape and type as a given array.

    Parameters
    ----------
    a : array_like
        The shape and data-type of `a` define these same attributes of
        the returned array.
    dtype : data-type, optional
        Overrides the data type of the result.

        .. versionadded:: 1.6.0
    order : {'C', 'F', 'A', or 'K'}, optional
        Overrides the memory layout of the result. 'C' means C-order,
        'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
        'C' otherwise. 'K' means match the layout of `a` as closely
        as possible.

        .. versionadded:: 1.6.0
    subok : bool, optional.
        If True, then the newly created array will use the sub-class
        type of `a`, otherwise it will be a base-class array. Defaults
        to True.
    shape : int or sequence of ints, optional.
        Overrides the shape of the result. If order='K' and the number of
        dimensions is unchanged, will try to keep order, otherwise,
        order='C' is implied.

        .. versionadded:: 1.17.0
    device : str, optional
        The device on which to place the created array. Default: None.
        For Array-API interoperability only, so must be ``"cpu"`` if passed.

        .. versionadded:: 2.0.0

    Returns
    -------
    out : ndarray
        Array of zeros with the same shape and type as `a`.

    See Also
    --------
    empty_like : Return an empty array with shape and type of input.
    ones_like : Return an array of ones with shape and type of input.
    full_like : Return a new array with shape of input filled with value.
    zeros : Return a new array setting values to zero.

    Examples
    --------
    >>> import numpy as np
    >>> x = np.arange(6)
    >>> x = x.reshape((2, 3))
    >>> x
    array([[0, 1, 2],
           [3, 4, 5]])
    >>> np.zeros_like(x)
    array([[0, 0, 0],
           [0, 0, 0]])

    >>> y = np.arange(3, dtype=float)
    >>> y
    array([0., 1., 2.])
    >>> np.zeros_like(y)
    array([0.,  0.,  0.])

Python Library Documentation: class OrderedDict in module collections

class OrderedDict(builtins.dict)
 |  Dictionary that remembers insertion order
 |
 |  Method resolution order:
 |      OrderedDict
 |      builtins.dict
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __delitem__(self, key, /)
 |      Delete self[key].
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __init__(self, /, *args, **kwargs)
 |      Initialize self.  See help(type(self)) for accurate signature.
 |
 |  __ior__(self, value, /)
 |      Return self|=value.
 |
 |  __iter__(self, /)
 |      Implement iter(self).
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __or__(self, value, /)
 |      Return self|value.
 |
 |  __reduce__(...)
 |      Return state information for pickling
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __reversed__(...)
 |      od.__reversed__() <==> reversed(od)
 |
 |  __ror__(self, value, /)
 |      Return value|self.
 |
 |  __setitem__(self, key, value, /)
 |      Set self[key] to value.
 |
 |  __sizeof__(...)
 |      D.__sizeof__() -> size of D in memory, in bytes
 |
 |  clear(...)
 |      od.clear() -> None.  Remove all items from od.
 |
 |  copy(...)
 |      od.copy() -> a shallow copy of od
 |
 |  items(...)
 |      D.items() -> a set-like object providing a view on D's items
 |
 |  keys(...)
 |      D.keys() -> a set-like object providing a view on D's keys
 |
 |  move_to_end(self, /, key, last=True)
 |      Move an existing element to the end (or beginning if last is false).
 |
 |      Raise KeyError if the element does not exist.
 |
 |  pop(...)
 |      od.pop(key[,default]) -> v, remove specified key and return the corresponding value.
 |
 |      If the key is not found, return the default if given; otherwise,
 |      raise a KeyError.
 |
 |  popitem(self, /, last=True)
 |      Remove and return a (key, value) pair from the dictionary.
 |
 |      Pairs are returned in LIFO order if last is true or FIFO order if false.
 |
 |  setdefault(self, /, key, default=None)
 |      Insert key with a value of default if key is not in the dictionary.
 |
 |      Return the value for key if key is in the dictionary, else default.
 |
 |  update(...)
 |      D.update([E, ]**F) -> None.  Update D from dict/iterable E and F.
 |      If E is present and has a .keys() method, then does:  for k in E: D[k] = E[k]
 |      If E is present and lacks a .keys() method, then does:  for k, v in E: D[k] = v
 |      In either case, this is followed by: for k in F:  D[k] = F[k]
 |
 |  values(...)
 |      D.values() -> an object providing a view on D's values
 |
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |
 |  fromkeys(iterable, value=None)
 |      Create a new ordered dictionary with keys from iterable and values set to value.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes defined here:
 |
 |  __hash__ = None
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from builtins.dict:
 |
 |  __contains__(self, key, /)
 |      True if the dictionary has the specified key, else False.
 |
 |  __getattribute__(self, name, /)
 |      Return getattr(self, name).
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  get(self, key, default=None, /)
 |      Return the value for key if key is in the dictionary, else default.
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from builtins.dict:
 |
 |  __class_getitem__(...)
 |      See PEP 585
 |
 |  ----------------------------------------------------------------------
 |  Static methods inherited from builtins.dict:
 |
 |  __new__(*args, **kwargs) class method of builtins.dict
 |      Create and return a new object.  See help(type) for accurate signature.

Python Library Documentation: class tuple in module autograd.builtins

class tuple(builtins.tuple)
 |  tuple(xs)
 |
 |  Method resolution order:
 |      tuple
 |      builtins.tuple
 |      builtins.object
 |
 |  Static methods defined here:
 |
 |  __new__(cls, xs)
 |      Create and return a new object.  See help(type) for accurate signature.
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __dict__
 |      dictionary for instance variables
 |
 |  ----------------------------------------------------------------------
 |  Methods inherited from builtins.tuple:
 |
 |  __add__(self, value, /)
 |      Return self+value.
 |
 |  __contains__(self, key, /)
 |      Return bool(key in self).
 |
 |  __eq__(self, value, /)
 |      Return self==value.
 |
 |  __ge__(self, value, /)
 |      Return self>=value.
 |
 |  __getattribute__(self, name, /)
 |      Return getattr(self, name).
 |
 |  __getitem__(self, key, /)
 |      Return self[key].
 |
 |  __getnewargs__(self, /)
 |
 |  __gt__(self, value, /)
 |      Return self>value.
 |
 |  __hash__(self, /)
 |      Return hash(self).
 |
 |  __iter__(self, /)
 |      Implement iter(self).
 |
 |  __le__(self, value, /)
 |      Return self<=value.
 |
 |  __len__(self, /)
 |      Return len(self).
 |
 |  __lt__(self, value, /)
 |      Return self<value.
 |
 |  __mul__(self, value, /)
 |      Return self*value.
 |
 |  __ne__(self, value, /)
 |      Return self!=value.
 |
 |  __repr__(self, /)
 |      Return repr(self).
 |
 |  __rmul__(self, value, /)
 |      Return value*self.
 |
 |  count(self, value, /)
 |      Return number of occurrences of value.
 |
 |  index(self, value, start=0, stop=9223372036854775807, /)
 |      Return first index of value.
 |
 |      Raises ValueError if the value is not present.
 |
 |  ----------------------------------------------------------------------
 |  Class methods inherited from builtins.tuple:
 |
 |  __class_getitem__(...)
 |      See PEP 585

Python Library Documentation: function checkpoint in module autograd.differential_operators

checkpoint(fun)
    Returns a checkpointed version of `fun`, where intermediate values
    computed during the forward pass of `fun` are discarded and then recomputed
    for the backward pass. Useful to save memory, effectively trading off time
    and memory. See e.g. arxiv.org/abs/1604.06174.

Python Library Documentation: function defvjp_argnum in module autograd.core

defvjp_argnum(fun, vjpmaker)

Python Library Documentation: function deriv in module autograd.wrap_util

deriv(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    None

Python Library Documentation: function elementwise_grad in module autograd.wrap_util

elementwise_grad(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    Returns a function that computes the sum of each column of the Jacobian of
    `fun`, in one pass. If the Jacobian is diagonal, then this is the diagonal
    of the Jacobian.

Python Library Documentation: function grad in module autograd.wrap_util

grad(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    Returns a function which computes the gradient of `fun` with respect to
    positional argument number `argnum`. The returned function takes the same
    arguments as `fun`, but returns the gradient instead. The function `fun`
    should be scalar-valued. The gradient has the same type as the argument.

Python Library Documentation: function grad_and_aux in module autograd.wrap_util

grad_and_aux(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    Builds a function that returns the gradient of the first output and the
    (unmodified) second output of a function that returns two outputs.

Python Library Documentation: function grad_named in module autograd.differential_operators

grad_named(fun, argname)
    Takes gradients with respect to a named argument.
    Doesn't work on *args or **kwargs.

Python Library Documentation: function hessian in module autograd.wrap_util

hessian(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    Returns a function that computes the exact Hessian.

Python Library Documentation: function hessian_tensor_product in module autograd.differential_operators

hessian_tensor_product(fun, argnum=0)
    Builds a function that returns the exact Hessian-tensor product.
    The returned function has arguments (*args, tensor, **kwargs), and for
    vectors takes roughly 4x as long to evaluate as the original function.

Python Library Documentation: function hessian_tensor_product in module autograd.differential_operators

hessian_tensor_product(fun, argnum=0)
    Builds a function that returns the exact Hessian-tensor product.
    The returned function has arguments (*args, tensor, **kwargs), and for
    vectors takes roughly 4x as long to evaluate as the original function.

Python Library Documentation: function holomorphic_grad in module autograd.wrap_util

holomorphic_grad(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    None

Python Library Documentation: function jacobian in module autograd.wrap_util

jacobian(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    Returns a function which computes the Jacobian of `fun` with respect to
    positional argument number `argnum`, which must be a scalar or array. Unlike
    `grad` it is not restricted to scalar-output functions, but also it cannot
    take derivatives with respect to some argument types (like lists or dicts).
    If the input to `fun` has shape (in1, in2, ...) and the output has shape
    (out1, out2, ...) then the Jacobian has shape (out1, out2, ..., in1, in2, ...).

Python Library Documentation: function make_ggnvp in module autograd.differential_operators

make_ggnvp(f, g=<function <lambda> at 0x000001DD17CB1B20>, f_argnum=0)
    Builds a function for evaluating generalized-Gauss-Newton-vector products
    at a point. Slightly more expensive than mixed-mode.

Python Library Documentation: function make_hvp in module autograd.wrap_util

make_hvp(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    Builds a function for evaluating the Hessian-vector product at a point,
    which may be useful when evaluating many Hessian-vector products at the same
    point while caching the results of the forward pass.

Python Library Documentation: function make_jvp in module autograd.wrap_util

make_jvp(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    None

Python Library Documentation: function make_jvp_reversemode in module autograd.wrap_util

make_jvp_reversemode(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    Builds a function for evaluating the Jacobian-vector product at a
    point. Roughly 1.5x more FLOPs than forward-mode, plus memory requirements
    that scale with the number of primitives applied in the evaluation of f, as
    well as other overheads. See j-towns.github.io/2017/06/12/A-new-trick.html.

Python Library Documentation: function make_vjp in module autograd.wrap_util

make_vjp(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    None

Python Library Documentation: function multigrad_dict in module autograd.differential_operators

multigrad_dict(fun)
    Takes gradients wrt all arguments simultaneously,

Python Library Documentation: function primitive in module autograd.tracer

primitive(f_raw)
    Wraps a function so that its gradient can be specified and its invocation
    can be recorded. For examples, see the docs.

Python Library Documentation: function tensor_jacobian_product in module autograd.differential_operators

tensor_jacobian_product(fun, argnum=0)
    Builds a function that returns the exact tensor-Jacobian product, that
    is the Jacobian matrix left-multiplied by tensor. The returned function
    has arguments (*args, tensor, **kwargs).

Python Library Documentation: function unary_to_nary in module autograd.wrap_util

unary_to_nary(unary_operator)

Python Library Documentation: function value_and_grad in module autograd.wrap_util

value_and_grad(fun, argnum=0, *nary_op_args, **nary_op_kwargs)
    Returns a function that returns both value and gradient. Suitable for use
    in scipy.optimize

Python Library Documentation: function tensor_jacobian_product in module autograd.differential_operators

tensor_jacobian_product(fun, argnum=0)
    Builds a function that returns the exact tensor-Jacobian product, that
    is the Jacobian matrix left-multiplied by tensor. The returned function
    has arguments (*args, tensor, **kwargs).

Python Library Documentation: function vspace in module autograd.core

vspace(value)