_torch_docs.py

# -*- coding: utf-8 -*-
"""Adds docstrings to functions defined in the torch._C"""

import re

import torch._C
from torch._C import _add_docstr as add_docstr


def parse_kwargs(desc):
    """Maps a description of args to a dictionary of {argname: description}.
    Input:
        ('    weight (Tensor): a weight tensor\n' +
         '        Some optional description')
    Output: {
        'weight': \
        'weight (Tensor): a weight tensor\n        Some optional description'
    }
    """
    # Split on exactly 4 spaces after a newline
    regx = re.compile(r"\n\s{4}(?!\s)")
    kwargs = [section.strip() for section in regx.split(desc)]
    kwargs = [section for section in kwargs if len(section) > 0]
    return {desc.split(' ')[0]: desc for desc in kwargs}


def merge_dicts(*dicts):
    return {x: d[x] for d in dicts for x in d}


common_args = parse_kwargs("""
    input (Tensor): the input tensor.
    generator (:class:`torch.Generator`, optional): a pseudorandom number generator for sampling
    out (Tensor, optional): the output tensor.
    memory_format (:class:`torch.memory_format`, optional): the desired memory format of
        returned tensor. Default: ``torch.preserve_format``.
""")

reduceops_common_args = merge_dicts(common_args, parse_kwargs("""
    dtype (:class:`torch.dtype`, optional): the desired data type of returned tensor.
        If specified, the input tensor is casted to :attr:`dtype` before the operation
        is performed. This is useful for preventing data type overflows. Default: None.
    keepdim (bool): whether the output tensor has :attr:`dim` retained or not.
"""))

multi_dim_common = merge_dicts(reduceops_common_args, parse_kwargs("""
    dim (int or tuple of ints): the dimension or dimensions to reduce.
"""), {'keepdim_details': """
If :attr:`keepdim` is ``True``, the output tensor is of the same size
as :attr:`input` except in the dimension(s) :attr:`dim` where it is of size 1.
Otherwise, :attr:`dim` is squeezed (see :func:`torch.squeeze`), resulting in the
output tensor having 1 (or ``len(dim)``) fewer dimension(s).
"""})

single_dim_common = merge_dicts(reduceops_common_args, parse_kwargs("""
    dim (int): the dimension to reduce.
"""), {'keepdim_details': """If :attr:`keepdim` is ``True``, the output tensor is of the same size
as :attr:`input` except in the dimension :attr:`dim` where it is of size 1.
Otherwise, :attr:`dim` is squeezed (see :func:`torch.squeeze`), resulting in
the output tensor having 1 fewer dimension than :attr:`input`."""})

factory_common_args = merge_dicts(common_args, parse_kwargs("""
    dtype (:class:`torch.dtype`, optional): the desired data type of returned tensor.
        Default: if ``None``, uses a global default (see :func:`torch.set_default_tensor_type`).
    layout (:class:`torch.layout`, optional): the desired layout of returned Tensor.
        Default: ``torch.strided``.
    device (:class:`torch.device`, optional): the desired device of returned tensor.
        Default: if ``None``, uses the current device for the default tensor type
        (see :func:`torch.set_default_tensor_type`). :attr:`device` will be the CPU
        for CPU tensor types and the current CUDA device for CUDA tensor types.
    requires_grad (bool, optional): If autograd should record operations on the
        returned tensor. Default: ``False``.
    pin_memory (bool, optional): If set, returned tensor would be allocated in
        the pinned memory. Works only for CPU tensors. Default: ``False``.
    memory_format (:class:`torch.memory_format`, optional): the desired memory format of
        returned Tensor. Default: ``torch.contiguous_format``.
"""))

factory_like_common_args = parse_kwargs("""
    input (Tensor): the size of :attr:`input` will determine size of the output tensor.
    layout (:class:`torch.layout`, optional): the desired layout of returned tensor.
        Default: if ``None``, defaults to the layout of :attr:`input`.
    dtype (:class:`torch.dtype`, optional): the desired data type of returned Tensor.
        Default: if ``None``, defaults to the dtype of :attr:`input`.
    device (:class:`torch.device`, optional): the desired device of returned tensor.
        Default: if ``None``, defaults to the device of :attr:`input`.
    requires_grad (bool, optional): If autograd should record operations on the
        returned tensor. Default: ``False``.
    pin_memory (bool, optional): If set, returned tensor would be allocated in
        the pinned memory. Works only for CPU tensors. Default: ``False``.
    memory_format (:class:`torch.memory_format`, optional): the desired memory format of
        returned Tensor. Default: ``torch.preserve_format``.
""")

factory_data_common_args = parse_kwargs("""
    data (array_like): Initial data for the tensor. Can be a list, tuple,
        NumPy ``ndarray``, scalar, and other types.
    dtype (:class:`torch.dtype`, optional): the desired data type of returned tensor.
        Default: if ``None``, infers data type from :attr:`data`.
    device (:class:`torch.device`, optional): the desired device of returned tensor.
        Default: if ``None``, uses the current device for the default tensor type
        (see :func:`torch.set_default_tensor_type`). :attr:`device` will be the CPU
        for CPU tensor types and the current CUDA device for CUDA tensor types.
    requires_grad (bool, optional): If autograd should record operations on the
        returned tensor. Default: ``False``.
    pin_memory (bool, optional): If set, returned tensor would be allocated in
        the pinned memory. Works only for CPU tensors. Default: ``False``.
""")

tf32_notes = {
    "tf32_note": """This operator supports :ref:`TensorFloat32<tf32_on_ampere>`."""
}


reproducibility_notes = {
    "forward_reproducibility_note": """This operation may behave nondeterministically when given tensors on \
a CUDA device. See :doc:`/notes/randomness` for more information.""",
    "backward_reproducibility_note": """This operation may produce nondeterministic gradients when given tensors on \
a CUDA device. See :doc:`/notes/randomness` for more information.""",
    "cudnn_reproducibility_note": """In some circumstances when given tensors on a CUDA device \
and using CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is \
undesirable, you can try to make the operation deterministic (potentially at \
a performance cost) by setting ``torch.backends.cudnn.deterministic = True``. \
See :doc:`/notes/randomness` for more information."""
}

add_docstr(torch.abs, r"""
abs(input, *, out=None) -> Tensor

Computes the absolute value of each element in :attr:`input`.

.. math::
    \text{out}_{i} = |\text{input}_{i}|
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> torch.abs(torch.tensor([-1, -2, 3]))
    tensor([ 1,  2,  3])
""".format(**common_args))

add_docstr(torch.absolute,
           r"""
absolute(input, *, out=None) -> Tensor

Alias for :func:`torch.abs`
""")

add_docstr(torch.acos, r"""
acos(input, *, out=None) -> Tensor

Computes the inverse cosine of each element in :attr:`input`.

.. math::
    \text{out}_{i} = \cos^{-1}(\text{input}_{i})
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([ 0.3348, -0.5889,  0.2005, -0.1584])
    >>> torch.acos(a)
    tensor([ 1.2294,  2.2004,  1.3690,  1.7298])
""".format(**common_args))

add_docstr(torch.arccos, r"""
arccos(input, *, out=None) -> Tensor

Alias for :func:`torch.acos`.
""")

add_docstr(torch.acosh, r"""
acosh(input, *, out=None) -> Tensor

Returns a new tensor with the inverse hyperbolic cosine of the elements of :attr:`input`.

.. math::
    \text{out}_{i} = \cosh^{-1}(\text{input}_{i})

Note:
    The domain of the inverse hyperbolic cosine is `[1, inf)` and values outside this range
    will be mapped to ``NaN``, except for `+ INF` for which the output is mapped to `+ INF`.
""" + r"""
Args:
    {input}

Keyword arguments:
    {out}

Example::

    >>> a = torch.randn(4).uniform_(1, 2)
    >>> a
    tensor([ 1.3192, 1.9915, 1.9674, 1.7151 ])
    >>> torch.acosh(a)
    tensor([ 0.7791, 1.3120, 1.2979, 1.1341 ])
""".format(**common_args))

add_docstr(torch.arccosh, r"""
arccosh(input, *, out=None) -> Tensor

Alias for :func:`torch.acosh`.
""")

add_docstr(torch.index_add, r"""
index_add(input, dim, index, source, *, alpha=1, out=None) -> Tensor

See :meth:`~Tensor.index_add_` for function description.
""")

add_docstr(torch.index_copy, r"""
index_copy(input, dim, index, source, *, out=None) -> Tensor

See :meth:`~Tensor.index_add_` for function description.
""")

add_docstr(torch.add, r"""
add(input, other, *, alpha=1, out=None) -> Tensor

Adds :attr:`other`, scaled by :attr:`alpha`, to :attr:`input`.

.. math::
    \text{{out}}_i = \text{{input}}_i + \text{{alpha}} \times \text{{other}}_i
""" + r"""

Supports :ref:`broadcasting to a common shape <broadcasting-semantics>`,
:ref:`type promotion <type-promotion-doc>`, and integer, float, and complex inputs.

Args:
    {input}
    other (Tensor or Number): the tensor or number to add to input.

Keyword arguments:
    alpha (Number): the multiplier for :attr:`other`.
    {out}

Examples::

    >>> a = torch.randn(4)
    >>> a
    tensor([ 0.0202,  1.0985,  1.3506, -0.6056])
    >>> torch.add(a, 20)
    tensor([ 20.0202,  21.0985,  21.3506,  19.3944])

    >>> b = torch.randn(4)
    >>> b
    tensor([-0.9732, -0.3497,  0.6245,  0.4022])
    >>> c = torch.randn(4, 1)
    >>> c
    tensor([[ 0.3743],
            [-1.7724],
            [-0.5811],
            [-0.8017]])
    >>> torch.add(b, c, alpha=10)
    tensor([[  2.7695,   3.3930,   4.3672,   4.1450],
            [-18.6971, -18.0736, -17.0994, -17.3216],
            [ -6.7845,  -6.1610,  -5.1868,  -5.4090],
            [ -8.9902,  -8.3667,  -7.3925,  -7.6147]])
""".format(**common_args))

add_docstr(torch.addbmm,
           r"""
addbmm(input, batch1, batch2, *, beta=1, alpha=1, out=None) -> Tensor

Performs a batch matrix-matrix product of matrices stored
in :attr:`batch1` and :attr:`batch2`,
with a reduced add step (all matrix multiplications get accumulated
along the first dimension).
:attr:`input` is added to the final result.

:attr:`batch1` and :attr:`batch2` must be 3-D tensors each containing the
same number of matrices.

If :attr:`batch1` is a :math:`(b \times n \times m)` tensor, :attr:`batch2` is a
:math:`(b \times m \times p)` tensor, :attr:`input` must be
:ref:`broadcastable <broadcasting-semantics>` with a :math:`(n \times p)` tensor
and :attr:`out` will be a :math:`(n \times p)` tensor.

.. math::
    out = \beta\ \text{input} + \alpha\ (\sum_{i=0}^{b-1} \text{batch1}_i \mathbin{@} \text{batch2}_i)

If :attr:`beta` is 0, then :attr:`input` will be ignored, and `nan` and `inf` in
it will not be propagated.
""" + r"""
For inputs of type `FloatTensor` or `DoubleTensor`, arguments :attr:`beta` and :attr:`alpha`
must be real numbers, otherwise they should be integers.

{tf32_note}

Args:
    batch1 (Tensor): the first batch of matrices to be multiplied
    batch2 (Tensor): the second batch of matrices to be multiplied

Keyword args:
    beta (Number, optional): multiplier for :attr:`input` (:math:`\beta`)
    input (Tensor): matrix to be added
    alpha (Number, optional): multiplier for `batch1 @ batch2` (:math:`\alpha`)
    {out}

Example::

    >>> M = torch.randn(3, 5)
    >>> batch1 = torch.randn(10, 3, 4)
    >>> batch2 = torch.randn(10, 4, 5)
    >>> torch.addbmm(M, batch1, batch2)
    tensor([[  6.6311,   0.0503,   6.9768, -12.0362,  -2.1653],
            [ -4.8185,  -1.4255,  -6.6760,   8.9453,   2.5743],
            [ -3.8202,   4.3691,   1.0943,  -1.1109,   5.4730]])
""".format(**common_args, **tf32_notes))

add_docstr(torch.addcdiv, r"""
addcdiv(input, tensor1, tensor2, *, value=1, out=None) -> Tensor

Performs the element-wise division of :attr:`tensor1` by :attr:`tensor2`,
multiply the result by the scalar :attr:`value` and add it to :attr:`input`.

.. warning::
    Integer division with addcdiv is no longer supported, and in a future
    release addcdiv will perform a true division of tensor1 and tensor2.
    The historic addcdiv behavior can be implemented as
    (input + value * torch.trunc(tensor1 / tensor2)).to(input.dtype)
    for integer inputs and as (input + value * tensor1 / tensor2) for float inputs.
    The future addcdiv behavior is just the latter implementation:
    (input + value * tensor1 / tensor2), for all dtypes.

.. math::
    \text{out}_i = \text{input}_i + \text{value} \times \frac{\text{tensor1}_i}{\text{tensor2}_i}
""" + r"""

The shapes of :attr:`input`, :attr:`tensor1`, and :attr:`tensor2` must be
:ref:`broadcastable <broadcasting-semantics>`.

For inputs of type `FloatTensor` or `DoubleTensor`, :attr:`value` must be
a real number, otherwise an integer.

Args:
    input (Tensor): the tensor to be added
    tensor1 (Tensor): the numerator tensor
    tensor2 (Tensor): the denominator tensor

Keyword args:
    value (Number, optional): multiplier for :math:`\text{{tensor1}} / \text{{tensor2}}`
    {out}

Example::

    >>> t = torch.randn(1, 3)
    >>> t1 = torch.randn(3, 1)
    >>> t2 = torch.randn(1, 3)
    >>> torch.addcdiv(t, t1, t2, value=0.1)
    tensor([[-0.2312, -3.6496,  0.1312],
            [-1.0428,  3.4292, -0.1030],
            [-0.5369, -0.9829,  0.0430]])
""".format(**common_args))

add_docstr(torch.addcmul,
           r"""
addcmul(input, tensor1, tensor2, *, value=1, out=None) -> Tensor

Performs the element-wise multiplication of :attr:`tensor1`
by :attr:`tensor2`, multiply the result by the scalar :attr:`value`
and add it to :attr:`input`.

.. math::
    \text{out}_i = \text{input}_i + \text{value} \times \text{tensor1}_i \times \text{tensor2}_i
""" + r"""
The shapes of :attr:`tensor`, :attr:`tensor1`, and :attr:`tensor2` must be
:ref:`broadcastable <broadcasting-semantics>`.

For inputs of type `FloatTensor` or `DoubleTensor`, :attr:`value` must be
a real number, otherwise an integer.

Args:
    input (Tensor): the tensor to be added
    tensor1 (Tensor): the tensor to be multiplied
    tensor2 (Tensor): the tensor to be multiplied

Keyword args:
    value (Number, optional): multiplier for :math:`tensor1 .* tensor2`
    {out}

Example::

    >>> t = torch.randn(1, 3)
    >>> t1 = torch.randn(3, 1)
    >>> t2 = torch.randn(1, 3)
    >>> torch.addcmul(t, t1, t2, value=0.1)
    tensor([[-0.8635, -0.6391,  1.6174],
            [-0.7617, -0.5879,  1.7388],
            [-0.8353, -0.6249,  1.6511]])
""".format(**common_args))

add_docstr(torch.addmm,
           r"""
addmm(input, mat1, mat2, *, beta=1, alpha=1, out=None) -> Tensor

Performs a matrix multiplication of the matrices :attr:`mat1` and :attr:`mat2`.
The matrix :attr:`input` is added to the final result.

If :attr:`mat1` is a :math:`(n \times m)` tensor, :attr:`mat2` is a
:math:`(m \times p)` tensor, then :attr:`input` must be
:ref:`broadcastable <broadcasting-semantics>` with a :math:`(n \times p)` tensor
and :attr:`out` will be a :math:`(n \times p)` tensor.

:attr:`alpha` and :attr:`beta` are scaling factors on matrix-vector product between
:attr:`mat1` and :attr:`mat2` and the added matrix :attr:`input` respectively.

.. math::
    \text{out} = \beta\ \text{input} + \alpha\ (\text{mat1}_i \mathbin{@} \text{mat2}_i)

If :attr:`beta` is 0, then :attr:`input` will be ignored, and `nan` and `inf` in
it will not be propagated.
""" + r"""
For inputs of type `FloatTensor` or `DoubleTensor`, arguments :attr:`beta` and
:attr:`alpha` must be real numbers, otherwise they should be integers.

{tf32_note}

Args:
    input (Tensor): matrix to be added
    mat1 (Tensor): the first matrix to be matrix multiplied
    mat2 (Tensor): the second matrix to be matrix multiplied

Keyword args:
    beta (Number, optional): multiplier for :attr:`input` (:math:`\beta`)
    alpha (Number, optional): multiplier for :math:`mat1 @ mat2` (:math:`\alpha`)
    {out}

Example::

    >>> M = torch.randn(2, 3)
    >>> mat1 = torch.randn(2, 3)
    >>> mat2 = torch.randn(3, 3)
    >>> torch.addmm(M, mat1, mat2)
    tensor([[-4.8716,  1.4671, -1.3746],
            [ 0.7573, -3.9555, -2.8681]])
""".format(**common_args, **tf32_notes))

add_docstr(torch.adjoint,
           r"""
adjoint(Tensor) -> Tensor
Returns a view of the tensor conjugated and with the last two dimensions transposed.

``x.adjoint()`` is equivalent to ``x.transpose(-2, -1).conj()`` for complex tensors and
to ``x.transpose(-2, -1)`` for real tensors.

Example::
    >>> x = torch.arange(4, dtype=torch.float)
    >>> A = torch.complex(x, x).reshape(2, 2)
    >>> A
    tensor([[0.+0.j, 1.+1.j],
            [2.+2.j, 3.+3.j]])
    >>> A.adjoint()
    tensor([[0.-0.j, 2.-2.j],
            [1.-1.j, 3.-3.j]])
    >>> (A.adjoint() == A.mH).all()
    tensor(True)
""")

add_docstr(torch.sspaddmm,
           r"""
sspaddmm(input, mat1, mat2, *, beta=1, alpha=1, out=None) -> Tensor

Matrix multiplies a sparse tensor :attr:`mat1` with a dense tensor
:attr:`mat2`, then adds the sparse tensor :attr:`input` to the result.

Note: This function is equivalent to :func:`torch.addmm`, except
:attr:`input` and :attr:`mat1` are sparse.

Args:
    input (Tensor): a sparse matrix to be added
    mat1 (Tensor): a sparse matrix to be matrix multiplied
    mat2 (Tensor): a dense matrix to be matrix multiplied

Keyword args:
    beta (Number, optional): multiplier for :attr:`mat` (:math:`\beta`)
    alpha (Number, optional): multiplier for :math:`mat1 @ mat2` (:math:`\alpha`)
    {out}
""".format(**common_args))

add_docstr(torch.smm,
           r"""
smm(input, mat) -> Tensor

Performs a matrix multiplication of the sparse matrix :attr:`input`
with the dense matrix :attr:`mat`.

Args:
    input (Tensor): a sparse matrix to be matrix multiplied
    mat (Tensor): a dense matrix to be matrix multiplied
""")

add_docstr(torch.addmv,
           r"""
addmv(input, mat, vec, *, beta=1, alpha=1, out=None) -> Tensor

Performs a matrix-vector product of the matrix :attr:`mat` and
the vector :attr:`vec`.
The vector :attr:`input` is added to the final result.

If :attr:`mat` is a :math:`(n \times m)` tensor, :attr:`vec` is a 1-D tensor of
size `m`, then :attr:`input` must be
:ref:`broadcastable <broadcasting-semantics>` with a 1-D tensor of size `n` and
:attr:`out` will be 1-D tensor of size `n`.

:attr:`alpha` and :attr:`beta` are scaling factors on matrix-vector product between
:attr:`mat` and :attr:`vec` and the added tensor :attr:`input` respectively.

.. math::
    \text{out} = \beta\ \text{input} + \alpha\ (\text{mat} \mathbin{@} \text{vec})

If :attr:`beta` is 0, then :attr:`input` will be ignored, and `nan` and `inf` in
it will not be propagated.
""" + r"""
For inputs of type `FloatTensor` or `DoubleTensor`, arguments :attr:`beta` and
:attr:`alpha` must be real numbers, otherwise they should be integers

Args:
    input (Tensor): vector to be added
    mat (Tensor): matrix to be matrix multiplied
    vec (Tensor): vector to be matrix multiplied

Keyword args:
    beta (Number, optional): multiplier for :attr:`input` (:math:`\beta`)
    alpha (Number, optional): multiplier for :math:`mat @ vec` (:math:`\alpha`)
    {out}

Example::

    >>> M = torch.randn(2)
    >>> mat = torch.randn(2, 3)
    >>> vec = torch.randn(3)
    >>> torch.addmv(M, mat, vec)
    tensor([-0.3768, -5.5565])
""".format(**common_args))

add_docstr(torch.addr,
           r"""
addr(input, vec1, vec2, *, beta=1, alpha=1, out=None) -> Tensor

Performs the outer-product of vectors :attr:`vec1` and :attr:`vec2`
and adds it to the matrix :attr:`input`.

Optional values :attr:`beta` and :attr:`alpha` are scaling factors on the
outer product between :attr:`vec1` and :attr:`vec2` and the added matrix
:attr:`input` respectively.

.. math::
    \text{out} = \beta\ \text{input} + \alpha\ (\text{vec1} \otimes \text{vec2})

If :attr:`beta` is 0, then :attr:`input` will be ignored, and `nan` and `inf` in
it will not be propagated.
""" + r"""
If :attr:`vec1` is a vector of size `n` and :attr:`vec2` is a vector
of size `m`, then :attr:`input` must be
:ref:`broadcastable <broadcasting-semantics>` with a matrix of size
:math:`(n \times m)` and :attr:`out` will be a matrix of size
:math:`(n \times m)`.

Args:
    input (Tensor): matrix to be added
    vec1 (Tensor): the first vector of the outer product
    vec2 (Tensor): the second vector of the outer product

Keyword args:
    beta (Number, optional): multiplier for :attr:`input` (:math:`\beta`)
    alpha (Number, optional): multiplier for :math:`\text{{vec1}} \otimes \text{{vec2}}` (:math:`\alpha`)
    {out}

Example::

    >>> vec1 = torch.arange(1., 4.)
    >>> vec2 = torch.arange(1., 3.)
    >>> M = torch.zeros(3, 2)
    >>> torch.addr(M, vec1, vec2)
    tensor([[ 1.,  2.],
            [ 2.,  4.],
            [ 3.,  6.]])
""".format(**common_args))

add_docstr(torch.allclose,
           r"""
allclose(input, other, rtol=1e-05, atol=1e-08, equal_nan=False) -> bool

This function checks if all :attr:`input` and :attr:`other` satisfy the condition:

.. math::
    \lvert \text{input} - \text{other} \rvert \leq \texttt{atol} + \texttt{rtol} \times \lvert \text{other} \rvert
""" + r"""
elementwise, for all elements of :attr:`input` and :attr:`other`. The behaviour of this function is analogous to
`numpy.allclose <https://docs.scipy.org/doc/numpy/reference/generated/numpy.allclose.html>`_

Args:
    input (Tensor): first tensor to compare
    other (Tensor): second tensor to compare
    atol (float, optional): absolute tolerance. Default: 1e-08
    rtol (float, optional): relative tolerance. Default: 1e-05
    equal_nan (bool, optional): if ``True``, then two ``NaN`` s will be considered equal. Default: ``False``

Example::

    >>> torch.allclose(torch.tensor([10000., 1e-07]), torch.tensor([10000.1, 1e-08]))
    False
    >>> torch.allclose(torch.tensor([10000., 1e-08]), torch.tensor([10000.1, 1e-09]))
    True
    >>> torch.allclose(torch.tensor([1.0, float('nan')]), torch.tensor([1.0, float('nan')]))
    False
    >>> torch.allclose(torch.tensor([1.0, float('nan')]), torch.tensor([1.0, float('nan')]), equal_nan=True)
    True
""")

add_docstr(torch.all,
           r"""
all(input) -> Tensor

Tests if all elements in :attr:`input` evaluate to `True`.

.. note:: This function matches the behaviour of NumPy in returning
          output of dtype `bool` for all supported dtypes except `uint8`.
          For `uint8` the dtype of output is `uint8` itself.

Example::

    >>> a = torch.rand(1, 2).bool()
    >>> a
    tensor([[False, True]], dtype=torch.bool)
    >>> torch.all(a)
    tensor(False, dtype=torch.bool)
    >>> a = torch.arange(0, 3)
    >>> a
    tensor([0, 1, 2])
    >>> torch.all(a)
    tensor(False)

.. function:: all(input, dim, keepdim=False, *, out=None) -> Tensor
   :noindex:

For each row of :attr:`input` in the given dimension :attr:`dim`,
returns `True` if all elements in the row evaluate to `True` and `False` otherwise.

{keepdim_details}

Args:
    {input}
    {dim}
    {keepdim}

Keyword args:
    {out}

Example::

    >>> a = torch.rand(4, 2).bool()
    >>> a
    tensor([[True, True],
            [True, False],
            [True, True],
            [True, True]], dtype=torch.bool)
    >>> torch.all(a, dim=1)
    tensor([ True, False,  True,  True], dtype=torch.bool)
    >>> torch.all(a, dim=0)
    tensor([ True, False], dtype=torch.bool)
""".format(**single_dim_common))

add_docstr(torch.any,
           r"""
any(input) -> Tensor

Tests if any element in :attr:`input` evaluates to `True`.

.. note:: This function matches the behaviour of NumPy in returning
          output of dtype `bool` for all supported dtypes except `uint8`.
          For `uint8` the dtype of output is `uint8` itself.

Example::

    >>> a = torch.rand(1, 2).bool()
    >>> a
    tensor([[False, True]], dtype=torch.bool)
    >>> torch.any(a)
    tensor(True, dtype=torch.bool)
    >>> a = torch.arange(0, 3)
    >>> a
    tensor([0, 1, 2])
    >>> torch.any(a)
    tensor(True)

.. function:: any(input, dim, keepdim=False, *, out=None) -> Tensor
   :noindex:

For each row of :attr:`input` in the given dimension :attr:`dim`,
returns `True` if any element in the row evaluate to `True` and `False` otherwise.

{keepdim_details}

Args:
    {input}
    {dim}
    {keepdim}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4, 2) < 0
    >>> a
    tensor([[ True,  True],
            [False,  True],
            [ True,  True],
            [False, False]])
    >>> torch.any(a, 1)
    tensor([ True,  True,  True, False])
    >>> torch.any(a, 0)
    tensor([True, True])
""".format(**single_dim_common))

add_docstr(torch.angle,
           r"""
angle(input, *, out=None) -> Tensor

Computes the element-wise angle (in radians) of the given :attr:`input` tensor.

.. math::
    \text{out}_{i} = angle(\text{input}_{i})
""" + r"""
Args:
    {input}

Keyword args:
    {out}

.. note:: Starting in PyTorch 1.8, angle returns pi for negative real numbers,
          zero for non-negative real numbers, and propagates NaNs. Previously
          the function would return zero for all real numbers and not propagate
          floating-point NaNs.

Example::

    >>> torch.angle(torch.tensor([-1 + 1j, -2 + 2j, 3 - 3j]))*180/3.14159
    tensor([ 135.,  135,  -45])
""".format(**common_args))

add_docstr(torch.as_strided,
           r"""
as_strided(input, size, stride, storage_offset=0) -> Tensor

Create a view of an existing `torch.Tensor` :attr:`input` with specified
:attr:`size`, :attr:`stride` and :attr:`storage_offset`.

.. warning::
    Prefer using other view functions, like :meth:`torch.Tensor.expand`,
    to setting a view's strides manually with `as_strided`, as this
    function's behavior depends on the implementation of a tensor's storage.
    The constructed view of the storage must only refer to elements within
    the storage or a runtime error will be thrown, and if the view is
    "overlapped" (with multiple indices referring to the same element in
    memory) its behavior is undefined.

Args:
    {input}
    size (tuple or ints): the shape of the output tensor
    stride (tuple or ints): the stride of the output tensor
    storage_offset (int, optional): the offset in the underlying storage of the output tensor

Example::

    >>> x = torch.randn(3, 3)
    >>> x
    tensor([[ 0.9039,  0.6291,  1.0795],
            [ 0.1586,  2.1939, -0.4900],
            [-0.1909, -0.7503,  1.9355]])
    >>> t = torch.as_strided(x, (2, 2), (1, 2))
    >>> t
    tensor([[0.9039, 1.0795],
            [0.6291, 0.1586]])
    >>> t = torch.as_strided(x, (2, 2), (1, 2), 1)
    tensor([[0.6291, 0.1586],
            [1.0795, 2.1939]])
""".format(**common_args))

add_docstr(torch.as_tensor,
           r"""
as_tensor(data, dtype=None, device=None) -> Tensor

Converts data into a tensor, sharing data and preserving autograd
history if possible.

If data is already a tensor with the requeseted dtype and device
then data itself is returned, but if data is a
tensor with a different dtype or device then it's copied as if using
`data.to(dtype=dtype, device=device)`.

If data is a NumPy array (an ndarray) with the same dtype and device then a
tensor is constructed using :func:`torch.from_numpy`.

.. seealso::

    :func:`torch.tensor` never shares its data and creates a new "leaf tensor" (see :doc:`/notes/autograd`).


Args:
    {data}
    {dtype}
    device (:class:`torch.device`, optional): the device of the constructed tensor. If None and data is a tensor
        then the device of data is used. If None and data is not a tensor then
        the result tensor is constructed on the CPU.


Example::

    >>> a = numpy.array([1, 2, 3])
    >>> t = torch.as_tensor(a)
    >>> t
    tensor([ 1,  2,  3])
    >>> t[0] = -1
    >>> a
    array([-1,  2,  3])

    >>> a = numpy.array([1, 2, 3])
    >>> t = torch.as_tensor(a, device=torch.device('cuda'))
    >>> t
    tensor([ 1,  2,  3])
    >>> t[0] = -1
    >>> a
    array([1,  2,  3])
""".format(**factory_data_common_args))

add_docstr(torch.asin, r"""
asin(input, *, out=None) -> Tensor

Returns a new tensor with the arcsine  of the elements of :attr:`input`.

.. math::
    \text{out}_{i} = \sin^{-1}(\text{input}_{i})
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([-0.5962,  1.4985, -0.4396,  1.4525])
    >>> torch.asin(a)
    tensor([-0.6387,     nan, -0.4552,     nan])
""".format(**common_args))

add_docstr(torch.arcsin, r"""
arcsin(input, *, out=None) -> Tensor

Alias for :func:`torch.asin`.
""")

add_docstr(torch.asinh,
           r"""
asinh(input, *, out=None) -> Tensor

Returns a new tensor with the inverse hyperbolic sine of the elements of :attr:`input`.

.. math::
    \text{out}_{i} = \sinh^{-1}(\text{input}_{i})
""" + r"""
Args:
    {input}

Keyword arguments:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([ 0.1606, -1.4267, -1.0899, -1.0250 ])
    >>> torch.asinh(a)
    tensor([ 0.1599, -1.1534, -0.9435, -0.8990 ])
""".format(**common_args))

add_docstr(torch.arcsinh, r"""
arcsinh(input, *, out=None) -> Tensor

Alias for :func:`torch.asinh`.
""")

add_docstr(torch.atan, r"""
atan(input, *, out=None) -> Tensor

Returns a new tensor with the arctangent  of the elements of :attr:`input`.

.. math::
    \text{out}_{i} = \tan^{-1}(\text{input}_{i})
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([ 0.2341,  0.2539, -0.6256, -0.6448])
    >>> torch.atan(a)
    tensor([ 0.2299,  0.2487, -0.5591, -0.5727])
""".format(**common_args))

add_docstr(torch.arctan, r"""
arctan(input, *, out=None) -> Tensor

Alias for :func:`torch.atan`.
""")

add_docstr(torch.atan2,
           r"""
atan2(input, other, *, out=None) -> Tensor

Element-wise arctangent of :math:`\text{{input}}_{{i}} / \text{{other}}_{{i}}`
with consideration of the quadrant. Returns a new tensor with the signed angles
in radians between vector :math:`(\text{{other}}_{{i}}, \text{{input}}_{{i}})`
and vector :math:`(1, 0)`. (Note that :math:`\text{{other}}_{{i}}`, the second
parameter, is the x-coordinate, while :math:`\text{{input}}_{{i}}`, the first
parameter, is the y-coordinate.)

The shapes of ``input`` and ``other`` must be
:ref:`broadcastable <broadcasting-semantics>`.

Args:
    input (Tensor): the first input tensor
    other (Tensor): the second input tensor

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([ 0.9041,  0.0196, -0.3108, -2.4423])
    >>> torch.atan2(a, torch.randn(4))
    tensor([ 0.9833,  0.0811, -1.9743, -1.4151])
""".format(**common_args))

add_docstr(torch.arctan2,
           r"""
arctan2(input, other, *, out=None) -> Tensor
Alias for :func:`torch.atan2`.
""")

add_docstr(torch.atanh, r"""
atanh(input, *, out=None) -> Tensor

Returns a new tensor with the inverse hyperbolic tangent of the elements of :attr:`input`.

Note:
    The domain of the inverse hyperbolic tangent is `(-1, 1)` and values outside this range
    will be mapped to ``NaN``, except for the values `1` and `-1` for which the output is
    mapped to `+/-INF` respectively.

.. math::
    \text{out}_{i} = \tanh^{-1}(\text{input}_{i})
""" + r"""
Args:
    {input}

Keyword arguments:
    {out}

Example::

    >>> a = torch.randn(4).uniform_(-1, 1)
    >>> a
    tensor([ -0.9385, 0.2968, -0.8591, -0.1871 ])
    >>> torch.atanh(a)
    tensor([ -1.7253, 0.3060, -1.2899, -0.1893 ])
""".format(**common_args))

add_docstr(torch.arctanh, r"""
arctanh(input, *, out=None) -> Tensor

Alias for :func:`torch.atanh`.
""")

add_docstr(torch.asarray,
           r"""
asarray(obj, *, dtype=None, device=None, copy=None, requires_grad=False) -> Tensor

Converts :attr:`obj` to a tensor.

:attr:`obj` can be one of:

1. a tensor
2. a NumPy array
3. a DLPack capsule
4. an object that implements Python's buffer protocol
5. a scalar
6. a sequence of scalars

When :attr:`obj` is a tensor, NumPy array, or DLPack capsule the returned tensor will,
by default, not require a gradient, have the same datatype as :attr:`obj`, be on the
same device, and share memory with it. These properties can be controlled with the
:attr:`dtype`, :attr:`device`, :attr:`copy`, and :attr:`requires_grad` keyword arguments.
If the returned tensor is of a different datatype, on a different device, or a copy is
requested then it will not share its memory with :attr:`obj`. If :attr:`requires_grad`
is ``True`` then the returned tensor will require a gradient, and if :attr:`obj` is
also a tensor with an autograd history then the returned tensor will have the same history.

When :attr:`obj` is not a tensor, NumPy Array, or DLPack capsule but implements Python's
buffer protocol then the buffer is interpreted as an array of bytes grouped according to
the size of the datatype passed to the :attr:`dtype` keyword argument. (If no datatype is
passed then the default floating point datatype is used, instead.) The returned tensor
will have the specified datatype (or default floating point datatype if none is specified)
and, by default, be on the CPU device and share memory with the buffer.

When :attr:`obj` is none of the above but a scalar or sequence of scalars then the
returned tensor will, by default, infer its datatype from the scalar values, be on the
CPU device, and not share its memory.

.. seealso::
    :func:`torch.tensor` creates a tensor that always copies the data from the input object.

    :func:`torch.from_numpy` creates a tensor that always shares memory from NumPy arrays.

    :func:`torch.frombuffer` creates a tensor that always shares memory from objects that
           implement the buffer protocol.

    :func:`torch.from_dlpack` creates a tensor that always shares memory from
           DLPack capsules.

Args:
    obj (object): a tensor, NumPy array, DLPack Capsule, object that implements Python's
           buffer protocol, scalar, or sequence of scalars.

Keyword args:
    dtype (:class:`torch.dtype`, optional): the datatype of the returned tensor.
           Default: ``None``, which causes the datatype of the returned tensor to be
           inferred from :attr:`obj`.
    copy (bool, optional): controls whether the returned tensor shares memory with :attr:`obj`.
           Default: ``None``, which causes the returned tensor to share memory with :attr:`obj`
           whenever possible. If ``True`` then the returned tensor does not share its memory.
           If ``False`` then the returned tensor shares its memory with :attr:`obj` and an
           error is thrown if it cannot.
    device (:class:`torch.device`, optional): the device of the returned tensor.
           Default: ``None``, which causes the device of :attr:`obj` to be used.
    requires_grad (bool, optional): whether the returned tensor requires grad.
           Default: ``False``, which causes the returned tensor not to require a gradient.
           If ``True``, then the returned tensor will require a gradient, and if :attr:`obj`
           is also a tensor with an autograd history then the returned tensor will have
           the same history.

Example::

    >>> a = torch.tensor([1, 2, 3])
    >>> # Shares memory with tensor 'a'
    >>> b = torch.asarray(a)
    >>> a.data_ptr() == b.data_ptr()
    True
    >>> # Forces memory copy
    >>> c = torch.asarray(a, copy=True)
    >>> a.data_ptr() == c.data_ptr()
    False

    >>> a = torch.tensor([1, 2, 3], requires_grad=True).float()
    >>> b = a + 2
    >>> b
    tensor([1., 2., 3.], grad_fn=<AddBackward0>)
    >>> # Shares memory with tensor 'b', with no grad
    >>> c = torch.asarray(b)
    >>> c
    tensor([1., 2., 3.])
    >>> # Shares memory with tensor 'b', retaining autograd history
    >>> d = torch.asarray(b, requires_grad=True)
    >>> d
    tensor([1., 2., 3.], grad_fn=<AddBackward0>)

    >>> array = numpy.array([1, 2, 3])
    >>> # Shares memory with array 'array'
    >>> t1 = torch.asarray(array)
    >>> array.__array_interface__['data'][0] == t1.data_ptr()
    True
    >>> # Copies memory due to dtype mismatch
    >>> t2 = torch.asarray(array, dtype=torch.float32)
    >>> array.__array_interface__['data'][0] == t1.data_ptr()
    False
""")

add_docstr(torch.baddbmm,
           r"""
baddbmm(input, batch1, batch2, *, beta=1, alpha=1, out=None) -> Tensor

Performs a batch matrix-matrix product of matrices in :attr:`batch1`
and :attr:`batch2`.
:attr:`input` is added to the final result.

:attr:`batch1` and :attr:`batch2` must be 3-D tensors each containing the same
number of matrices.

If :attr:`batch1` is a :math:`(b \times n \times m)` tensor, :attr:`batch2` is a
:math:`(b \times m \times p)` tensor, then :attr:`input` must be
:ref:`broadcastable <broadcasting-semantics>` with a
:math:`(b \times n \times p)` tensor and :attr:`out` will be a
:math:`(b \times n \times p)` tensor. Both :attr:`alpha` and :attr:`beta` mean the
same as the scaling factors used in :meth:`torch.addbmm`.

.. math::
    \text{out}_i = \beta\ \text{input}_i + \alpha\ (\text{batch1}_i \mathbin{@} \text{batch2}_i)

If :attr:`beta` is 0, then :attr:`input` will be ignored, and `nan` and `inf` in
it will not be propagated.
""" + r"""
For inputs of type `FloatTensor` or `DoubleTensor`, arguments :attr:`beta` and
:attr:`alpha` must be real numbers, otherwise they should be integers.

{tf32_note}

Args:
    input (Tensor): the tensor to be added
    batch1 (Tensor): the first batch of matrices to be multiplied
    batch2 (Tensor): the second batch of matrices to be multiplied

Keyword args:
    beta (Number, optional): multiplier for :attr:`input` (:math:`\beta`)
    alpha (Number, optional): multiplier for :math:`\text{{batch1}} \mathbin{{@}} \text{{batch2}}` (:math:`\alpha`)
    {out}

Example::

    >>> M = torch.randn(10, 3, 5)
    >>> batch1 = torch.randn(10, 3, 4)
    >>> batch2 = torch.randn(10, 4, 5)
    >>> torch.baddbmm(M, batch1, batch2).size()
    torch.Size([10, 3, 5])
""".format(**common_args, **tf32_notes))

add_docstr(torch.bernoulli,
           r"""
bernoulli(input, *, generator=None, out=None) -> Tensor

Draws binary random numbers (0 or 1) from a Bernoulli distribution.

The :attr:`input` tensor should be a tensor containing probabilities
to be used for drawing the binary random number.
Hence, all values in :attr:`input` have to be in the range:
:math:`0 \leq \text{input}_i \leq 1`.

The :math:`\text{i}^{th}` element of the output tensor will draw a
value :math:`1` according to the :math:`\text{i}^{th}` probability value given
in :attr:`input`.

.. math::
    \text{out}_{i} \sim \mathrm{Bernoulli}(p = \text{input}_{i})
""" + r"""
The returned :attr:`out` tensor only has values 0 or 1 and is of the same
shape as :attr:`input`.

:attr:`out` can have integral ``dtype``, but :attr:`input` must have floating
point ``dtype``.

Args:
    input (Tensor): the input tensor of probability values for the Bernoulli distribution

Keyword args:
    {generator}
    {out}

Example::

    >>> a = torch.empty(3, 3).uniform_(0, 1)  # generate a uniform random matrix with range [0, 1]
    >>> a
    tensor([[ 0.1737,  0.0950,  0.3609],
            [ 0.7148,  0.0289,  0.2676],
            [ 0.9456,  0.8937,  0.7202]])
    >>> torch.bernoulli(a)
    tensor([[ 1.,  0.,  0.],
            [ 0.,  0.,  0.],
            [ 1.,  1.,  1.]])

    >>> a = torch.ones(3, 3) # probability of drawing "1" is 1
    >>> torch.bernoulli(a)
    tensor([[ 1.,  1.,  1.],
            [ 1.,  1.,  1.],
            [ 1.,  1.,  1.]])
    >>> a = torch.zeros(3, 3) # probability of drawing "1" is 0
    >>> torch.bernoulli(a)
    tensor([[ 0.,  0.,  0.],
            [ 0.,  0.,  0.],
            [ 0.,  0.,  0.]])
""".format(**common_args))

add_docstr(torch.bincount,
           r"""
bincount(input, weights=None, minlength=0) -> Tensor

Count the frequency of each value in an array of non-negative ints.

The number of bins (size 1) is one larger than the largest value in
:attr:`input` unless :attr:`input` is empty, in which case the result is a
tensor of size 0. If :attr:`minlength` is specified, the number of bins is at least
:attr:`minlength` and if :attr:`input` is empty, then the result is tensor of size
:attr:`minlength` filled with zeros. If ``n`` is the value at position ``i``,
``out[n] += weights[i]`` if :attr:`weights` is specified else
``out[n] += 1``.

Note:
    {backward_reproducibility_note}

Arguments:
    input (Tensor): 1-d int tensor
    weights (Tensor): optional, weight for each value in the input tensor.
        Should be of same size as input tensor.
    minlength (int): optional, minimum number of bins. Should be non-negative.

Returns:
    output (Tensor): a tensor of shape ``Size([max(input) + 1])`` if
    :attr:`input` is non-empty, else ``Size(0)``

Example::

    >>> input = torch.randint(0, 8, (5,), dtype=torch.int64)
    >>> weights = torch.linspace(0, 1, steps=5)
    >>> input, weights
    (tensor([4, 3, 6, 3, 4]),
     tensor([ 0.0000,  0.2500,  0.5000,  0.7500,  1.0000])

    >>> torch.bincount(input)
    tensor([0, 0, 0, 2, 2, 0, 1])

    >>> input.bincount(weights)
    tensor([0.0000, 0.0000, 0.0000, 1.0000, 1.0000, 0.0000, 0.5000])
""".format(**reproducibility_notes))

add_docstr(torch.bitwise_not,
           r"""
bitwise_not(input, *, out=None) -> Tensor

Computes the bitwise NOT of the given input tensor. The input tensor must be of
integral or Boolean types. For bool tensors, it computes the logical NOT.

Args:
    {input}

Keyword args:
    {out}

Example:

    >>> torch.bitwise_not(torch.tensor([-1, -2, 3], dtype=torch.int8))
    tensor([ 0,  1, -4], dtype=torch.int8)
""".format(**common_args))

add_docstr(torch.bmm,
           r"""
bmm(input, mat2, *, out=None) -> Tensor

Performs a batch matrix-matrix product of matrices stored in :attr:`input`
and :attr:`mat2`.

:attr:`input` and :attr:`mat2` must be 3-D tensors each containing
the same number of matrices.

If :attr:`input` is a :math:`(b \times n \times m)` tensor, :attr:`mat2` is a
:math:`(b \times m \times p)` tensor, :attr:`out` will be a
:math:`(b \times n \times p)` tensor.

.. math::
    \text{out}_i = \text{input}_i \mathbin{@} \text{mat2}_i
""" + r"""
{tf32_note}

.. note:: This function does not :ref:`broadcast <broadcasting-semantics>`.
          For broadcasting matrix products, see :func:`torch.matmul`.

Args:
    input (Tensor): the first batch of matrices to be multiplied
    mat2 (Tensor): the second batch of matrices to be multiplied

Keyword Args:
    {out}

Example::

    >>> input = torch.randn(10, 3, 4)
    >>> mat2 = torch.randn(10, 4, 5)
    >>> res = torch.bmm(input, mat2)
    >>> res.size()
    torch.Size([10, 3, 5])
""".format(**common_args, **tf32_notes))

add_docstr(torch.bitwise_and,
           r"""
bitwise_and(input, other, *, out=None) -> Tensor

Computes the bitwise AND of :attr:`input` and :attr:`other`. The input tensor must be of
integral or Boolean types. For bool tensors, it computes the logical AND.

Args:
    input: the first input tensor
    other: the second input tensor

Keyword args:
    {out}

Example:

    >>> torch.bitwise_and(torch.tensor([-1, -2, 3], dtype=torch.int8), torch.tensor([1, 0, 3], dtype=torch.int8))
    tensor([1, 0,  3], dtype=torch.int8)
    >>> torch.bitwise_and(torch.tensor([True, True, False]), torch.tensor([False, True, False]))
    tensor([ False, True, False])
""".format(**common_args))

add_docstr(torch.bitwise_or,
           r"""
bitwise_or(input, other, *, out=None) -> Tensor

Computes the bitwise OR of :attr:`input` and :attr:`other`. The input tensor must be of
integral or Boolean types. For bool tensors, it computes the logical OR.

Args:
    input: the first input tensor
    other: the second input tensor

Keyword args:
    {out}

Example:

    >>> torch.bitwise_or(torch.tensor([-1, -2, 3], dtype=torch.int8), torch.tensor([1, 0, 3], dtype=torch.int8))
    tensor([-1, -2,  3], dtype=torch.int8)
    >>> torch.bitwise_or(torch.tensor([True, True, False]), torch.tensor([False, True, False]))
    tensor([ True, True, False])
""".format(**common_args))

add_docstr(torch.bitwise_xor,
           r"""
bitwise_xor(input, other, *, out=None) -> Tensor

Computes the bitwise XOR of :attr:`input` and :attr:`other`. The input tensor must be of
integral or Boolean types. For bool tensors, it computes the logical XOR.

Args:
    input: the first input tensor
    other: the second input tensor

Keyword args:
    {out}

Example:

    >>> torch.bitwise_xor(torch.tensor([-1, -2, 3], dtype=torch.int8), torch.tensor([1, 0, 3], dtype=torch.int8))
    tensor([-2, -2,  0], dtype=torch.int8)
    >>> torch.bitwise_xor(torch.tensor([True, True, False]), torch.tensor([False, True, False]))
    tensor([ True, False, False])
""".format(**common_args))

add_docstr(torch.bitwise_left_shift,
           r"""
bitwise_left_shift(input, other, *, out=None) -> Tensor

Computes the left arithmetic shift of :attr:`input` by :attr:`other` bits.
The result will have the same dtype as :attr:`input`.

The operation applied is:

.. math::
    \text{{out}}_i = \text{{input}}_i \times 2 ^ {{\text{{other}}_i}}

Args:
    input (Tensor or Scalar): the first input tensor
    other (Tensor or Scalar): the second input tensor

Keyword args:
    {out}

Example:

    >>> torch.bitwise_left_shift(torch.tensor([-1, -2, 3], dtype=torch.int8), torch.tensor([1, 0, 3], dtype=torch.int8))
    tensor([-2, -2, 24], dtype=torch.int8)
""".format(**common_args))

add_docstr(torch.bitwise_right_shift,
           r"""
bitwise_right_shift(input, other, *, out=None) -> Tensor

Computes the right arithmetic shift of :attr:`input` by :attr:`other` bits.
The result will have the same dtype as :attr:`input`.

The operation applied is:

.. math::
    \text{{out}}_i = \text{{input}}_i / 2 ^ {{\text{{other}}_i}}

Args:
    input (Tensor or Scalar): the first input tensor
    other (Tensor or Scalar): the second input tensor

Keyword args:
    {out}

Example:

    >>> torch.bitwise_right_shift(torch.tensor([-2, -7, 31], dtype=torch.int8), torch.tensor([1, 0, 3], dtype=torch.int8))
    tensor([-1, -7,  3], dtype=torch.int8)
""".format(**common_args))

add_docstr(torch.broadcast_to,
           r"""
broadcast_to(input, shape) -> Tensor

Broadcasts :attr:`input` to the shape :attr:`\shape`.
Equivalent to calling ``input.expand(shape)``. See :meth:`~Tensor.expand` for details.

Args:
    {input}
    shape (list, tuple, or :class:`torch.Size`): the new shape.

Example::

    >>> x = torch.tensor([1, 2, 3])
    >>> torch.broadcast_to(x, (3, 3))
    tensor([[1, 2, 3],
            [1, 2, 3],
            [1, 2, 3]])
""".format(**common_args))

add_docstr(torch.stack,
           r"""
stack(tensors, dim=0, *, out=None) -> Tensor

Concatenates a sequence of tensors along a new dimension.

All tensors need to be of the same size.

Arguments:
    tensors (sequence of Tensors): sequence of tensors to concatenate
    dim (int): dimension to insert. Has to be between 0 and the number
        of dimensions of concatenated tensors (inclusive)

Keyword args:
    {out}
""".format(**common_args))

add_docstr(torch.hstack,
           r"""
hstack(tensors, *, out=None) -> Tensor

Stack tensors in sequence horizontally (column wise).

This is equivalent to concatenation along the first axis for 1-D tensors, and along the second axis for all other tensors.

Args:
    tensors (sequence of Tensors): sequence of tensors to concatenate

Keyword args:
    {out}

Example::

    >>> a = torch.tensor([1, 2, 3])
    >>> b = torch.tensor([4, 5, 6])
    >>> torch.hstack((a,b))
    tensor([1, 2, 3, 4, 5, 6])
    >>> a = torch.tensor([[1],[2],[3]])
    >>> b = torch.tensor([[4],[5],[6]])
    >>> torch.hstack((a,b))
    tensor([[1, 4],
            [2, 5],
            [3, 6]])

""".format(**common_args))

add_docstr(torch.vstack,
           r"""
vstack(tensors, *, out=None) -> Tensor

Stack tensors in sequence vertically (row wise).

This is equivalent to concatenation along the first axis after all 1-D tensors have been reshaped by :func:`torch.atleast_2d`.

Args:
    tensors (sequence of Tensors): sequence of tensors to concatenate

Keyword args:
    {out}

Example::

    >>> a = torch.tensor([1, 2, 3])
    >>> b = torch.tensor([4, 5, 6])
    >>> torch.vstack((a,b))
    tensor([[1, 2, 3],
            [4, 5, 6]])
    >>> a = torch.tensor([[1],[2],[3]])
    >>> b = torch.tensor([[4],[5],[6]])
    >>> torch.vstack((a,b))
    tensor([[1],
            [2],
            [3],
            [4],
            [5],
            [6]])


""".format(**common_args))

add_docstr(torch.dstack,
           r"""
dstack(tensors, *, out=None) -> Tensor

Stack tensors in sequence depthwise (along third axis).

This is equivalent to concatenation along the third axis after 1-D and 2-D tensors have been reshaped by :func:`torch.atleast_3d`.

Args:
    tensors (sequence of Tensors): sequence of tensors to concatenate

Keyword args:
    {out}

Example::

    >>> a = torch.tensor([1, 2, 3])
    >>> b = torch.tensor([4, 5, 6])
    >>> torch.dstack((a,b))
    tensor([[[1, 4],
             [2, 5],
             [3, 6]]])
    >>> a = torch.tensor([[1],[2],[3]])
    >>> b = torch.tensor([[4],[5],[6]])
    >>> torch.dstack((a,b))
    tensor([[[1, 4]],
            [[2, 5]],
            [[3, 6]]])


""".format(**common_args))

add_docstr(torch.tensor_split,
           r"""
tensor_split(input, indices_or_sections, dim=0) -> List of Tensors

Splits a tensor into multiple sub-tensors, all of which are views of :attr:`input`,
along dimension :attr:`dim` according to the indices or number of sections specified
by :attr:`indices_or_sections`. This function is based on NumPy's
:func:`numpy.array_split`.

Args:
    input (Tensor): the tensor to split
    indices_or_sections (Tensor, int or list or tuple of ints):
        If :attr:`indices_or_sections` is an integer ``n`` or a zero dimensional long tensor
        with value ``n``, :attr:`input` is split into ``n`` sections along dimension :attr:`dim`.
        If :attr:`input` is divisible by ``n`` along dimension :attr:`dim`, each
        section will be of equal size, :code:`input.size(dim) / n`. If :attr:`input`
        is not divisible by ``n``, the sizes of the first :code:`int(input.size(dim) % n)`
        sections will have size :code:`int(input.size(dim) / n) + 1`, and the rest will
        have size :code:`int(input.size(dim) / n)`.

        If :attr:`indices_or_sections` is a list or tuple of ints, or a one-dimensional long
        tensor, then :attr:`input` is split along dimension :attr:`dim` at each of the indices
        in the list, tuple or tensor. For instance, :code:`indices_or_sections=[2, 3]` and :code:`dim=0`
        would result in the tensors :code:`input[:2]`, :code:`input[2:3]`, and :code:`input[3:]`.

        If indices_or_sections is a tensor, it must be a zero-dimensional or one-dimensional
        long tensor on the CPU.

    dim (int, optional): dimension along which to split the tensor. Default: ``0``

Example::

    >>> x = torch.arange(8)
    >>> torch.tensor_split(x, 3)
    (tensor([0, 1, 2]), tensor([3, 4, 5]), tensor([6, 7]))

    >>> x = torch.arange(7)
    >>> torch.tensor_split(x, 3)
    (tensor([0, 1, 2]), tensor([3, 4]), tensor([5, 6]))
    >>> torch.tensor_split(x, (1, 6))
    (tensor([0]), tensor([1, 2, 3, 4, 5]), tensor([6]))

    >>> x = torch.arange(14).reshape(2, 7)
    >>> x
    tensor([[ 0,  1,  2,  3,  4,  5,  6],
            [ 7,  8,  9, 10, 11, 12, 13]])
    >>> torch.tensor_split(x, 3, dim=1)
    (tensor([[0, 1, 2],
            [7, 8, 9]]),
     tensor([[ 3,  4],
            [10, 11]]),
     tensor([[ 5,  6],
            [12, 13]]))
    >>> torch.tensor_split(x, (1, 6), dim=1)
    (tensor([[0],
            [7]]),
     tensor([[ 1,  2,  3,  4,  5],
            [ 8,  9, 10, 11, 12]]),
     tensor([[ 6],
            [13]]))
""")

add_docstr(torch.chunk,
           r"""
chunk(input, chunks, dim=0) -> List of Tensors

Attempts to split a tensor into the specified number of chunks. Each chunk is a view of
the input tensor.


.. note::

    This function may return less then the specified number of chunks!

.. seealso::

    :func:`torch.tensor_split` a function that always returns exactly the specified number of chunks

If the tensor size along the given dimesion :attr:`dim` is divisible by :attr:`chunks`,
all returned chunks will be the same size.
If the tensor size along the given dimension :attr:`dim` is not divisible by :attr:`chunks`,
all returned chunks will be the same size, except the last one.
If such division is not possible, this function may return less
than the specified number of chunks.

Arguments:
    input (Tensor): the tensor to split
    chunks (int): number of chunks to return
    dim (int): dimension along which to split the tensor

Example::
    >>> torch.arange(11).chunk(6)
    (tensor([0, 1]),
     tensor([2, 3]),
     tensor([4, 5]),
     tensor([6, 7]),
     tensor([8, 9]),
     tensor([10]))
    >>> torch.arange(12).chunk(6)
    (tensor([0, 1]),
     tensor([2, 3]),
     tensor([4, 5]),
     tensor([6, 7]),
     tensor([8, 9]),
     tensor([10, 11]))
    >>> torch.arange(13).chunk(6)
    (tensor([0, 1, 2]),
     tensor([3, 4, 5]),
     tensor([6, 7, 8]),
     tensor([ 9, 10, 11]),
     tensor([12]))
""")

add_docstr(torch.unsafe_chunk,
           r"""
unsafe_chunk(input, chunks, dim=0) -> List of Tensors

Works like :func:`torch.chunk` but without enforcing the autograd restrictions
on inplace modification of the outputs.

.. warning::
    This function is safe to use as long as only the input, or only the outputs
    are modified inplace after calling this function. It is user's
    responsibility to ensure that is the case. If both the input and one or more
    of the outputs are modified inplace, gradients computed by autograd will be
    silently incorrect.
""")

add_docstr(torch.unsafe_split,
           r"""
unsafe_split(tensor, split_size_or_sections, dim=0) -> List of Tensors

Works like :func:`torch.split` but without enforcing the autograd restrictions
on inplace modification of the outputs.

.. warning::
    This function is safe to use as long as only the input, or only the outputs
    are modified inplace after calling this function. It is user's
    responsibility to ensure that is the case. If both the input and one or more
    of the outputs are modified inplace, gradients computed by autograd will be
    silently incorrect.
""")

add_docstr(torch.hsplit,
           r"""
hsplit(input, indices_or_sections) -> List of Tensors

Splits :attr:`input`, a tensor with one or more dimensions, into multiple tensors
horizontally according to :attr:`indices_or_sections`. Each split is a view of
:attr:`input`.

If :attr:`input` is one dimensional this is equivalent to calling
torch.tensor_split(input, indices_or_sections, dim=0) (the split dimension is
zero), and if :attr:`input` has two or more dimensions it's equivalent to calling
torch.tensor_split(input, indices_or_sections, dim=1) (the split dimension is 1),
except that if :attr:`indices_or_sections` is an integer it must evenly divide
the split dimension or a runtime error will be thrown.

This function is based on NumPy's :func:`numpy.hsplit`.

Args:
    input (Tensor): tensor to split.
    indices_or_sections (Tensor, int or list or tuple of ints): See argument in :func:`torch.tensor_split`.

Example::
    >>> t = torch.arange(16.0).reshape(4,4)
    >>> t
    tensor([[ 0.,  1.,  2.,  3.],
            [ 4.,  5.,  6.,  7.],
            [ 8.,  9., 10., 11.],
            [12., 13., 14., 15.]])
    >>> torch.hsplit(t, 2)
    (tensor([[ 0.,  1.],
             [ 4.,  5.],
             [ 8.,  9.],
             [12., 13.]]),
     tensor([[ 2.,  3.],
             [ 6.,  7.],
             [10., 11.],
             [14., 15.]]))
    >>> torch.hsplit(t, [3, 6])
    (tensor([[ 0.,  1.,  2.],
             [ 4.,  5.,  6.],
             [ 8.,  9., 10.],
             [12., 13., 14.]]),
     tensor([[ 3.],
             [ 7.],
             [11.],
             [15.]]),
     tensor([], size=(4, 0)))

""")

add_docstr(torch.vsplit,
           r"""
vsplit(input, indices_or_sections) -> List of Tensors

Splits :attr:`input`, a tensor with two or more dimensions, into multiple tensors
vertically according to :attr:`indices_or_sections`. Each split is a view of
:attr:`input`.

This is equivalent to calling torch.tensor_split(input, indices_or_sections, dim=0)
(the split dimension is 0), except that if :attr:`indices_or_sections` is an integer
it must evenly divide the split dimension or a runtime error will be thrown.

This function is based on NumPy's :func:`numpy.vsplit`.

Args:
    input (Tensor): tensor to split.
    indices_or_sections (Tensor, int or list or tuple of ints): See argument in :func:`torch.tensor_split`.

Example::
    >>> t = torch.arange(16.0).reshape(4,4)
    >>> t
    tensor([[ 0.,  1.,  2.,  3.],
            [ 4.,  5.,  6.,  7.],
            [ 8.,  9., 10., 11.],
            [12., 13., 14., 15.]])
    >>> torch.vsplit(t, 2)
    (tensor([[0., 1., 2., 3.],
             [4., 5., 6., 7.]]),
     tensor([[ 8.,  9., 10., 11.],
             [12., 13., 14., 15.]]))
    >>> torch.vsplit(t, [3, 6])
    (tensor([[ 0.,  1.,  2.,  3.],
             [ 4.,  5.,  6.,  7.],
             [ 8.,  9., 10., 11.]]),
     tensor([[12., 13., 14., 15.]]),
     tensor([], size=(0, 4)))

""")

add_docstr(torch.dsplit,
           r"""
dsplit(input, indices_or_sections) -> List of Tensors

Splits :attr:`input`, a tensor with three or more dimensions, into multiple tensors
depthwise according to :attr:`indices_or_sections`. Each split is a view of
:attr:`input`.

This is equivalent to calling torch.tensor_split(input, indices_or_sections, dim=2)
(the split dimension is 2), except that if :attr:`indices_or_sections` is an integer
it must evenly divide the split dimension or a runtime error will be thrown.

This function is based on NumPy's :func:`numpy.dsplit`.

Args:
    input (Tensor): tensor to split.
    indices_or_sections (Tensor, int or list or tuple of ints): See argument in :func:`torch.tensor_split`.

Example::
    >>> t = torch.arange(16.0).reshape(2, 2, 4)
    >>> t
    tensor([[[ 0.,  1.,  2.,  3.],
             [ 4.,  5.,  6.,  7.]],
            [[ 8.,  9., 10., 11.],
             [12., 13., 14., 15.]]])
    >>> torch.dsplit(t, 2)
    (tensor([[[ 0.,  1.],
            [ 4.,  5.]],
           [[ 8.,  9.],
            [12., 13.]]]),
     tensor([[[ 2.,  3.],
              [ 6.,  7.]],
             [[10., 11.],
              [14., 15.]]]))

    >>> torch.dsplit(t, [3, 6])
    (tensor([[[ 0.,  1.,  2.],
              [ 4.,  5.,  6.]],
             [[ 8.,  9., 10.],
              [12., 13., 14.]]]),
     tensor([[[ 3.],
              [ 7.]],
             [[11.],
              [15.]]]),
     tensor([], size=(2, 2, 0)))

""")

add_docstr(torch.can_cast,
           r"""
can_cast(from, to) -> bool

Determines if a type conversion is allowed under PyTorch casting rules
described in the type promotion :ref:`documentation <type-promotion-doc>`.

Args:
    from (dtype): The original :class:`torch.dtype`.
    to (dtype): The target :class:`torch.dtype`.

Example::

    >>> torch.can_cast(torch.double, torch.float)
    True
    >>> torch.can_cast(torch.float, torch.int)
    False
""")

add_docstr(torch.corrcoef, r"""
corrcoef(input) -> Tensor

Estimates the Pearson product-moment correlation coefficient matrix of the variables given by the :attr:`input` matrix,
where rows are the variables and columns are the observations.

.. note::

    The correlation coefficient matrix R is computed using the covariance matrix C as given by
    :math:`R_{ij} = \frac{ C_{ij} } { \sqrt{ C_{ii} * C_{jj} } }`

.. note::

    Due to floating point rounding, the resulting array may not be Hermitian and its diagonal elements may not be 1.
    The real and imaginary values are clipped to the interval [-1, 1] in an attempt to improve this situation.

Args:
    input (Tensor): A 2D matrix containing multiple variables and observations, or a
        Scalar or 1D vector representing a single variable.

Returns:
    (Tensor) The correlation coefficient matrix of the variables.

.. seealso::

        :func:`torch.cov` covariance matrix.

Example::

    >>> x = torch.tensor([[0, 1, 2], [2, 1, 0]])
    >>> torch.corrcoef(x)
    tensor([[ 1., -1.],
            [-1.,  1.]])
    >>> x = torch.randn(2, 4)
    >>> x
    tensor([[-0.2678, -0.0908, -0.3766,  0.2780],
            [-0.5812,  0.1535,  0.2387,  0.2350]])
    >>> torch.corrcoef(x)
    tensor([[1.0000, 0.3582],
            [0.3582, 1.0000]])
    >>> torch.corrcoef(x[0])
    tensor(1.)
""")

add_docstr(torch.cov, r"""
cov(input, *, correction=1, fweights=None, aweights=None) -> Tensor

Estimates the covariance matrix of the variables given by the :attr:`input` matrix, where rows are
the variables and columns are the observations.

A covariance matrix is a square matrix giving the covariance of each pair of variables. The diagonal contains
the variance of each variable (covariance of a variable with itself). By definition, if :attr:`input` represents
a single variable (Scalar or 1D) then its variance is returned.

The unbiased sample covariance of the variables :math:`x` and :math:`y` is given by:

.. math::
    \text{cov}_w(x,y) = \frac{\sum^{N}_{i = 1}(x_{i} - \bar{x})(y_{i} - \bar{y})}{N~-~1}

where :math:`\bar{x}` and :math:`\bar{y}` are the simple means of the :math:`x` and :math:`y` respectively.

If :attr:`fweights` and/or :attr:`aweights` are provided, the unbiased weighted covariance
is calculated, which is given by:

.. math::
    \text{cov}_w(x,y) = \frac{\sum^{N}_{i = 1}w_i(x_{i} - \mu_x^*)(y_{i} - \mu_y^*)}{\sum^{N}_{i = 1}w_i~-~1}

where :math:`w` denotes :attr:`fweights` or :attr:`aweights` based on whichever is provided, or
:math:`w = fweights \times aweights` if both are provided, and
:math:`\mu_x^* = \frac{\sum^{N}_{i = 1}w_ix_{i} }{\sum^{N}_{i = 1}w_i}` is the weighted mean of the variable.

Args:
    input (Tensor): A 2D matrix containing multiple variables and observations, or a
        Scalar or 1D vector representing a single variable.

Keyword Args:
    correction (int, optional): difference between the sample size and sample degrees of freedom.
        Defaults to Bessel's correction, ``correction = 1`` which returns the unbiased estimate,
        even if both :attr:`fweights` and :attr:`aweights` are specified. ``correction = 0``
        will return the simple average. Defaults to ``1``.
    fweights (tensor, optional): A Scalar or 1D tensor of observation vector frequencies representing the number of
        times each observation should be repeated. Its numel must equal the number of columns of :attr:`input`.
        Must have integral dtype. Ignored if ``None``. `Defaults to ``None``.
    aweights (tensor, optional): A Scalar or 1D array of observation vector weights.
        These relative weights are typically large for observations considered “important” and smaller for
        observations considered less “important”. Its numel must equal the number of columns of :attr:`input`.
        Must have floating point dtype. Ignored if ``None``. `Defaults to ``None``.

Returns:
    (Tensor) The covariance matrix of the variables.

.. seealso::

        :func:`torch.corrcoef` normalized covariance matrix.

Example::
    >>> x = torch.tensor([[0, 2], [1, 1], [2, 0]]).T
    >>> x
    tensor([[0, 1, 2],
            [2, 1, 0]])
    >>> torch.cov(x)
    tensor([[ 1., -1.],
            [-1.,  1.]])
    >>> torch.cov(x, correction=0)
    tensor([[ 0.6667, -0.6667],
            [-0.6667,  0.6667]])
    >>> fw = torch.randint(1, 10, (3,))
    >>> fw
    tensor([1, 6, 9])
    >>> aw = torch.rand(3)
    >>> aw
    tensor([0.4282, 0.0255, 0.4144])
    >>> torch.cov(x, fweights=fw, aweights=aw)
    tensor([[ 0.4169, -0.4169],
            [-0.4169,  0.4169]])
""")

add_docstr(torch.cat,
           r"""
cat(tensors, dim=0, *, out=None) -> Tensor

Concatenates the given sequence of :attr:`seq` tensors in the given dimension.
All tensors must either have the same shape (except in the concatenating
dimension) or be empty.

:func:`torch.cat` can be seen as an inverse operation for :func:`torch.split`
and :func:`torch.chunk`.

:func:`torch.cat` can be best understood via examples.

Args:
    tensors (sequence of Tensors): any python sequence of tensors of the same type.
        Non-empty tensors provided must have the same shape, except in the
        cat dimension.
    dim (int, optional): the dimension over which the tensors are concatenated

Keyword args:
    {out}

Example::

    >>> x = torch.randn(2, 3)
    >>> x
    tensor([[ 0.6580, -1.0969, -0.4614],
            [-0.1034, -0.5790,  0.1497]])
    >>> torch.cat((x, x, x), 0)
    tensor([[ 0.6580, -1.0969, -0.4614],
            [-0.1034, -0.5790,  0.1497],
            [ 0.6580, -1.0969, -0.4614],
            [-0.1034, -0.5790,  0.1497],
            [ 0.6580, -1.0969, -0.4614],
            [-0.1034, -0.5790,  0.1497]])
    >>> torch.cat((x, x, x), 1)
    tensor([[ 0.6580, -1.0969, -0.4614,  0.6580, -1.0969, -0.4614,  0.6580,
             -1.0969, -0.4614],
            [-0.1034, -0.5790,  0.1497, -0.1034, -0.5790,  0.1497, -0.1034,
             -0.5790,  0.1497]])
""".format(**common_args))

add_docstr(torch.concat,
           r"""
concat(tensors, dim=0, *, out=None) -> Tensor

Alias of :func:`torch.cat`.
""")

add_docstr(torch.ceil,
           r"""
ceil(input, *, out=None) -> Tensor

Returns a new tensor with the ceil of the elements of :attr:`input`,
the smallest integer greater than or equal to each element.

.. math::
    \text{out}_{i} = \left\lceil \text{input}_{i} \right\rceil
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([-0.6341, -1.4208, -1.0900,  0.5826])
    >>> torch.ceil(a)
    tensor([-0., -1., -1.,  1.])
""".format(**common_args))

add_docstr(torch.real,
           r"""
real(input) -> Tensor

Returns a new tensor containing real values of the :attr:`self` tensor.
The returned tensor and :attr:`self` share the same underlying storage.

.. warning::
    :func:`real` is only supported for tensors with complex dtypes.

Args:
    {input}

Example::

    >>> x=torch.randn(4, dtype=torch.cfloat)
    >>> x
    tensor([(0.3100+0.3553j), (-0.5445-0.7896j), (-1.6492-0.0633j), (-0.0638-0.8119j)])
    >>> x.real
    tensor([ 0.3100, -0.5445, -1.6492, -0.0638])

""".format(**common_args))

add_docstr(torch.imag,
           r"""
imag(input) -> Tensor

Returns a new tensor containing imaginary values of the :attr:`self` tensor.
The returned tensor and :attr:`self` share the same underlying storage.

.. warning::
    :func:`imag` is only supported for tensors with complex dtypes.

Args:
    {input}

Example::

    >>> x=torch.randn(4, dtype=torch.cfloat)
    >>> x
    tensor([(0.3100+0.3553j), (-0.5445-0.7896j), (-1.6492-0.0633j), (-0.0638-0.8119j)])
    >>> x.imag
    tensor([ 0.3553, -0.7896, -0.0633, -0.8119])

""".format(**common_args))

add_docstr(torch.view_as_real,
           r"""
view_as_real(input) -> Tensor

Returns a view of :attr:`input` as a real tensor. For an input complex tensor of
:attr:`size` :math:`m1, m2, \dots, mi`, this function returns a new
real tensor of size :math:`m1, m2, \dots, mi, 2`, where the last dimension of size 2
represents the real and imaginary components of complex numbers.

.. warning::
    :func:`view_as_real` is only supported for tensors with ``complex dtypes``.

Args:
    {input}

Example::

    >>> x=torch.randn(4, dtype=torch.cfloat)
    >>> x
    tensor([(0.4737-0.3839j), (-0.2098-0.6699j), (0.3470-0.9451j), (-0.5174-1.3136j)])
    >>> torch.view_as_real(x)
    tensor([[ 0.4737, -0.3839],
            [-0.2098, -0.6699],
            [ 0.3470, -0.9451],
            [-0.5174, -1.3136]])
""".format(**common_args))

add_docstr(torch.view_as_complex,
           r"""
view_as_complex(input) -> Tensor

Returns a view of :attr:`input` as a complex tensor. For an input complex
tensor of :attr:`size` :math:`m1, m2, \dots, mi, 2`, this function returns a
new complex tensor of :attr:`size` :math:`m1, m2, \dots, mi` where the last
dimension of the input tensor is expected to represent the real and imaginary
components of complex numbers.

.. warning::
    :func:`view_as_complex` is only supported for tensors with
    :class:`torch.dtype` ``torch.float64`` and ``torch.float32``.  The input is
    expected to have the last dimension of :attr:`size` 2. In addition, the
    tensor must have a `stride` of 1 for its last dimension. The strides of all
    other dimensions must be even numbers.

Args:
    {input}

Example::

    >>> x=torch.randn(4, 2)
    >>> x
    tensor([[ 1.6116, -0.5772],
            [-1.4606, -0.9120],
            [ 0.0786, -1.7497],
            [-0.6561, -1.6623]])
    >>> torch.view_as_complex(x)
    tensor([(1.6116-0.5772j), (-1.4606-0.9120j), (0.0786-1.7497j), (-0.6561-1.6623j)])
""".format(**common_args))

add_docstr(torch.reciprocal,
           r"""
reciprocal(input, *, out=None) -> Tensor

Returns a new tensor with the reciprocal of the elements of :attr:`input`

.. math::
    \text{out}_{i} = \frac{1}{\text{input}_{i}}

.. note::
    Unlike NumPy's reciprocal, torch.reciprocal supports integral inputs. Integral
    inputs to reciprocal are automatically :ref:`promoted <type-promotion-doc>` to
    the default scalar type.
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([-0.4595, -2.1219, -1.4314,  0.7298])
    >>> torch.reciprocal(a)
    tensor([-2.1763, -0.4713, -0.6986,  1.3702])
""".format(**common_args))

add_docstr(torch.cholesky, r"""
cholesky(input, upper=False, *, out=None) -> Tensor

Computes the Cholesky decomposition of a symmetric positive-definite
matrix :math:`A` or for batches of symmetric positive-definite matrices.

If :attr:`upper` is ``True``, the returned matrix ``U`` is upper-triangular, and
the decomposition has the form:

.. math::

  A = U^TU

If :attr:`upper` is ``False``, the returned matrix ``L`` is lower-triangular, and
the decomposition has the form:

.. math::

    A = LL^T

If :attr:`upper` is ``True``, and :math:`A` is a batch of symmetric positive-definite
matrices, then the returned tensor will be composed of upper-triangular Cholesky factors
of each of the individual matrices. Similarly, when :attr:`upper` is ``False``, the returned
tensor will be composed of lower-triangular Cholesky factors of each of the individual
matrices.

.. warning::

    :func:`torch.cholesky` is deprecated in favor of :func:`torch.linalg.cholesky`
    and will be removed in a future PyTorch release.

    ``L = torch.cholesky(A)`` should be replaced with

    .. code:: python

        L = torch.linalg.cholesky(A)

    ``U = torch.cholesky(A, upper=True)`` should be replaced with

    .. code:: python

        U = torch.linalg.cholesky(A).mH

    This transform will produce equivalent results for all valid (symmetric positive definite) inputs.

Args:
    input (Tensor): the input tensor :math:`A` of size :math:`(*, n, n)` where `*` is zero or more
                batch dimensions consisting of symmetric positive-definite matrices.
    upper (bool, optional): flag that indicates whether to return a
                            upper or lower triangular matrix. Default: ``False``

Keyword args:
    out (Tensor, optional): the output matrix

Example::

    >>> a = torch.randn(3, 3)
    >>> a = a @ a.mT + 1e-3 # make symmetric positive-definite
    >>> l = torch.cholesky(a)
    >>> a
    tensor([[ 2.4112, -0.7486,  1.4551],
            [-0.7486,  1.3544,  0.1294],
            [ 1.4551,  0.1294,  1.6724]])
    >>> l
    tensor([[ 1.5528,  0.0000,  0.0000],
            [-0.4821,  1.0592,  0.0000],
            [ 0.9371,  0.5487,  0.7023]])
    >>> l @ l.mT
    tensor([[ 2.4112, -0.7486,  1.4551],
            [-0.7486,  1.3544,  0.1294],
            [ 1.4551,  0.1294,  1.6724]])
    >>> a = torch.randn(3, 2, 2) # Example for batched input
    >>> a = a @ a.mT + 1e-03 # make symmetric positive-definite
    >>> l = torch.cholesky(a)
    >>> z = l @ l.mT
    >>> torch.dist(z, a)
    tensor(2.3842e-07)
""")

add_docstr(torch.cholesky_solve, r"""
cholesky_solve(input, input2, upper=False, *, out=None) -> Tensor

Solves a linear system of equations with a positive semidefinite
matrix to be inverted given its Cholesky factor matrix :math:`u`.

If :attr:`upper` is ``False``, :math:`u` is and lower triangular and `c` is
returned such that:

.. math::
    c = (u u^T)^{{-1}} b

If :attr:`upper` is ``True`` or not provided, :math:`u` is upper triangular
and `c` is returned such that:

.. math::
    c = (u^T u)^{{-1}} b

`torch.cholesky_solve(b, u)` can take in 2D inputs `b, u` or inputs that are
batches of 2D matrices. If the inputs are batches, then returns
batched outputs `c`

Supports real-valued and complex-valued inputs.
For the complex-valued inputs the transpose operator above is the conjugate transpose.

Args:
    input (Tensor): input matrix :math:`b` of size :math:`(*, m, k)`,
                where :math:`*` is zero or more batch dimensions
    input2 (Tensor): input matrix :math:`u` of size :math:`(*, m, m)`,
                where :math:`*` is zero of more batch dimensions composed of
                upper or lower triangular Cholesky factor
    upper (bool, optional): whether to consider the Cholesky factor as a
                            lower or upper triangular matrix. Default: ``False``.

Keyword args:
    out (Tensor, optional): the output tensor for `c`

Example::

    >>> a = torch.randn(3, 3)
    >>> a = torch.mm(a, a.t()) # make symmetric positive definite
    >>> u = torch.linalg.cholesky(a)
    >>> a
    tensor([[ 0.7747, -1.9549,  1.3086],
            [-1.9549,  6.7546, -5.4114],
            [ 1.3086, -5.4114,  4.8733]])
    >>> b = torch.randn(3, 2)
    >>> b
    tensor([[-0.6355,  0.9891],
            [ 0.1974,  1.4706],
            [-0.4115, -0.6225]])
    >>> torch.cholesky_solve(b, u)
    tensor([[ -8.1625,  19.6097],
            [ -5.8398,  14.2387],
            [ -4.3771,  10.4173]])
    >>> torch.mm(a.inverse(), b)
    tensor([[ -8.1626,  19.6097],
            [ -5.8398,  14.2387],
            [ -4.3771,  10.4173]])
""")

add_docstr(torch.cholesky_inverse, r"""
cholesky_inverse(input, upper=False, *, out=None) -> Tensor

Computes the inverse of a symmetric positive-definite matrix :math:`A` using its
Cholesky factor :math:`u`: returns matrix ``inv``. The inverse is computed using
LAPACK routines ``dpotri`` and ``spotri`` (and the corresponding MAGMA routines).

If :attr:`upper` is ``False``, :math:`u` is lower triangular
such that the returned tensor is

.. math::
    inv = (uu^{{T}})^{{-1}}

If :attr:`upper` is ``True`` or not provided, :math:`u` is upper
triangular such that the returned tensor is

.. math::
    inv = (u^T u)^{{-1}}

Supports input of float, double, cfloat and cdouble dtypes.
Also supports batches of matrices, and if :math:`A` is a batch of matrices then the output has the same batch dimensions.

Args:
    input (Tensor): the input tensor :math:`A` of size :math:`(*, n, n)`,
                consisting of symmetric positive-definite matrices
                where :math:`*` is zero or more batch dimensions.
    upper (bool, optional): flag that indicates whether to return a
                upper or lower triangular matrix. Default: False

Keyword args:
    out (Tensor, optional): the output tensor for `inv`

Example::

    >>> a = torch.randn(3, 3)
    >>> a = torch.mm(a, a.t()) + 1e-05 * torch.eye(3) # make symmetric positive definite
    >>> u = torch.linalg.cholesky(a)
    >>> a
    tensor([[  0.9935,  -0.6353,   1.5806],
            [ -0.6353,   0.8769,  -1.7183],
            [  1.5806,  -1.7183,  10.6618]])
    >>> torch.cholesky_inverse(u)
    tensor([[ 1.9314,  1.2251, -0.0889],
            [ 1.2251,  2.4439,  0.2122],
            [-0.0889,  0.2122,  0.1412]])
    >>> a.inverse()
    tensor([[ 1.9314,  1.2251, -0.0889],
            [ 1.2251,  2.4439,  0.2122],
            [-0.0889,  0.2122,  0.1412]])
    >>> a = torch.randn(3, 2, 2) # Example for batched input
    >>> a = a @ a.mT + 1e-03 # make symmetric positive-definite
    >>> l = torch.linalg.cholesky(a)
    >>> z = l @ l.mT
    >>> torch.dist(z, a)
    tensor(3.5894e-07)
""")

add_docstr(torch.clone, r"""
clone(input, *, memory_format=torch.preserve_format) -> Tensor

Returns a copy of :attr:`input`.

.. note::

    This function is differentiable, so gradients will flow back from the
    result of this operation to :attr:`input`. To create a tensor without an
    autograd relationship to :attr:`input` see :meth:`~Tensor.detach`.

Args:
    {input}

Keyword args:
    {memory_format}
""".format(**common_args))

add_docstr(torch.clamp, r"""
clamp(input, min=None, max=None, *, out=None) -> Tensor

Clamps all elements in :attr:`input` into the range `[` :attr:`min`, :attr:`max` `]`.
Letting min_value and max_value be :attr:`min` and :attr:`max`, respectively, this returns:

.. math::
    y_i = \min(\max(x_i, \text{min\_value}_i), \text{max\_value}_i)

If :attr:`min` is ``None``, there is no lower bound.
Or, if :attr:`max` is ``None`` there is no upper bound.
""" + r"""

.. note::
    If :attr:`min` is greater than :attr:`max` :func:`torch.clamp(..., min, max) <torch.clamp>`
    sets all elements in :attr:`input` to the value of :attr:`max`.

Args:
    {input}
    min (Number or Tensor, optional): lower-bound of the range to be clamped to
    max (Number or Tensor, optional): upper-bound of the range to be clamped to

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([-1.7120,  0.1734, -0.0478, -0.0922])
    >>> torch.clamp(a, min=-0.5, max=0.5)
    tensor([-0.5000,  0.1734, -0.0478, -0.0922])

    >>> min = torch.linspace(-1, 1, steps=4)
    >>> torch.clamp(a, min=min)
    tensor([-1.0000,  0.1734,  0.3333,  1.0000])

""".format(**common_args))

add_docstr(torch.clip, r"""
clip(input, min=None, max=None, *, out=None) -> Tensor

Alias for :func:`torch.clamp`.
""")

add_docstr(torch.column_stack,
           r"""
column_stack(tensors, *, out=None) -> Tensor

Creates a new tensor by horizontally stacking the tensors in :attr:`tensors`.

Equivalent to ``torch.hstack(tensors)``, except each zero or one dimensional tensor ``t``
in :attr:`tensors` is first reshaped into a ``(t.numel(), 1)`` column before being stacked horizontally.

Args:
    tensors (sequence of Tensors): sequence of tensors to concatenate

Keyword args:
    {out}

Example::

    >>> a = torch.tensor([1, 2, 3])
    >>> b = torch.tensor([4, 5, 6])
    >>> torch.column_stack((a, b))
    tensor([[1, 4],
        [2, 5],
        [3, 6]])
    >>> a = torch.arange(5)
    >>> b = torch.arange(10).reshape(5, 2)
    >>> torch.column_stack((a, b, b))
    tensor([[0, 0, 1, 0, 1],
            [1, 2, 3, 2, 3],
            [2, 4, 5, 4, 5],
            [3, 6, 7, 6, 7],
            [4, 8, 9, 8, 9]])

""".format(**common_args))

add_docstr(torch.complex,
           r"""
complex(real, imag, *, out=None) -> Tensor

Constructs a complex tensor with its real part equal to :attr:`real` and its
imaginary part equal to :attr:`imag`.

Args:
    real (Tensor): The real part of the complex tensor. Must be float or double.
    imag (Tensor): The imaginary part of the complex tensor. Must be same dtype
        as :attr:`real`.

Keyword args:
    out (Tensor): If the inputs are ``torch.float32``, must be
        ``torch.complex64``. If the inputs are ``torch.float64``, must be
        ``torch.complex128``.

Example::

    >>> real = torch.tensor([1, 2], dtype=torch.float32)
    >>> imag = torch.tensor([3, 4], dtype=torch.float32)
    >>> z = torch.complex(real, imag)
    >>> z
    tensor([(1.+3.j), (2.+4.j)])
    >>> z.dtype
    torch.complex64

""")

add_docstr(torch.polar,
           r"""
polar(abs, angle, *, out=None) -> Tensor

Constructs a complex tensor whose elements are Cartesian coordinates
corresponding to the polar coordinates with absolute value :attr:`abs` and angle
:attr:`angle`.

.. math::
    \text{out} = \text{abs} \cdot \cos(\text{angle}) + \text{abs} \cdot \sin(\text{angle}) \cdot j

.. note::
    `torch.polar` is similar to
    `std::polar <https://en.cppreference.com/w/cpp/numeric/complex/polar>`_
    and does not compute the polar decomposition
    of a complex tensor like Python's `cmath.polar` and SciPy's `linalg.polar` do.
    The behavior of this function is undefined if `abs` is negative or NaN, or if `angle` is
    infinite.

""" + r"""
Args:
    abs (Tensor): The absolute value the complex tensor. Must be float or double.
    angle (Tensor): The angle of the complex tensor. Must be same dtype as
        :attr:`abs`.

Keyword args:
    out (Tensor): If the inputs are ``torch.float32``, must be
        ``torch.complex64``. If the inputs are ``torch.float64``, must be
        ``torch.complex128``.

Example::

    >>> import numpy as np
    >>> abs = torch.tensor([1, 2], dtype=torch.float64)
    >>> angle = torch.tensor([np.pi / 2, 5 * np.pi / 4], dtype=torch.float64)
    >>> z = torch.polar(abs, angle)
    >>> z
    tensor([(0.0000+1.0000j), (-1.4142-1.4142j)], dtype=torch.complex128)
""")

add_docstr(torch.conj_physical,
           r"""
conj_physical(input, *, out=None) -> Tensor

Computes the element-wise conjugate of the given :attr:`input` tensor.
If :attr:`input` has a non-complex dtype, this function just returns :attr:`input`.

.. note::
   This performs the conjugate operation regardless of the fact conjugate bit is set or not.

.. warning:: In the future, :func:`torch.conj_physical` may return a non-writeable view for an :attr:`input` of
             non-complex dtype. It's recommended that programs not modify the tensor returned by :func:`torch.conj_physical`
             when :attr:`input` is of non-complex dtype to be compatible with this change.

.. math::
    \text{out}_{i} = conj(\text{input}_{i})
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> torch.conj_physical(torch.tensor([-1 + 1j, -2 + 2j, 3 - 3j]))
    tensor([-1 - 1j, -2 - 2j, 3 + 3j])
""".format(**common_args))

add_docstr(torch.conj,
           r"""
conj(input) -> Tensor

Returns a view of :attr:`input` with a flipped conjugate bit. If :attr:`input` has a non-complex dtype,
this function just returns :attr:`input`.

.. note::
    :func:`torch.conj` performs a lazy conjugation, but the actual conjugated tensor can be materialized
    at any time using :func:`torch.resolve_conj`.

.. warning:: In the future, :func:`torch.conj` may return a non-writeable view for an :attr:`input` of
             non-complex dtype. It's recommended that programs not modify the tensor returned by :func:`torch.conj_physical`
             when :attr:`input` is of non-complex dtype to be compatible with this change.

Args:
    {input}

Example::

    >>> x = torch.tensor([-1 + 1j, -2 + 2j, 3 - 3j])
    >>> x.is_conj()
    False
    >>> y = torch.conj(x)
    >>> y.is_conj()
    True
""".format(**common_args))

add_docstr(torch.resolve_conj,
           r"""
resolve_conj(input) -> Tensor

Returns a new tensor with materialized conjugation if :attr:`input`'s conjugate bit is set to `True`,
else returns :attr:`input`. The output tensor will always have its conjugate bit set to `False`.

Args:
    {input}

Example::

    >>> x = torch.tensor([-1 + 1j, -2 + 2j, 3 - 3j])
    >>> y = x.conj()
    >>> y.is_conj()
    True
    >>> z = y.resolve_conj()
    >>> z
    tensor([-1 - 1j, -2 - 2j, 3 + 3j])
    >>> z.is_conj()
    False
""".format(**common_args))

add_docstr(torch.resolve_neg,
           r"""
resolve_neg(input) -> Tensor

Returns a new tensor with materialized negation if :attr:`input`'s negative bit is set to `True`,
else returns :attr:`input`. The output tensor will always have its negative bit set to `False`.
Args:
    {input}

Example::

    >>> x = torch.tensor([-1 + 1j, -2 + 2j, 3 - 3j])
    >>> y = x.conj()
    >>> z = y.imag
    >>> z.is_neg()
    True
    >>> out = y.resolve_neg()
    >>> out
    tensor([-1, -2, -3])
    >>> out.is_neg()
    False

""".format(**common_args))

add_docstr(torch.copysign,
           r"""
copysign(input, other, *, out=None) -> Tensor

Create a new floating-point tensor with the magnitude of :attr:`input` and the sign of :attr:`other`, elementwise.

.. math::
    \text{out}_{i} = \begin{cases}
        -|\text{input}_{i}| & \text{if} \text{other}_{i} \leq -0.0 \\
        |\text{input}_{i}| & \text{if} \text{other}_{i} \geq 0.0 \\
    \end{cases}
""" + r"""

Supports :ref:`broadcasting to a common shape <broadcasting-semantics>`,
and integer and float inputs.

Args:
    input (Tensor): magnitudes.
    other (Tensor or Number): contains value(s) whose signbit(s) are
        applied to the magnitudes in :attr:`input`.

Keyword args:
    {out}

Example::

    >>> a = torch.randn(5)
    >>> a
    tensor([-1.2557, -0.0026, -0.5387,  0.4740, -0.9244])
    >>> torch.copysign(a, 1)
    tensor([1.2557, 0.0026, 0.5387, 0.4740, 0.9244])
    >>> a = torch.randn(4, 4)
    >>> a
    tensor([[ 0.7079,  0.2778, -1.0249,  0.5719],
            [-0.0059, -0.2600, -0.4475, -1.3948],
            [ 0.3667, -0.9567, -2.5757, -0.1751],
            [ 0.2046, -0.0742,  0.2998, -0.1054]])
    >>> b = torch.randn(4)
    tensor([ 0.2373,  0.3120,  0.3190, -1.1128])
    >>> torch.copysign(a, b)
    tensor([[ 0.7079,  0.2778,  1.0249, -0.5719],
            [ 0.0059,  0.2600,  0.4475, -1.3948],
            [ 0.3667,  0.9567,  2.5757, -0.1751],
            [ 0.2046,  0.0742,  0.2998, -0.1054]])

""".format(**common_args))

add_docstr(torch.cos,
           r"""
cos(input, *, out=None) -> Tensor

Returns a new tensor with the cosine  of the elements of :attr:`input`.

.. math::
    \text{out}_{i} = \cos(\text{input}_{i})
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([ 1.4309,  1.2706, -0.8562,  0.9796])
    >>> torch.cos(a)
    tensor([ 0.1395,  0.2957,  0.6553,  0.5574])
""".format(**common_args))

add_docstr(torch.cosh,
           r"""
cosh(input, *, out=None) -> Tensor

Returns a new tensor with the hyperbolic cosine  of the elements of
:attr:`input`.

.. math::
    \text{out}_{i} = \cosh(\text{input}_{i})
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([ 0.1632,  1.1835, -0.6979, -0.7325])
    >>> torch.cosh(a)
    tensor([ 1.0133,  1.7860,  1.2536,  1.2805])

.. note::
   When :attr:`input` is on the CPU, the implementation of torch.cosh may use
   the Sleef library, which rounds very large results to infinity or negative
   infinity. See `here <https://sleef.org/purec.xhtml>`_ for details.
""".format(**common_args))

add_docstr(torch.cross,
           r"""
cross(input, other, dim=None, *, out=None) -> Tensor


Returns the cross product of vectors in dimension :attr:`dim` of :attr:`input`
and :attr:`other`.

Supports input of float, double, cfloat and cdouble dtypes. Also supports batches
of vectors, for which it computes the product along the dimension :attr:`dim`.
In this case, the output has the same batch dimensions as the inputs.

If :attr:`dim` is not given, it defaults to the first dimension found with the
size 3. Note that this might be unexpected.

.. seealso::
        :func:`torch.linalg.cross` which requires specifying dim (defaulting to -1).

.. warning:: This function may change in a future PyTorch release to match
        the default behaviour in :func:`torch.linalg.cross`. We recommend using
        :func:`torch.linalg.cross`.

Args:
    {input}
    other (Tensor): the second input tensor
    dim  (int, optional): the dimension to take the cross-product in.

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4, 3)
    >>> a
    tensor([[-0.3956,  1.1455,  1.6895],
            [-0.5849,  1.3672,  0.3599],
            [-1.1626,  0.7180, -0.0521],
            [-0.1339,  0.9902, -2.0225]])
    >>> b = torch.randn(4, 3)
    >>> b
    tensor([[-0.0257, -1.4725, -1.2251],
            [-1.1479, -0.7005, -1.9757],
            [-1.3904,  0.3726, -1.1836],
            [-0.9688, -0.7153,  0.2159]])
    >>> torch.cross(a, b, dim=1)
    tensor([[ 1.0844, -0.5281,  0.6120],
            [-2.4490, -1.5687,  1.9792],
            [-0.8304, -1.3037,  0.5650],
            [-1.2329,  1.9883,  1.0551]])
    >>> torch.cross(a, b)
    tensor([[ 1.0844, -0.5281,  0.6120],
            [-2.4490, -1.5687,  1.9792],
            [-0.8304, -1.3037,  0.5650],
            [-1.2329,  1.9883,  1.0551]])
""".format(**common_args))

add_docstr(torch.logcumsumexp,
           r"""
logcumsumexp(input, dim, *, out=None) -> Tensor
Returns the logarithm of the cumulative summation of the exponentiation of
elements of :attr:`input` in the dimension :attr:`dim`.

For summation index :math:`j` given by `dim` and other indices :math:`i`, the result is

    .. math::
        \text{{logcumsumexp}}(x)_{{ij}} = \log \sum\limits_{{j=0}}^{{i}} \exp(x_{{ij}})

Args:
    {input}
    dim  (int): the dimension to do the operation over

Keyword args:
    {out}

Example::

    >>> a = torch.randn(10)
    >>> torch.logcumsumexp(a, dim=0)
    tensor([-0.42296738, -0.04462666,  0.86278635,  0.94622083,  1.05277811,
             1.39202815,  1.83525007,  1.84492621,  2.06084887,  2.06844475]))
""".format(**reduceops_common_args))

add_docstr(torch.cummax,
           r"""
cummax(input, dim, *, out=None) -> (Tensor, LongTensor)
Returns a namedtuple ``(values, indices)`` where ``values`` is the cumulative maximum of
elements of :attr:`input` in the dimension :attr:`dim`. And ``indices`` is the index
location of each maximum value found in the dimension :attr:`dim`.

.. math::
    y_i = max(x_1, x_2, x_3, \dots, x_i)

Args:
    {input}
    dim  (int): the dimension to do the operation over

Keyword args:
    out (tuple, optional): the result tuple of two output tensors (values, indices)

Example::

    >>> a = torch.randn(10)
    >>> a
    tensor([-0.3449, -1.5447,  0.0685, -1.5104, -1.1706,  0.2259,  1.4696, -1.3284,
         1.9946, -0.8209])
    >>> torch.cummax(a, dim=0)
    torch.return_types.cummax(
        values=tensor([-0.3449, -0.3449,  0.0685,  0.0685,  0.0685,  0.2259,  1.4696,  1.4696,
         1.9946,  1.9946]),
        indices=tensor([0, 0, 2, 2, 2, 5, 6, 6, 8, 8]))
""".format(**reduceops_common_args))

add_docstr(torch.cummin,
           r"""
cummin(input, dim, *, out=None) -> (Tensor, LongTensor)
Returns a namedtuple ``(values, indices)`` where ``values`` is the cumulative minimum of
elements of :attr:`input` in the dimension :attr:`dim`. And ``indices`` is the index
location of each maximum value found in the dimension :attr:`dim`.

.. math::
    y_i = min(x_1, x_2, x_3, \dots, x_i)

Args:
    {input}
    dim  (int): the dimension to do the operation over

Keyword args:
    out (tuple, optional): the result tuple of two output tensors (values, indices)

Example::

    >>> a = torch.randn(10)
    >>> a
    tensor([-0.2284, -0.6628,  0.0975,  0.2680, -1.3298, -0.4220, -0.3885,  1.1762,
         0.9165,  1.6684])
    >>> torch.cummin(a, dim=0)
    torch.return_types.cummin(
        values=tensor([-0.2284, -0.6628, -0.6628, -0.6628, -1.3298, -1.3298, -1.3298, -1.3298,
        -1.3298, -1.3298]),
        indices=tensor([0, 1, 1, 1, 4, 4, 4, 4, 4, 4]))
""".format(**reduceops_common_args))

add_docstr(torch.cumprod,
           r"""
cumprod(input, dim, *, dtype=None, out=None) -> Tensor

Returns the cumulative product of elements of :attr:`input` in the dimension
:attr:`dim`.

For example, if :attr:`input` is a vector of size N, the result will also be
a vector of size N, with elements.

.. math::
    y_i = x_1 \times x_2\times x_3\times \dots \times x_i

Args:
    {input}
    dim  (int): the dimension to do the operation over

Keyword args:
    {dtype}
    {out}

Example::

    >>> a = torch.randn(10)
    >>> a
    tensor([ 0.6001,  0.2069, -0.1919,  0.9792,  0.6727,  1.0062,  0.4126,
            -0.2129, -0.4206,  0.1968])
    >>> torch.cumprod(a, dim=0)
    tensor([ 0.6001,  0.1241, -0.0238, -0.0233, -0.0157, -0.0158, -0.0065,
             0.0014, -0.0006, -0.0001])

    >>> a[5] = 0.0
    >>> torch.cumprod(a, dim=0)
    tensor([ 0.6001,  0.1241, -0.0238, -0.0233, -0.0157, -0.0000, -0.0000,
             0.0000, -0.0000, -0.0000])
""".format(**reduceops_common_args))

add_docstr(torch.cumsum,
           r"""
cumsum(input, dim, *, dtype=None, out=None) -> Tensor

Returns the cumulative sum of elements of :attr:`input` in the dimension
:attr:`dim`.

For example, if :attr:`input` is a vector of size N, the result will also be
a vector of size N, with elements.

.. math::
    y_i = x_1 + x_2 + x_3 + \dots + x_i

Args:
    {input}
    dim  (int): the dimension to do the operation over

Keyword args:
    {dtype}
    {out}

Example::

    >>> a = torch.randn(10)
    >>> a
    tensor([-0.8286, -0.4890,  0.5155,  0.8443,  0.1865, -0.1752, -2.0595,
             0.1850, -1.1571, -0.4243])
    >>> torch.cumsum(a, dim=0)
    tensor([-0.8286, -1.3175, -0.8020,  0.0423,  0.2289,  0.0537, -2.0058,
            -1.8209, -2.9780, -3.4022])
""".format(**reduceops_common_args))

add_docstr(torch.count_nonzero,
           r"""
count_nonzero(input, dim=None) -> Tensor

Counts the number of non-zero values in the tensor :attr:`input` along the given :attr:`dim`.
If no dim is specified then all non-zeros in the tensor are counted.

Args:
    {input}
    dim (int or tuple of ints, optional): Dim or tuple of dims along which to count non-zeros.

Example::

    >>> x = torch.zeros(3,3)
    >>> x[torch.randn(3,3) > 0.5] = 1
    >>> x
    tensor([[0., 1., 1.],
            [0., 0., 0.],
            [0., 0., 1.]])
    >>> torch.count_nonzero(x)
    tensor(3)
    >>> torch.count_nonzero(x, dim=0)
    tensor([0, 1, 2])
""".format(**reduceops_common_args))

add_docstr(torch.dequantize,
           r"""
dequantize(tensor) -> Tensor

Returns an fp32 Tensor by dequantizing a quantized Tensor

Args:
    tensor (Tensor): A quantized Tensor

.. function:: dequantize(tensors) -> sequence of Tensors
   :noindex:

Given a list of quantized Tensors, dequantize them and return a list of fp32 Tensors

Args:
     tensors (sequence of Tensors): A list of quantized Tensors
""")

add_docstr(torch.diag,
           r"""
diag(input, diagonal=0, *, out=None) -> Tensor

- If :attr:`input` is a vector (1-D tensor), then returns a 2-D square tensor
  with the elements of :attr:`input` as the diagonal.
- If :attr:`input` is a matrix (2-D tensor), then returns a 1-D tensor with
  the diagonal elements of :attr:`input`.

The argument :attr:`diagonal` controls which diagonal to consider:

- If :attr:`diagonal` = 0, it is the main diagonal.
- If :attr:`diagonal` > 0, it is above the main diagonal.
- If :attr:`diagonal` < 0, it is below the main diagonal.

Args:
    {input}
    diagonal (int, optional): the diagonal to consider

Keyword args:
    {out}

.. seealso::

        :func:`torch.diagonal` always returns the diagonal of its input.

        :func:`torch.diagflat` always constructs a tensor with diagonal elements
        specified by the input.

Examples:

Get the square matrix where the input vector is the diagonal::

    >>> a = torch.randn(3)
    >>> a
    tensor([ 0.5950,-0.0872, 2.3298])
    >>> torch.diag(a)
    tensor([[ 0.5950, 0.0000, 0.0000],
            [ 0.0000,-0.0872, 0.0000],
            [ 0.0000, 0.0000, 2.3298]])
    >>> torch.diag(a, 1)
    tensor([[ 0.0000, 0.5950, 0.0000, 0.0000],
            [ 0.0000, 0.0000,-0.0872, 0.0000],
            [ 0.0000, 0.0000, 0.0000, 2.3298],
            [ 0.0000, 0.0000, 0.0000, 0.0000]])

Get the k-th diagonal of a given matrix::

    >>> a = torch.randn(3, 3)
    >>> a
    tensor([[-0.4264, 0.0255,-0.1064],
            [ 0.8795,-0.2429, 0.1374],
            [ 0.1029,-0.6482,-1.6300]])
    >>> torch.diag(a, 0)
    tensor([-0.4264,-0.2429,-1.6300])
    >>> torch.diag(a, 1)
    tensor([ 0.0255, 0.1374])
""".format(**common_args))

add_docstr(torch.diag_embed,
           r"""
diag_embed(input, offset=0, dim1=-2, dim2=-1) -> Tensor

Creates a tensor whose diagonals of certain 2D planes (specified by
:attr:`dim1` and :attr:`dim2`) are filled by :attr:`input`.
To facilitate creating batched diagonal matrices, the 2D planes formed by
the last two dimensions of the returned tensor are chosen by default.

The argument :attr:`offset` controls which diagonal to consider:

- If :attr:`offset` = 0, it is the main diagonal.
- If :attr:`offset` > 0, it is above the main diagonal.
- If :attr:`offset` < 0, it is below the main diagonal.

The size of the new matrix will be calculated to make the specified diagonal
of the size of the last input dimension.
Note that for :attr:`offset` other than :math:`0`, the order of :attr:`dim1`
and :attr:`dim2` matters. Exchanging them is equivalent to changing the
sign of :attr:`offset`.

Applying :meth:`torch.diagonal` to the output of this function with
the same arguments yields a matrix identical to input. However,
:meth:`torch.diagonal` has different default dimensions, so those
need to be explicitly specified.

Args:
    {input} Must be at least 1-dimensional.
    offset (int, optional): which diagonal to consider. Default: 0
        (main diagonal).
    dim1 (int, optional): first dimension with respect to which to
        take diagonal. Default: -2.
    dim2 (int, optional): second dimension with respect to which to
        take diagonal. Default: -1.

Example::

    >>> a = torch.randn(2, 3)
    >>> torch.diag_embed(a)
    tensor([[[ 1.5410,  0.0000,  0.0000],
             [ 0.0000, -0.2934,  0.0000],
             [ 0.0000,  0.0000, -2.1788]],

            [[ 0.5684,  0.0000,  0.0000],
             [ 0.0000, -1.0845,  0.0000],
             [ 0.0000,  0.0000, -1.3986]]])

    >>> torch.diag_embed(a, offset=1, dim1=0, dim2=2)
    tensor([[[ 0.0000,  1.5410,  0.0000,  0.0000],
             [ 0.0000,  0.5684,  0.0000,  0.0000]],

            [[ 0.0000,  0.0000, -0.2934,  0.0000],
             [ 0.0000,  0.0000, -1.0845,  0.0000]],

            [[ 0.0000,  0.0000,  0.0000, -2.1788],
             [ 0.0000,  0.0000,  0.0000, -1.3986]],

            [[ 0.0000,  0.0000,  0.0000,  0.0000],
             [ 0.0000,  0.0000,  0.0000,  0.0000]]])
""".format(**common_args))


add_docstr(torch.diagflat,
           r"""
diagflat(input, offset=0) -> Tensor

- If :attr:`input` is a vector (1-D tensor), then returns a 2-D square tensor
  with the elements of :attr:`input` as the diagonal.
- If :attr:`input` is a tensor with more than one dimension, then returns a
  2-D tensor with diagonal elements equal to a flattened :attr:`input`.

The argument :attr:`offset` controls which diagonal to consider:

- If :attr:`offset` = 0, it is the main diagonal.
- If :attr:`offset` > 0, it is above the main diagonal.
- If :attr:`offset` < 0, it is below the main diagonal.

Args:
    {input}
    offset (int, optional): the diagonal to consider. Default: 0 (main
        diagonal).

Examples::

    >>> a = torch.randn(3)
    >>> a
    tensor([-0.2956, -0.9068,  0.1695])
    >>> torch.diagflat(a)
    tensor([[-0.2956,  0.0000,  0.0000],
            [ 0.0000, -0.9068,  0.0000],
            [ 0.0000,  0.0000,  0.1695]])
    >>> torch.diagflat(a, 1)
    tensor([[ 0.0000, -0.2956,  0.0000,  0.0000],
            [ 0.0000,  0.0000, -0.9068,  0.0000],
            [ 0.0000,  0.0000,  0.0000,  0.1695],
            [ 0.0000,  0.0000,  0.0000,  0.0000]])

    >>> a = torch.randn(2, 2)
    >>> a
    tensor([[ 0.2094, -0.3018],
            [-0.1516,  1.9342]])
    >>> torch.diagflat(a)
    tensor([[ 0.2094,  0.0000,  0.0000,  0.0000],
            [ 0.0000, -0.3018,  0.0000,  0.0000],
            [ 0.0000,  0.0000, -0.1516,  0.0000],
            [ 0.0000,  0.0000,  0.0000,  1.9342]])
""".format(**common_args))

add_docstr(torch.diagonal,
           r"""
diagonal(input, offset=0, dim1=0, dim2=1) -> Tensor

Returns a partial view of :attr:`input` with the its diagonal elements
with respect to :attr:`dim1` and :attr:`dim2` appended as a dimension
at the end of the shape.

The argument :attr:`offset` controls which diagonal to consider:

- If :attr:`offset` = 0, it is the main diagonal.
- If :attr:`offset` > 0, it is above the main diagonal.
- If :attr:`offset` < 0, it is below the main diagonal.

Applying :meth:`torch.diag_embed` to the output of this function with
the same arguments yields a diagonal matrix with the diagonal entries
of the input. However, :meth:`torch.diag_embed` has different default
dimensions, so those need to be explicitly specified.

Args:
    {input} Must be at least 2-dimensional.
    offset (int, optional): which diagonal to consider. Default: 0
        (main diagonal).
    dim1 (int, optional): first dimension with respect to which to
        take diagonal. Default: 0.
    dim2 (int, optional): second dimension with respect to which to
        take diagonal. Default: 1.

.. note::  To take a batch diagonal, pass in dim1=-2, dim2=-1.

Examples::

    >>> a = torch.randn(3, 3)
    >>> a
    tensor([[-1.0854,  1.1431, -0.1752],
            [ 0.8536, -0.0905,  0.0360],
            [ 0.6927, -0.3735, -0.4945]])


    >>> torch.diagonal(a, 0)
    tensor([-1.0854, -0.0905, -0.4945])


    >>> torch.diagonal(a, 1)
    tensor([ 1.1431,  0.0360])


    >>> x = torch.randn(2, 5, 4, 2)
    >>> torch.diagonal(x, offset=-1, dim1=1, dim2=2)
    tensor([[[-1.2631,  0.3755, -1.5977, -1.8172],
             [-1.1065,  1.0401, -0.2235, -0.7938]],

            [[-1.7325, -0.3081,  0.6166,  0.2335],
             [ 1.0500,  0.7336, -0.3836, -1.1015]]])
""".format(**common_args))

add_docstr(torch.diagonal_scatter,
           r"""
diagonal_scatter(input, src, offset=0, dim1=0, dim2=1) -> Tensor

Embeds the values of the :attr:`src` tensor into :attr:`input` along
the diagonal elements of :attr:`input`, with respect to :attr:`dim1`
and :attr:`dim2`.

This function returns a tensor with fresh storage; it does not
return a view.

The argument :attr:`offset` controls which diagonal to consider:

- If :attr:`offset` = 0, it is the main diagonal.
- If :attr:`offset` > 0, it is above the main diagonal.
- If :attr:`offset` < 0, it is below the main diagonal.

Args:
    {input} Must be at least 2-dimensional.
    src (Tensor): the tensor to embed into :attr:`input`.
    offset (int, optional): which diagonal to consider. Default: 0
        (main diagonal).
    dim1 (int, optional): first dimension with respect to which to
        take diagonal. Default: 0.
    dim2 (int, optional): second dimension with respect to which to
        take diagonal. Default: 1.

.. note::

    :attr:`src` must be of the proper size in order to be embedded
    into :attr:`input`. Specifically, it should have the same shape as
    ``torch.diagonal(input, offset, dim1, dim2)``

Examples::

    >>> a = torch.zeros(3, 3)
    >>> a
    tensor([[0., 0., 0.],
            [0., 0., 0.],
            [0., 0., 0.]])

    >>> torch.diagonal_scatter(a, torch.ones(3), 0)
    tensor([[1., 0., 0.],
            [0., 1., 0.],
            [0., 0., 1.]])

    >>> torch.diagonal_scatter(a, torch.ones(2), 1)
    tensor([[0., 1., 0.],
            [0., 0., 1.],
            [0., 0., 0.]])
""".format(**common_args))

add_docstr(torch.diff, r"""
diff(input, n=1, dim=-1, prepend=None, append=None) -> Tensor

Computes the n-th forward difference along the given dimension.

The first-order differences are given by `out[i] = input[i + 1] - input[i]`. Higher-order
differences are calculated by using :func:`torch.diff` recursively.

Args:
    input (Tensor): the tensor to compute the differences on
    n (int, optional): the number of times to recursively compute the difference
    dim (int, optional): the dimension to compute the difference along.
        Default is the last dimension.
    prepend, append (Tensor, optional): values to prepend or append to
        :attr:`input` along :attr:`dim` before computing the difference.
        Their dimensions must be equivalent to that of input, and their shapes
        must match input's shape except on :attr:`dim`.

Keyword args:
    {out}

Example::

    >>> a = torch.tensor([1, 3, 2])
    >>> torch.diff(a)
    tensor([ 2, -1])
    >>> b = torch.tensor([4, 5])
    >>> torch.diff(a, append=b)
    tensor([ 2, -1,  2,  1])
    >>> c = torch.tensor([[1, 2, 3], [3, 4, 5]])
    >>> torch.diff(c, dim=0)
    tensor([[2, 2, 2]])
    >>> torch.diff(c, dim=1)
    tensor([[1, 1],
            [1, 1]])
""".format(**common_args))

add_docstr(torch.digamma, r"""
digamma(input, *, out=None) -> Tensor

Alias for :func:`torch.special.digamma`.
""")

add_docstr(torch.dist,
           r"""
dist(input, other, p=2) -> Tensor

Returns the p-norm of (:attr:`input` - :attr:`other`)

The shapes of :attr:`input` and :attr:`other` must be
:ref:`broadcastable <broadcasting-semantics>`.

Args:
    {input}
    other (Tensor): the Right-hand-side input tensor
    p (float, optional): the norm to be computed

Example::

    >>> x = torch.randn(4)
    >>> x
    tensor([-1.5393, -0.8675,  0.5916,  1.6321])
    >>> y = torch.randn(4)
    >>> y
    tensor([ 0.0967, -1.0511,  0.6295,  0.8360])
    >>> torch.dist(x, y, 3.5)
    tensor(1.6727)
    >>> torch.dist(x, y, 3)
    tensor(1.6973)
    >>> torch.dist(x, y, 0)
    tensor(inf)
    >>> torch.dist(x, y, 1)
    tensor(2.6537)
""".format(**common_args))

add_docstr(torch.div, r"""
div(input, other, *, rounding_mode=None, out=None) -> Tensor

Divides each element of the input ``input`` by the corresponding element of
:attr:`other`.

.. math::
    \text{{out}}_i = \frac{{\text{{input}}_i}}{{\text{{other}}_i}}

.. note::
    By default, this performs a "true" division like Python 3.
    See the :attr:`rounding_mode` argument for floor division.

Supports :ref:`broadcasting to a common shape <broadcasting-semantics>`,
:ref:`type promotion <type-promotion-doc>`, and integer, float, and complex inputs.
Always promotes integer types to the default scalar type.

Args:
    input (Tensor): the dividend
    other (Tensor or Number): the divisor

Keyword args:
    rounding_mode (str, optional): Type of rounding applied to the result:

        * None - default behavior. Performs no rounding and, if both :attr:`input` and
          :attr:`other` are integer types, promotes the inputs to the default scalar type.
          Equivalent to true division in Python (the ``/`` operator) and NumPy's ``np.true_divide``.
        * ``"trunc"`` - rounds the results of the division towards zero.
          Equivalent to C-style integer division.
        * ``"floor"`` - rounds the results of the division down.
          Equivalent to floor division in Python (the ``//`` operator) and NumPy's ``np.floor_divide``.

    {out}

Examples::

    >>> x = torch.tensor([ 0.3810,  1.2774, -0.2972, -0.3719,  0.4637])
    >>> torch.div(x, 0.5)
    tensor([ 0.7620,  2.5548, -0.5944, -0.7438,  0.9274])

    >>> a = torch.tensor([[-0.3711, -1.9353, -0.4605, -0.2917],
    ...                   [ 0.1815, -1.0111,  0.9805, -1.5923],
    ...                   [ 0.1062,  1.4581,  0.7759, -1.2344],
    ...                   [-0.1830, -0.0313,  1.1908, -1.4757]])
    >>> b = torch.tensor([ 0.8032,  0.2930, -0.8113, -0.2308])
    >>> torch.div(a, b)
    tensor([[-0.4620, -6.6051,  0.5676,  1.2639],
            [ 0.2260, -3.4509, -1.2086,  6.8990],
            [ 0.1322,  4.9764, -0.9564,  5.3484],
            [-0.2278, -0.1068, -1.4678,  6.3938]])

    >>> torch.div(a, b, rounding_mode='trunc')
    tensor([[-0., -6.,  0.,  1.],
            [ 0., -3., -1.,  6.],
            [ 0.,  4., -0.,  5.],
            [-0., -0., -1.,  6.]])

    >>> torch.div(a, b, rounding_mode='floor')
    tensor([[-1., -7.,  0.,  1.],
            [ 0., -4., -2.,  6.],
            [ 0.,  4., -1.,  5.],
            [-1., -1., -2.,  6.]])

""".format(**common_args))

add_docstr(torch.divide, r"""
divide(input, other, *, rounding_mode=None, out=None) -> Tensor

Alias for :func:`torch.div`.
""")

add_docstr(torch.dot,
           r"""
dot(input, other, *, out=None) -> Tensor

Computes the dot product of two 1D tensors.

.. note::

    Unlike NumPy's dot, torch.dot intentionally only supports computing the dot product
    of two 1D tensors with the same number of elements.

Args:
    input (Tensor): first tensor in the dot product, must be 1D.
    other (Tensor): second tensor in the dot product, must be 1D.

Keyword args:
    {out}

Example::

    >>> torch.dot(torch.tensor([2, 3]), torch.tensor([2, 1]))
    tensor(7)
""".format(**common_args))

add_docstr(torch.vdot,
           r"""
vdot(input, other, *, out=None) -> Tensor

Computes the dot product of two 1D tensors. 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::

    Unlike NumPy's vdot, torch.vdot intentionally only supports computing the dot product
    of two 1D tensors with the same number of elements.

Args:
    input (Tensor): first tensor in the dot product, must be 1D. Its conjugate is used if it's complex.
    other (Tensor): second tensor in the dot product, must be 1D.

Keyword args:
    {out}

Example::

    >>> torch.vdot(torch.tensor([2, 3]), torch.tensor([2, 1]))
    tensor(7)
    >>> a = torch.tensor((1 +2j, 3 - 1j))
    >>> b = torch.tensor((2 +1j, 4 - 0j))
    >>> torch.vdot(a, b)
    tensor([16.+1.j])
    >>> torch.vdot(b, a)
    tensor([16.-1.j])
""".format(**common_args))

add_docstr(torch.eig,
           r"""
eig(input, eigenvectors=False, *, out=None) -> (Tensor, Tensor)

Computes the eigenvalues and eigenvectors of a real square matrix.

.. note::
    Since eigenvalues and eigenvectors might be complex, backward pass is supported only
    if eigenvalues and eigenvectors are all real valued.

    When :attr:`input` is on CUDA, :func:`torch.eig() <torch.eig>` causes
    host-device synchronization.

.. warning::

    :func:`torch.eig` is deprecated in favor of :func:`torch.linalg.eig`
    and will be removed in a future PyTorch release.
    :func:`torch.linalg.eig` returns complex tensors of dtype `cfloat` or `cdouble`
    rather than real tensors mimicking complex tensors.

    ``L, _ = torch.eig(A)`` should be replaced with

    .. code :: python

        L_complex = torch.linalg.eigvals(A)

    ``L, V = torch.eig(A, eigenvectors=True)`` should be replaced with

    .. code :: python

        L_complex, V_complex = torch.linalg.eig(A)

Args:
    input (Tensor): the square matrix of shape :math:`(n \times n)` for which the eigenvalues and eigenvectors
        will be computed
    eigenvectors (bool): ``True`` to compute both eigenvalues and eigenvectors;
        otherwise, only eigenvalues will be computed

Keyword args:
    out (tuple, optional): the output tensors

Returns:
    (Tensor, Tensor): A namedtuple (eigenvalues, eigenvectors) containing

        - **eigenvalues** (*Tensor*): Shape :math:`(n \times 2)`. Each row is an eigenvalue of ``input``,
          where the first element is the real part and the second element is the imaginary part.
          The eigenvalues are not necessarily ordered.
        - **eigenvectors** (*Tensor*): If ``eigenvectors=False``, it's an empty tensor.
          Otherwise, this tensor of shape :math:`(n \times n)` can be used to compute normalized (unit length)
          eigenvectors of corresponding eigenvalues as follows.
          If the corresponding `eigenvalues[j]` is a real number, column `eigenvectors[:, j]` is the eigenvector
          corresponding to `eigenvalues[j]`.
          If the corresponding `eigenvalues[j]` and `eigenvalues[j + 1]` form a complex conjugate pair, then the
          true eigenvectors can be computed as
          :math:`\text{true eigenvector}[j] = eigenvectors[:, j] + i \times eigenvectors[:, j + 1]`,
          :math:`\text{true eigenvector}[j + 1] = eigenvectors[:, j] - i \times eigenvectors[:, j + 1]`.

Example::

    Trivial example with a diagonal matrix. By default, only eigenvalues are computed:

    >>> a = torch.diag(torch.tensor([1, 2, 3], dtype=torch.double))
    >>> e, v = torch.eig(a)
    >>> e
    tensor([[1., 0.],
            [2., 0.],
            [3., 0.]], dtype=torch.float64)
    >>> v
    tensor([], dtype=torch.float64)

    Compute also the eigenvectors:

    >>> e, v = torch.eig(a, eigenvectors=True)
    >>> e
    tensor([[1., 0.],
            [2., 0.],
            [3., 0.]], dtype=torch.float64)
    >>> v
    tensor([[1., 0., 0.],
            [0., 1., 0.],
            [0., 0., 1.]], dtype=torch.float64)

""")

add_docstr(torch.eq, r"""
eq(input, other, *, out=None) -> Tensor

Computes element-wise equality

The second argument can be a number or a tensor whose shape is
:ref:`broadcastable <broadcasting-semantics>` with the first argument.

Args:
    input (Tensor): the tensor to compare
    other (Tensor or float): the tensor or value to compare

Keyword args:
    {out}

Returns:
    A boolean tensor that is True where :attr:`input` is equal to :attr:`other` and False elsewhere

Example::

    >>> torch.eq(torch.tensor([[1, 2], [3, 4]]), torch.tensor([[1, 1], [4, 4]]))
    tensor([[ True, False],
            [False, True]])
""".format(**common_args))

add_docstr(torch.equal,
           r"""
equal(input, other) -> bool

``True`` if two tensors have the same size and elements, ``False`` otherwise.

Example::

    >>> torch.equal(torch.tensor([1, 2]), torch.tensor([1, 2]))
    True
""")

add_docstr(torch.erf,
           r"""
erf(input, *, out=None) -> Tensor

Alias for :func:`torch.special.erf`.
""")

add_docstr(torch.erfc,
           r"""
erfc(input, *, out=None) -> Tensor

Alias for :func:`torch.special.erfc`.
""")

add_docstr(torch.erfinv,
           r"""
erfinv(input, *, out=None) -> Tensor

Alias for :func:`torch.special.erfinv`.
""")

add_docstr(torch.exp,
           r"""
exp(input, *, out=None) -> Tensor

Returns a new tensor with the exponential of the elements
of the input tensor :attr:`input`.

.. math::
    y_{i} = e^{x_{i}}
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> torch.exp(torch.tensor([0, math.log(2.)]))
    tensor([ 1.,  2.])
""".format(**common_args))

add_docstr(torch.exp2,
           r"""
exp2(input, *, out=None) -> Tensor

Alias for :func:`torch.special.exp2`.
""")

add_docstr(torch.expm1,
           r"""
expm1(input, *, out=None) -> Tensor

Alias for :func:`torch.special.expm1`.
""")

add_docstr(torch.eye,
           r"""
eye(n, m=None, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) -> Tensor

Returns a 2-D tensor with ones on the diagonal and zeros elsewhere.

Args:
    n (int): the number of rows
    m (int, optional): the number of columns with default being :attr:`n`

Keyword arguments:
    {out}
    {dtype}
    {layout}
    {device}
    {requires_grad}

Returns:
    Tensor: A 2-D tensor with ones on the diagonal and zeros elsewhere

Example::

    >>> torch.eye(3)
    tensor([[ 1.,  0.,  0.],
            [ 0.,  1.,  0.],
            [ 0.,  0.,  1.]])
""".format(**factory_common_args))

add_docstr(torch.floor,
           r"""
floor(input, *, out=None) -> Tensor

Returns a new tensor with the floor of the elements of :attr:`input`,
the largest integer less than or equal to each element.

.. math::
    \text{out}_{i} = \left\lfloor \text{input}_{i} \right\rfloor
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([-0.8166,  1.5308, -0.2530, -0.2091])
    >>> torch.floor(a)
    tensor([-1.,  1., -1., -1.])
""".format(**common_args))

add_docstr(torch.floor_divide, r"""
floor_divide(input, other, *, out=None) -> Tensor

.. warning::

    :func:`torch.floor_divide` is deprecated and will be removed in a future PyTorch
    release. Its name is a misnomer because it actually rounds the quotient
    towards zero instead of taking its floor. To keep the current behavior use
    :func:`torch.div` with ``rounding_mode='trunc'``. To actually perform floor
    division, use :func:`torch.div` with ``rounding_mode='floor'``.

Computes :attr:`input` divided by :attr:`other`, elementwise, and rounds each
quotient towards zero. Equivalently, it truncates the quotient(s):

.. math::
    \text{{out}}_i = \text{trunc} \left( \frac{{\text{{input}}_i}}{{\text{{other}}_i}} \right)

""" + r"""

Supports broadcasting to a common shape, type promotion, and integer and float inputs.

Args:
    input (Tensor or Number): the dividend
    other (Tensor or Number): the divisor

Keyword args:
    {out}

Example::

    >>> a = torch.tensor([4.0, 3.0])
    >>> b = torch.tensor([2.0, 2.0])
    >>> torch.floor_divide(a, b)
    tensor([2.0, 1.0])
    >>> torch.floor_divide(a, 1.4)
    tensor([2.0, 2.0])
""".format(**common_args))

add_docstr(torch.fmod,
           r"""
fmod(input, other, *, out=None) -> Tensor

Applies C++'s `std::fmod <https://en.cppreference.com/w/cpp/numeric/math/fmod>`_ entrywise.
The result has the same sign as the dividend :attr:`input` and its absolute value
is less than that of :attr:`other`.

This function may be defined in terms of :func:`torch.div` as

.. code:: python

    torch.fmod(a, b) == a - a.div(b, rounding_mode="trunc") * b

Supports :ref:`broadcasting to a common shape <broadcasting-semantics>`,
:ref:`type promotion <type-promotion-doc>`, and integer and float inputs.

.. note::

    When the divisor is zero, returns ``NaN`` for floating point dtypes
    on both CPU and GPU; raises ``RuntimeError`` for integer division by
    zero on CPU; Integer division by zero on GPU may return any value.

.. note::

   Complex inputs are not supported. In some cases, it is not mathematically
   possible to satisfy the definition of a modulo operation with complex numbers.

.. seealso::

    :func:`torch.remainder` which implements Python's modulus operator.
    This one is defined using division rounding down the result.

Args:
    input (Tensor): the dividend
    other (Tensor or Scalar): the divisor

Keyword args:
    {out}

Example::

    >>> torch.fmod(torch.tensor([-3., -2, -1, 1, 2, 3]), 2)
    tensor([-1., -0., -1.,  1.,  0.,  1.])
    >>> torch.fmod(torch.tensor([1, 2, 3, 4, 5]), -1.5)
    tensor([1.0000, 0.5000, 0.0000, 1.0000, 0.5000])

""".format(**common_args))

add_docstr(torch.frac,
           r"""
frac(input, *, out=None) -> Tensor

Computes the fractional portion of each element in :attr:`input`.

.. math::
    \text{out}_{i} = \text{input}_{i} - \left\lfloor |\text{input}_{i}| \right\rfloor * \operatorname{sgn}(\text{input}_{i})

Example::

    >>> torch.frac(torch.tensor([1, 2.5, -3.2]))
    tensor([ 0.0000,  0.5000, -0.2000])
""")

add_docstr(torch.frexp,
           r"""
frexp(input, *, out=None) -> (Tensor mantissa, Tensor exponent)

Decomposes :attr:`input` into mantissa and exponent tensors
such that :math:`\text{input} = \text{mantissa} \times 2^{\text{exponent}}`.

The range of mantissa is the open interval (-1, 1).

Supports float inputs.

Args:
    input (Tensor): the input tensor


Keyword args:
    out (tuple, optional): the output tensors

Example::

    >>> x = torch.arange(9.)
    >>> mantissa, exponent = torch.frexp(x)
    >>> mantissa
    tensor([0.0000, 0.5000, 0.5000, 0.7500, 0.5000, 0.6250, 0.7500, 0.8750, 0.5000])
    >>> exponent
    tensor([0, 1, 2, 2, 3, 3, 3, 3, 4], dtype=torch.int32)
    >>> torch.ldexp(mantissa, exponent)
    tensor([0., 1., 2., 3., 4., 5., 6., 7., 8.])
""")

add_docstr(torch.from_numpy,
           r"""
from_numpy(ndarray) -> Tensor

Creates a :class:`Tensor` from a :class:`numpy.ndarray`.

The returned tensor and :attr:`ndarray` share the same memory. Modifications to
the tensor will be reflected in the :attr:`ndarray` and vice versa. The returned
tensor is not resizable.

It currently accepts :attr:`ndarray` with dtypes of ``numpy.float64``,
``numpy.float32``, ``numpy.float16``, ``numpy.complex64``, ``numpy.complex128``,
``numpy.int64``, ``numpy.int32``, ``numpy.int16``, ``numpy.int8``, ``numpy.uint8``,
and ``numpy.bool``.

.. warning::
    Writing to a tensor created from a read-only NumPy array is not supported and will result in undefined behavior.

Example::

    >>> a = numpy.array([1, 2, 3])
    >>> t = torch.from_numpy(a)
    >>> t
    tensor([ 1,  2,  3])
    >>> t[0] = -1
    >>> a
    array([-1,  2,  3])
""")

add_docstr(torch.frombuffer,
           r"""
frombuffer(buffer, *, dtype, count=-1, offset=0, requires_grad=False) -> Tensor

Creates a 1-dimensional :class:`Tensor` from an object that implements
the Python buffer protocol.

Skips the first :attr:`offset` bytes in the buffer, and interprets the rest of
the raw bytes as a 1-dimensional tensor of type :attr:`dtype` with :attr:`count`
elements.

Note that either of the following must be true:

1. :attr:`count` is a positive non-zero number, and the total number of bytes
in the buffer is less than :attr:`offset` plus :attr:`count` times the size
(in bytes) of :attr:`dtype`.

2. :attr:`count` is negative, and the length (number of bytes) of the buffer
subtracted by the :attr:`offset` is a multiple of the size (in bytes) of
:attr:`dtype`.

The returned tensor and buffer share the same memory. Modifications to
the tensor will be reflected in the buffer and vice versa. The returned
tensor is not resizable.

.. note::
    This function increments the reference count for the object that
    owns the shared memory. Therefore, such memory will not be deallocated
    before the returned tensor goes out of scope.

.. warning::
    This function's behavior is undefined when passed an object implementing
    the buffer protocol whose data is not on the CPU. Doing so is likely to
    cause a segmentation fault.

.. warning::
    This function does not try to infer the :attr:`dtype` (hence, it is not
    optional). Passing a different :attr:`dtype` than its source may result
    in unexpected behavior.

Args:
    buffer (object): a Python object that exposes the buffer interface.

Keyword args:
    dtype (:class:`torch.dtype`): the desired data type of returned tensor.
    count (int, optional): the number of desired elements to be read.
        If negative, all the elements (until the end of the buffer) will be
        read. Default: -1.
    offset (int, optional): the number of bytes to skip at the start of
        the buffer. Default: 0.
    {requires_grad}

Example::

    >>> import array
    >>> a = array.array('i', [1, 2, 3])
    >>> t = torch.frombuffer(a, dtype=torch.int32)
    >>> t
    tensor([ 1,  2,  3])
    >>> t[0] = -1
    >>> a
    array([-1,  2,  3])

    >>> # Interprets the signed char bytes as 32-bit integers.
    >>> # Each 4 signed char elements will be interpreted as
    >>> # 1 signed 32-bit integer.
    >>> import array
    >>> a = array.array('b', [-1, 0, 0, 0])
    >>> torch.frombuffer(a, dtype=torch.int32)
    tensor([255], dtype=torch.int32)
""".format(**factory_common_args))

add_docstr(torch.flatten,
           r"""
flatten(input, start_dim=0, end_dim=-1) -> Tensor

Flattens :attr:`input` by reshaping it into a one-dimensional tensor. If :attr:`start_dim` or :attr:`end_dim`
are passed, only dimensions starting with :attr:`start_dim` and ending with :attr:`end_dim` are flattened.
The order of elements in :attr:`input` is unchanged.

Unlike NumPy's flatten, which always copies input's data, this function may return the original object, a view,
or copy. If no dimensions are flattened, then the original object :attr:`input` is returned. Otherwise, if input can
be viewed as the flattened shape, then that view is returned. Finally, only if the input cannot be viewed as the
flattened shape is input's data copied. See :meth:`torch.Tensor.view` for details on when a view will be returned.

.. note::
    Flattening a zero-dimensional tensor will return a one-dimensional view.

Args:
    {input}
    start_dim (int): the first dim to flatten
    end_dim (int): the last dim to flatten

Example::

    >>> t = torch.tensor([[[1, 2],
    ...                    [3, 4]],
    ...                   [[5, 6],
    ...                    [7, 8]]])
    >>> torch.flatten(t)
    tensor([1, 2, 3, 4, 5, 6, 7, 8])
    >>> torch.flatten(t, start_dim=1)
    tensor([[1, 2, 3, 4],
            [5, 6, 7, 8]])
""".format(**common_args))

add_docstr(torch.gather,
           r"""
gather(input, dim, index, *, sparse_grad=False, out=None) -> Tensor

Gathers values along an axis specified by `dim`.

For a 3-D tensor the output is specified by::

    out[i][j][k] = input[index[i][j][k]][j][k]  # if dim == 0
    out[i][j][k] = input[i][index[i][j][k]][k]  # if dim == 1
    out[i][j][k] = input[i][j][index[i][j][k]]  # if dim == 2

:attr:`input` and :attr:`index` must have the same number of dimensions.
It is also required that ``index.size(d) <= input.size(d)`` for all
dimensions ``d != dim``.  :attr:`out` will have the same shape as :attr:`index`.
Note that ``input`` and ``index`` do not broadcast against each other.

Args:
    input (Tensor): the source tensor
    dim (int): the axis along which to index
    index (LongTensor): the indices of elements to gather

Keyword arguments:
    sparse_grad (bool, optional): If ``True``, gradient w.r.t. :attr:`input` will be a sparse tensor.
    out (Tensor, optional): the destination tensor

Example::

    >>> t = torch.tensor([[1, 2], [3, 4]])
    >>> torch.gather(t, 1, torch.tensor([[0, 0], [1, 0]]))
    tensor([[ 1,  1],
            [ 4,  3]])
""")


add_docstr(torch.gcd,
           r"""
gcd(input, other, *, out=None) -> Tensor

Computes the element-wise greatest common divisor (GCD) of :attr:`input` and :attr:`other`.

Both :attr:`input` and :attr:`other` must have integer types.

.. note::
    This defines :math:`gcd(0, 0) = 0`.

Args:
    {input}
    other (Tensor): the second input tensor

Keyword arguments:
    {out}

Example::

    >>> a = torch.tensor([5, 10, 15])
    >>> b = torch.tensor([3, 4, 5])
    >>> torch.gcd(a, b)
    tensor([1, 2, 5])
    >>> c = torch.tensor([3])
    >>> torch.gcd(a, c)
    tensor([1, 1, 3])
""".format(**common_args))

add_docstr(torch.ge, r"""
ge(input, other, *, out=None) -> Tensor

Computes :math:`\text{input} \geq \text{other}` element-wise.
""" + r"""

The second argument can be a number or a tensor whose shape is
:ref:`broadcastable <broadcasting-semantics>` with the first argument.

Args:
    input (Tensor): the tensor to compare
    other (Tensor or float): the tensor or value to compare

Keyword args:
    {out}

Returns:
    A boolean tensor that is True where :attr:`input` is greater than or equal to :attr:`other` and False elsewhere

Example::

    >>> torch.ge(torch.tensor([[1, 2], [3, 4]]), torch.tensor([[1, 1], [4, 4]]))
    tensor([[True, True], [False, True]])
""".format(**common_args))

add_docstr(torch.greater_equal, r"""
greater_equal(input, other, *, out=None) -> Tensor

Alias for :func:`torch.ge`.
""")

add_docstr(torch.gradient,
           r"""
gradient(input, *, spacing=1, dim=None, edge_order=1) -> List of Tensors

Estimates the gradient of a function :math:`g : \mathbb{R}^n \rightarrow \mathbb{R}` in
one or more dimensions using the `second-order accurate central differences method
<https://www.ams.org/journals/mcom/1988-51-184/S0025-5718-1988-0935077-0/S0025-5718-1988-0935077-0.pdf>`_.

The gradient of :math:`g` is estimated using samples. By default, when :attr:`spacing` is not
specified, the samples are entirely described by :attr:`input`, and the mapping of input coordinates
to an output is the same as the tensor's mapping of indices to values. For example, for a three-dimensional
:attr:`input` the function described is :math:`g : \mathbb{R}^3 \rightarrow \mathbb{R}`, and
:math:`g(1, 2, 3)\ == input[1, 2, 3]`.

When :attr:`spacing` is specified, it modifies the relationship between :attr:`input` and input coordinates.
This is detailed in the "Keyword Arguments" section below.

The gradient is estimated by estimating each partial derivative of :math:`g` independently. This estimation is
accurate if :math:`g` is in :math:`C^3` (it has at least 3 continuous derivatives), and the estimation can be
improved by providing closer samples. Mathematically, the value at each interior point of a partial derivative
is estimated using `Taylor’s theorem with remainder <https://en.wikipedia.org/wiki/Taylor%27s_theorem>`_.
Letting :math:`x` be an interior point and  :math:`x+h_r` be point neighboring it, the partial gradient at
:math:`f(x+h_r)` is estimated using:

.. math::
    \begin{aligned}
        f(x+h_r) = f(x) + h_r f'(x) + {h_r}^2  \frac{f''(x)}{2} + {h_r}^3 \frac{f'''(x_r)}{6} \\
    \end{aligned}

where :math:`x_r` is a number in the interval :math:`[x, x+ h_r]`  and using the fact that :math:`f \in C^3`
we derive :

.. math::
    f'(x) \approx \frac{ {h_l}^2 f(x+h_r) - {h_r}^2 f(x-h_l)
          + ({h_r}^2-{h_l}^2 ) f(x) }{ {h_r} {h_l}^2 + {h_r}^2 {h_l} }

.. note::
    We estimate the gradient of functions in complex domain
    :math:`g : \mathbb{C}^n \rightarrow \mathbb{C}` in the same way.

The value of each partial derivative at the boundary points is computed differently. See edge_order below.

Args:
    input (``Tensor``): the tensor that represents the values of the function

Keyword args:
    spacing (``scalar``, ``list of scalar``, ``list of Tensor``, optional): :attr:`spacing` can be used to modify
        how the :attr:`input` tensor's indices relate to sample coordinates. If :attr:`spacing` is a scalar then
        the indices are multiplied by the scalar to produce the coordinates. For example, if :attr:`spacing=2` the
        indices (1, 2, 3) become coordinates (2, 4, 6). If :attr:`spacing` is a list of scalars then the corresponding
        indices are multiplied. For example, if :attr:`spacing=(2, -1, 3)` the indices (1, 2, 3) become coordinates (2, -2, 9).
        Finally, if :attr:`spacing` is a list of one-dimensional tensors then each tensor specifies the coordinates for
        the corresponding dimension. For example, if the indices are (1, 2, 3) and the tensors are (t0, t1, t2), then
        the coordinates are (t0[1], t1[2], t2[3])

    dim (``int``, ``list of int``, optional): the dimension or dimensions to approximate the gradient over.  By default
        the partial  gradient in every dimension is computed. Note that when :attr:`dim` is  specified the elements of
        the :attr:`spacing` argument must correspond with the specified dims."

    edge_order (``int``, optional): 1 or 2, for `first-order
        <https://www.ams.org/journals/mcom/1988-51-184/S0025-5718-1988-0935077-0/S0025-5718-1988-0935077-0.pdf>`_ or
        `second-order <https://www.ams.org/journals/mcom/1988-51-184/S0025-5718-1988-0935077-0/S0025-5718-1988-0935077-0.pdf>`_
        estimation of the boundary ("edge") values, respectively.

Examples::

    >>> # Estimates the gradient of f(x)=x^2 at points [-2, -1, 2, 4]
    >>> coordinates = (torch.tensor([-2., -1., 1., 4.]),)
    >>> values = torch.tensor([4., 1., 1., 16.], )
    >>> torch.gradient(values, spacing = coordinates)
    (tensor([-3., -2., 2., 5.]),)

    >>> # Estimates the gradient of the R^2 -> R function whose samples are
    >>> # described by the tensor t. Implicit coordinates are [0, 1] for the outermost
    >>> # dimension and [0, 1, 2, 3] for the innermost dimension, and function estimates
    >>> # partial derivative for both dimensions.
    >>> t = torch.tensor([[1, 2, 4, 8], [10, 20, 40, 80]])
    >>> torch.gradient(t)
    (tensor([[ 9., 18., 36., 72.],
             [ 9., 18., 36., 72.]]),
     tensor([[ 1.0000, 1.5000, 3.0000, 4.0000],
             [10.0000, 15.0000, 30.0000, 40.0000]]))

    >>> # A scalar value for spacing modifies the relationship between tensor indices
    >>> # and input coordinates by multiplying the indices to find the
    >>> # coordinates. For example, below the indices of the innermost
    >>> # 0, 1, 2, 3 translate to coordinates of [0, 2, 4, 6], and the indices of
    >>> # the outermost dimension 0, 1 translate to coordinates of [0, 2].
    >>> torch.gradient(t, spacing = 2.0) # dim = None (implicitly [0, 1])
    (tensor([[ 4.5000, 9.0000, 18.0000, 36.0000],
              [ 4.5000, 9.0000, 18.0000, 36.0000]]),
     tensor([[ 0.5000, 0.7500, 1.5000, 2.0000],
              [ 5.0000, 7.5000, 15.0000, 20.0000]]))
    >>> # doubling the spacing between samples halves the estimated partial gradients.

    >>>
    >>> # Estimates only the partial derivative for dimension 1
    >>> torch.gradient(t, dim = 1) # spacing = None (implicitly 1.)
    (tensor([[ 1.0000, 1.5000, 3.0000, 4.0000],
             [10.0000, 15.0000, 30.0000, 40.0000]]),)

    >>> # When spacing is a list of scalars, the relationship between the tensor
    >>> # indices and input coordinates changes based on dimension.
    >>> # For example, below, the indices of the innermost dimension 0, 1, 2, 3 translate
    >>> # to coordinates of [0, 3, 6, 9], and the indices of the outermost dimension
    >>> # 0, 1 translate to coordinates of [0, 2].
    >>> torch.gradient(t, spacing = [3., 2.])
    (tensor([[ 4.5000, 9.0000, 18.0000, 36.0000],
             [ 4.5000, 9.0000, 18.0000, 36.0000]]),
     tensor([[ 0.3333, 0.5000, 1.0000, 1.3333],
             [ 3.3333, 5.0000, 10.0000, 13.3333]]))

    >>> # The following example is a replication of the previous one with explicit
    >>> # coordinates.
    >>> coords = (torch.tensor([0, 2]), torch.tensor([0, 3, 6, 9]))
    >>> torch.gradient(t, spacing = coords)
    (tensor([[ 4.5000, 9.0000, 18.0000, 36.0000],
             [ 4.5000, 9.0000, 18.0000, 36.0000]]),
     tensor([[ 0.3333, 0.5000, 1.0000, 1.3333],
             [ 3.3333, 5.0000, 10.0000, 13.3333]]))

""")

add_docstr(torch.geqrf,
           r"""
geqrf(input, *, out=None) -> (Tensor, Tensor)

This is a low-level function for calling LAPACK's geqrf directly. This function
returns a namedtuple (a, tau) as defined in `LAPACK documentation for geqrf`_ .

Computes a QR decomposition of :attr:`input`.
Both `Q` and `R` matrices are stored in the same output tensor `a`.
The elements of `R` are stored on and above the diagonal.
Elementary reflectors (or Householder vectors) implicitly defining matrix `Q`
are stored below the diagonal.
The results of this function can be used together with :func:`torch.linalg.householder_product`
to obtain the `Q` matrix or
with :func:`torch.ormqr`, which uses an implicit representation of the `Q` matrix,
for an efficient matrix-matrix multiplication.

See `LAPACK documentation for geqrf`_ for further details.

.. note::
    See also :func:`torch.linalg.qr`, which computes Q and R matrices, and :func:`torch.linalg.lstsq`
    with the ``driver="gels"`` option for a function that can solve matrix equations using a QR decomposition.

Args:
    input (Tensor): the input matrix

Keyword args:
    out (tuple, optional): the output tuple of (Tensor, Tensor). Ignored if `None`. Default: `None`.

.. _LAPACK documentation for geqrf:
    http://www.netlib.org/lapack/explore-html/df/dc5/group__variants_g_ecomputational_ga3766ea903391b5cf9008132f7440ec7b.html

""")

add_docstr(torch.inner, r"""
inner(input, other, *, out=None) -> Tensor

Computes the dot product for 1D tensors. For higher dimensions, sums the product
of elements from :attr:`input` and :attr:`other` along their last dimension.

.. note::

    If either :attr:`input` or :attr:`other` is a scalar, the result is equivalent
    to `torch.mul(input, other)`.

    If both :attr:`input` and :attr:`other` are non-scalars, the size of their last
    dimension must match and the result is equivalent to `torch.tensordot(input,
    other, dims=([-1], [-1]))`

Args:
    input (Tensor): First input tensor
    other (Tensor): Second input tensor

Keyword args:
    out (Tensor, optional): Optional output tensor to write result into. The output
                            shape is `input.shape[:-1] + other.shape[:-1]`.

Example::

    # Dot product
    >>> torch.inner(torch.tensor([1, 2, 3]), torch.tensor([0, 2, 1]))
    tensor(7)

    # Multidimensional input tensors
    >>> a = torch.randn(2, 3)
    >>> a
    tensor([[0.8173, 1.0874, 1.1784],
            [0.3279, 0.1234, 2.7894]])
    >>> b = torch.randn(2, 4, 3)
    >>> b
    tensor([[[-0.4682, -0.7159,  0.1506],
            [ 0.4034, -0.3657,  1.0387],
            [ 0.9892, -0.6684,  0.1774],
            [ 0.9482,  1.3261,  0.3917]],

            [[ 0.4537,  0.7493,  1.1724],
            [ 0.2291,  0.5749, -0.2267],
            [-0.7920,  0.3607, -0.3701],
            [ 1.3666, -0.5850, -1.7242]]])
    >>> torch.inner(a, b)
    tensor([[[-0.9837,  1.1560,  0.2907,  2.6785],
            [ 2.5671,  0.5452, -0.6912, -1.5509]],

            [[ 0.1782,  2.9843,  0.7366,  1.5672],
            [ 3.5115, -0.4864, -1.2476, -4.4337]]])

    # Scalar input
    >>> torch.inner(a, torch.tensor(2))
    tensor([[1.6347, 2.1748, 2.3567],
            [0.6558, 0.2469, 5.5787]])
""")

add_docstr(torch.outer, r"""
outer(input, vec2, *, out=None) -> Tensor

Outer product of :attr:`input` and :attr:`vec2`.
If :attr:`input` is a vector of size :math:`n` and :attr:`vec2` is a vector of
size :math:`m`, then :attr:`out` must be a matrix of size :math:`(n \times m)`.

.. note:: This function does not :ref:`broadcast <broadcasting-semantics>`.

Args:
    input (Tensor): 1-D input vector
    vec2 (Tensor): 1-D input vector

Keyword args:
    out (Tensor, optional): optional output matrix

Example::

    >>> v1 = torch.arange(1., 5.)
    >>> v2 = torch.arange(1., 4.)
    >>> torch.outer(v1, v2)
    tensor([[  1.,   2.,   3.],
            [  2.,   4.,   6.],
            [  3.,   6.,   9.],
            [  4.,   8.,  12.]])
""")

add_docstr(torch.ger,
           r"""
ger(input, vec2, *, out=None) -> Tensor

Alias of :func:`torch.outer`.

.. warning::
    This function is deprecated and will be removed in a future PyTorch release.
    Use :func:`torch.outer` instead.
""")

add_docstr(torch.solve,
           r"""
torch.solve(input, A, *, out=None) -> (Tensor, Tensor)

This function returns the solution to the system of linear
equations represented by :math:`AX = B` and the LU factorization of
A, in order as a namedtuple `solution, LU`.

`LU` contains `L` and `U` factors for LU factorization of `A`.

`torch.solve(B, A)` can take in 2D inputs `B, A` or inputs that are
batches of 2D matrices. If the inputs are batches, then returns
batched outputs `solution, LU`.

Supports real-valued and complex-valued inputs.

.. warning::

    :func:`torch.solve` is deprecated in favor of :func:`torch.linalg.solve`
    and will be removed in a future PyTorch release.
    :func:`torch.linalg.solve` has its arguments reversed and does not return the
    LU factorization of the input. To get the LU factorization see :func:`torch.lu`,
    which may be used with :func:`torch.lu_solve` and :func:`torch.lu_unpack`.

    ``X = torch.solve(B, A).solution`` should be replaced with

    .. code:: python

        X = torch.linalg.solve(A, B)

.. note::

    Irrespective of the original strides, the returned matrices
    `solution` and `LU` will be transposed, i.e. with strides like
    `B.contiguous().mT.stride()` and
    `A.contiguous().mT.stride()` respectively.

Args:
    input (Tensor): input matrix :math:`B` of size :math:`(*, m, k)` , where :math:`*`
                is zero or more batch dimensions.
    A (Tensor): input square matrix of size :math:`(*, m, m)`, where
                :math:`*` is zero or more batch dimensions.

Keyword args:
    out ((Tensor, Tensor), optional): optional output tuple.

Example::

    >>> A = torch.tensor([[6.80, -2.11,  5.66,  5.97,  8.23],
    ...                   [-6.05, -3.30,  5.36, -4.44,  1.08],
    ...                   [-0.45,  2.58, -2.70,  0.27,  9.04],
    ...                   [8.32,  2.71,  4.35,  -7.17,  2.14],
    ...                   [-9.67, -5.14, -7.26,  6.08, -6.87]]).t()
    >>> B = torch.tensor([[4.02,  6.19, -8.22, -7.57, -3.03],
    ...                   [-1.56,  4.00, -8.67,  1.75,  2.86],
    ...                   [9.81, -4.09, -4.57, -8.61,  8.99]]).t()
    >>> X, LU = torch.solve(B, A)
    >>> torch.dist(B, torch.mm(A, X))
    tensor(1.00000e-06 *
           7.0977)

    >>> # Batched solver example
    >>> A = torch.randn(2, 3, 1, 4, 4)
    >>> B = torch.randn(2, 3, 1, 4, 6)
    >>> X, LU = torch.solve(B, A)
    >>> torch.dist(B, A.matmul(X))
    tensor(1.00000e-06 *
       3.6386)

""")

add_docstr(torch.get_default_dtype,
           r"""
get_default_dtype() -> torch.dtype

Get the current default floating point :class:`torch.dtype`.

Example::

    >>> torch.get_default_dtype()  # initial default for floating point is torch.float32
    torch.float32
    >>> torch.set_default_dtype(torch.float64)
    >>> torch.get_default_dtype()  # default is now changed to torch.float64
    torch.float64
    >>> torch.set_default_tensor_type(torch.FloatTensor)  # setting tensor type also affects this
    >>> torch.get_default_dtype()  # changed to torch.float32, the dtype for torch.FloatTensor
    torch.float32

""")

add_docstr(torch.get_num_threads,
           r"""
get_num_threads() -> int

Returns the number of threads used for parallelizing CPU operations
""")

add_docstr(torch.get_num_interop_threads,
           r"""
get_num_interop_threads() -> int

Returns the number of threads used for inter-op parallelism on CPU
(e.g. in JIT interpreter)
""")

add_docstr(torch.gt, r"""
gt(input, other, *, out=None) -> Tensor

Computes :math:`\text{input} > \text{other}` element-wise.
""" + r"""

The second argument can be a number or a tensor whose shape is
:ref:`broadcastable <broadcasting-semantics>` with the first argument.

Args:
    input (Tensor): the tensor to compare
    other (Tensor or float): the tensor or value to compare

Keyword args:
    {out}

Returns:
    A boolean tensor that is True where :attr:`input` is greater than :attr:`other` and False elsewhere

Example::

    >>> torch.gt(torch.tensor([[1, 2], [3, 4]]), torch.tensor([[1, 1], [4, 4]]))
    tensor([[False, True], [False, False]])
""".format(**common_args))

add_docstr(torch.greater, r"""
greater(input, other, *, out=None) -> Tensor

Alias for :func:`torch.gt`.
""")

add_docstr(torch.histc,
           r"""
histc(input, bins=100, min=0, max=0, *, out=None) -> Tensor

Computes the histogram of a tensor.

The elements are sorted into equal width bins between :attr:`min` and
:attr:`max`. If :attr:`min` and :attr:`max` are both zero, the minimum and
maximum values of the data are used.

Elements lower than min and higher than max are ignored.

Args:
    {input}
    bins (int): number of histogram bins
    min (Scalar): lower end of the range (inclusive)
    max (Scalar): upper end of the range (inclusive)

Keyword args:
    {out}

Returns:
    Tensor: Histogram represented as a tensor

Example::

    >>> torch.histc(torch.tensor([1., 2, 1]), bins=4, min=0, max=3)
    tensor([ 0.,  2.,  1.,  0.])
""".format(**common_args))

add_docstr(torch.histogram,
           r"""
histogram(input, bins, *, range=None, weight=None, density=False, out=None) -> (Tensor, Tensor)

Computes a histogram of the values in a tensor.

:attr:`bins` can be an integer or a 1D tensor.

If :attr:`bins` is an int, it specifies the number of equal-width bins.
By default, the lower and upper range of the bins is determined by the
minimum and maximum elements of the input tensor. The :attr:`range`
argument can be provided to specify a range for the bins.

If :attr:`bins` is a 1D tensor, it specifies the sequence of bin edges
including the rightmost edge. It should contain at least 2 elements
and its elements should be increasing.

Args:
    {input}
    bins: int or 1D Tensor. If int, defines the number of equal-width bins. If tensor,
          defines the sequence of bin edges including the rightmost edge.

Keyword args:
    range (tuple of float): Defines the range of the bins.
    weight (Tensor): If provided, weight should have the same shape as input. Each value in
                     input contributes its associated weight towards its bin's result.
    density (bool): If False, the result will contain the count (or total weight) in each bin.
                    If True, the result is the value of the probability density function over the bins,
                    normalized such that the integral over the range of the bins is 1.
    {out} (tuple, optional): The result tuple of two output tensors (hist, bin_edges).

Returns:
    hist (Tensor): 1D Tensor containing the values of the histogram.
    bin_edges(Tensor): 1D Tensor containing the edges of the histogram bins.

Example::

    >>> torch.histogram(torch.tensor([1., 2, 1]), bins=4, range=(0., 3.), weight=torch.tensor([1., 2., 4.]))
    (tensor([ 0.,  5.,  2.,  0.]), tensor([0., 0.75, 1.5, 2.25, 3.]))
    >>> torch.histogram(torch.tensor([1., 2, 1]), bins=4, range=(0., 3.), weight=torch.tensor([1., 2., 4.]), density=True)
    (tensor([ 0.,  0.9524,  0.3810,  0.]), tensor([0., 0.75, 1.5, 2.25, 3.]))
""".format(**common_args))

add_docstr(torch.hypot,
           r"""
hypot(input, other, *, out=None) -> Tensor

Given the legs of a right triangle, return its hypotenuse.

.. math::
    \text{out}_{i} = \sqrt{\text{input}_{i}^{2} + \text{other}_{i}^{2}}

The shapes of ``input`` and ``other`` must be
:ref:`broadcastable <broadcasting-semantics>`.
""" + r"""
Args:
    input (Tensor): the first input tensor
    other (Tensor): the second input tensor

Keyword args:
    {out}

Example::

    >>> a = torch.hypot(torch.tensor([4.0]), torch.tensor([3.0, 4.0, 5.0]))
    tensor([5.0000, 5.6569, 6.4031])

""".format(**common_args))

add_docstr(torch.i0,
           r"""
i0(input, *, out=None) -> Tensor

Alias for :func:`torch.special.i0`.
""")

add_docstr(torch.igamma,
           r"""
igamma(input, other, *, out=None) -> Tensor

Alias for :func:`torch.special.gammainc`.
""")

add_docstr(torch.igammac,
           r"""
igammac(input, other, *, out=None) -> Tensor

Alias for :func:`torch.special.gammaincc`.
""")

add_docstr(torch.index_select,
           r"""
index_select(input, dim, index, *, out=None) -> Tensor

Returns a new tensor which indexes the :attr:`input` tensor along dimension
:attr:`dim` using the entries in :attr:`index` which is a `LongTensor`.

The returned tensor has the same number of dimensions as the original tensor
(:attr:`input`).  The :attr:`dim`\ th dimension has the same size as the length
of :attr:`index`; other dimensions have the same size as in the original tensor.

.. note:: The returned tensor does **not** use the same storage as the original
          tensor.  If :attr:`out` has a different shape than expected, we
          silently change it to the correct shape, reallocating the underlying
          storage if necessary.

Args:
    {input}
    dim (int): the dimension in which we index
    index (IntTensor or LongTensor): the 1-D tensor containing the indices to index

Keyword args:
    {out}

Example::

    >>> x = torch.randn(3, 4)
    >>> x
    tensor([[ 0.1427,  0.0231, -0.5414, -1.0009],
            [-0.4664,  0.2647, -0.1228, -1.1068],
            [-1.1734, -0.6571,  0.7230, -0.6004]])
    >>> indices = torch.tensor([0, 2])
    >>> torch.index_select(x, 0, indices)
    tensor([[ 0.1427,  0.0231, -0.5414, -1.0009],
            [-1.1734, -0.6571,  0.7230, -0.6004]])
    >>> torch.index_select(x, 1, indices)
    tensor([[ 0.1427, -0.5414],
            [-0.4664, -0.1228],
            [-1.1734,  0.7230]])
""".format(**common_args))

add_docstr(torch.inverse, r"""
inverse(input, *, out=None) -> Tensor

Alias for :func:`torch.linalg.inv`
""")

add_docstr(torch.isin, r"""
isin(elements, test_elements, *, assume_unique=False, invert=False) -> Tensor

Tests if each element of :attr:`elements` is in :attr:`test_elements`. Returns
a boolean tensor of the same shape as :attr:`elements` that is True for elements
in :attr:`test_elements` and False otherwise.

.. note::
    One of :attr:`elements` or :attr:`test_elements` can be a scalar, but not both.

Args:
    elements (Tensor or Scalar): Input elements
    test_elements (Tensor or Scalar): Values against which to test for each input element
    assume_unique (bool, optional): If True, assumes both :attr:`elements` and
        :attr:`test_elements` contain unique elements, which can speed up the
        calculation. Default: False
    invert (bool, optional): If True, inverts the boolean return tensor, resulting in True
        values for elements *not* in :attr:`test_elements`. Default: False

Returns:
    A boolean tensor of the same shape as :attr:`elements` that is True for elements in
    :attr:`test_elements` and False otherwise

Example:
    >>> torch.isin(torch.tensor([[1, 2], [3, 4]]), torch.tensor([2, 3]))
    tensor([[False,  True],
            [ True, False]])
""")

add_docstr(torch.isinf, r"""
isinf(input) -> Tensor

Tests if each element of :attr:`input` is infinite
(positive or negative infinity) or not.

.. note::
    Complex values are infinite when their real or imaginary part is
    infinite.

Args:
    {input}

Returns:
    A boolean tensor that is True where :attr:`input` is infinite and False elsewhere

Example::

    >>> torch.isinf(torch.tensor([1, float('inf'), 2, float('-inf'), float('nan')]))
    tensor([False,  True,  False,  True,  False])
""".format(**common_args))

add_docstr(torch.isposinf,
           r"""
isposinf(input, *, out=None) -> Tensor
Tests if each element of :attr:`input` is positive infinity or not.

Args:
  {input}

Keyword args:
  {out}

Example::

    >>> a = torch.tensor([-float('inf'), float('inf'), 1.2])
    >>> torch.isposinf(a)
    tensor([False,  True, False])
""".format(**common_args))

add_docstr(torch.isneginf,
           r"""
isneginf(input, *, out=None) -> Tensor
Tests if each element of :attr:`input` is negative infinity or not.

Args:
  {input}

Keyword args:
  {out}

Example::

    >>> a = torch.tensor([-float('inf'), float('inf'), 1.2])
    >>> torch.isneginf(a)
    tensor([ True, False, False])
""".format(**common_args))

add_docstr(torch.isclose, r"""
isclose(input, other, rtol=1e-05, atol=1e-08, equal_nan=False) -> Tensor

Returns a new tensor with boolean elements representing if each element of
:attr:`input` is "close" to the corresponding element of :attr:`other`.
Closeness is defined as:

.. math::
    \lvert \text{input} - \text{other} \rvert \leq \texttt{atol} + \texttt{rtol} \times \lvert \text{other} \rvert
""" + r"""

where :attr:`input` and :attr:`other` are finite. Where :attr:`input`
and/or :attr:`other` are nonfinite they are close if and only if
they are equal, with NaNs being considered equal to each other when
:attr:`equal_nan` is True.

Args:
    input (Tensor): first tensor to compare
    other (Tensor): second tensor to compare
    atol (float, optional): absolute tolerance. Default: 1e-08
    rtol (float, optional): relative tolerance. Default: 1e-05
    equal_nan (bool, optional): if ``True``, then two ``NaN`` s will be considered equal. Default: ``False``

Examples::

    >>> torch.isclose(torch.tensor((1., 2, 3)), torch.tensor((1 + 1e-10, 3, 4)))
    tensor([ True, False, False])
    >>> torch.isclose(torch.tensor((float('inf'), 4)), torch.tensor((float('inf'), 6)), rtol=.5)
    tensor([True, True])
""")

add_docstr(torch.isfinite, r"""
isfinite(input) -> Tensor

Returns a new tensor with boolean elements representing if each element is `finite` or not.

Real values are finite when they are not NaN, negative infinity, or infinity.
Complex values are finite when both their real and imaginary parts are finite.

Args:
    {input}

Returns:
    A boolean tensor that is True where :attr:`input` is finite and False elsewhere

Example::

    >>> torch.isfinite(torch.tensor([1, float('inf'), 2, float('-inf'), float('nan')]))
    tensor([True,  False,  True,  False,  False])
""".format(**common_args))

add_docstr(torch.isnan, r"""
isnan(input) -> Tensor

Returns a new tensor with boolean elements representing if each element of :attr:`input`
is NaN or not. Complex values are considered NaN when either their real
and/or imaginary part is NaN.

Arguments:
    {input}

Returns:
    A boolean tensor that is True where :attr:`input` is NaN and False elsewhere

Example::

    >>> torch.isnan(torch.tensor([1, float('nan'), 2]))
    tensor([False, True, False])
""".format(**common_args))

add_docstr(torch.isreal, r"""
isreal(input) -> Tensor

Returns a new tensor with boolean elements representing if each element of :attr:`input` is real-valued or not.
All real-valued types are considered real. Complex values are considered real when their imaginary part is 0.

Arguments:
    {input}

Returns:
    A boolean tensor that is True where :attr:`input` is real and False elsewhere

Example::

    >>> torch.isreal(torch.tensor([1, 1+1j, 2+0j]))
    tensor([True, False, True])
""".format(**common_args))

add_docstr(torch.is_floating_point, r"""
is_floating_point(input) -> (bool)

Returns True if the data type of :attr:`input` is a floating point data type i.e.,
one of ``torch.float64``, ``torch.float32``, ``torch.float16``, and ``torch.bfloat16``.

Args:
    {input}
""".format(**common_args))

add_docstr(torch.is_complex, r"""
is_complex(input) -> (bool)

Returns True if the data type of :attr:`input` is a complex data type i.e.,
one of ``torch.complex64``, and ``torch.complex128``.

Args:
    {input}
""".format(**common_args))

add_docstr(torch.is_grad_enabled, r"""
is_grad_enabled() -> (bool)

Returns True if grad mode is currently enabled.
""".format(**common_args))

add_docstr(torch.is_inference_mode_enabled, r"""
is_inference_mode_enabled() -> (bool)

Returns True if inference mode is currently enabled.
""".format(**common_args))

add_docstr(torch.is_inference, r"""
is_inference(input) -> (bool)

Returns True if :attr:`input` is an inference tensor.

A non-view tensor is an inference tensor if and only if it was
allocated during inference mode. A view tensor is an inference
tensor if and only if the tensor it is a view of is an inference tensor.

For details on inference mode please see
`Inference Mode <https://pytorch.org/cppdocs/notes/inference_mode.html>`_.

Args:
    {input}
""".format(**common_args))

add_docstr(torch.is_conj, r"""
is_conj(input) -> (bool)

Returns True if the :attr:`input` is a conjugated tensor, i.e. its conjugate bit is set to `True`.

Args:
    {input}
""".format(**common_args))

add_docstr(torch.is_nonzero, r"""
is_nonzero(input) -> (bool)

Returns True if the :attr:`input` is a single element tensor which is not equal to zero
after type conversions.
i.e. not equal to ``torch.tensor([0.])`` or ``torch.tensor([0])`` or
``torch.tensor([False])``.
Throws a ``RuntimeError`` if ``torch.numel() != 1`` (even in case
of sparse tensors).

Args:
    {input}

Examples::

    >>> torch.is_nonzero(torch.tensor([0.]))
    False
    >>> torch.is_nonzero(torch.tensor([1.5]))
    True
    >>> torch.is_nonzero(torch.tensor([False]))
    False
    >>> torch.is_nonzero(torch.tensor([3]))
    True
    >>> torch.is_nonzero(torch.tensor([1, 3, 5]))
    Traceback (most recent call last):
    ...
    RuntimeError: bool value of Tensor with more than one value is ambiguous
    >>> torch.is_nonzero(torch.tensor([]))
    Traceback (most recent call last):
    ...
    RuntimeError: bool value of Tensor with no values is ambiguous
""".format(**common_args))

add_docstr(torch.kron,
           r"""
kron(input, other, *, out=None) -> Tensor

Computes the Kronecker product, denoted by :math:`\otimes`, of :attr:`input` and :attr:`other`.

If :attr:`input` is a :math:`(a_0 \times a_1 \times \dots \times a_n)` tensor and :attr:`other` is a
:math:`(b_0 \times b_1 \times \dots \times b_n)` tensor, the result will be a
:math:`(a_0*b_0 \times a_1*b_1 \times \dots \times a_n*b_n)` tensor with the following entries:

.. math::
    (\text{input} \otimes \text{other})_{k_0, k_1, \dots, k_n} =
        \text{input}_{i_0, i_1, \dots, i_n} * \text{other}_{j_0, j_1, \dots, j_n},

where :math:`k_t = i_t * b_t + j_t` for :math:`0 \leq t \leq n`.
If one tensor has fewer dimensions than the other it is unsqueezed until it has the same number of dimensions.

Supports real-valued and complex-valued inputs.

.. note::
    This function generalizes the typical definition of the Kronecker product for two matrices to two tensors,
    as described above. When :attr:`input` is a :math:`(m \times n)` matrix and :attr:`other` is a
    :math:`(p \times q)` matrix, the result will be a :math:`(p*m \times q*n)` block matrix:

    .. math::
        \mathbf{A} \otimes \mathbf{B}=\begin{bmatrix}
        a_{11} \mathbf{B} & \cdots & a_{1 n} \mathbf{B} \\
        \vdots & \ddots & \vdots \\
        a_{m 1} \mathbf{B} & \cdots & a_{m n} \mathbf{B} \end{bmatrix}

    where :attr:`input` is :math:`\mathbf{A}` and :attr:`other` is :math:`\mathbf{B}`.

Arguments:
    input (Tensor)
    other (Tensor)

Keyword args:
    out (Tensor, optional): The output tensor. Ignored if ``None``. Default: ``None``

Examples::

    >>> mat1 = torch.eye(2)
    >>> mat2 = torch.ones(2, 2)
    >>> torch.kron(mat1, mat2)
    tensor([[1., 1., 0., 0.],
            [1., 1., 0., 0.],
            [0., 0., 1., 1.],
            [0., 0., 1., 1.]])

    >>> mat1 = torch.eye(2)
    >>> mat2 = torch.arange(1, 5).reshape(2, 2)
    >>> torch.kron(mat1, mat2)
    tensor([[1., 2., 0., 0.],
            [3., 4., 0., 0.],
            [0., 0., 1., 2.],
            [0., 0., 3., 4.]])
""")

add_docstr(torch.kthvalue,
           r"""
kthvalue(input, k, dim=None, keepdim=False, *, out=None) -> (Tensor, LongTensor)

Returns a namedtuple ``(values, indices)`` where ``values`` is the :attr:`k` th
smallest element of each row of the :attr:`input` tensor in the given dimension
:attr:`dim`. And ``indices`` is the index location of each element found.

If :attr:`dim` is not given, the last dimension of the `input` is chosen.

If :attr:`keepdim` is ``True``, both the :attr:`values` and :attr:`indices` tensors
are the same size as :attr:`input`, except in the dimension :attr:`dim` where
they are of size 1. Otherwise, :attr:`dim` is squeezed
(see :func:`torch.squeeze`), resulting in both the :attr:`values` and
:attr:`indices` tensors having 1 fewer dimension than the :attr:`input` tensor.

.. note::
    When :attr:`input` is a CUDA tensor and there are multiple valid
    :attr:`k` th values, this function may nondeterministically return
    :attr:`indices` for any of them.

Args:
    {input}
    k (int): k for the k-th smallest element
    dim (int, optional): the dimension to find the kth value along
    {keepdim}

Keyword args:
    out (tuple, optional): the output tuple of (Tensor, LongTensor)
                           can be optionally given to be used as output buffers

Example::

    >>> x = torch.arange(1., 6.)
    >>> x
    tensor([ 1.,  2.,  3.,  4.,  5.])
    >>> torch.kthvalue(x, 4)
    torch.return_types.kthvalue(values=tensor(4.), indices=tensor(3))

    >>> x=torch.arange(1.,7.).resize_(2,3)
    >>> x
    tensor([[ 1.,  2.,  3.],
            [ 4.,  5.,  6.]])
    >>> torch.kthvalue(x, 2, 0, True)
    torch.return_types.kthvalue(values=tensor([[4., 5., 6.]]), indices=tensor([[1, 1, 1]]))
""".format(**single_dim_common))

add_docstr(torch.lcm,
           r"""
lcm(input, other, *, out=None) -> Tensor

Computes the element-wise least common multiple (LCM) of :attr:`input` and :attr:`other`.

Both :attr:`input` and :attr:`other` must have integer types.

.. note::
    This defines :math:`lcm(0, 0) = 0` and :math:`lcm(0, a) = 0`.

Args:
    {input}
    other (Tensor): the second input tensor

Keyword arguments:
    {out}

Example::

    >>> a = torch.tensor([5, 10, 15])
    >>> b = torch.tensor([3, 4, 5])
    >>> torch.lcm(a, b)
    tensor([15, 20, 15])
    >>> c = torch.tensor([3])
    >>> torch.lcm(a, c)
    tensor([15, 30, 15])
""".format(**common_args))

add_docstr(torch.ldexp, r"""
ldexp(input, other, *, out=None) -> Tensor

Multiplies :attr:`input` by 2**:attr:`other`.

.. math::
    \text{{out}}_i = \text{{input}}_i * 2^\text{{other}}_i
""" + r"""

Typically this function is used to construct floating point numbers by multiplying
mantissas in :attr:`input` with integral powers of two created from the exponents
in :attr:`other`.

Args:
    {input}
    other (Tensor): a tensor of exponents, typically integers.

Keyword args:
    {out}

Example::

    >>> torch.ldexp(torch.tensor([1.]), torch.tensor([1]))
    tensor([2.])
    >>> torch.ldexp(torch.tensor([1.0]), torch.tensor([1, 2, 3, 4]))
    tensor([ 2.,  4.,  8., 16.])


""".format(**common_args))

add_docstr(torch.le, r"""
le(input, other, *, out=None) -> Tensor

Computes :math:`\text{input} \leq \text{other}` element-wise.
""" + r"""

The second argument can be a number or a tensor whose shape is
:ref:`broadcastable <broadcasting-semantics>` with the first argument.

Args:
    input (Tensor): the tensor to compare
    other (Tensor or Scalar): the tensor or value to compare

Keyword args:
    {out}

Returns:
    A boolean tensor that is True where :attr:`input` is less than or equal to
    :attr:`other` and False elsewhere

Example::

    >>> torch.le(torch.tensor([[1, 2], [3, 4]]), torch.tensor([[1, 1], [4, 4]]))
    tensor([[True, False], [True, True]])
""".format(**common_args))

add_docstr(torch.less_equal, r"""
less_equal(input, other, *, out=None) -> Tensor

Alias for :func:`torch.le`.
""")

add_docstr(torch.lerp,
           r"""
lerp(input, end, weight, *, out=None)

Does a linear interpolation of two tensors :attr:`start` (given by :attr:`input`) and :attr:`end` based
on a scalar or tensor :attr:`weight` and returns the resulting :attr:`out` tensor.

.. math::
    \text{out}_i = \text{start}_i + \text{weight}_i \times (\text{end}_i - \text{start}_i)
""" + r"""
The shapes of :attr:`start` and :attr:`end` must be
:ref:`broadcastable <broadcasting-semantics>`. If :attr:`weight` is a tensor, then
the shapes of :attr:`weight`, :attr:`start`, and :attr:`end` must be :ref:`broadcastable <broadcasting-semantics>`.

Args:
    input (Tensor): the tensor with the starting points
    end (Tensor): the tensor with the ending points
    weight (float or tensor): the weight for the interpolation formula

Keyword args:
    {out}

Example::

    >>> start = torch.arange(1., 5.)
    >>> end = torch.empty(4).fill_(10)
    >>> start
    tensor([ 1.,  2.,  3.,  4.])
    >>> end
    tensor([ 10.,  10.,  10.,  10.])
    >>> torch.lerp(start, end, 0.5)
    tensor([ 5.5000,  6.0000,  6.5000,  7.0000])
    >>> torch.lerp(start, end, torch.full_like(start, 0.5))
    tensor([ 5.5000,  6.0000,  6.5000,  7.0000])
""".format(**common_args))

add_docstr(torch.lgamma,
           r"""
lgamma(input, *, out=None) -> Tensor

Computes the natural logarithm of the absolute value of the gamma function on :attr:`input`.

.. math::
    \text{out}_{i} = \ln \Gamma(|\text{input}_{i}|)
""" + """
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.arange(0.5, 2, 0.5)
    >>> torch.lgamma(a)
    tensor([ 0.5724,  0.0000, -0.1208])
""".format(**common_args))

add_docstr(torch.linspace, r"""
linspace(start, end, steps, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) -> Tensor

Creates a one-dimensional tensor of size :attr:`steps` whose values are evenly
spaced from :attr:`start` to :attr:`end`, inclusive. That is, the value are:

.. math::
    (\text{start},
    \text{start} + \frac{\text{end} - \text{start}}{\text{steps} - 1},
    \ldots,
    \text{start} + (\text{steps} - 2) * \frac{\text{end} - \text{start}}{\text{steps} - 1},
    \text{end})
""" + """

From PyTorch 1.11 linspace requires the steps argument. Use steps=100 to restore the previous behavior.

Args:
    start (float): the starting value for the set of points
    end (float): the ending value for the set of points
    steps (int): size of the constructed tensor

Keyword arguments:
    {out}
    dtype (torch.dtype, optional): the data type to perform the computation in.
        Default: if None, uses the global default dtype (see torch.get_default_dtype())
        when both :attr:`start` and :attr:`end` are real,
        and corresponding complex dtype when either is complex.
    {layout}
    {device}
    {requires_grad}


Example::

    >>> torch.linspace(3, 10, steps=5)
    tensor([  3.0000,   4.7500,   6.5000,   8.2500,  10.0000])
    >>> torch.linspace(-10, 10, steps=5)
    tensor([-10.,  -5.,   0.,   5.,  10.])
    >>> torch.linspace(start=-10, end=10, steps=5)
    tensor([-10.,  -5.,   0.,   5.,  10.])
    >>> torch.linspace(start=-10, end=10, steps=1)
    tensor([-10.])
""".format(**factory_common_args))

add_docstr(torch.log,
           r"""
log(input, *, out=None) -> Tensor

Returns a new tensor with the natural logarithm of the elements
of :attr:`input`.

.. math::
    y_{i} = \log_{e} (x_{i})
""" + r"""

Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(5)
    >>> a
    tensor([-0.7168, -0.5471, -0.8933, -1.4428, -0.1190])
    >>> torch.log(a)
    tensor([ nan,  nan,  nan,  nan,  nan])
""".format(**common_args))

add_docstr(torch.log10,
           r"""
log10(input, *, out=None) -> Tensor

Returns a new tensor with the logarithm to the base 10 of the elements
of :attr:`input`.

.. math::
    y_{i} = \log_{10} (x_{i})
""" + r"""

Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.rand(5)
    >>> a
    tensor([ 0.5224,  0.9354,  0.7257,  0.1301,  0.2251])


    >>> torch.log10(a)
    tensor([-0.2820, -0.0290, -0.1392, -0.8857, -0.6476])

""".format(**common_args))

add_docstr(torch.log1p,
           r"""
log1p(input, *, out=None) -> Tensor

Returns a new tensor with the natural logarithm of (1 + :attr:`input`).

.. math::
    y_i = \log_{e} (x_i + 1)
""" + r"""
.. note:: This function is more accurate than :func:`torch.log` for small
          values of :attr:`input`

Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(5)
    >>> a
    tensor([-1.0090, -0.9923,  1.0249, -0.5372,  0.2492])
    >>> torch.log1p(a)
    tensor([    nan, -4.8653,  0.7055, -0.7705,  0.2225])
""".format(**common_args))

add_docstr(torch.log2,
           r"""
log2(input, *, out=None) -> Tensor

Returns a new tensor with the logarithm to the base 2 of the elements
of :attr:`input`.

.. math::
    y_{i} = \log_{2} (x_{i})
""" + r"""

Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.rand(5)
    >>> a
    tensor([ 0.8419,  0.8003,  0.9971,  0.5287,  0.0490])


    >>> torch.log2(a)
    tensor([-0.2483, -0.3213, -0.0042, -0.9196, -4.3504])

""".format(**common_args))

add_docstr(torch.logaddexp,
           r"""
logaddexp(input, other, *, out=None) -> Tensor

Logarithm of the sum of exponentiations of the inputs.

Calculates pointwise :math:`\log\left(e^x + e^y\right)`. 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.

This op should be disambiguated with :func:`torch.logsumexp` which performs a
reduction on a single tensor.

Args:
    {input}
    other (Tensor): the second input tensor

Keyword arguments:
    {out}

Example::

    >>> torch.logaddexp(torch.tensor([-1.0]), torch.tensor([-1.0, -2, -3]))
    tensor([-0.3069, -0.6867, -0.8731])
    >>> torch.logaddexp(torch.tensor([-100.0, -200, -300]), torch.tensor([-1.0, -2, -3]))
    tensor([-1., -2., -3.])
    >>> torch.logaddexp(torch.tensor([1.0, 2000, 30000]), torch.tensor([-1.0, -2, -3]))
    tensor([1.1269e+00, 2.0000e+03, 3.0000e+04])
""".format(**common_args))

add_docstr(torch.logaddexp2,
           r"""
logaddexp2(input, other, *, out=None) -> Tensor

Logarithm of the sum of exponentiations of the inputs in base-2.

Calculates pointwise :math:`\log_2\left(2^x + 2^y\right)`. See
:func:`torch.logaddexp` for more details.

Args:
    {input}
    other (Tensor): the second input tensor

Keyword arguments:
    {out}
""".format(**common_args))

add_docstr(torch.xlogy,
           r"""
xlogy(input, other, *, out=None) -> Tensor

Alias for :func:`torch.special.xlogy`.
""")

add_docstr(torch.logical_and,
           r"""
logical_and(input, other, *, out=None) -> Tensor

Computes the element-wise logical AND of the given input tensors. Zeros are treated as ``False`` and nonzeros are
treated as ``True``.

Args:
    {input}
    other (Tensor): the tensor to compute AND with

Keyword args:
    {out}

Example::

    >>> torch.logical_and(torch.tensor([True, False, True]), torch.tensor([True, False, False]))
    tensor([ True, False, False])
    >>> a = torch.tensor([0, 1, 10, 0], dtype=torch.int8)
    >>> b = torch.tensor([4, 0, 1, 0], dtype=torch.int8)
    >>> torch.logical_and(a, b)
    tensor([False, False,  True, False])
    >>> torch.logical_and(a.double(), b.double())
    tensor([False, False,  True, False])
    >>> torch.logical_and(a.double(), b)
    tensor([False, False,  True, False])
    >>> torch.logical_and(a, b, out=torch.empty(4, dtype=torch.bool))
    tensor([False, False,  True, False])
""".format(**common_args))

add_docstr(torch.logical_not,
           r"""
logical_not(input, *, out=None) -> Tensor

Computes the element-wise logical NOT of the given input tensor. If not specified, the output tensor will have the bool
dtype. If the input tensor is not a bool tensor, zeros are treated as ``False`` and non-zeros are treated as ``True``.

Args:
    {input}

Keyword args:
    {out}

Example::

    >>> torch.logical_not(torch.tensor([True, False]))
    tensor([False,  True])
    >>> torch.logical_not(torch.tensor([0, 1, -10], dtype=torch.int8))
    tensor([ True, False, False])
    >>> torch.logical_not(torch.tensor([0., 1.5, -10.], dtype=torch.double))
    tensor([ True, False, False])
    >>> torch.logical_not(torch.tensor([0., 1., -10.], dtype=torch.double), out=torch.empty(3, dtype=torch.int16))
    tensor([1, 0, 0], dtype=torch.int16)
""".format(**common_args))

add_docstr(torch.logical_or,
           r"""
logical_or(input, other, *, out=None) -> Tensor

Computes the element-wise logical OR of the given input tensors. Zeros are treated as ``False`` and nonzeros are
treated as ``True``.

Args:
    {input}
    other (Tensor): the tensor to compute OR with

Keyword args:
    {out}

Example::

    >>> torch.logical_or(torch.tensor([True, False, True]), torch.tensor([True, False, False]))
    tensor([ True, False,  True])
    >>> a = torch.tensor([0, 1, 10, 0], dtype=torch.int8)
    >>> b = torch.tensor([4, 0, 1, 0], dtype=torch.int8)
    >>> torch.logical_or(a, b)
    tensor([ True,  True,  True, False])
    >>> torch.logical_or(a.double(), b.double())
    tensor([ True,  True,  True, False])
    >>> torch.logical_or(a.double(), b)
    tensor([ True,  True,  True, False])
    >>> torch.logical_or(a, b, out=torch.empty(4, dtype=torch.bool))
    tensor([ True,  True,  True, False])
""".format(**common_args))

add_docstr(torch.logical_xor,
           r"""
logical_xor(input, other, *, out=None) -> Tensor

Computes the element-wise logical XOR of the given input tensors. Zeros are treated as ``False`` and nonzeros are
treated as ``True``.

Args:
    {input}
    other (Tensor): the tensor to compute XOR with

Keyword args:
    {out}

Example::

    >>> torch.logical_xor(torch.tensor([True, False, True]), torch.tensor([True, False, False]))
    tensor([False, False,  True])
    >>> a = torch.tensor([0, 1, 10, 0], dtype=torch.int8)
    >>> b = torch.tensor([4, 0, 1, 0], dtype=torch.int8)
    >>> torch.logical_xor(a, b)
    tensor([ True,  True, False, False])
    >>> torch.logical_xor(a.double(), b.double())
    tensor([ True,  True, False, False])
    >>> torch.logical_xor(a.double(), b)
    tensor([ True,  True, False, False])
    >>> torch.logical_xor(a, b, out=torch.empty(4, dtype=torch.bool))
    tensor([ True,  True, False, False])
""".format(**common_args))

add_docstr(torch.logspace, """
logspace(start, end, steps, base=10.0, *, \
         out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) -> Tensor
""" + r"""

Creates a one-dimensional tensor of size :attr:`steps` whose values are evenly
spaced from :math:`{{\text{{base}}}}^{{\text{{start}}}}` to
:math:`{{\text{{base}}}}^{{\text{{end}}}}`, inclusive, on a logarithmic scale
with base :attr:`base`. That is, the values are:

.. math::
    (\text{base}^{\text{start}},
    \text{base}^{(\text{start} + \frac{\text{end} - \text{start}}{ \text{steps} - 1})},
    \ldots,
    \text{base}^{(\text{start} + (\text{steps} - 2) * \frac{\text{end} - \text{start}}{ \text{steps} - 1})},
    \text{base}^{\text{end}})
""" + """


From PyTorch 1.11 logspace requires the steps argument. Use steps=100 to restore the previous behavior.

Args:
    start (float): the starting value for the set of points
    end (float): the ending value for the set of points
    steps (int): size of the constructed tensor
    base (float, optional): base of the logarithm function. Default: ``10.0``.

Keyword arguments:
    {out}
    dtype (torch.dtype, optional): the data type to perform the computation in.
        Default: if None, uses the global default dtype (see torch.get_default_dtype())
        when both :attr:`start` and :attr:`end` are real,
        and corresponding complex dtype when either is complex.
    {layout}
    {device}
    {requires_grad}

Example::

    >>> torch.logspace(start=-10, end=10, steps=5)
    tensor([ 1.0000e-10,  1.0000e-05,  1.0000e+00,  1.0000e+05,  1.0000e+10])
    >>> torch.logspace(start=0.1, end=1.0, steps=5)
    tensor([  1.2589,   2.1135,   3.5481,   5.9566,  10.0000])
    >>> torch.logspace(start=0.1, end=1.0, steps=1)
    tensor([1.2589])
    >>> torch.logspace(start=2, end=2, steps=1, base=2)
    tensor([4.0])
""".format(**factory_common_args))

add_docstr(torch.logsumexp,
           r"""
logsumexp(input, dim, keepdim=False, *, out=None)

Returns the log of summed exponentials of each row of the :attr:`input`
tensor in the given dimension :attr:`dim`. The computation is numerically
stabilized.

For summation index :math:`j` given by `dim` and other indices :math:`i`, the result is

    .. math::
        \text{{logsumexp}}(x)_{{i}} = \log \sum_j \exp(x_{{ij}})

{keepdim_details}

Args:
    {input}
    {dim}
    {keepdim}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(3, 3)
    >>> torch.logsumexp(a, 1)
    tensor([1.4907, 1.0593, 1.5696])
    >>> torch.dist(torch.logsumexp(a, 1), torch.log(torch.sum(torch.exp(a), 1)))
    tensor(1.6859e-07)
""".format(**multi_dim_common))

add_docstr(torch.lstsq,
           r"""
lstsq(input, A, *, out=None) -> (Tensor, Tensor)

Computes the solution to the least squares and least norm problems for a full
rank matrix :math:`A` of size :math:`(m \times n)` and a matrix :math:`B` of
size :math:`(m \times k)`.

If :math:`m \geq n`, :func:`lstsq` solves the least-squares problem:

.. math::

   \begin{array}{ll}
   \min_X & \|AX-B\|_2.
   \end{array}

If :math:`m < n`, :func:`lstsq` solves the least-norm problem:

.. math::

   \begin{array}{llll}
   \min_X & \|X\|_2 & \text{subject to} & AX = B.
   \end{array}

Returned tensor :math:`X` has shape :math:`(\max(m, n) \times k)`. The first :math:`n`
rows of :math:`X` contains the solution. If :math:`m \geq n`, the residual sum of squares
for the solution in each column is given by the sum of squares of elements in the
remaining :math:`m - n` rows of that column.

.. warning::

    :func:`torch.lstsq` is deprecated in favor of :func:`torch.linalg.lstsq`
    and will be removed in a future PyTorch release. :func:`torch.linalg.lstsq`
    has reversed arguments and does not return the QR decomposition in the returned tuple,
    (it returns other information about the problem).
    The returned `solution` in :func:`torch.lstsq` stores the residuals of the solution in the
    last `m - n` columns in the case `m > n`. In :func:`torch.linalg.lstsq`, the residuals
    are in the field 'residuals' of the returned named tuple.

    Unpacking the solution as ``X = torch.lstsq(B, A).solution[:A.size(1)]`` should be replaced with

    .. code:: python

        X = torch.linalg.lstsq(A, B).solution

.. note::
    The case when :math:`m < n` is not supported on the GPU.

Args:
    input (Tensor): the matrix :math:`B`
    A (Tensor): the :math:`m` by :math:`n` matrix :math:`A`

Keyword args:
    out (tuple, optional): the optional destination tensor

Returns:
    (Tensor, Tensor): A namedtuple (solution, QR) containing:

        - **solution** (*Tensor*): the least squares solution
        - **QR** (*Tensor*): the details of the QR factorization

.. note::

    The returned matrices will always be transposed, irrespective of the strides
    of the input matrices. That is, they will have stride `(1, m)` instead of
    `(m, 1)`.

Example::

    >>> A = torch.tensor([[1., 1, 1],
    ...                   [2, 3, 4],
    ...                   [3, 5, 2],
    ...                   [4, 2, 5],
    ...                   [5, 4, 3]])
    >>> B = torch.tensor([[-10., -3],
    ...                   [ 12, 14],
    ...                   [ 14, 12],
    ...                   [ 16, 16],
    ...                   [ 18, 16]])
    >>> X, _ = torch.lstsq(B, A)
    >>> X
    tensor([[  2.0000,   1.0000],
            [  1.0000,   1.0000],
            [  1.0000,   2.0000],
            [ 10.9635,   4.8501],
            [  8.9332,   5.2418]])
""")

add_docstr(torch.lt, r"""
lt(input, other, *, out=None) -> Tensor

Computes :math:`\text{input} < \text{other}` element-wise.
""" + r"""

The second argument can be a number or a tensor whose shape is
:ref:`broadcastable <broadcasting-semantics>` with the first argument.

Args:
    input (Tensor): the tensor to compare
    other (Tensor or float): the tensor or value to compare

Keyword args:
    {out}

Returns:
    A boolean tensor that is True where :attr:`input` is less than :attr:`other` and False elsewhere

Example::

    >>> torch.lt(torch.tensor([[1, 2], [3, 4]]), torch.tensor([[1, 1], [4, 4]]))
    tensor([[False, False], [True, False]])
""".format(**common_args))

add_docstr(torch.lu_unpack, r"""
lu_unpack(LU_data, LU_pivots, unpack_data=True, unpack_pivots=True, *, out=None) -> (Tensor, Tensor, Tensor)

Unpacks the data and pivots from a LU factorization of a tensor into tensors ``L`` and ``U`` and a permutation tensor ``P``
such that ``LU_data, LU_pivots = (P @ L @ U).lu()``.

Returns a tuple of tensors as ``(the P tensor (permutation matrix), the L tensor, the U tensor)``.

.. note:: ``P.dtype == LU_data.dtype`` and ``P.dtype`` is not an integer type so that matrix products with ``P``
          are possible without casting it to a floating type.

Args:
    LU_data (Tensor): the packed LU factorization data
    LU_pivots (Tensor): the packed LU factorization pivots
    unpack_data (bool): flag indicating if the data should be unpacked.
                        If ``False``, then the returned ``L`` and ``U`` are ``None``.
                        Default: ``True``
    unpack_pivots (bool): flag indicating if the pivots should be unpacked into a permutation matrix ``P``.
                          If ``False``, then the returned ``P`` is  ``None``.
                          Default: ``True``
    out (tuple, optional): a tuple of three tensors to use for the outputs ``(P, L, U)``.

Examples::

    >>> A = torch.randn(2, 3, 3)
    >>> A_LU, pivots = A.lu()
    >>> P, A_L, A_U = torch.lu_unpack(A_LU, pivots)
    >>>
    >>> # can recover A from factorization
    >>> A_ = torch.bmm(P, torch.bmm(A_L, A_U))

    >>> # LU factorization of a rectangular matrix:
    >>> A = torch.randn(2, 3, 2)
    >>> A_LU, pivots = A.lu()
    >>> P, A_L, A_U = torch.lu_unpack(A_LU, pivots)
    >>> P
    tensor([[[1., 0., 0.],
             [0., 1., 0.],
             [0., 0., 1.]],

            [[0., 0., 1.],
             [0., 1., 0.],
             [1., 0., 0.]]])
    >>> A_L
    tensor([[[ 1.0000,  0.0000],
             [ 0.4763,  1.0000],
             [ 0.3683,  0.1135]],

            [[ 1.0000,  0.0000],
             [ 0.2957,  1.0000],
             [-0.9668, -0.3335]]])
    >>> A_U
    tensor([[[ 2.1962,  1.0881],
             [ 0.0000, -0.8681]],

            [[-1.0947,  0.3736],
             [ 0.0000,  0.5718]]])
    >>> A_ = torch.bmm(P, torch.bmm(A_L, A_U))
    >>> torch.norm(A_ - A)
    tensor(2.9802e-08)
""".format(**common_args))

add_docstr(torch.less, r"""
less(input, other, *, out=None) -> Tensor

Alias for :func:`torch.lt`.
""")

add_docstr(torch.lu_solve,
           r"""
lu_solve(b, LU_data, LU_pivots, *, out=None) -> Tensor

Returns the LU solve of the linear system :math:`Ax = b` using the partially pivoted
LU factorization of A from :meth:`torch.lu`.

This function supports ``float``, ``double``, ``cfloat`` and ``cdouble`` dtypes for :attr:`input`.

Arguments:
    b (Tensor): the RHS tensor of size :math:`(*, m, k)`, where :math:`*`
                is zero or more batch dimensions.
    LU_data (Tensor): the pivoted LU factorization of A from :meth:`torch.lu` of size :math:`(*, m, m)`,
                       where :math:`*` is zero or more batch dimensions.
    LU_pivots (IntTensor): the pivots of the LU factorization from :meth:`torch.lu` of size :math:`(*, m)`,
                           where :math:`*` is zero or more batch dimensions.
                           The batch dimensions of :attr:`LU_pivots` must be equal to the batch dimensions of
                           :attr:`LU_data`.

Keyword args:
    {out}

Example::

    >>> A = torch.randn(2, 3, 3)
    >>> b = torch.randn(2, 3, 1)
    >>> A_LU = torch.lu(A)
    >>> x = torch.lu_solve(b, *A_LU)
    >>> torch.norm(torch.bmm(A, x) - b)
    tensor(1.00000e-07 *
           2.8312)
""".format(**common_args))

add_docstr(torch.masked_select,
           r"""
masked_select(input, mask, *, out=None) -> Tensor

Returns a new 1-D tensor which indexes the :attr:`input` tensor according to
the boolean mask :attr:`mask` which is a `BoolTensor`.

The shapes of the :attr:`mask` tensor and the :attr:`input` tensor don't need
to match, but they must be :ref:`broadcastable <broadcasting-semantics>`.

.. note:: The returned tensor does **not** use the same storage
          as the original tensor

Args:
    {input}
    mask  (BoolTensor): the tensor containing the binary mask to index with

Keyword args:
    {out}

Example::

    >>> x = torch.randn(3, 4)
    >>> x
    tensor([[ 0.3552, -2.3825, -0.8297,  0.3477],
            [-1.2035,  1.2252,  0.5002,  0.6248],
            [ 0.1307, -2.0608,  0.1244,  2.0139]])
    >>> mask = x.ge(0.5)
    >>> mask
    tensor([[False, False, False, False],
            [False, True, True, True],
            [False, False, False, True]])
    >>> torch.masked_select(x, mask)
    tensor([ 1.2252,  0.5002,  0.6248,  2.0139])
""".format(**common_args))

add_docstr(torch.matrix_rank, r"""
matrix_rank(input, tol=None, symmetric=False, *, out=None) -> Tensor

Returns the numerical rank of a 2-D tensor. The method to compute the
matrix rank is done using SVD by default. If :attr:`symmetric` is ``True``,
then :attr:`input` is assumed to be symmetric, and the computation of the
rank is done by obtaining the eigenvalues.

:attr:`tol` is the threshold below which the singular values (or the eigenvalues
when :attr:`symmetric` is ``True``) are considered to be 0. If :attr:`tol` is not
specified, :attr:`tol` is set to ``S.max() * max(S.size()) * eps`` where `S` is the
singular values (or the eigenvalues when :attr:`symmetric` is ``True``), and ``eps``
is the epsilon value for the datatype of :attr:`input`.

.. warning::

    :func:`torch.matrix_rank` is deprecated in favor of :func:`torch.linalg.matrix_rank`
    and will be removed in a future PyTorch release. The parameter :attr:`symmetric` was
    renamed in :func:`torch.linalg.matrix_rank` to :attr:`hermitian`.

Args:
    input (Tensor): the input 2-D tensor
    tol (float, optional): the tolerance value. Default: ``None``
    symmetric(bool, optional): indicates whether :attr:`input` is symmetric.
                               Default: ``False``

Keyword args:
    {out}

Example::

    >>> a = torch.eye(10)
    >>> torch.matrix_rank(a)
    tensor(10)
    >>> b = torch.eye(10)
    >>> b[0, 0] = 0
    >>> torch.matrix_rank(b)
    tensor(9)
""".format(**common_args))

add_docstr(torch.matrix_power, r"""
matrix_power(input, n, *, out=None) -> Tensor

Alias for :func:`torch.linalg.matrix_power`
""")

add_docstr(torch.matrix_exp, r"""
matrix_exp(A) -> Tensor

Alias for :func:`torch.linalg.matrix_exp`.
""")

add_docstr(torch.max,
           r"""
max(input) -> Tensor

Returns the maximum value of all elements in the ``input`` tensor.

.. warning::
    This function produces deterministic (sub)gradients unlike ``max(dim=0)``

Args:
    {input}

Example::

    >>> a = torch.randn(1, 3)
    >>> a
    tensor([[ 0.6763,  0.7445, -2.2369]])
    >>> torch.max(a)
    tensor(0.7445)

.. function:: max(input, dim, keepdim=False, *, out=None) -> (Tensor, LongTensor)
   :noindex:

Returns a namedtuple ``(values, indices)`` where ``values`` is the maximum
value of each row of the :attr:`input` tensor in the given dimension
:attr:`dim`. And ``indices`` is the index location of each maximum value found
(argmax).

If ``keepdim`` is ``True``, the output tensors are of the same size
as ``input`` except in the dimension ``dim`` where they are of size 1.
Otherwise, ``dim`` is squeezed (see :func:`torch.squeeze`), resulting
in the output tensors having 1 fewer dimension than ``input``.

.. note:: If there are multiple maximal values in a reduced row then
          the indices of the first maximal value are returned.

Args:
    {input}
    {dim}
    {keepdim} Default: ``False``.

Keyword args:
    out (tuple, optional): the result tuple of two output tensors (max, max_indices)

Example::

    >>> a = torch.randn(4, 4)
    >>> a
    tensor([[-1.2360, -0.2942, -0.1222,  0.8475],
            [ 1.1949, -1.1127, -2.2379, -0.6702],
            [ 1.5717, -0.9207,  0.1297, -1.8768],
            [-0.6172,  1.0036, -0.6060, -0.2432]])
    >>> torch.max(a, 1)
    torch.return_types.max(values=tensor([0.8475, 1.1949, 1.5717, 1.0036]), indices=tensor([3, 0, 0, 1]))

.. function:: max(input, other, *, out=None) -> Tensor
   :noindex:

See :func:`torch.maximum`.

""".format(**single_dim_common))

add_docstr(torch.maximum, r"""
maximum(input, other, *, out=None) -> Tensor

Computes the element-wise maximum of :attr:`input` and :attr:`other`.

.. note::
    If one of the elements being compared is a NaN, then that element is returned.
    :func:`maximum` is not supported for tensors with complex dtypes.

Args:
    {input}
    other (Tensor): the second input tensor

Keyword args:
    {out}

Example::

    >>> a = torch.tensor((1, 2, -1))
    >>> b = torch.tensor((3, 0, 4))
    >>> torch.maximum(a, b)
    tensor([3, 2, 4])
""".format(**common_args))

add_docstr(torch.fmax, r"""
fmax(input, other, *, out=None) -> Tensor

Computes the element-wise maximum of :attr:`input` and :attr:`other`.

This is like :func:`torch.maximum` except it handles NaNs differently:
if exactly one of the two elements being compared is a NaN then the non-NaN element is taken as the maximum.
Only if both elements are NaN is NaN propagated.

This function is a wrapper around C++'s ``std::fmax`` and is similar to NumPy's ``fmax`` function.

Supports :ref:`broadcasting to a common shape <broadcasting-semantics>`,
:ref:`type promotion <type-promotion-doc>`, and integer and floating-point inputs.

Args:
    {input}
    other (Tensor): the second input tensor

Keyword args:
    {out}

Example::

    >>> a = torch.tensor([9.7, float('nan'), 3.1, float('nan')])
    >>> b = torch.tensor([-2.2, 0.5, float('nan'), float('nan')])
    >>> torch.fmax(a, b)
    tensor([9.7000, 0.5000, 3.1000,    nan])
""".format(**common_args))

add_docstr(torch.amax,
           r"""
amax(input, dim, keepdim=False, *, out=None) -> Tensor

Returns the maximum value of each slice of the :attr:`input` tensor in the given
dimension(s) :attr:`dim`.

.. note::
    The difference between ``max``/``min`` and ``amax``/``amin`` is:
        - ``amax``/``amin`` supports reducing on multiple dimensions,
        - ``amax``/``amin`` does not return indices,
        - ``amax``/``amin`` evenly distributes gradient between equal values,
          while ``max(dim)``/``min(dim)`` propagates gradient only to a single
          index in the source tensor.

{keepdim_details}

Args:
    {input}
    {dim}
    {keepdim}

Keyword args:
  {out}

Example::

    >>> a = torch.randn(4, 4)
    >>> a
    tensor([[ 0.8177,  1.4878, -0.2491,  0.9130],
            [-0.7158,  1.1775,  2.0992,  0.4817],
            [-0.0053,  0.0164, -1.3738, -0.0507],
            [ 1.9700,  1.1106, -1.0318, -1.0816]])
    >>> torch.amax(a, 1)
    tensor([1.4878, 2.0992, 0.0164, 1.9700])
""".format(**multi_dim_common))

add_docstr(torch.argmax,
           r"""
argmax(input) -> LongTensor

Returns the indices of the maximum value of all elements in the :attr:`input` tensor.

This is the second value returned by :meth:`torch.max`. See its
documentation for the exact semantics of this method.

.. note:: If there are multiple maximal values then the indices of the first maximal value are returned.

Args:
    {input}

Example::

    >>> a = torch.randn(4, 4)
    >>> a
    tensor([[ 1.3398,  0.2663, -0.2686,  0.2450],
            [-0.7401, -0.8805, -0.3402, -1.1936],
            [ 0.4907, -1.3948, -1.0691, -0.3132],
            [-1.6092,  0.5419, -0.2993,  0.3195]])
    >>> torch.argmax(a)
    tensor(0)

.. function:: argmax(input, dim, keepdim=False) -> LongTensor
   :noindex:

Returns the indices of the maximum values of a tensor across a dimension.

This is the second value returned by :meth:`torch.max`. See its
documentation for the exact semantics of this method.

Args:
    {input}
    {dim} If ``None``, the argmax of the flattened input is returned.
    {keepdim} Ignored if ``dim=None``.

Example::

    >>> a = torch.randn(4, 4)
    >>> a
    tensor([[ 1.3398,  0.2663, -0.2686,  0.2450],
            [-0.7401, -0.8805, -0.3402, -1.1936],
            [ 0.4907, -1.3948, -1.0691, -0.3132],
            [-1.6092,  0.5419, -0.2993,  0.3195]])
    >>> torch.argmax(a, dim=1)
    tensor([ 0,  2,  0,  1])
""".format(**single_dim_common))

add_docstr(torch.argwhere,
           r"""
argwhere(input) -> Tensor

Returns a tensor containing the indices of all non-zero elements of
:attr:`input`.  Each row in the result contains the indices of a non-zero
element in :attr:`input`. The result is sorted lexicographically, with
the last index changing the fastest (C-style).

If :attr:`input` has :math:`n` dimensions, then the resulting indices tensor
:attr:`out` is of size :math:`(z \times n)`, where :math:`z` is the total number of
non-zero elements in the :attr:`input` tensor.

.. note::
    This function is similar to NumPy's `argwhere`.

    When :attr:`input` is on CUDA, this function causes host-device synchronization.

Args:
    {input}

Example::

    >>> t = torch.tensor([1, 0, 1])
    >>> torch.argwhere(t)
    tensor([[0],
            [2]])
    >>> t = torch.tensor([[1, 0, 1], [0, 1, 1]])
    >>> torch.argwhere(t)
    tensor([[0, 0],
            [0, 2],
            [1, 1],
            [1, 2]])
""")

add_docstr(torch.mean, r"""
mean(input, *, dtype=None) -> Tensor

Returns the mean value of all elements in the :attr:`input` tensor.

Args:
    {input}

Keyword args:
    {dtype}

Example::

    >>> a = torch.randn(1, 3)
    >>> a
    tensor([[ 0.2294, -0.5481,  1.3288]])
    >>> torch.mean(a)
    tensor(0.3367)

.. function:: mean(input, dim, keepdim=False, *, dtype=None, out=None) -> Tensor
   :noindex:

Returns the mean value of each row of the :attr:`input` tensor in the given
dimension :attr:`dim`. If :attr:`dim` is a list of dimensions,
reduce over all of them.

{keepdim_details}

Args:
    {input}
    {dim}
    {keepdim}

Keyword args:
    {dtype}
    {out}

.. seealso::

    :func:`torch.nanmean` computes the mean value of `non-NaN` elements.

Example::

    >>> a = torch.randn(4, 4)
    >>> a
    tensor([[-0.3841,  0.6320,  0.4254, -0.7384],
            [-0.9644,  1.0131, -0.6549, -1.4279],
            [-0.2951, -1.3350, -0.7694,  0.5600],
            [ 1.0842, -0.9580,  0.3623,  0.2343]])
    >>> torch.mean(a, 1)
    tensor([-0.0163, -0.5085, -0.4599,  0.1807])
    >>> torch.mean(a, 1, True)
    tensor([[-0.0163],
            [-0.5085],
            [-0.4599],
            [ 0.1807]])
""".format(**multi_dim_common))

add_docstr(torch.nanmean, r"""
nanmean(input, dim=None, keepdim=False, *, dtype=None, out=None) -> Tensor

Computes the mean of all `non-NaN` elements along the specified dimensions.

This function is identical to :func:`torch.mean` when there are no `NaN` values
in the :attr:`input` tensor. In the presence of `NaN`, :func:`torch.mean` will
propagate the `NaN` to the output whereas :func:`torch.nanmean` will ignore the
`NaN` values (`torch.nanmean(a)` is equivalent to `torch.mean(a[~a.isnan()])`).

{keepdim_details}

Args:
    {input}
    {dim} If `None`, reduces all dimensions. Default is `None`.
    {keepdim}

Keyword args:
    {dtype}
    {out}

.. seealso::

    :func:`torch.mean` computes the mean value, propagating `NaN`.

Example::

    >>> x = torch.tensor([[torch.nan, 1, 2], [1, 2, 3]])
    >>> x.mean()
    tensor(nan)
    >>> x.nanmean()
    tensor(1.8000)
    >>> x.mean(dim=0)
    tensor([   nan, 1.5000, 2.5000])
    >>> x.nanmean(dim=0)
    tensor([1.0000, 1.5000, 2.5000])

    # If all elements in the reduced dimensions are NaN then the result is NaN
    >>> torch.tensor([torch.nan]).nanmean()
    tensor(nan)
""".format(**multi_dim_common))

add_docstr(torch.median,
           r"""
median(input) -> Tensor

Returns the median of the values in :attr:`input`.

.. note::
    The median is not unique for :attr:`input` tensors with an even number
    of elements. In this case the lower of the two medians is returned. To
    compute the mean of both medians, use :func:`torch.quantile` with ``q=0.5`` instead.

.. warning::
    This function produces deterministic (sub)gradients unlike ``median(dim=0)``

Args:
    {input}

Example::

    >>> a = torch.randn(1, 3)
    >>> a
    tensor([[ 1.5219, -1.5212,  0.2202]])
    >>> torch.median(a)
    tensor(0.2202)

.. function:: median(input, dim=-1, keepdim=False, *, out=None) -> (Tensor, LongTensor)
   :noindex:

Returns a namedtuple ``(values, indices)`` where ``values`` contains the median of each row of :attr:`input`
in the dimension :attr:`dim`, and ``indices`` contains the index of the median values found in the dimension :attr:`dim`.

By default, :attr:`dim` is the last dimension of the :attr:`input` tensor.

If :attr:`keepdim` is ``True``, the output tensors are of the same size
as :attr:`input` except in the dimension :attr:`dim` where they are of size 1.
Otherwise, :attr:`dim` is squeezed (see :func:`torch.squeeze`), resulting in
the outputs tensor having 1 fewer dimension than :attr:`input`.

.. note::
    The median is not unique for :attr:`input` tensors with an even number
    of elements in the dimension :attr:`dim`. In this case the lower of the
    two medians is returned. To compute the mean of both medians in
    :attr:`input`, use :func:`torch.quantile` with ``q=0.5`` instead.

.. warning::
    ``indices`` does not necessarily contain the first occurrence of each
    median value found, unless it is unique.
    The exact implementation details are device-specific.
    Do not expect the same result when run on CPU and GPU in general.
    For the same reason do not expect the gradients to be deterministic.

Args:
    {input}
    {dim}
    {keepdim}

Keyword args:
    out ((Tensor, Tensor), optional): The first tensor will be populated with the median values and the second
                                      tensor, which must have dtype long, with their indices in the dimension
                                      :attr:`dim` of :attr:`input`.

Example::

    >>> a = torch.randn(4, 5)
    >>> a
    tensor([[ 0.2505, -0.3982, -0.9948,  0.3518, -1.3131],
            [ 0.3180, -0.6993,  1.0436,  0.0438,  0.2270],
            [-0.2751,  0.7303,  0.2192,  0.3321,  0.2488],
            [ 1.0778, -1.9510,  0.7048,  0.4742, -0.7125]])
    >>> torch.median(a, 1)
    torch.return_types.median(values=tensor([-0.3982,  0.2270,  0.2488,  0.4742]), indices=tensor([1, 4, 4, 3]))
""".format(**single_dim_common))

add_docstr(torch.nanmedian,
           r"""
nanmedian(input) -> Tensor

Returns the median of the values in :attr:`input`, ignoring ``NaN`` values.

This function is identical to :func:`torch.median` when there are no ``NaN`` values in :attr:`input`.
When :attr:`input` has one or more ``NaN`` values, :func:`torch.median` will always return ``NaN``,
while this function will return the median of the non-``NaN`` elements in :attr:`input`.
If all the elements in :attr:`input` are ``NaN`` it will also return ``NaN``.

Args:
    {input}

Example::

    >>> a = torch.tensor([1, float('nan'), 3, 2])
    >>> a.median()
    tensor(nan)
    >>> a.nanmedian()
    tensor(2.)

.. function:: nanmedian(input, dim=-1, keepdim=False, *, out=None) -> (Tensor, LongTensor)
   :noindex:

Returns a namedtuple ``(values, indices)`` where ``values`` contains the median of each row of :attr:`input`
in the dimension :attr:`dim`, ignoring ``NaN`` values, and ``indices`` contains the index of the median values
found in the dimension :attr:`dim`.

This function is identical to :func:`torch.median` when there are no ``NaN`` values in a reduced row. When a reduced row has
one or more ``NaN`` values, :func:`torch.median` will always reduce it to ``NaN``, while this function will reduce it to the
median of the non-``NaN`` elements. If all the elements in a reduced row are ``NaN`` then it will be reduced to ``NaN``, too.

Args:
    {input}
    {dim}
    {keepdim}

Keyword args:
    out ((Tensor, Tensor), optional): The first tensor will be populated with the median values and the second
                                      tensor, which must have dtype long, with their indices in the dimension
                                      :attr:`dim` of :attr:`input`.

Example::

    >>> a = torch.tensor([[2, 3, 1], [float('nan'), 1, float('nan')]])
    >>> a
    tensor([[2., 3., 1.],
            [nan, 1., nan]])
    >>> a.median(0)
    torch.return_types.median(values=tensor([nan, 1., nan]), indices=tensor([1, 1, 1]))
    >>> a.nanmedian(0)
    torch.return_types.nanmedian(values=tensor([2., 1., 1.]), indices=tensor([0, 1, 0]))
""".format(**single_dim_common))

add_docstr(torch.quantile, r"""
quantile(input, q, dim=None, keepdim=False, *, interpolation='linear', out=None) -> Tensor

Computes the q-th quantiles of each row of the :attr:`input` tensor along the dimension :attr:`dim`.

To compute the quantile, we map q in [0, 1] to the range of indices [0, n] to find the location
of the quantile in the sorted input. If the quantile lies between two data points ``a < b`` with
indices ``i`` and ``j`` in the sorted order, result is computed according to the given
:attr:`interpolation` method as follows:

- ``linear``: ``a + (b - a) * fraction``, where ``fraction`` is the fractional part of the computed quantile index.
- ``lower``: ``a``.
- ``higher``: ``b``.
- ``nearest``: ``a`` or ``b``, whichever's index is closer to the computed quantile index (rounding down for .5 fractions).
- ``midpoint``: ``(a + b) / 2``.

If :attr:`q` is a 1D tensor, the first dimension of the output represents the quantiles and has size
equal to the size of :attr:`q`, the remaining dimensions are what remains from the reduction.

.. note::
    By default :attr:`dim` is ``None`` resulting in the :attr:`input` tensor being flattened before computation.

Args:
    {input}
    q (float or Tensor): a scalar or 1D tensor of values in the range [0, 1].
    {dim}
    {keepdim}

Keyword arguments:
    interpolation (string): interpolation method to use when the desired quantile lies between two data points.
                            Can be ``linear``, ``lower``, ``higher``, ``midpoint`` and ``nearest``.
                            Default is ``linear``.
    {out}

Example::

    >>> a = torch.randn(2, 3)
    >>> a
    tensor([[ 0.0795, -1.2117,  0.9765],
            [ 1.1707,  0.6706,  0.4884]])
    >>> q = torch.tensor([0.25, 0.5, 0.75])
    >>> torch.quantile(a, q, dim=1, keepdim=True)
    tensor([[[-0.5661],
            [ 0.5795]],

            [[ 0.0795],
            [ 0.6706]],

            [[ 0.5280],
            [ 0.9206]]])
    >>> torch.quantile(a, q, dim=1, keepdim=True).shape
    torch.Size([3, 2, 1])
    >>> a = torch.arange(4.)
    >>> a
    tensor([0., 1., 2., 3.])
    >>> torch.quantile(a, 0.6, interpolation='linear')
    tensor(1.8000)
    >>> torch.quantile(a, 0.6, interpolation='lower')
    tensor(1.)
    >>> torch.quantile(a, 0.6, interpolation='higher')
    tensor(2.)
    >>> torch.quantile(a, 0.6, interpolation='midpoint')
    tensor(1.5000)
    >>> torch.quantile(a, 0.6, interpolation='nearest')
    tensor(2.)
    >>> torch.quantile(a, 0.4, interpolation='nearest')
    tensor(1.)
""".format(**single_dim_common))

add_docstr(torch.nanquantile, r"""
nanquantile(input, q, dim=None, keepdim=False, *, interpolation='linear', out=None) -> Tensor

This is a variant of :func:`torch.quantile` that "ignores" ``NaN`` values,
computing the quantiles :attr:`q` as if ``NaN`` values in :attr:`input` did
not exist. If all values in a reduced row are ``NaN`` then the quantiles for
that reduction will be ``NaN``. See the documentation for :func:`torch.quantile`.

Args:
    {input}
    q (float or Tensor): a scalar or 1D tensor of quantile values in the range [0, 1]
    {dim}
    {keepdim}

Keyword arguments:
    interpolation (string): interpolation method to use when the desired quantile lies between two data points.
                            Can be ``linear``, ``lower``, ``higher``, ``midpoint`` and ``nearest``.
                            Default is ``linear``.
    {out}

Example::

    >>> t = torch.tensor([float('nan'), 1, 2])
    >>> t.quantile(0.5)
    tensor(nan)
    >>> t.nanquantile(0.5)
    tensor(1.5000)
    >>> t = torch.tensor([[float('nan'), float('nan')], [1, 2]])
    >>> t
    tensor([[nan, nan],
            [1., 2.]])
    >>> t.nanquantile(0.5, dim=0)
    tensor([1., 2.])
    >>> t.nanquantile(0.5, dim=1)
    tensor([   nan, 1.5000])
""".format(**single_dim_common))

add_docstr(torch.min,
           r"""
min(input) -> Tensor

Returns the minimum value of all elements in the :attr:`input` tensor.

.. warning::
    This function produces deterministic (sub)gradients unlike ``min(dim=0)``

Args:
    {input}

Example::

    >>> a = torch.randn(1, 3)
    >>> a
    tensor([[ 0.6750,  1.0857,  1.7197]])
    >>> torch.min(a)
    tensor(0.6750)

.. function:: min(input, dim, keepdim=False, *, out=None) -> (Tensor, LongTensor)
   :noindex:

Returns a namedtuple ``(values, indices)`` where ``values`` is the minimum
value of each row of the :attr:`input` tensor in the given dimension
:attr:`dim`. And ``indices`` is the index location of each minimum value found
(argmin).

If :attr:`keepdim` is ``True``, the output tensors are of the same size as
:attr:`input` except in the dimension :attr:`dim` where they are of size 1.
Otherwise, :attr:`dim` is squeezed (see :func:`torch.squeeze`), resulting in
the output tensors having 1 fewer dimension than :attr:`input`.

.. note:: If there are multiple minimal values in a reduced row then
          the indices of the first minimal value are returned.

Args:
    {input}
    {dim}
    {keepdim}

Keyword args:
    out (tuple, optional): the tuple of two output tensors (min, min_indices)

Example::

    >>> a = torch.randn(4, 4)
    >>> a
    tensor([[-0.6248,  1.1334, -1.1899, -0.2803],
            [-1.4644, -0.2635, -0.3651,  0.6134],
            [ 0.2457,  0.0384,  1.0128,  0.7015],
            [-0.1153,  2.9849,  2.1458,  0.5788]])
    >>> torch.min(a, 1)
    torch.return_types.min(values=tensor([-1.1899, -1.4644,  0.0384, -0.1153]), indices=tensor([2, 0, 1, 0]))

.. function:: min(input, other, *, out=None) -> Tensor
   :noindex:

See :func:`torch.minimum`.
""".format(**single_dim_common))

add_docstr(torch.minimum, r"""
minimum(input, other, *, out=None) -> Tensor

Computes the element-wise minimum of :attr:`input` and :attr:`other`.

.. note::
    If one of the elements being compared is a NaN, then that element is returned.
    :func:`minimum` is not supported for tensors with complex dtypes.

Args:
    {input}
    other (Tensor): the second input tensor

Keyword args:
    {out}

Example::

    >>> a = torch.tensor((1, 2, -1))
    >>> b = torch.tensor((3, 0, 4))
    >>> torch.minimum(a, b)
    tensor([1, 0, -1])
""".format(**common_args))

add_docstr(torch.fmin, r"""
fmin(input, other, *, out=None) -> Tensor

Computes the element-wise minimum of :attr:`input` and :attr:`other`.

This is like :func:`torch.minimum` except it handles NaNs differently:
if exactly one of the two elements being compared is a NaN then the non-NaN element is taken as the minimum.
Only if both elements are NaN is NaN propagated.

This function is a wrapper around C++'s ``std::fmin`` and is similar to NumPy's ``fmin`` function.

Supports :ref:`broadcasting to a common shape <broadcasting-semantics>`,
:ref:`type promotion <type-promotion-doc>`, and integer and floating-point inputs.

Args:
    {input}
    other (Tensor): the second input tensor

Keyword args:
    {out}

Example::

    >>> a = torch.tensor([2.2, float('nan'), 2.1, float('nan')])
    >>> b = torch.tensor([-9.3, 0.1, float('nan'), float('nan')])
    >>> torch.fmin(a, b)
    tensor([-9.3000, 0.1000, 2.1000,    nan])
""".format(**common_args))

add_docstr(torch.amin,
           r"""
amin(input, dim, keepdim=False, *, out=None) -> Tensor

Returns the minimum value of each slice of the :attr:`input` tensor in the given
dimension(s) :attr:`dim`.

.. note::
    The difference between ``max``/``min`` and ``amax``/``amin`` is:
        - ``amax``/``amin`` supports reducing on multiple dimensions,
        - ``amax``/``amin`` does not return indices,
        - ``amax``/``amin`` evenly distributes gradient between equal values,
          while ``max(dim)``/``min(dim)`` propagates gradient only to a single
          index in the source tensor.

{keepdim_details}

Args:
    {input}
    {dim}
    {keepdim}

Keyword args:
  {out}

Example::

    >>> a = torch.randn(4, 4)
    >>> a
    tensor([[ 0.6451, -0.4866,  0.2987, -1.3312],
            [-0.5744,  1.2980,  1.8397, -0.2713],
            [ 0.9128,  0.9214, -1.7268, -0.2995],
            [ 0.9023,  0.4853,  0.9075, -1.6165]])
    >>> torch.amin(a, 1)
    tensor([-1.3312, -0.5744, -1.7268, -1.6165])
""".format(**multi_dim_common))

add_docstr(torch.aminmax, r"""
aminmax(input, *, dim=None, keepdim=False, out=None) -> (Tensor min, Tensor max)

Computes the minimum and maximum values of the :attr:`input` tensor.

Args:
    input (Tensor):
        The input tensor

Keyword Args:
    dim (Optional[int]):
        The dimension along which to compute the values. If `None`,
        computes the values over the entire :attr:`input` tensor.
        Default is `None`.
    keepdim (bool):
        If `True`, the reduced dimensions will be kept in the output
        tensor as dimensions with size 1 for broadcasting, otherwise
        they will be removed, as if calling (:func:`torch.squeeze`).
        Default is `False`.
    out (Optional[Tuple[Tensor, Tensor]]):
        Optional tensors on which to write the result. Must have the same
        shape and dtype as the expected output.
        Default is `None`.

Returns:
    A named tuple `(min, max)` containing the minimum and maximum values.

Raises:
    RuntimeError
        If any of the dimensions to compute the values over has size 0.

.. note::
    NaN values are propagated to the output if at least one value is NaN.

.. seealso::
    :func:`torch.amin` computes just the minimum value
    :func:`torch.amax` computes just the maximum value

Example::

    >>> torch.aminmax(torch.tensor([1, -3, 5]))
    torch.return_types.aminmax(
    min=tensor(-3),
    max=tensor(5))

    >>> # aminmax propagates NaNs
    >>> torch.aminmax(torch.tensor([1, -3, 5, torch.nan]))
    torch.return_types.aminmax(
    min=tensor(nan),
    max=tensor(nan))

    >>> t = torch.arange(10).view(2, 5)
    >>> t
    tensor([[0, 1, 2, 3, 4],
            [5, 6, 7, 8, 9]])
    >>> t.aminmax(dim=0, keepdim=True)
    torch.return_types.aminmax(
    min=tensor([[0, 1, 2, 3, 4]]),
    max=tensor([[5, 6, 7, 8, 9]]))
""")

add_docstr(torch.argmin,
           r"""
argmin(input, dim=None, keepdim=False) -> LongTensor

Returns the indices of the minimum value(s) of the flattened tensor or along a dimension

This is the second value returned by :meth:`torch.min`. See its
documentation for the exact semantics of this method.

.. note:: If there are multiple minimal values then the indices of the first minimal value are returned.

Args:
    {input}
    {dim} If ``None``, the argmin of the flattened input is returned.
    {keepdim} Ignored if ``dim=None``.

Example::

    >>> a = torch.randn(4, 4)
    >>> a
    tensor([[ 0.1139,  0.2254, -0.1381,  0.3687],
            [ 1.0100, -1.1975, -0.0102, -0.4732],
            [-0.9240,  0.1207, -0.7506, -1.0213],
            [ 1.7809, -1.2960,  0.9384,  0.1438]])
    >>> torch.argmin(a)
    tensor(13)
    >>> torch.argmin(a, dim=1)
    tensor([ 2,  1,  3,  1])
    >>> torch.argmin(a, dim=1, keepdim=True)
    tensor([[2],
            [1],
            [3],
            [1]])
""".format(**single_dim_common))

add_docstr(torch.mm,
           r"""
mm(input, mat2, *, out=None) -> Tensor

Performs a matrix multiplication of the matrices :attr:`input` and :attr:`mat2`.

If :attr:`input` is a :math:`(n \times m)` tensor, :attr:`mat2` is a
:math:`(m \times p)` tensor, :attr:`out` will be a :math:`(n \times p)` tensor.

.. note:: This function does not :ref:`broadcast <broadcasting-semantics>`.
          For broadcasting matrix products, see :func:`torch.matmul`.

Supports strided and sparse 2-D tensors as inputs, autograd with
respect to strided inputs.

{tf32_note}

Args:
    input (Tensor): the first matrix to be matrix multiplied
    mat2 (Tensor): the second matrix to be matrix multiplied

Keyword args:
    {out}

Example::

    >>> mat1 = torch.randn(2, 3)
    >>> mat2 = torch.randn(3, 3)
    >>> torch.mm(mat1, mat2)
    tensor([[ 0.4851,  0.5037, -0.3633],
            [-0.0760, -3.6705,  2.4784]])
""".format(**common_args, **tf32_notes))

add_docstr(torch.hspmm,
           r"""
hspmm(mat1, mat2, *, out=None) -> Tensor

Performs a matrix multiplication of a :ref:`sparse COO matrix
<sparse-coo-docs>` :attr:`mat1` and a strided matrix :attr:`mat2`. The
result is a (1 + 1)-dimensional :ref:`hybrid COO matrix
<sparse-hybrid-coo-docs>`.

Args:
    mat1 (Tensor): the first sparse matrix to be matrix multiplied
    mat2 (Tensor): the second strided matrix to be matrix multiplied

Keyword args:
    {out}
""".format(**common_args))

add_docstr(torch.matmul,
           r"""
matmul(input, other, *, out=None) -> Tensor

Matrix product of two tensors.

The behavior depends on the dimensionality of the tensors as follows:

- If both tensors are 1-dimensional, the dot product (scalar) is returned.
- If both arguments are 2-dimensional, the matrix-matrix product is returned.
- If the first argument is 1-dimensional and the second argument is 2-dimensional,
  a 1 is prepended to its dimension for the purpose of the matrix multiply.
  After the matrix multiply, the prepended dimension is removed.
- If the first argument is 2-dimensional and the second argument is 1-dimensional,
  the matrix-vector product is returned.
- If both arguments are at least 1-dimensional and at least one argument is
  N-dimensional (where N > 2), then a batched matrix multiply is returned.  If the first
  argument is 1-dimensional, a 1 is prepended to its dimension for the purpose of the
  batched matrix multiply and removed after.  If the second argument is 1-dimensional, a
  1 is appended to its dimension for the purpose of the batched matrix multiple and removed after.
  The non-matrix (i.e. batch) dimensions are :ref:`broadcasted <broadcasting-semantics>` (and thus
  must be broadcastable).  For example, if :attr:`input` is a
  :math:`(j \times 1 \times n \times n)` tensor and :attr:`other` is a :math:`(k \times n \times n)`
  tensor, :attr:`out` will be a :math:`(j \times k \times n \times n)` tensor.

  Note that the broadcasting logic only looks at the batch dimensions when determining if the inputs
  are broadcastable, and not the matrix dimensions. For example, if :attr:`input` is a
  :math:`(j \times 1 \times n \times m)` tensor and :attr:`other` is a :math:`(k \times m \times p)`
  tensor, these inputs are valid for broadcasting even though the final two dimensions (i.e. the
  matrix dimensions) are different. :attr:`out` will be a :math:`(j \times k \times n \times p)` tensor.

{tf32_note}

.. note::

    The 1-dimensional dot product version of this function does not support an :attr:`out` parameter.

Arguments:
    input (Tensor): the first tensor to be multiplied
    other (Tensor): the second tensor to be multiplied

Keyword args:
    {out}

Example::

    >>> # vector x vector
    >>> tensor1 = torch.randn(3)
    >>> tensor2 = torch.randn(3)
    >>> torch.matmul(tensor1, tensor2).size()
    torch.Size([])
    >>> # matrix x vector
    >>> tensor1 = torch.randn(3, 4)
    >>> tensor2 = torch.randn(4)
    >>> torch.matmul(tensor1, tensor2).size()
    torch.Size([3])
    >>> # batched matrix x broadcasted vector
    >>> tensor1 = torch.randn(10, 3, 4)
    >>> tensor2 = torch.randn(4)
    >>> torch.matmul(tensor1, tensor2).size()
    torch.Size([10, 3])
    >>> # batched matrix x batched matrix
    >>> tensor1 = torch.randn(10, 3, 4)
    >>> tensor2 = torch.randn(10, 4, 5)
    >>> torch.matmul(tensor1, tensor2).size()
    torch.Size([10, 3, 5])
    >>> # batched matrix x broadcasted matrix
    >>> tensor1 = torch.randn(10, 3, 4)
    >>> tensor2 = torch.randn(4, 5)
    >>> torch.matmul(tensor1, tensor2).size()
    torch.Size([10, 3, 5])

""".format(**common_args, **tf32_notes))

add_docstr(torch.mode,
           r"""
mode(input, dim=-1, keepdim=False, *, out=None) -> (Tensor, LongTensor)

Returns a namedtuple ``(values, indices)`` where ``values`` is the mode
value of each row of the :attr:`input` tensor in the given dimension
:attr:`dim`, i.e. a value which appears most often
in that row, and ``indices`` is the index location of each mode value found.

By default, :attr:`dim` is the last dimension of the :attr:`input` tensor.

If :attr:`keepdim` is ``True``, the output tensors are of the same size as
:attr:`input` except in the dimension :attr:`dim` where they are of size 1.
Otherwise, :attr:`dim` is squeezed (see :func:`torch.squeeze`), resulting
in the output tensors having 1 fewer dimension than :attr:`input`.

.. note:: This function is not defined for ``torch.cuda.Tensor`` yet.

Args:
    {input}
    {dim}
    {keepdim}

Keyword args:
    out (tuple, optional): the result tuple of two output tensors (values, indices)

Example::

    >>> a = torch.randint(10, (5,))
    >>> a
    tensor([6, 5, 1, 0, 2])
    >>> b = a + (torch.randn(50, 1) * 5).long()
    >>> torch.mode(b, 0)
    torch.return_types.mode(values=tensor([6, 5, 1, 0, 2]), indices=tensor([2, 2, 2, 2, 2]))
""".format(**single_dim_common))

add_docstr(torch.mul, r"""
mul(input, other, *, out=None) -> Tensor

Multiplies :attr:`input` by :attr:`other`.


.. math::
    \text{out}_i = \text{input}_i \times \text{other}_i
""" + r"""

Supports :ref:`broadcasting to a common shape <broadcasting-semantics>`,
:ref:`type promotion <type-promotion-doc>`, and integer, float, and complex inputs.

Args:
    {input}
    other (Tensor or Number) - the tensor or number to multiply input by.

Keyword args:
    {out}

Examples::

    >>> a = torch.randn(3)
    >>> a
    tensor([ 0.2015, -0.4255,  2.6087])
    >>> torch.mul(a, 100)
    tensor([  20.1494,  -42.5491,  260.8663])

    >>> b = torch.randn(4, 1)
    >>> b
    tensor([[ 1.1207],
            [-0.3137],
            [ 0.0700],
            [ 0.8378]])
    >>> c = torch.randn(1, 4)
    >>> c
    tensor([[ 0.5146,  0.1216, -0.5244,  2.2382]])
    >>> torch.mul(b, c)
    tensor([[ 0.5767,  0.1363, -0.5877,  2.5083],
            [-0.1614, -0.0382,  0.1645, -0.7021],
            [ 0.0360,  0.0085, -0.0367,  0.1567],
            [ 0.4312,  0.1019, -0.4394,  1.8753]])
""".format(**common_args))

add_docstr(torch.multiply, r"""
multiply(input, other, *, out=None)

Alias for :func:`torch.mul`.
""")

add_docstr(torch.multinomial,
           r"""
multinomial(input, num_samples, replacement=False, *, generator=None, out=None) -> LongTensor

Returns a tensor where each row contains :attr:`num_samples` indices sampled
from the multinomial probability distribution located in the corresponding row
of tensor :attr:`input`.

.. note::
    The rows of :attr:`input` do not need to sum to one (in which case we use
    the values as weights), but must be non-negative, finite and have
    a non-zero sum.

Indices are ordered from left to right according to when each was sampled
(first samples are placed in first column).

If :attr:`input` is a vector, :attr:`out` is a vector of size :attr:`num_samples`.

If :attr:`input` is a matrix with `m` rows, :attr:`out` is an matrix of shape
:math:`(m \times \text{{num\_samples}})`.

If replacement is ``True``, samples are drawn with replacement.

If not, they are drawn without replacement, which means that when a
sample index is drawn for a row, it cannot be drawn again for that row.

.. note::
    When drawn without replacement, :attr:`num_samples` must be lower than
    number of non-zero elements in :attr:`input` (or the min number of non-zero
    elements in each row of :attr:`input` if it is a matrix).

Args:
    input (Tensor): the input tensor containing probabilities
    num_samples (int): number of samples to draw
    replacement (bool, optional): whether to draw with replacement or not

Keyword args:
    {generator}
    {out}

Example::

    >>> weights = torch.tensor([0, 10, 3, 0], dtype=torch.float) # create a tensor of weights
    >>> torch.multinomial(weights, 2)
    tensor([1, 2])
    >>> torch.multinomial(weights, 4) # ERROR!
    RuntimeError: invalid argument 2: invalid multinomial distribution (with replacement=False,
    not enough non-negative category to sample) at ../aten/src/TH/generic/THTensorRandom.cpp:320
    >>> torch.multinomial(weights, 4, replacement=True)
    tensor([ 2,  1,  1,  1])
""".format(**common_args))

add_docstr(torch.mv,
           r"""
mv(input, vec, *, out=None) -> Tensor

Performs a matrix-vector product of the matrix :attr:`input` and the vector
:attr:`vec`.

If :attr:`input` is a :math:`(n \times m)` tensor, :attr:`vec` is a 1-D tensor of
size :math:`m`, :attr:`out` will be 1-D of size :math:`n`.

.. note:: This function does not :ref:`broadcast <broadcasting-semantics>`.

Args:
    input (Tensor): matrix to be multiplied
    vec (Tensor): vector to be multiplied

Keyword args:
    {out}

Example::

    >>> mat = torch.randn(2, 3)
    >>> vec = torch.randn(3)
    >>> torch.mv(mat, vec)
    tensor([ 1.0404, -0.6361])
""".format(**common_args))

add_docstr(torch.mvlgamma,
           r"""
mvlgamma(input, p, *, out=None) -> Tensor

Alias for :func:`torch.special.multigammaln`.
""")

add_docstr(torch.movedim, r"""
movedim(input, source, destination) -> Tensor

Moves the dimension(s) of :attr:`input` at the position(s) in :attr:`source`
to the position(s) in :attr:`destination`.

Other dimensions of :attr:`input` that are not explicitly moved remain in
their original order and appear at the positions not specified in :attr:`destination`.

Args:
    {input}
    source (int or tuple of ints): Original positions of the dims to move. These must be unique.
    destination (int or tuple of ints): Destination positions for each of the original dims. These must also be unique.

Examples::

    >>> t = torch.randn(3,2,1)
    >>> t
    tensor([[[-0.3362],
            [-0.8437]],

            [[-0.9627],
            [ 0.1727]],

            [[ 0.5173],
            [-0.1398]]])
    >>> torch.movedim(t, 1, 0).shape
    torch.Size([2, 3, 1])
    >>> torch.movedim(t, 1, 0)
    tensor([[[-0.3362],
            [-0.9627],
            [ 0.5173]],

            [[-0.8437],
            [ 0.1727],
            [-0.1398]]])
    >>> torch.movedim(t, (1, 2), (0, 1)).shape
    torch.Size([2, 1, 3])
    >>> torch.movedim(t, (1, 2), (0, 1))
    tensor([[[-0.3362, -0.9627,  0.5173]],

            [[-0.8437,  0.1727, -0.1398]]])
""".format(**common_args))

add_docstr(torch.moveaxis, r"""
moveaxis(input, source, destination) -> Tensor

Alias for :func:`torch.movedim`.

This function is equivalent to NumPy's moveaxis function.

Examples::

    >>> t = torch.randn(3,2,1)
    >>> t
    tensor([[[-0.3362],
            [-0.8437]],

            [[-0.9627],
            [ 0.1727]],

            [[ 0.5173],
            [-0.1398]]])
    >>> torch.moveaxis(t, 1, 0).shape
    torch.Size([2, 3, 1])
    >>> torch.moveaxis(t, 1, 0)
    tensor([[[-0.3362],
            [-0.9627],
            [ 0.5173]],

            [[-0.8437],
            [ 0.1727],
            [-0.1398]]])
    >>> torch.moveaxis(t, (1, 2), (0, 1)).shape
    torch.Size([2, 1, 3])
    >>> torch.moveaxis(t, (1, 2), (0, 1))
    tensor([[[-0.3362, -0.9627,  0.5173]],

            [[-0.8437,  0.1727, -0.1398]]])
""".format(**common_args))

add_docstr(torch.swapdims, r"""
swapdims(input, dim0, dim1) -> Tensor

Alias for :func:`torch.transpose`.

This function is equivalent to NumPy's swapaxes function.

Examples::

    >>> x = torch.tensor([[[0,1],[2,3]],[[4,5],[6,7]]])
    >>> x
    tensor([[[0, 1],
            [2, 3]],

            [[4, 5],
            [6, 7]]])
    >>> torch.swapdims(x, 0, 1)
    tensor([[[0, 1],
            [4, 5]],

            [[2, 3],
            [6, 7]]])
    >>> torch.swapdims(x, 0, 2)
    tensor([[[0, 4],
            [2, 6]],

            [[1, 5],
            [3, 7]]])
""".format(**common_args))

add_docstr(torch.swapaxes, r"""
swapaxes(input, axis0, axis1) -> Tensor

Alias for :func:`torch.transpose`.

This function is equivalent to NumPy's swapaxes function.

Examples::

    >>> x = torch.tensor([[[0,1],[2,3]],[[4,5],[6,7]]])
    >>> x
    tensor([[[0, 1],
            [2, 3]],

            [[4, 5],
            [6, 7]]])
    >>> torch.swapaxes(x, 0, 1)
    tensor([[[0, 1],
            [4, 5]],

            [[2, 3],
            [6, 7]]])
    >>> torch.swapaxes(x, 0, 2)
    tensor([[[0, 4],
            [2, 6]],

            [[1, 5],
            [3, 7]]])
""".format(**common_args))

add_docstr(torch.narrow,
           r"""
narrow(input, dim, start, length) -> Tensor

Returns a new tensor that is a narrowed version of :attr:`input` tensor. The
dimension :attr:`dim` is input from :attr:`start` to ``start + length``. The
returned tensor and :attr:`input` tensor share the same underlying storage.

Args:
    input (Tensor): the tensor to narrow
    dim (int): the dimension along which to narrow
    start (int): the starting dimension
    length (int): the distance to the ending dimension

Example::

    >>> x = torch.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
    >>> torch.narrow(x, 0, 0, 2)
    tensor([[ 1,  2,  3],
            [ 4,  5,  6]])
    >>> torch.narrow(x, 1, 1, 2)
    tensor([[ 2,  3],
            [ 5,  6],
            [ 8,  9]])
""")

add_docstr(torch.nan_to_num,
           r"""
nan_to_num(input, nan=0.0, posinf=None, neginf=None, *, out=None) -> Tensor

Replaces :literal:`NaN`, positive infinity, and negative infinity values in :attr:`input`
with the values specified by :attr:`nan`, :attr:`posinf`, and :attr:`neginf`, respectively.
By default, :literal:`NaN`\ s are replaced with zero, positive infinity is replaced with the
greatest finite value representable by :attr:`input`'s dtype, and negative infinity
is replaced with the least finite value representable by :attr:`input`'s dtype.

Args:
    {input}
    nan (Number, optional): the value to replace :literal:`NaN`\s with. Default is zero.
    posinf (Number, optional): if a Number, the value to replace positive infinity values with.
        If None, positive infinity values are replaced with the greatest finite value representable by :attr:`input`'s dtype.
        Default is None.
    neginf (Number, optional): if a Number, the value to replace negative infinity values with.
        If None, negative infinity values are replaced with the lowest finite value representable by :attr:`input`'s dtype.
        Default is None.

Keyword args:
    {out}

Example::

    >>> x = torch.tensor([float('nan'), float('inf'), -float('inf'), 3.14])
    >>> torch.nan_to_num(x)
    tensor([ 0.0000e+00,  3.4028e+38, -3.4028e+38,  3.1400e+00])
    >>> torch.nan_to_num(x, nan=2.0)
    tensor([ 2.0000e+00,  3.4028e+38, -3.4028e+38,  3.1400e+00])
    >>> torch.nan_to_num(x, nan=2.0, posinf=1.0)
    tensor([ 2.0000e+00,  1.0000e+00, -3.4028e+38,  3.1400e+00])

""".format(**common_args))

add_docstr(torch.ne, r"""
ne(input, other, *, out=None) -> Tensor

Computes :math:`\text{input} \neq \text{other}` element-wise.
""" + r"""

The second argument can be a number or a tensor whose shape is
:ref:`broadcastable <broadcasting-semantics>` with the first argument.

Args:
    input (Tensor): the tensor to compare
    other (Tensor or float): the tensor or value to compare

Keyword args:
    {out}

Returns:
    A boolean tensor that is True where :attr:`input` is not equal to :attr:`other` and False elsewhere

Example::

    >>> torch.ne(torch.tensor([[1, 2], [3, 4]]), torch.tensor([[1, 1], [4, 4]]))
    tensor([[False, True], [True, False]])
""".format(**common_args))

add_docstr(torch.not_equal, r"""
not_equal(input, other, *, out=None) -> Tensor

Alias for :func:`torch.ne`.
""")

add_docstr(torch.neg,
           r"""
neg(input, *, out=None) -> Tensor

Returns a new tensor with the negative of the elements of :attr:`input`.

.. math::
    \text{out} = -1 \times \text{input}
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(5)
    >>> a
    tensor([ 0.0090, -0.2262, -0.0682, -0.2866,  0.3940])
    >>> torch.neg(a)
    tensor([-0.0090,  0.2262,  0.0682,  0.2866, -0.3940])
""".format(**common_args))

add_docstr(torch.negative,
           r"""
negative(input, *, out=None) -> Tensor

Alias for :func:`torch.neg`
""")

add_docstr(torch.nextafter,
           r"""
nextafter(input, other, *, out=None) -> Tensor

Return the next floating-point value after :attr:`input` towards :attr:`other`, elementwise.

The shapes of ``input`` and ``other`` must be
:ref:`broadcastable <broadcasting-semantics>`.

Args:
    input (Tensor): the first input tensor
    other (Tensor): the second input tensor

Keyword args:
    {out}

Example::

    >>> eps = torch.finfo(torch.float32).eps
    >>> torch.nextafter(torch.tensor([1.0, 2.0]), torch.tensor([2.0, 1.0])) == torch.tensor([eps + 1, 2 - eps])
    tensor([True, True])

""".format(**common_args))

add_docstr(torch.nonzero,
           r"""
nonzero(input, *, out=None, as_tuple=False) -> LongTensor or tuple of LongTensors

.. note::
    :func:`torch.nonzero(..., as_tuple=False) <torch.nonzero>` (default) returns a
    2-D tensor where each row is the index for a nonzero value.

    :func:`torch.nonzero(..., as_tuple=True) <torch.nonzero>` returns a tuple of 1-D
    index tensors, allowing for advanced indexing, so ``x[x.nonzero(as_tuple=True)]``
    gives all nonzero values of tensor ``x``. Of the returned tuple, each index tensor
    contains nonzero indices for a certain dimension.

    See below for more details on the two behaviors.

    When :attr:`input` is on CUDA, :func:`torch.nonzero() <torch.nonzero>` causes
    host-device synchronization.

**When** :attr:`as_tuple` **is** ``False`` **(default)**:

Returns a tensor containing the indices of all non-zero elements of
:attr:`input`.  Each row in the result contains the indices of a non-zero
element in :attr:`input`. The result is sorted lexicographically, with
the last index changing the fastest (C-style).

If :attr:`input` has :math:`n` dimensions, then the resulting indices tensor
:attr:`out` is of size :math:`(z \times n)`, where :math:`z` is the total number of
non-zero elements in the :attr:`input` tensor.

**When** :attr:`as_tuple` **is** ``True``:

Returns a tuple of 1-D tensors, one for each dimension in :attr:`input`,
each containing the indices (in that dimension) of all non-zero elements of
:attr:`input` .

If :attr:`input` has :math:`n` dimensions, then the resulting tuple contains :math:`n`
tensors of size :math:`z`, where :math:`z` is the total number of
non-zero elements in the :attr:`input` tensor.

As a special case, when :attr:`input` has zero dimensions and a nonzero scalar
value, it is treated as a one-dimensional tensor with one element.

Args:
    {input}

Keyword args:
    out (LongTensor, optional): the output tensor containing indices

Returns:
    LongTensor or tuple of LongTensor: If :attr:`as_tuple` is ``False``, the output
    tensor containing indices. If :attr:`as_tuple` is ``True``, one 1-D tensor for
    each dimension, containing the indices of each nonzero element along that
    dimension.

Example::

    >>> torch.nonzero(torch.tensor([1, 1, 1, 0, 1]))
    tensor([[ 0],
            [ 1],
            [ 2],
            [ 4]])
    >>> torch.nonzero(torch.tensor([[0.6, 0.0, 0.0, 0.0],
    ...                             [0.0, 0.4, 0.0, 0.0],
    ...                             [0.0, 0.0, 1.2, 0.0],
    ...                             [0.0, 0.0, 0.0,-0.4]]))
    tensor([[ 0,  0],
            [ 1,  1],
            [ 2,  2],
            [ 3,  3]])
    >>> torch.nonzero(torch.tensor([1, 1, 1, 0, 1]), as_tuple=True)
    (tensor([0, 1, 2, 4]),)
    >>> torch.nonzero(torch.tensor([[0.6, 0.0, 0.0, 0.0],
    ...                             [0.0, 0.4, 0.0, 0.0],
    ...                             [0.0, 0.0, 1.2, 0.0],
    ...                             [0.0, 0.0, 0.0,-0.4]]), as_tuple=True)
    (tensor([0, 1, 2, 3]), tensor([0, 1, 2, 3]))
    >>> torch.nonzero(torch.tensor(5), as_tuple=True)
    (tensor([0]),)
""".format(**common_args))

add_docstr(torch.normal,
           r"""
normal(mean, std, *, generator=None, out=None) -> Tensor

Returns a tensor of random numbers drawn from separate normal distributions
whose mean and standard deviation are given.

The :attr:`mean` is a tensor with the mean of
each output element's normal distribution

The :attr:`std` is a tensor with the standard deviation of
each output element's normal distribution

The shapes of :attr:`mean` and :attr:`std` don't need to match, but the
total number of elements in each tensor need to be the same.

.. note:: When the shapes do not match, the shape of :attr:`mean`
          is used as the shape for the returned output tensor

.. note:: When :attr:`std` is a CUDA tensor, this function synchronizes
          its device with the CPU.

Args:
    mean (Tensor): the tensor of per-element means
    std (Tensor): the tensor of per-element standard deviations

Keyword args:
    {generator}
    {out}

Example::

    >>> torch.normal(mean=torch.arange(1., 11.), std=torch.arange(1, 0, -0.1))
    tensor([  1.0425,   3.5672,   2.7969,   4.2925,   4.7229,   6.2134,
              8.0505,   8.1408,   9.0563,  10.0566])

.. function:: normal(mean=0.0, std, *, out=None) -> Tensor
   :noindex:

Similar to the function above, but the means are shared among all drawn
elements.

Args:
    mean (float, optional): the mean for all distributions
    std (Tensor): the tensor of per-element standard deviations

Keyword args:
    {out}

Example::

    >>> torch.normal(mean=0.5, std=torch.arange(1., 6.))
    tensor([-1.2793, -1.0732, -2.0687,  5.1177, -1.2303])

.. function:: normal(mean, std=1.0, *, out=None) -> Tensor
   :noindex:

Similar to the function above, but the standard deviations are shared among
all drawn elements.

Args:
    mean (Tensor): the tensor of per-element means
    std (float, optional): the standard deviation for all distributions

Keyword args:
    out (Tensor, optional): the output tensor

Example::

    >>> torch.normal(mean=torch.arange(1., 6.))
    tensor([ 1.1552,  2.6148,  2.6535,  5.8318,  4.2361])

.. function:: normal(mean, std, size, *, out=None) -> Tensor
   :noindex:

Similar to the function above, but the means and standard deviations are shared
among all drawn elements. The resulting tensor has size given by :attr:`size`.

Args:
    mean (float): the mean for all distributions
    std (float): the standard deviation for all distributions
    size (int...): a sequence of integers defining the shape of the output tensor.

Keyword args:
    {out}

Example::

    >>> torch.normal(2, 3, size=(1, 4))
    tensor([[-1.3987, -1.9544,  3.6048,  0.7909]])
""".format(**common_args))

add_docstr(torch.numel,
           r"""
numel(input) -> int

Returns the total number of elements in the :attr:`input` tensor.

Args:
    {input}

Example::

    >>> a = torch.randn(1, 2, 3, 4, 5)
    >>> torch.numel(a)
    120
    >>> a = torch.zeros(4,4)
    >>> torch.numel(a)
    16

""".format(**common_args))

add_docstr(torch.ones,
           r"""
ones(*size, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) -> Tensor

Returns a tensor filled with the scalar value `1`, with the shape defined
by the variable argument :attr:`size`.

Args:
    size (int...): a sequence of integers defining the shape of the output tensor.
        Can be a variable number of arguments or a collection like a list or tuple.

Keyword arguments:
    {out}
    {dtype}
    {layout}
    {device}
    {requires_grad}

Example::

    >>> torch.ones(2, 3)
    tensor([[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]])

    >>> torch.ones(5)
    tensor([ 1.,  1.,  1.,  1.,  1.])

""".format(**factory_common_args))

add_docstr(torch.ones_like,
           r"""
ones_like(input, *, dtype=None, layout=None, device=None, requires_grad=False, memory_format=torch.preserve_format) -> Tensor

Returns a tensor filled with the scalar value `1`, with the same size as
:attr:`input`. ``torch.ones_like(input)`` is equivalent to
``torch.ones(input.size(), dtype=input.dtype, layout=input.layout, device=input.device)``.

.. warning::
    As of 0.4, this function does not support an :attr:`out` keyword. As an alternative,
    the old ``torch.ones_like(input, out=output)`` is equivalent to
    ``torch.ones(input.size(), out=output)``.

Args:
    {input}

Keyword arguments:
    {dtype}
    {layout}
    {device}
    {requires_grad}
    {memory_format}

Example::

    >>> input = torch.empty(2, 3)
    >>> torch.ones_like(input)
    tensor([[ 1.,  1.,  1.],
            [ 1.,  1.,  1.]])
""".format(**factory_like_common_args))

add_docstr(torch.orgqr,
           r"""
orgqr(input, tau) -> Tensor

Alias for :func:`torch.linalg.householder_product`.
""")

add_docstr(torch.ormqr,
           r"""
ormqr(input, tau, other, left=True, transpose=False, *, out=None) -> Tensor

Computes the matrix-matrix multiplication of a product of Householder matrices with a general matrix.

Multiplies a :math:`m \times n` matrix `C` (given by :attr:`other`) with a matrix `Q`,
where `Q` is represented using Householder reflectors `(input, tau)`.
See `Representation of Orthogonal or Unitary Matrices`_ for further details.

If :attr:`left` is `True` then `op(Q)` times `C` is computed, otherwise the result is `C` times `op(Q)`.
When :attr:`left` is `True`, the implicit matrix `Q` has size :math:`m \times m`.
It has size :math:`n \times n` otherwise.
If :attr:`transpose` is `True` then `op` is the conjugate transpose operation, otherwise it's a no-op.

Supports inputs of float, double, cfloat and cdouble dtypes.
Also supports batched inputs, and, if the input is batched, the output is batched with the same dimensions.

.. seealso::

        :func:`torch.geqrf` can be used to form the Householder representation `(input, tau)` of matrix `Q`
        from the QR decomposition.

Args:
    input (Tensor): tensor of shape `(*, mn, k)` where `*` is zero or more batch dimensions
                    and `mn` equals to `m` or `n` depending on the :attr:`left`.
    tau (Tensor): tensor of shape `(*, min(mn, k))` where `*` is zero or more batch dimensions.
    other (Tensor): tensor of shape `(*, m, n)` where `*` is zero or more batch dimensions.
    left (bool): controls the order of multiplication.
    transpose (bool): controls whether the matrix `Q` is conjugate transposed or not.

Keyword args:
    out (Tensor, optional): the output Tensor. Ignored if `None`. Default: `None`.

.. _Representation of Orthogonal or Unitary Matrices:
    https://www.netlib.org/lapack/lug/node128.html
""")

add_docstr(torch.permute,
           r"""
permute(input, dims) -> Tensor

Returns a view of the original tensor :attr:`input` with its dimensions permuted.

Args:
    {input}
    dims (tuple of ints): The desired ordering of dimensions

Example:
    >>> x = torch.randn(2, 3, 5)
    >>> x.size()
    torch.Size([2, 3, 5])
    >>> torch.permute(x, (2, 0, 1)).size()
    torch.Size([5, 2, 3])
""".format(**common_args))

add_docstr(torch.poisson,
           r"""
poisson(input, generator=None) -> Tensor

Returns a tensor of the same size as :attr:`input` with each element
sampled from a Poisson distribution with rate parameter given by the corresponding
element in :attr:`input` i.e.,

.. math::
    \text{{out}}_i \sim \text{{Poisson}}(\text{{input}}_i)

Args:
    input (Tensor): the input tensor containing the rates of the Poisson distribution

Keyword args:
    {generator}

Example::

    >>> rates = torch.rand(4, 4) * 5  # rate parameter between 0 and 5
    >>> torch.poisson(rates)
    tensor([[9., 1., 3., 5.],
            [8., 6., 6., 0.],
            [0., 4., 5., 3.],
            [2., 1., 4., 2.]])
""".format(**common_args))

add_docstr(torch.polygamma,
           r"""
polygamma(n, input, *, out=None) -> Tensor

Alias for :func:`torch.special.polygamma`.
""")

add_docstr(torch.positive,
           r"""
positive(input) -> Tensor

Returns :attr:`input`.
Throws a runtime error if :attr:`input` is a bool tensor.
""" + r"""
Args:
    {input}

Example::

    >>> t = torch.randn(5)
    >>> t
    tensor([ 0.0090, -0.2262, -0.0682, -0.2866,  0.3940])
    >>> torch.positive(t)
    tensor([ 0.0090, -0.2262, -0.0682, -0.2866,  0.3940])
""".format(**common_args))

add_docstr(torch.pow,
           r"""
pow(input, exponent, *, out=None) -> Tensor

Takes the power of each element in :attr:`input` with :attr:`exponent` and
returns a tensor with the result.

:attr:`exponent` can be either a single ``float`` number or a `Tensor`
with the same number of elements as :attr:`input`.

When :attr:`exponent` is a scalar value, the operation applied is:

.. math::
    \text{out}_i = x_i ^ \text{exponent}

When :attr:`exponent` is a tensor, the operation applied is:

.. math::
    \text{out}_i = x_i ^ {\text{exponent}_i}
""" + r"""
When :attr:`exponent` is a tensor, the shapes of :attr:`input`
and :attr:`exponent` must be :ref:`broadcastable <broadcasting-semantics>`.

Args:
    {input}
    exponent (float or tensor): the exponent value

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([ 0.4331,  1.2475,  0.6834, -0.2791])
    >>> torch.pow(a, 2)
    tensor([ 0.1875,  1.5561,  0.4670,  0.0779])
    >>> exp = torch.arange(1., 5.)

    >>> a = torch.arange(1., 5.)
    >>> a
    tensor([ 1.,  2.,  3.,  4.])
    >>> exp
    tensor([ 1.,  2.,  3.,  4.])
    >>> torch.pow(a, exp)
    tensor([   1.,    4.,   27.,  256.])

.. function:: pow(self, exponent, *, out=None) -> Tensor
   :noindex:

:attr:`self` is a scalar ``float`` value, and :attr:`exponent` is a tensor.
The returned tensor :attr:`out` is of the same shape as :attr:`exponent`

The operation applied is:

.. math::
    \text{{out}}_i = \text{{self}} ^ {{\text{{exponent}}_i}}

Args:
    self (float): the scalar base value for the power operation
    exponent (Tensor): the exponent tensor

Keyword args:
    {out}

Example::

    >>> exp = torch.arange(1., 5.)
    >>> base = 2
    >>> torch.pow(base, exp)
    tensor([  2.,   4.,   8.,  16.])
""".format(**common_args))

add_docstr(torch.float_power,
           r"""
float_power(input, exponent, *, out=None) -> Tensor

Raises :attr:`input` to the power of :attr:`exponent`, elementwise, in double precision.
If neither input is complex returns a ``torch.float64`` tensor,
and if one or more inputs is complex returns a ``torch.complex128`` tensor.

.. note::
    This function always computes in double precision, unlike :func:`torch.pow`,
    which implements more typical :ref:`type promotion <type-promotion-doc>`.
    This is useful when the computation needs to be performed in a wider or more precise dtype,
    or the results of the computation may contain fractional values not representable in the input dtypes,
    like when an integer base is raised to a negative integer exponent.

Args:
    input (Tensor or Number): the base value(s)
    exponent (Tensor or Number): the exponent value(s)

Keyword args:
    {out}

Example::

    >>> a = torch.randint(10, (4,))
    >>> a
    tensor([6, 4, 7, 1])
    >>> torch.float_power(a, 2)
    tensor([36., 16., 49.,  1.], dtype=torch.float64)

    >>> a = torch.arange(1, 5)
    >>> a
    tensor([ 1,  2,  3,  4])
    >>> exp = torch.tensor([2, -3, 4, -5])
    >>> exp
    tensor([ 2, -3,  4, -5])
    >>> torch.float_power(a, exp)
    tensor([1.0000e+00, 1.2500e-01, 8.1000e+01, 9.7656e-04], dtype=torch.float64)
""".format(**common_args))

add_docstr(torch.prod,
           r"""
prod(input, *, dtype=None) -> Tensor

Returns the product of all elements in the :attr:`input` tensor.

Args:
    {input}

Keyword args:
    {dtype}

Example::

    >>> a = torch.randn(1, 3)
    >>> a
    tensor([[-0.8020,  0.5428, -1.5854]])
    >>> torch.prod(a)
    tensor(0.6902)

.. function:: prod(input, dim, keepdim=False, *, dtype=None) -> Tensor
   :noindex:

Returns the product of each row of the :attr:`input` tensor in the given
dimension :attr:`dim`.

{keepdim_details}

Args:
    {input}
    {dim}
    {keepdim}

Keyword args:
    {dtype}

Example::

    >>> a = torch.randn(4, 2)
    >>> a
    tensor([[ 0.5261, -0.3837],
            [ 1.1857, -0.2498],
            [-1.1646,  0.0705],
            [ 1.1131, -1.0629]])
    >>> torch.prod(a, 1)
    tensor([-0.2018, -0.2962, -0.0821, -1.1831])
""".format(**single_dim_common))

add_docstr(torch.promote_types,
           r"""
promote_types(type1, type2) -> dtype

Returns the :class:`torch.dtype` with the smallest size and scalar kind that is
not smaller nor of lower kind than either `type1` or `type2`. See type promotion
:ref:`documentation <type-promotion-doc>` for more information on the type
promotion logic.

Args:
    type1 (:class:`torch.dtype`)
    type2 (:class:`torch.dtype`)

Example::

    >>> torch.promote_types(torch.int32, torch.float32)
    torch.float32
    >>> torch.promote_types(torch.uint8, torch.long)
    torch.long
""")

add_docstr(torch.qr,
           r"""
qr(input, some=True, *, out=None) -> (Tensor, Tensor)

Computes the QR decomposition of a matrix or a batch of matrices :attr:`input`,
and returns a namedtuple (Q, R) of tensors such that :math:`\text{input} = Q R`
with :math:`Q` being an orthogonal matrix or batch of orthogonal matrices and
:math:`R` being an upper triangular matrix or batch of upper triangular matrices.

If :attr:`some` is ``True``, then this function returns the thin (reduced) QR factorization.
Otherwise, if :attr:`some` is ``False``, this function returns the complete QR factorization.

.. warning::

    :func:`torch.qr` is deprecated in favor of :func:`torch.linalg.qr`
    and will be removed in a future PyTorch release. The boolean parameter :attr:`some` has been
    replaced with a string parameter :attr:`mode`.

    ``Q, R = torch.qr(A)`` should be replaced with

    .. code:: python

        Q, R = torch.linalg.qr(A)

    ``Q, R = torch.qr(A, some=False)`` should be replaced with

    .. code:: python

        Q, R = torch.linalg.qr(A, mode="complete")

.. warning::
          If you plan to backpropagate through QR, note that the current backward implementation
          is only well-defined when the first :math:`\min(input.size(-1), input.size(-2))`
          columns of :attr:`input` are linearly independent.
          This behavior will propably change once QR supports pivoting.

.. note:: This function uses LAPACK for CPU inputs and MAGMA for CUDA inputs,
          and may produce different (valid) decompositions on different device types
          or different platforms.

Args:
    input (Tensor): the input tensor of size :math:`(*, m, n)` where `*` is zero or more
                batch dimensions consisting of matrices of dimension :math:`m \times n`.
    some (bool, optional): Set to ``True`` for reduced QR decomposition and ``False`` for
                complete QR decomposition. If `k = min(m, n)` then:

                  * ``some=True`` : returns `(Q, R)` with dimensions (m, k), (k, n) (default)

                  * ``'some=False'``: returns `(Q, R)` with dimensions (m, m), (m, n)

Keyword args:
    out (tuple, optional): tuple of `Q` and `R` tensors.
                The dimensions of `Q` and `R` are detailed in the description of :attr:`some` above.

Example::

    >>> a = torch.tensor([[12., -51, 4], [6, 167, -68], [-4, 24, -41]])
    >>> q, r = torch.qr(a)
    >>> q
    tensor([[-0.8571,  0.3943,  0.3314],
            [-0.4286, -0.9029, -0.0343],
            [ 0.2857, -0.1714,  0.9429]])
    >>> r
    tensor([[ -14.0000,  -21.0000,   14.0000],
            [   0.0000, -175.0000,   70.0000],
            [   0.0000,    0.0000,  -35.0000]])
    >>> torch.mm(q, r).round()
    tensor([[  12.,  -51.,    4.],
            [   6.,  167.,  -68.],
            [  -4.,   24.,  -41.]])
    >>> torch.mm(q.t(), q).round()
    tensor([[ 1.,  0.,  0.],
            [ 0.,  1., -0.],
            [ 0., -0.,  1.]])
    >>> a = torch.randn(3, 4, 5)
    >>> q, r = torch.qr(a, some=False)
    >>> torch.allclose(torch.matmul(q, r), a)
    True
    >>> torch.allclose(torch.matmul(q.mT, q), torch.eye(5))
    True
""")

add_docstr(torch.rad2deg,
           r"""
rad2deg(input, *, out=None) -> Tensor

Returns a new tensor with each of the elements of :attr:`input`
converted from angles in radians to degrees.

Args:
    {input}

Keyword arguments:
    {out}

Example::

    >>> a = torch.tensor([[3.142, -3.142], [6.283, -6.283], [1.570, -1.570]])
    >>> torch.rad2deg(a)
    tensor([[ 180.0233, -180.0233],
            [ 359.9894, -359.9894],
            [  89.9544,  -89.9544]])

""".format(**common_args))

add_docstr(torch.deg2rad,
           r"""
deg2rad(input, *, out=None) -> Tensor

Returns a new tensor with each of the elements of :attr:`input`
converted from angles in degrees to radians.

Args:
    {input}

Keyword arguments:
    {out}

Example::

    >>> a = torch.tensor([[180.0, -180.0], [360.0, -360.0], [90.0, -90.0]])
    >>> torch.deg2rad(a)
    tensor([[ 3.1416, -3.1416],
            [ 6.2832, -6.2832],
            [ 1.5708, -1.5708]])

""".format(**common_args))

add_docstr(torch.heaviside,
           r"""
heaviside(input, values, *, out=None) -> Tensor

Computes the Heaviside step function for each element in :attr:`input`.
The Heaviside step function is defined as:

.. math::
    \text{{heaviside}}(input, values) = \begin{cases}
        0, & \text{if input < 0}\\
        values, & \text{if input == 0}\\
        1, & \text{if input > 0}
    \end{cases}
""" + r"""

Args:
    {input}
    values (Tensor): The values to use where :attr:`input` is zero.

Keyword arguments:
    {out}

Example::

    >>> input = torch.tensor([-1.5, 0, 2.0])
    >>> values = torch.tensor([0.5])
    >>> torch.heaviside(input, values)
    tensor([0.0000, 0.5000, 1.0000])
    >>> values = torch.tensor([1.2, -2.0, 3.5])
    >>> torch.heaviside(input, values)
    tensor([0., -2., 1.])

""".format(**common_args))

add_docstr(torch.rand,
           r"""
rand(*size, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) -> Tensor

Returns a tensor filled with random numbers from a uniform distribution
on the interval :math:`[0, 1)`

The shape of the tensor is defined by the variable argument :attr:`size`.

Args:
    size (int...): a sequence of integers defining the shape of the output tensor.
        Can be a variable number of arguments or a collection like a list or tuple.

Keyword args:
    {generator}
    {out}
    {dtype}
    {layout}
    {device}
    {requires_grad}

Example::

    >>> torch.rand(4)
    tensor([ 0.5204,  0.2503,  0.3525,  0.5673])
    >>> torch.rand(2, 3)
    tensor([[ 0.8237,  0.5781,  0.6879],
            [ 0.3816,  0.7249,  0.0998]])
""".format(**factory_common_args))

add_docstr(torch.rand_like,
           r"""
rand_like(input, *, dtype=None, layout=None, device=None, requires_grad=False, memory_format=torch.preserve_format) -> Tensor

Returns a tensor with the same size as :attr:`input` that is filled with
random numbers from a uniform distribution on the interval :math:`[0, 1)`.
``torch.rand_like(input)`` is equivalent to
``torch.rand(input.size(), dtype=input.dtype, layout=input.layout, device=input.device)``.

Args:
    {input}

Keyword args:
    {dtype}
    {layout}
    {device}
    {requires_grad}
    {memory_format}

""".format(**factory_like_common_args))

add_docstr(torch.randint,
           """
randint(low=0, high, size, \\*, generator=None, out=None, \
dtype=None, layout=torch.strided, device=None, requires_grad=False) -> Tensor

Returns a tensor filled with random integers generated uniformly
between :attr:`low` (inclusive) and :attr:`high` (exclusive).

The shape of the tensor is defined by the variable argument :attr:`size`.

.. note::
    With the global dtype default (``torch.float32``), this function returns
    a tensor with dtype ``torch.int64``.

Args:
    low (int, optional): Lowest integer to be drawn from the distribution. Default: 0.
    high (int): One above the highest integer to be drawn from the distribution.
    size (tuple): a tuple defining the shape of the output tensor.

Keyword args:
    {generator}
    {out}
    dtype (`torch.dtype`, optional) - the desired data type of returned tensor. Default: if ``None``,
        this function returns a tensor with dtype ``torch.int64``.
    {layout}
    {device}
    {requires_grad}

Example::

    >>> torch.randint(3, 5, (3,))
    tensor([4, 3, 4])


    >>> torch.randint(10, (2, 2))
    tensor([[0, 2],
            [5, 5]])


    >>> torch.randint(3, 10, (2, 2))
    tensor([[4, 5],
            [6, 7]])


""".format(**factory_common_args))

add_docstr(torch.randint_like,
           """
randint_like(input, low=0, high, \\*, dtype=None, layout=torch.strided, device=None, requires_grad=False, \
memory_format=torch.preserve_format) -> Tensor

Returns a tensor with the same shape as Tensor :attr:`input` filled with
random integers generated uniformly between :attr:`low` (inclusive) and
:attr:`high` (exclusive).

.. note:
    With the global dtype default (``torch.float32``), this function returns
    a tensor with dtype ``torch.int64``.

Args:
    {input}
    low (int, optional): Lowest integer to be drawn from the distribution. Default: 0.
    high (int): One above the highest integer to be drawn from the distribution.

Keyword args:
    {dtype}
    {layout}
    {device}
    {requires_grad}
    {memory_format}

""".format(**factory_like_common_args))

add_docstr(torch.randn,
           r"""
randn(*size, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) -> Tensor

Returns a tensor filled with random numbers from a normal distribution
with mean `0` and variance `1` (also called the standard normal
distribution).

.. math::
    \text{{out}}_{{i}} \sim \mathcal{{N}}(0, 1)

The shape of the tensor is defined by the variable argument :attr:`size`.

Args:
    size (int...): a sequence of integers defining the shape of the output tensor.
        Can be a variable number of arguments or a collection like a list or tuple.

Keyword args:
    {generator}
    {out}
    {dtype}
    {layout}
    {device}
    {requires_grad}

Example::

    >>> torch.randn(4)
    tensor([-2.1436,  0.9966,  2.3426, -0.6366])
    >>> torch.randn(2, 3)
    tensor([[ 1.5954,  2.8929, -1.0923],
            [ 1.1719, -0.4709, -0.1996]])
""".format(**factory_common_args))

add_docstr(torch.randn_like,
           r"""
randn_like(input, *, dtype=None, layout=None, device=None, requires_grad=False, memory_format=torch.preserve_format) -> Tensor

Returns a tensor with the same size as :attr:`input` that is filled with
random numbers from a normal distribution with mean 0 and variance 1.
``torch.randn_like(input)`` is equivalent to
``torch.randn(input.size(), dtype=input.dtype, layout=input.layout, device=input.device)``.

Args:
    {input}

Keyword args:
    {dtype}
    {layout}
    {device}
    {requires_grad}
    {memory_format}

""".format(**factory_like_common_args))

add_docstr(torch.randperm,
           """
randperm(n, *, generator=None, out=None, dtype=torch.int64,layout=torch.strided, \
device=None, requires_grad=False, pin_memory=False) -> Tensor
""" + r"""
Returns a random permutation of integers from ``0`` to ``n - 1``.

Args:
    n (int): the upper bound (exclusive)

Keyword args:
    {generator}
    {out}
    dtype (:class:`torch.dtype`, optional): the desired data type of returned tensor.
        Default: ``torch.int64``.
    {layout}
    {device}
    {requires_grad}
    {pin_memory}

Example::

    >>> torch.randperm(4)
    tensor([2, 1, 0, 3])
""".format(**factory_common_args))

add_docstr(torch.tensor,
           r"""
tensor(data, *, dtype=None, device=None, requires_grad=False, pin_memory=False) -> Tensor

Constructs a tensor with no autograd history (also known as a "leaf tensor", see :doc:`/notes/autograd`) by copying :attr:`data`.

.. warning::

    When working with tensors prefer using :func:`torch.Tensor.clone`,
    :func:`torch.Tensor.detach`, and :func:`torch.Tensor.requires_grad_` for
    readability. Letting `t` be a tensor, ``torch.tensor(t)`` is equivalent to
    ``t.clone().detach()``, and ``torch.tensor(t, requires_grad=True)``
    is equivalent to ``t.clone().detach().requires_grad_(True)``.

.. seealso::

    :func:`torch.as_tensor` preserves autograd history and avoids copies where possible.
    :func:`torch.from_numpy` creates a tensor that shares storage with a NumPy array.

Args:
    {data}

Keyword args:
    {dtype}
    device (:class:`torch.device`, optional): the device of the constructed tensor. If None and data is a tensor
        then the device of data is used. If None and data is not a tensor then
        the result tensor is constructed on the CPU.
    {requires_grad}
    {pin_memory}


Example::

    >>> torch.tensor([[0.1, 1.2], [2.2, 3.1], [4.9, 5.2]])
    tensor([[ 0.1000,  1.2000],
            [ 2.2000,  3.1000],
            [ 4.9000,  5.2000]])

    >>> torch.tensor([0, 1])  # Type inference on data
    tensor([ 0,  1])

    >>> torch.tensor([[0.11111, 0.222222, 0.3333333]],
    ...              dtype=torch.float64,
    ...              device=torch.device('cuda:0'))  # creates a double tensor on a CUDA device
    tensor([[ 0.1111,  0.2222,  0.3333]], dtype=torch.float64, device='cuda:0')

    >>> torch.tensor(3.14159)  # Create a zero-dimensional (scalar) tensor
    tensor(3.1416)

    >>> torch.tensor([])  # Create an empty tensor (of size (0,))
    tensor([])
""".format(**factory_data_common_args))

add_docstr(torch.range,
           r"""
range(start=0, end, step=1, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) -> Tensor

Returns a 1-D tensor of size :math:`\left\lfloor \frac{\text{end} - \text{start}}{\text{step}} \right\rfloor + 1`
with values from :attr:`start` to :attr:`end` with step :attr:`step`. Step is
the gap between two values in the tensor.

.. math::
    \text{out}_{i+1} = \text{out}_i + \text{step}.
""" + r"""
.. warning::
    This function is deprecated and will be removed in a future release because its behavior is inconsistent with
    Python's range builtin. Instead, use :func:`torch.arange`, which produces values in [start, end).

Args:
    start (float): the starting value for the set of points. Default: ``0``.
    end (float): the ending value for the set of points
    step (float): the gap between each pair of adjacent points. Default: ``1``.

Keyword args:
    {out}
    {dtype} If `dtype` is not given, infer the data type from the other input
        arguments. If any of `start`, `end`, or `stop` are floating-point, the
        `dtype` is inferred to be the default dtype, see
        :meth:`~torch.get_default_dtype`. Otherwise, the `dtype` is inferred to
        be `torch.int64`.
    {layout}
    {device}
    {requires_grad}

Example::

    >>> torch.range(1, 4)
    tensor([ 1.,  2.,  3.,  4.])
    >>> torch.range(1, 4, 0.5)
    tensor([ 1.0000,  1.5000,  2.0000,  2.5000,  3.0000,  3.5000,  4.0000])
""".format(**factory_common_args))

add_docstr(torch.arange,
           r"""
arange(start=0, end, step=1, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) -> Tensor

Returns a 1-D tensor of size :math:`\left\lceil \frac{\text{end} - \text{start}}{\text{step}} \right\rceil`
with values from the interval ``[start, end)`` taken with common difference
:attr:`step` beginning from `start`.

Note that non-integer :attr:`step` is subject to floating point rounding errors when
comparing against :attr:`end`; to avoid inconsistency, we advise adding a small epsilon to :attr:`end`
in such cases.

.. math::
    \text{out}_{{i+1}} = \text{out}_{i} + \text{step}
""" + r"""
Args:
    start (Number): the starting value for the set of points. Default: ``0``.
    end (Number): the ending value for the set of points
    step (Number): the gap between each pair of adjacent points. Default: ``1``.

Keyword args:
    {out}
    {dtype} If `dtype` is not given, infer the data type from the other input
        arguments. If any of `start`, `end`, or `stop` are floating-point, the
        `dtype` is inferred to be the default dtype, see
        :meth:`~torch.get_default_dtype`. Otherwise, the `dtype` is inferred to
        be `torch.int64`.
    {layout}
    {device}
    {requires_grad}

Example::

    >>> torch.arange(5)
    tensor([ 0,  1,  2,  3,  4])
    >>> torch.arange(1, 4)
    tensor([ 1,  2,  3])
    >>> torch.arange(1, 2.5, 0.5)
    tensor([ 1.0000,  1.5000,  2.0000])
""".format(**factory_common_args))

add_docstr(torch.ravel,
           r"""
ravel(input) -> Tensor

Return a contiguous flattened tensor. A copy is made only if needed.

Args:
    {input}

Example::

    >>> t = torch.tensor([[[1, 2],
    ...                    [3, 4]],
    ...                   [[5, 6],
    ...                    [7, 8]]])
    >>> torch.ravel(t)
    tensor([1, 2, 3, 4, 5, 6, 7, 8])
""".format(**common_args))

add_docstr(torch.remainder,
           r"""
remainder(input, other, *, out=None) -> Tensor

Computes
`Python's modulus operation <https://docs.python.org/3/reference/expressions.html#binary-arithmetic-operations>`_
entrywise.  The result has the same sign as the divisor :attr:`other` and its absolute value
is less than that of :attr:`other`.

It may also be defined in terms of :func:`torch.div` as

.. code:: python

    torch.remainder(a, b) == a - a.div(b, rounding_mode="floor") * b

Supports :ref:`broadcasting to a common shape <broadcasting-semantics>`,
:ref:`type promotion <type-promotion-doc>`, and integer and float inputs.

.. note::
    Complex inputs are not supported. In some cases, it is not mathematically
    possible to satisfy the definition of a modulo operation with complex numbers.
    See :func:`torch.fmod` for how division by zero is handled.

.. seealso::

    :func:`torch.fmod` which implements C++'s `std::fmod <https://en.cppreference.com/w/cpp/numeric/math/fmod>`_.
    This one is defined in terms of division rounding towards zero.

Args:
    input (Tensor or Scalar): the dividend
    other (Tensor or Scalar): the divisor

Keyword args:
    {out}

Example::

    >>> torch.remainder(torch.tensor([-3., -2, -1, 1, 2, 3]), 2)
    tensor([ 1.,  0.,  1.,  1.,  0.,  1.])
    >>> torch.remainder(torch.tensor([1, 2, 3, 4, 5]), -1.5)
    tensor([ -0.5000, -1.0000,  0.0000, -0.5000, -1.0000 ])
""".format(**common_args))

add_docstr(torch.renorm,
           r"""
renorm(input, p, dim, maxnorm, *, out=None) -> Tensor

Returns a tensor where each sub-tensor of :attr:`input` along dimension
:attr:`dim` is normalized such that the `p`-norm of the sub-tensor is lower
than the value :attr:`maxnorm`

.. note:: If the norm of a row is lower than `maxnorm`, the row is unchanged

Args:
    {input}
    p (float): the power for the norm computation
    dim (int): the dimension to slice over to get the sub-tensors
    maxnorm (float): the maximum norm to keep each sub-tensor under

Keyword args:
    {out}

Example::

    >>> x = torch.ones(3, 3)
    >>> x[1].fill_(2)
    tensor([ 2.,  2.,  2.])
    >>> x[2].fill_(3)
    tensor([ 3.,  3.,  3.])
    >>> x
    tensor([[ 1.,  1.,  1.],
            [ 2.,  2.,  2.],
            [ 3.,  3.,  3.]])
    >>> torch.renorm(x, 1, 0, 5)
    tensor([[ 1.0000,  1.0000,  1.0000],
            [ 1.6667,  1.6667,  1.6667],
            [ 1.6667,  1.6667,  1.6667]])
""".format(**common_args))

add_docstr(torch.reshape,
           r"""
reshape(input, shape) -> Tensor

Returns a tensor with the same data and number of elements as :attr:`input`,
but with the specified shape. When possible, the returned tensor will be a view
of :attr:`input`. Otherwise, it will be a copy. Contiguous inputs and inputs
with compatible strides can be reshaped without copying, but you should not
depend on the copying vs. viewing behavior.

See :meth:`torch.Tensor.view` on when it is possible to return a view.

A single dimension may be -1, in which case it's inferred from the remaining
dimensions and the number of elements in :attr:`input`.

Args:
    input (Tensor): the tensor to be reshaped
    shape (tuple of ints): the new shape

Example::

    >>> a = torch.arange(4.)
    >>> torch.reshape(a, (2, 2))
    tensor([[ 0.,  1.],
            [ 2.,  3.]])
    >>> b = torch.tensor([[0, 1], [2, 3]])
    >>> torch.reshape(b, (-1,))
    tensor([ 0,  1,  2,  3])
""")


add_docstr(torch.result_type,
           r"""
result_type(tensor1, tensor2) -> dtype

Returns the :class:`torch.dtype` that would result from performing an arithmetic
operation on the provided input tensors. See type promotion :ref:`documentation <type-promotion-doc>`
for more information on the type promotion logic.

Args:
    tensor1 (Tensor or Number): an input tensor or number
    tensor2 (Tensor or Number): an input tensor or number

Example::

    >>> torch.result_type(torch.tensor([1, 2], dtype=torch.int), 1.0)
    torch.float32
    >>> torch.result_type(torch.tensor([1, 2], dtype=torch.uint8), torch.tensor(1))
    torch.uint8
""")

add_docstr(torch.row_stack,
           r"""
row_stack(tensors, *, out=None) -> Tensor

Alias of :func:`torch.vstack`.
""")

add_docstr(torch.round, r"""
round(input, *, decimals=0, out=None) -> Tensor

Rounds elements of :attr:`input` to the nearest integer.

.. note::
    This function implements the "round half to even" to
    break ties when a number is equidistant from two
    integers (e.g. `round(2.5)` is 2).

    When the :attr:\`decimals\` argument is specified the
    algorithm used is similar to NumPy's `around`. This
    algorithm is fast but inexact and it can easily
    overflow for low precision dtypes.
    Eg. `round(tensor([10000], dtype=torch.float16), decimals=3)` is `inf`.

.. seealso::
    :func:`torch.ceil`, which rounds up.
    :func:`torch.floor`, which rounds down.
    :func:`torch.trunc`, which rounds towards zero.

Args:
    {input}
    decimals (int): 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.

Keyword args:
    {out}

Example::

    >>> torch.round(torch.tensor((4.7, -2.3, 9.1, -7.7)))
    tensor([ 5.,  -2.,  9., -8.])

    >>> # Values equidistant from two integers are rounded towards the
    >>> #   the nearest even value (zero is treated as even)
    >>> torch.round(torch.tensor([-0.5, 0.5, 1.5, 2.5]))
    tensor([-0., 0., 2., 2.])

    >>> # A positive decimals argument rounds to the to that decimal place
    >>> torch.round(torch.tensor([0.1234567]), decimals=3)
    tensor([0.1230])

    >>> # A negative decimals argument rounds to the left of the decimal
    >>> torch.round(torch.tensor([1200.1234567]), decimals=-3)
    tensor([1000.])
""".format(**common_args))

add_docstr(torch.rsqrt,
           r"""
rsqrt(input, *, out=None) -> Tensor

Returns a new tensor with the reciprocal of the square-root of each of
the elements of :attr:`input`.

.. math::
    \text{out}_{i} = \frac{1}{\sqrt{\text{input}_{i}}}
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([-0.0370,  0.2970,  1.5420, -0.9105])
    >>> torch.rsqrt(a)
    tensor([    nan,  1.8351,  0.8053,     nan])
""".format(**common_args))

add_docstr(torch.scatter,
           r"""
scatter(input, dim, index, src) -> Tensor

Out-of-place version of :meth:`torch.Tensor.scatter_`
""")

add_docstr(torch.scatter_add,
           r"""
scatter_add(input, dim, index, src) -> Tensor

Out-of-place version of :meth:`torch.Tensor.scatter_add_`
""")

add_docstr(torch.scatter_reduce, r"""
scatter_reduce(input, dim, index, src, reduce, *, include_self=True) -> Tensor

Reduces all values from the :attr:`input` tensor to the indices specified in
the :attr:`index` tensor. For each value in :attr:`input`, its output index is
specified by its index in :attr:`input` for ``dimension != dim`` and by the
corresponding value in :attr:`index` for ``dimension = dim``.
The applied reduction for non-unique indices is defined via the :attr:`reduce`
argument (:obj:`"sum"`, :obj:`"prod"`, :obj:`"mean"`, :obj:`"amax"`, :obj:`"amin"`).
For non-existing indices, the output will be filled with the identity of the
applied reduction (1 for :obj:`"prod"` and 0 otherwise).

It is also required that ``index.size(d) == input.size(d)`` for all dimensions ``d``.
Moreover, if :attr:`output_size` is defined the the values of :attr:`index` must be
between ``0`` and ``output_size - 1`` inclusive.


For a 3-D tensor with :obj:`reduce="sum"`, the output is given as::

    out[index[i][j][k]][j][k] += input[i][j][k]  # if dim == 0
    out[i][index[i][j][k]][k] += input[i][j][k]  # if dim == 1
    out[i][j][index[i][j][k]] += input[i][j][k]  # if dim == 2

Note:
    This out-of-place operation is similar to the in-place versions of
    :meth:`~torch.Tensor.scatter_` and :meth:`~torch.Tensor.scatter_add_`,
    in which the output tensor is automatically created according to the
    maximum values in :attr:`index` and filled based on the identity of the
    applied reduction.

Note:
    {forward_reproducibility_note}

Args:
    input (Tensor): the input tensor
    dim (int): the axis along which to index
    index (LongTensor): the indices of elements to scatter and reduce.
    src (Tensor): the source elements to scatter and reduce
    reduce (str): the reduction operation to apply for non-unique indices
        (:obj:`"sum"`, :obj:`"prod"`, :obj:`"mean"`, :obj:`"amax"`, :obj:`"amin"`)

Example::

    >>> src = torch.tensor([1, 2, 3, 4, 5, 6])
    >>> index = torch.tensor([0, 1, 0, 1, 2, 1])
    >>> input = torch.zeros(3)
    >>> torch.scatter_reduce(input, 0, index, src, reduce="sum")
    tensor([4, 12, 5])

""".format(**reproducibility_notes))

add_docstr(torch.select,
           r"""
select(input, dim, index) -> Tensor

Slices the :attr:`input` tensor along the selected dimension at the given index.
This function returns a view of the original tensor with the given dimension removed.

Args:
    {input}
    dim (int): the dimension to slice
    index (int): the index to select with

.. note::

    :meth:`select` is equivalent to slicing. For example,
    ``tensor.select(0, index)`` is equivalent to ``tensor[index]`` and
    ``tensor.select(2, index)`` is equivalent to ``tensor[:,:,index]``.
""".format(**common_args))

add_docstr(torch.select_scatter,
           r"""
select_scatter(input, src, dim, index) -> Tensor

Embeds the values of the :attr:`src` tensor into :attr:`input` at the given index.
This function returns a tensor with fresh storage; it does not create a view.


Args:
    {input}
    src (Tensor): The tensor to embed into :attr:`input`
    dim (int): the dimension to insert the slice into.
    index (int): the index to select with

.. note::

    :attr:`src` must be of the proper size in order to be embedded
    into :attr:`input`. Specifically, it should have the same shape as
    ``torch.select(input, dim, index)``

Example::

    >>> a = torch.zeros(2, 2)
    >>> b = torch.ones(2)
    >>> a.select_scatter(b, 0, 0)
    tensor([[1., 1.],
            [0., 0.]])
""".format(**common_args))

add_docstr(torch.slice_scatter,
           r"""
slice_scatter(input, src, dim=0, start=None, end=None, step=1) -> Tensor

Embeds the values of the :attr:`src` tensor into :attr:`input` at the given
dimension.
This function returns a tensor with fresh storage; it does not create a view.


Args:
    {input}
    src (Tensor): The tensor to embed into :attr:`input`
    dim (int): the dimension to insert the slice into
    start (Optional[int]): the start index of where to insert the slice
    end (Optional[int]): the end index of where to insert the slice
    step (int): the how many elements to skip in

Example::

    >>> a = torch.zeros(8, 8)
    >>> b = torch.ones(8)
    >>> a.slice_scatter(b, start=6)
    tensor([[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.],
            [0., 0., 0., 0., 0., 0., 0., 0.],
            [1., 1., 1., 1., 1., 1., 1., 1.],
            [1., 1., 1., 1., 1., 1., 1., 1.]])

    >>> b = torch.ones(2)
    >>> a.slice_scatter(b, dim=1, start=2, end=6, step=2)
    tensor([[0., 0., 1., 0., 1., 0., 0., 0.],
            [0., 0., 1., 0., 1., 0., 0., 0.],
            [0., 0., 1., 0., 1., 0., 0., 0.],
            [0., 0., 1., 0., 1., 0., 0., 0.],
            [0., 0., 1., 0., 1., 0., 0., 0.],
            [0., 0., 1., 0., 1., 0., 0., 0.],
            [0., 0., 1., 0., 1., 0., 0., 0.],
            [0., 0., 1., 0., 1., 0., 0., 0.]])
""".format(**common_args))

add_docstr(torch.set_flush_denormal,
           r"""
set_flush_denormal(mode) -> bool

Disables denormal floating numbers on CPU.

Returns ``True`` if your system supports flushing denormal numbers and it
successfully configures flush denormal mode.  :meth:`~torch.set_flush_denormal`
is only supported on x86 architectures supporting SSE3.

Args:
    mode (bool): Controls whether to enable flush denormal mode or not

Example::

    >>> torch.set_flush_denormal(True)
    True
    >>> torch.tensor([1e-323], dtype=torch.float64)
    tensor([ 0.], dtype=torch.float64)
    >>> torch.set_flush_denormal(False)
    True
    >>> torch.tensor([1e-323], dtype=torch.float64)
    tensor(9.88131e-324 *
           [ 1.0000], dtype=torch.float64)
""")

add_docstr(torch.set_num_threads, r"""
set_num_threads(int)

Sets the number of threads used for intraop parallelism on CPU.

.. warning::
    To ensure that the correct number of threads is used, set_num_threads
    must be called before running eager, JIT or autograd code.
""")

add_docstr(torch.set_num_interop_threads, r"""
set_num_interop_threads(int)

Sets the number of threads used for interop parallelism
(e.g. in JIT interpreter) on CPU.

.. warning::
    Can only be called once and before any inter-op parallel work
    is started (e.g. JIT execution).
""")

add_docstr(torch.sigmoid, r"""
sigmoid(input, *, out=None) -> Tensor

Alias for :func:`torch.special.expit`.
""")

add_docstr(torch.logit,
           r"""
logit(input, eps=None, *, out=None) -> Tensor

Alias for :func:`torch.special.logit`.
""")

add_docstr(torch.sign,
           r"""
sign(input, *, out=None) -> Tensor

Returns a new tensor with the signs of the elements of :attr:`input`.

.. math::
    \text{out}_{i} = \operatorname{sgn}(\text{input}_{i})
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.tensor([0.7, -1.2, 0., 2.3])
    >>> a
    tensor([ 0.7000, -1.2000,  0.0000,  2.3000])
    >>> torch.sign(a)
    tensor([ 1., -1.,  0.,  1.])
""".format(**common_args))

add_docstr(torch.signbit,
           r"""
signbit(input, *, out=None) -> Tensor

Tests if each element of :attr:`input` has its sign bit set (is less than zero) or not.

Args:
  {input}

Keyword args:
  {out}

Example::

    >>> a = torch.tensor([0.7, -1.2, 0., 2.3])
    >>> torch.signbit(a)
    tensor([ False, True,  False,  False])
""".format(**common_args))

add_docstr(torch.sgn,
           r"""
sgn(input, *, out=None) -> Tensor

This function is an extension of torch.sign() to complex tensors.
It computes a new tensor whose elements have
the same angles as the corresponding elements of :attr:`input` and
absolute values (i.e. magnitudes) of one for complex tensors and
is equivalent to torch.sign() for non-complex tensors.

.. math::
    \text{out}_{i} = \begin{cases}
                    0 & |\text{{input}}_i| == 0 \\
                    \frac{{\text{{input}}_i}}{|{\text{{input}}_i}|} & \text{otherwise}
                    \end{cases}

""" + r"""
Args:
    {input}

Keyword args:
  {out}

Example::

    >>> t = torch.tensor([3+4j, 7-24j, 0, 1+2j])
    >>> t.sgn()
    tensor([0.6000+0.8000j, 0.2800-0.9600j, 0.0000+0.0000j, 0.4472+0.8944j])
""".format(**common_args))

add_docstr(torch.sin,
           r"""
sin(input, *, out=None) -> Tensor

Returns a new tensor with the sine of the elements of :attr:`input`.

.. math::
    \text{out}_{i} = \sin(\text{input}_{i})
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([-0.5461,  0.1347, -2.7266, -0.2746])
    >>> torch.sin(a)
    tensor([-0.5194,  0.1343, -0.4032, -0.2711])
""".format(**common_args))

add_docstr(torch.sinc,
           r"""
sinc(input, *, out=None) -> Tensor

Alias for :func:`torch.special.sinc`.
""")

add_docstr(torch.sinh,
           r"""
sinh(input, *, out=None) -> Tensor

Returns a new tensor with the hyperbolic sine of the elements of
:attr:`input`.

.. math::
    \text{out}_{i} = \sinh(\text{input}_{i})
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([ 0.5380, -0.8632, -0.1265,  0.9399])
    >>> torch.sinh(a)
    tensor([ 0.5644, -0.9744, -0.1268,  1.0845])

.. note::
   When :attr:`input` is on the CPU, the implementation of torch.sinh may use
   the Sleef library, which rounds very large results to infinity or negative
   infinity. See `here <https://sleef.org/purec.xhtml>`_ for details.
""".format(**common_args))

add_docstr(torch.sort,
           r"""
sort(input, dim=-1, descending=False, stable=False, *, out=None) -> (Tensor, LongTensor)

Sorts the elements of the :attr:`input` tensor along a given dimension
in ascending order by value.

If :attr:`dim` is not given, the last dimension of the `input` is chosen.

If :attr:`descending` is ``True`` then the elements are sorted in descending
order by value.

If :attr:`stable` is ``True`` then the sorting routine becomes stable, preserving
the order of equivalent elements.

A namedtuple of (values, indices) is returned, where the `values` are the
sorted values and `indices` are the indices of the elements in the original
`input` tensor.

Args:
    {input}
    dim (int, optional): the dimension to sort along
    descending (bool, optional): controls the sorting order (ascending or descending)
    stable (bool, optional): makes the sorting routine stable, which guarantees that the order
       of equivalent elements is preserved.

Keyword args:
    out (tuple, optional): the output tuple of (`Tensor`, `LongTensor`) that can
        be optionally given to be used as output buffers

Example::

    >>> x = torch.randn(3, 4)
    >>> sorted, indices = torch.sort(x)
    >>> sorted
    tensor([[-0.2162,  0.0608,  0.6719,  2.3332],
            [-0.5793,  0.0061,  0.6058,  0.9497],
            [-0.5071,  0.3343,  0.9553,  1.0960]])
    >>> indices
    tensor([[ 1,  0,  2,  3],
            [ 3,  1,  0,  2],
            [ 0,  3,  1,  2]])

    >>> sorted, indices = torch.sort(x, 0)
    >>> sorted
    tensor([[-0.5071, -0.2162,  0.6719, -0.5793],
            [ 0.0608,  0.0061,  0.9497,  0.3343],
            [ 0.6058,  0.9553,  1.0960,  2.3332]])
    >>> indices
    tensor([[ 2,  0,  0,  1],
            [ 0,  1,  1,  2],
            [ 1,  2,  2,  0]])
    >>> x = torch.tensor([0, 1] * 9)
    >>> x.sort()
    torch.return_types.sort(
        values=tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]),
        indices=tensor([ 2, 16,  4,  6, 14,  8,  0, 10, 12,  9, 17, 15, 13, 11,  7,  5,  3,  1]))
    >>> x.sort(stable=True)
    torch.return_types.sort(
        values=tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]),
        indices=tensor([ 0,  2,  4,  6,  8, 10, 12, 14, 16,  1,  3,  5,  7,  9, 11, 13, 15, 17]))
""".format(**common_args))

add_docstr(torch.argsort,
           r"""
argsort(input, dim=-1, descending=False) -> LongTensor

Returns the indices that sort a tensor along a given dimension in ascending
order by value.

This is the second value returned by :meth:`torch.sort`.  See its documentation
for the exact semantics of this method.

Args:
    {input}
    dim (int, optional): the dimension to sort along
    descending (bool, optional): controls the sorting order (ascending or descending)

Example::

    >>> a = torch.randn(4, 4)
    >>> a
    tensor([[ 0.0785,  1.5267, -0.8521,  0.4065],
            [ 0.1598,  0.0788, -0.0745, -1.2700],
            [ 1.2208,  1.0722, -0.7064,  1.2564],
            [ 0.0669, -0.2318, -0.8229, -0.9280]])


    >>> torch.argsort(a, dim=1)
    tensor([[2, 0, 3, 1],
            [3, 2, 1, 0],
            [2, 1, 0, 3],
            [3, 2, 1, 0]])
""".format(**common_args))

add_docstr(torch.msort,
           r"""
msort(input, *, out=None) -> Tensor

Sorts the elements of the :attr:`input` tensor along its first dimension
in ascending order by value.

.. note:: `torch.msort(t)` is equivalent to `torch.sort(t, dim=0)[0]`.
          See also :func:`torch.sort`.

Args:
    {input}

Keyword args:
    {out}

Example::

    >>> t = torch.randn(3, 4)
    >>> t
    tensor([[-0.1321,  0.4370, -1.2631, -1.1289],
            [-2.0527, -1.1250,  0.2275,  0.3077],
            [-0.0881, -0.1259, -0.5495,  1.0284]])
    >>> torch.msort(t)
    tensor([[-2.0527, -1.1250, -1.2631, -1.1289],
            [-0.1321, -0.1259, -0.5495,  0.3077],
            [-0.0881,  0.4370,  0.2275,  1.0284]])
""".format(**common_args))

add_docstr(torch.sparse_csr_tensor,
           r"""
sparse_csr_tensor(crow_indices, col_indices, values, size=None, *, dtype=None, device=None, requires_grad=False) -> Tensor

Constructs a :ref:`sparse tensor in CSR (Compressed Sparse Row) <sparse-csr-docs>` with specified
values at the given :attr:`crow_indices` and :attr:`col_indices`. Sparse matrix multiplication operations
in CSR format are typically faster than that for sparse tensors in COO format. Make you have a look
at :ref:`the note on the data type of the indices <sparse-csr-docs>`.

Args:
    crow_indices (array_like): One-dimensional array of size size[0] + 1. The last element
        is the number of non-zeros. This tensor encodes the index in values and col_indices
        depending on where the given row starts. Each successive number in the tensor
        subtracted by the number before it denotes the number of elements in a given row.
    col_indices (array_like): Column co-ordinates of each element in values. Strictly one
        dimensional tensor with the same length as values.
    values (array_list): Initial values for the tensor. Can be a list, tuple, NumPy ``ndarray``, scalar,
        and other types.
    size (list, tuple, :class:`torch.Size`, optional): Size of the sparse tensor. If not provided, the
        size will be inferred as the minimum size big enough to hold all non-zero elements.

Keyword args:
    dtype (:class:`torch.dtype`, optional): the desired data type of returned tensor.
        Default: if None, infers data type from :attr:`values`.
    device (:class:`torch.device`, optional): the desired device of returned tensor.
        Default: if None, uses the current device for the default tensor type
        (see :func:`torch.set_default_tensor_type`). :attr:`device` will be the CPU
        for CPU tensor types and the current CUDA device for CUDA tensor types.
    {requires_grad}

Example ::
    >>> crow_indices = [0, 2, 4]
    >>> col_indices = [0, 1, 0, 1]
    >>> values = [1, 2, 3, 4]
    >>> torch.sparse_csr_tensor(torch.tensor(crow_indices, dtype=torch.int64),
    ...                         torch.tensor(col_indices, dtype=torch.int64),
    ...                         torch.tensor(values), dtype=torch.double)
    tensor(crow_indices=tensor([0, 2, 4]),
           col_indices=tensor([0, 1, 0, 1]),
           values=tensor([1., 2., 3., 4.]), size=(2, 2), nnz=4,
           dtype=torch.float64, layout=torch.sparse_csr)
""".format(**factory_common_args))

add_docstr(torch.sparse_coo_tensor,
           r"""
sparse_coo_tensor(indices, values, size=None, *, dtype=None, device=None, requires_grad=False) -> Tensor

Constructs a :ref:`sparse tensor in COO(rdinate) format
<sparse-coo-docs>` with specified values at the given
:attr:`indices`.

.. note::

   This function returns an :ref:`uncoalesced tensor <sparse-uncoalesced-coo-docs>`.

Args:
    indices (array_like): Initial data for the tensor. Can be a list, tuple,
        NumPy ``ndarray``, scalar, and other types. Will be cast to a :class:`torch.LongTensor`
        internally. The indices are the coordinates of the non-zero values in the matrix, and thus
        should be two-dimensional where the first dimension is the number of tensor dimensions and
        the second dimension is the number of non-zero values.
    values (array_like): Initial values for the tensor. Can be a list, tuple,
        NumPy ``ndarray``, scalar, and other types.
    size (list, tuple, or :class:`torch.Size`, optional): Size of the sparse tensor. If not
        provided the size will be inferred as the minimum size big enough to hold all non-zero
        elements.

Keyword args:
    dtype (:class:`torch.dtype`, optional): the desired data type of returned tensor.
        Default: if None, infers data type from :attr:`values`.
    device (:class:`torch.device`, optional): the desired device of returned tensor.
        Default: if None, uses the current device for the default tensor type
        (see :func:`torch.set_default_tensor_type`). :attr:`device` will be the CPU
        for CPU tensor types and the current CUDA device for CUDA tensor types.
    {requires_grad}


Example::

    >>> i = torch.tensor([[0, 1, 1],
    ...                   [2, 0, 2]])
    >>> v = torch.tensor([3, 4, 5], dtype=torch.float32)
    >>> torch.sparse_coo_tensor(i, v, [2, 4])
    tensor(indices=tensor([[0, 1, 1],
                           [2, 0, 2]]),
           values=tensor([3., 4., 5.]),
           size=(2, 4), nnz=3, layout=torch.sparse_coo)

    >>> torch.sparse_coo_tensor(i, v)  # Shape inference
    tensor(indices=tensor([[0, 1, 1],
                           [2, 0, 2]]),
           values=tensor([3., 4., 5.]),
           size=(2, 3), nnz=3, layout=torch.sparse_coo)

    >>> torch.sparse_coo_tensor(i, v, [2, 4],
    ...                         dtype=torch.float64,
    ...                         device=torch.device('cuda:0'))
    tensor(indices=tensor([[0, 1, 1],
                           [2, 0, 2]]),
           values=tensor([3., 4., 5.]),
           device='cuda:0', size=(2, 4), nnz=3, dtype=torch.float64,
           layout=torch.sparse_coo)

    # Create an empty sparse tensor with the following invariants:
    #   1. sparse_dim + dense_dim = len(SparseTensor.shape)
    #   2. SparseTensor._indices().shape = (sparse_dim, nnz)
    #   3. SparseTensor._values().shape = (nnz, SparseTensor.shape[sparse_dim:])
    #
    # For instance, to create an empty sparse tensor with nnz = 0, dense_dim = 0 and
    # sparse_dim = 1 (hence indices is a 2D tensor of shape = (1, 0))
    >>> S = torch.sparse_coo_tensor(torch.empty([1, 0]), [], [1])
    tensor(indices=tensor([], size=(1, 0)),
           values=tensor([], size=(0,)),
           size=(1,), nnz=0, layout=torch.sparse_coo)

    # and to create an empty sparse tensor with nnz = 0, dense_dim = 1 and
    # sparse_dim = 1
    >>> S = torch.sparse_coo_tensor(torch.empty([1, 0]), torch.empty([0, 2]), [1, 2])
    tensor(indices=tensor([], size=(1, 0)),
           values=tensor([], size=(0, 2)),
           size=(1, 2), nnz=0, layout=torch.sparse_coo)

.. _torch.sparse: https://pytorch.org/docs/stable/sparse.html
""".format(**factory_common_args))

add_docstr(torch.sqrt,
           r"""
sqrt(input, *, out=None) -> Tensor

Returns a new tensor with the square-root of the elements of :attr:`input`.

.. math::
    \text{out}_{i} = \sqrt{\text{input}_{i}}
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([-2.0755,  1.0226,  0.0831,  0.4806])
    >>> torch.sqrt(a)
    tensor([    nan,  1.0112,  0.2883,  0.6933])
""".format(**common_args))

add_docstr(torch.square,
           r"""
square(input, *, out=None) -> Tensor

Returns a new tensor with the square of the elements of :attr:`input`.

Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([-2.0755,  1.0226,  0.0831,  0.4806])
    >>> torch.square(a)
    tensor([ 4.3077,  1.0457,  0.0069,  0.2310])
""".format(**common_args))

add_docstr(torch.squeeze,
           r"""
squeeze(input, dim=None, *, out=None) -> Tensor

Returns a tensor with all the dimensions of :attr:`input` of size `1` removed.

For example, if `input` is of shape:
:math:`(A \times 1 \times B \times C \times 1 \times D)` then the `out` tensor
will be of shape: :math:`(A \times B \times C \times D)`.

When :attr:`dim` is given, a squeeze operation is done only in the given
dimension. If `input` is of shape: :math:`(A \times 1 \times B)`,
``squeeze(input, 0)`` leaves the tensor unchanged, but ``squeeze(input, 1)``
will squeeze the tensor to the shape :math:`(A \times B)`.

.. note:: The returned tensor shares the storage with the input tensor,
          so changing the contents of one will change the contents of the other.

.. warning:: If the tensor has a batch dimension of size 1, then `squeeze(input)`
          will also remove the batch dimension, which can lead to unexpected
          errors.

Args:
    {input}
    dim (int, optional): if given, the input will be squeezed only in
           this dimension

Keyword args:
    {out}

Example::

    >>> x = torch.zeros(2, 1, 2, 1, 2)
    >>> x.size()
    torch.Size([2, 1, 2, 1, 2])
    >>> y = torch.squeeze(x)
    >>> y.size()
    torch.Size([2, 2, 2])
    >>> y = torch.squeeze(x, 0)
    >>> y.size()
    torch.Size([2, 1, 2, 1, 2])
    >>> y = torch.squeeze(x, 1)
    >>> y.size()
    torch.Size([2, 2, 1, 2])
""".format(**common_args))

add_docstr(torch.std, r"""
std(input, dim, unbiased, keepdim=False, *, out=None) -> Tensor

If :attr:`unbiased` is ``True``, Bessel's correction will be used.
Otherwise, the sample deviation is calculated, without any correction.

Args:
    {input}
    {dim}

Keyword args:
    unbiased (bool): whether to use Bessel's correction (:math:`\delta N = 1`).
    {keepdim}
    {out}


.. function:: std(input, unbiased) -> Tensor
   :noindex:

Calculates the standard deviation of all elements in the :attr:`input` tensor.

If :attr:`unbiased` is ``True``, Bessel's correction will be used.
Otherwise, the sample deviation is calculated, without any correction.

Args:
    {input}
    unbiased (bool): whether to use Bessel's correction (:math:`\delta N = 1`).

Example::

    >>> a = torch.tensor([[-0.8166, -1.3802, -0.3560]])
    >>> torch.std(a, unbiased=False)
    tensor(0.4188)
""".format(**multi_dim_common))

add_docstr(torch.std_mean,
           r"""
std_mean(input, dim, unbiased, keepdim=False, *, out=None) -> (Tensor, Tensor)

If :attr:`unbiased` is ``True``, Bessel's correction will be used to calculate
the standard deviation. Otherwise, the sample deviation is calculated, without
any correction.

Args:
    {input}
    {dim}

Keyword args:
    unbiased (bool): whether to use Bessel's correction (:math:`\delta N = 1`).
    {keepdim}
    {out}

Returns:
    A tuple (std, mean) containing the standard deviation and mean.

.. function:: std_mean(input, unbiased) -> (Tensor, Tensor)
   :noindex:

Calculates the standard deviation and mean of all elements in the :attr:`input`
tensor.

If :attr:`unbiased` is ``True``, Bessel's correction will be used.
Otherwise, the sample deviation is calculated, without any correction.

Args:
    {input}
    unbiased (bool): whether to use Bessel's correction (:math:`\delta N = 1`).

Returns:
    A tuple (std, mean) containing the standard deviation and mean.

Example::

    >>> a = torch.tensor([[-0.8166, -1.3802, -0.3560]])
    >>> torch.std_mean(a, unbiased=False)
    (tensor(0.4188), tensor(-0.8509))
""".format(**multi_dim_common))

add_docstr(torch.sub, r"""
sub(input, other, *, alpha=1, out=None) -> Tensor

Subtracts :attr:`other`, scaled by :attr:`alpha`, from :attr:`input`.

.. math::
    \text{{out}}_i = \text{{input}}_i - \text{{alpha}} \times \text{{other}}_i
""" + r"""

Supports :ref:`broadcasting to a common shape <broadcasting-semantics>`,
:ref:`type promotion <type-promotion-doc>`, and integer, float, and complex inputs.

Args:
    {input}
    other (Tensor or Number): the tensor or number to subtract from :attr:`input`.

Keyword args:
    alpha (Number): the multiplier for :attr:`other`.
    {out}

Example::

    >>> a = torch.tensor((1, 2))
    >>> b = torch.tensor((0, 1))
    >>> torch.sub(a, b, alpha=2)
    tensor([1, 0])
""".format(**common_args))

add_docstr(torch.subtract, r"""
subtract(input, other, *, alpha=1, out=None) -> Tensor

Alias for :func:`torch.sub`.
""")

add_docstr(torch.sum,
           r"""
sum(input, *, dtype=None) -> Tensor

Returns the sum of all elements in the :attr:`input` tensor.

Args:
    {input}

Keyword args:
    {dtype}

Example::

    >>> a = torch.randn(1, 3)
    >>> a
    tensor([[ 0.1133, -0.9567,  0.2958]])
    >>> torch.sum(a)
    tensor(-0.5475)

.. function:: sum(input, dim, keepdim=False, *, dtype=None) -> Tensor
   :noindex:

Returns the sum of each row of the :attr:`input` tensor in the given
dimension :attr:`dim`. If :attr:`dim` is a list of dimensions,
reduce over all of them.

{keepdim_details}

Args:
    {input}
    {dim}
    {keepdim}

Keyword args:
    {dtype}

Example::

    >>> a = torch.randn(4, 4)
    >>> a
    tensor([[ 0.0569, -0.2475,  0.0737, -0.3429],
            [-0.2993,  0.9138,  0.9337, -1.6864],
            [ 0.1132,  0.7892, -0.1003,  0.5688],
            [ 0.3637, -0.9906, -0.4752, -1.5197]])
    >>> torch.sum(a, 1)
    tensor([-0.4598, -0.1381,  1.3708, -2.6217])
    >>> b = torch.arange(4 * 5 * 6).view(4, 5, 6)
    >>> torch.sum(b, (2, 1))
    tensor([  435.,  1335.,  2235.,  3135.])
""".format(**multi_dim_common))

add_docstr(torch.nansum,
           r"""
nansum(input, *, dtype=None) -> Tensor

Returns the sum of all elements, treating Not a Numbers (NaNs) as zero.

Args:
    {input}

Keyword args:
    {dtype}

Example::

    >>> a = torch.tensor([1., 2., float('nan'), 4.])
    >>> torch.nansum(a)
    tensor(7.)

.. function:: nansum(input, dim, keepdim=False, *, dtype=None) -> Tensor
   :noindex:

Returns the sum of each row of the :attr:`input` tensor in the given
dimension :attr:`dim`, treating Not a Numbers (NaNs) as zero.
If :attr:`dim` is a list of dimensions, reduce over all of them.

{keepdim_details}

Args:
    {input}
    {dim}
    {keepdim}

Keyword args:
    {dtype}

Example::

    >>> torch.nansum(torch.tensor([1., float("nan")]))
    1.0
    >>> a = torch.tensor([[1, 2], [3., float("nan")]])
    >>> torch.nansum(a)
    tensor(6.)
    >>> torch.nansum(a, dim=0)
    tensor([4., 2.])
    >>> torch.nansum(a, dim=1)
    tensor([3., 3.])
""".format(**multi_dim_common))

add_docstr(torch.svd,
           r"""
svd(input, some=True, compute_uv=True, *, out=None) -> (Tensor, Tensor, Tensor)

Computes the singular value decomposition of either a matrix or batch of
matrices :attr:`input`. The singular value decomposition is represented as a
namedtuple `(U, S, V)`, such that :attr:`input` :math:`= U \text{diag}(S) V^{\text{H}}`.
where :math:`V^{\text{H}}` is the transpose of `V` for real inputs,
and the conjugate transpose of `V` for complex inputs.
If :attr:`input` is a batch of matrices, then `U`, `S`, and `V` are also
batched with the same batch dimensions as :attr:`input`.

If :attr:`some` is `True` (default), the method returns the reduced singular
value decomposition. In this case, if the last two dimensions of :attr:`input` are
`m` and `n`, then the returned `U` and `V` matrices will contain only
`min(n, m)` orthonormal columns.

If :attr:`compute_uv` is `False`, the returned `U` and `V` will be
zero-filled matrices of shape `(m, m)` and `(n, n)`
respectively, and the same device as :attr:`input`. The argument :attr:`some`
has no effect when :attr:`compute_uv` is `False`.

Supports :attr:`input` of float, double, cfloat and cdouble data types.
The dtypes of `U` and `V` are the same as :attr:`input`'s. `S` will
always be real-valued, even if :attr:`input` is complex.

.. warning::

    :func:`torch.svd` is deprecated in favor of :func:`torch.linalg.svd`
    and will be removed in a future PyTorch release.

    ``U, S, V = torch.svd(A, some=some, compute_uv=True)`` (default) should be replaced with

    .. code:: python

        U, S, Vh = torch.linalg.svd(A, full_matrices=not some)
        V = Vh.mH

    ``_, S, _ = torch.svd(A, some=some, compute_uv=False)`` should be replaced with

    .. code:: python

        S = torch.linalg.svdvals(A)

.. note:: Differences with :func:`torch.linalg.svd`:

             * :attr:`some` is the opposite of
               :func:`torch.linalg.svd`'s :attr:`full_matrices`. Note that
               default value for both is `True`, so the default behavior is
               effectively the opposite.
             * :func:`torch.svd` returns `V`, whereas :func:`torch.linalg.svd` returns
               `Vh`, that is, :math:`V^{\text{H}}`.
             * If :attr:`compute_uv` is `False`, :func:`torch.svd` returns zero-filled
               tensors for `U` and `Vh`, whereas :func:`torch.linalg.svd` returns
               empty tensors.

.. note:: The singular values are returned in descending order. If :attr:`input` is a batch of matrices,
          then the singular values of each matrix in the batch are returned in descending order.

.. note:: The `S` tensor can only be used to compute gradients if :attr:`compute_uv` is `True`.

.. note:: When :attr:`some` is `False`, the gradients on `U[..., :, min(m, n):]`
          and `V[..., :, min(m, n):]` will be ignored in the backward pass, as those vectors
          can be arbitrary bases of the corresponding subspaces.

.. note:: The implementation of :func:`torch.linalg.svd` on CPU uses LAPACK's routine `?gesdd`
          (a divide-and-conquer algorithm) instead of `?gesvd` for speed. Analogously,
          on GPU, it uses cuSOLVER's routines `gesvdj` and `gesvdjBatched` on CUDA 10.1.243
          and later, and MAGMA's routine `gesdd` on earlier versions of CUDA.

.. note:: The returned `U` will not be contiguous. The matrix (or batch of matrices) will
          be represented as a column-major matrix (i.e. Fortran-contiguous).

.. warning:: The gradients with respect to `U` and `V` will only be finite when the input does not
             have zero nor repeated singular values.

.. warning:: If the distance between any two singular values is close to zero, the gradients with respect to
             `U` and `V` will be numerically unstable, as they depends on
             :math:`\frac{1}{\min_{i \neq j} \sigma_i^2 - \sigma_j^2}`. The same happens when the matrix
             has small singular values, as these gradients also depend on `S⁻¹`.

.. warning:: For complex-valued :attr:`input` the singular value decomposition is not unique,
             as `U` and `V` may be multiplied by an arbitrary phase factor :math:`e^{i \phi}` on every column.
             The same happens when :attr:`input` has repeated singular values, where one may multiply
             the columns of the spanning subspace in `U` and `V` by a rotation matrix
             and `the resulting vectors will span the same subspace`_.
             Different platforms, like NumPy, or inputs on different device types,
             may produce different `U` and `V` tensors.

Args:
    input (Tensor): the input tensor of size `(*, m, n)` where `*` is zero or more
                    batch dimensions consisting of `(m, n)` matrices.
    some (bool, optional): controls whether to compute the reduced or full decomposition, and
                           consequently, the shape of returned `U` and `V`. Default: `True`.
    compute_uv (bool, optional): controls whether to compute `U` and `V`. Default: `True`.

Keyword args:
    out (tuple, optional): the output tuple of tensors

Example::

    >>> a = torch.randn(5, 3)
    >>> a
    tensor([[ 0.2364, -0.7752,  0.6372],
            [ 1.7201,  0.7394, -0.0504],
            [-0.3371, -1.0584,  0.5296],
            [ 0.3550, -0.4022,  1.5569],
            [ 0.2445, -0.0158,  1.1414]])
    >>> u, s, v = torch.svd(a)
    >>> u
    tensor([[ 0.4027,  0.0287,  0.5434],
            [-0.1946,  0.8833,  0.3679],
            [ 0.4296, -0.2890,  0.5261],
            [ 0.6604,  0.2717, -0.2618],
            [ 0.4234,  0.2481, -0.4733]])
    >>> s
    tensor([2.3289, 2.0315, 0.7806])
    >>> v
    tensor([[-0.0199,  0.8766,  0.4809],
            [-0.5080,  0.4054, -0.7600],
            [ 0.8611,  0.2594, -0.4373]])
    >>> torch.dist(a, torch.mm(torch.mm(u, torch.diag(s)), v.t()))
    tensor(8.6531e-07)
    >>> a_big = torch.randn(7, 5, 3)
    >>> u, s, v = torch.svd(a_big)
    >>> torch.dist(a_big, torch.matmul(torch.matmul(u, torch.diag_embed(s)), v.mT))
    tensor(2.6503e-06)

.. _the resulting vectors will span the same subspace:
       (https://en.wikipedia.org/wiki/Singular_value_decomposition#Singular_values,_singular_vectors,_and_their_relation_to_the_SVD)
""")

add_docstr(torch.symeig, r"""
symeig(input, eigenvectors=False, upper=True, *, out=None) -> (Tensor, Tensor)

This function returns eigenvalues and eigenvectors
of a real symmetric or complex Hermitian matrix :attr:`input` or a batch thereof,
represented by a namedtuple (eigenvalues, eigenvectors).

This function calculates all eigenvalues (and vectors) of :attr:`input`
such that :math:`\text{input} = V \text{diag}(e) V^T`.

The boolean argument :attr:`eigenvectors` defines computation of
both eigenvectors and eigenvalues or eigenvalues only.

If it is ``False``, only eigenvalues are computed. If it is ``True``,
both eigenvalues and eigenvectors are computed.

Since the input matrix :attr:`input` is supposed to be symmetric or Hermitian,
only the upper triangular portion is used by default.

If :attr:`upper` is ``False``, then lower triangular portion is used.

.. warning::

    :func:`torch.symeig` is deprecated in favor of :func:`torch.linalg.eigh`
    and will be removed in a future PyTorch release. The default behavior has changed
    from using the upper triangular portion of the matrix by default to using the
    lower triangular portion.

    ``L, _ = torch.symeig(A, upper=upper)`` should be replaced with

    .. code :: python

        UPLO = "U" if upper else "L"
        L = torch.linalg.eigvalsh(A, UPLO=UPLO)

    ``L, V = torch.symeig(A, eigenvectors=True, upper=upper)`` should be replaced with

    .. code :: python

        UPLO = "U" if upper else "L"
        L, V = torch.linalg.eigh(A, UPLO=UPLO)

.. note:: The eigenvalues are returned in ascending order. If :attr:`input` is a batch of matrices,
          then the eigenvalues of each matrix in the batch is returned in ascending order.

.. note:: Irrespective of the original strides, the returned matrix `V` will
          be transposed, i.e. with strides `V.contiguous().mT.stride()`.

.. warning:: Extra care needs to be taken when backward through outputs. Such
             operation is only stable when all eigenvalues are distinct and becomes
             less stable the smaller :math:`\min_{i \neq j} |\lambda_i - \lambda_j|` is.

Args:
    input (Tensor): the input tensor of size :math:`(*, n, n)` where `*` is zero or more
                    batch dimensions consisting of symmetric or Hermitian matrices.
    eigenvectors(bool, optional): controls whether eigenvectors have to be computed
    upper(boolean, optional): controls whether to consider upper-triangular or lower-triangular region

Keyword args:
    out (tuple, optional): the output tuple of (Tensor, Tensor)

Returns:
    (Tensor, Tensor): A namedtuple (eigenvalues, eigenvectors) containing

        - **eigenvalues** (*Tensor*): Shape :math:`(*, m)`. The eigenvalues in ascending order.
        - **eigenvectors** (*Tensor*): Shape :math:`(*, m, m)`.
          If ``eigenvectors=False``, it's an empty tensor.
          Otherwise, this tensor contains the orthonormal eigenvectors of the ``input``.

Examples::


    >>> a = torch.randn(5, 5)
    >>> a = a + a.t()  # To make a symmetric
    >>> a
    tensor([[-5.7827,  4.4559, -0.2344, -1.7123, -1.8330],
            [ 4.4559,  1.4250, -2.8636, -3.2100, -0.1798],
            [-0.2344, -2.8636,  1.7112, -5.5785,  7.1988],
            [-1.7123, -3.2100, -5.5785, -2.6227,  3.1036],
            [-1.8330, -0.1798,  7.1988,  3.1036, -5.1453]])
    >>> e, v = torch.symeig(a, eigenvectors=True)
    >>> e
    tensor([-13.7012,  -7.7497,  -2.3163,   5.2477,   8.1050])
    >>> v
    tensor([[ 0.1643,  0.9034, -0.0291,  0.3508,  0.1817],
            [-0.2417, -0.3071, -0.5081,  0.6534,  0.4026],
            [-0.5176,  0.1223, -0.0220,  0.3295, -0.7798],
            [-0.4850,  0.2695, -0.5773, -0.5840,  0.1337],
            [ 0.6415, -0.0447, -0.6381, -0.0193, -0.4230]])
    >>> a_big = torch.randn(5, 2, 2)
    >>> a_big = a_big + a_big.mT  # To make a_big symmetric
    >>> e, v = a_big.symeig(eigenvectors=True)
    >>> torch.allclose(torch.matmul(v, torch.matmul(e.diag_embed(), v.mT)), a_big)
    True
""")

add_docstr(torch.t,
           r"""
t(input) -> Tensor

Expects :attr:`input` to be <= 2-D tensor and transposes dimensions 0
and 1.

0-D and 1-D tensors are returned as is. When input is a 2-D tensor this
is equivalent to ``transpose(input, 0, 1)``.

Args:
    {input}

Example::

    >>> x = torch.randn(())
    >>> x
    tensor(0.1995)
    >>> torch.t(x)
    tensor(0.1995)
    >>> x = torch.randn(3)
    >>> x
    tensor([ 2.4320, -0.4608,  0.7702])
    >>> torch.t(x)
    tensor([ 2.4320, -0.4608,  0.7702])
    >>> x = torch.randn(2, 3)
    >>> x
    tensor([[ 0.4875,  0.9158, -0.5872],
            [ 0.3938, -0.6929,  0.6932]])
    >>> torch.t(x)
    tensor([[ 0.4875,  0.3938],
            [ 0.9158, -0.6929],
            [-0.5872,  0.6932]])

See also :func:`torch.transpose`.
""".format(**common_args))

add_docstr(torch.flip,
           r"""
flip(input, dims) -> Tensor

Reverse the order of a n-D tensor along given axis in dims.

.. note::
    `torch.flip` makes a copy of :attr:`input`'s data. This is different from NumPy's `np.flip`,
    which returns a view in constant time. Since copying a tensor's data is more work than viewing that data,
    `torch.flip` is expected to be slower than `np.flip`.

Args:
    {input}
    dims (a list or tuple): axis to flip on

Example::

    >>> x = torch.arange(8).view(2, 2, 2)
    >>> x
    tensor([[[ 0,  1],
             [ 2,  3]],

            [[ 4,  5],
             [ 6,  7]]])
    >>> torch.flip(x, [0, 1])
    tensor([[[ 6,  7],
             [ 4,  5]],

            [[ 2,  3],
             [ 0,  1]]])
""".format(**common_args))

add_docstr(torch.fliplr,
           r"""
fliplr(input) -> Tensor

Flip tensor in the left/right direction, returning a new tensor.

Flip the entries in each row in the left/right direction.
Columns are preserved, but appear in a different order than before.

Note:
    Requires the tensor to be at least 2-D.

.. note::
    `torch.fliplr` makes a copy of :attr:`input`'s data. This is different from NumPy's `np.fliplr`,
    which returns a view in constant time. Since copying a tensor's data is more work than viewing that data,
    `torch.fliplr` is expected to be slower than `np.fliplr`.

Args:
    input (Tensor): Must be at least 2-dimensional.

Example::

    >>> x = torch.arange(4).view(2, 2)
    >>> x
    tensor([[0, 1],
            [2, 3]])
    >>> torch.fliplr(x)
    tensor([[1, 0],
            [3, 2]])
""".format(**common_args))

add_docstr(torch.flipud,
           r"""
flipud(input) -> Tensor

Flip tensor in the up/down direction, returning a new tensor.

Flip the entries in each column in the up/down direction.
Rows are preserved, but appear in a different order than before.

Note:
    Requires the tensor to be at least 1-D.

.. note::
    `torch.flipud` makes a copy of :attr:`input`'s data. This is different from NumPy's `np.flipud`,
    which returns a view in constant time. Since copying a tensor's data is more work than viewing that data,
    `torch.flipud` is expected to be slower than `np.flipud`.

Args:
    input (Tensor): Must be at least 1-dimensional.

Example::

    >>> x = torch.arange(4).view(2, 2)
    >>> x
    tensor([[0, 1],
            [2, 3]])
    >>> torch.flipud(x)
    tensor([[2, 3],
            [0, 1]])
""".format(**common_args))

add_docstr(torch.roll,
           r"""
roll(input, shifts, dims=None) -> Tensor

Roll the tensor :attr:`input` along the given dimension(s). Elements that are
shifted beyond the last position are re-introduced at the first position. If
:attr:`dims` is `None`, the tensor will be flattened before rolling and then
restored to the original shape.

Args:
    {input}
    shifts (int or tuple of ints): The number of places by which the elements
        of the tensor are shifted. If shifts is a tuple, dims must be a tuple of
        the same size, and each dimension will be rolled by the corresponding
        value
    dims (int or tuple of ints): Axis along which to roll

Example::

    >>> x = torch.tensor([1, 2, 3, 4, 5, 6, 7, 8]).view(4, 2)
    >>> x
    tensor([[1, 2],
            [3, 4],
            [5, 6],
            [7, 8]])
    >>> torch.roll(x, 1)
    tensor([[8, 1],
            [2, 3],
            [4, 5],
            [6, 7]])
    >>> torch.roll(x, 1, 0)
    tensor([[7, 8],
            [1, 2],
            [3, 4],
            [5, 6]])
    >>> torch.roll(x, -1, 0)
    tensor([[3, 4],
            [5, 6],
            [7, 8],
            [1, 2]])
    >>> torch.roll(x, shifts=(2, 1), dims=(0, 1))
    tensor([[6, 5],
            [8, 7],
            [2, 1],
            [4, 3]])
""".format(**common_args))

add_docstr(torch.rot90,
           r"""
rot90(input, k, dims) -> Tensor

Rotate a n-D tensor by 90 degrees in the plane specified by dims axis.
Rotation direction is from the first towards the second axis if k > 0, and from the second towards the first for k < 0.

Args:
    {input}
    k (int): number of times to rotate
    dims (a list or tuple): axis to rotate

Example::

    >>> x = torch.arange(4).view(2, 2)
    >>> x
    tensor([[0, 1],
            [2, 3]])
    >>> torch.rot90(x, 1, [0, 1])
    tensor([[1, 3],
            [0, 2]])

    >>> x = torch.arange(8).view(2, 2, 2)
    >>> x
    tensor([[[0, 1],
             [2, 3]],

            [[4, 5],
             [6, 7]]])
    >>> torch.rot90(x, 1, [1, 2])
    tensor([[[1, 3],
             [0, 2]],

            [[5, 7],
             [4, 6]]])
""".format(**common_args))

add_docstr(torch.take,
           r"""
take(input, index) -> Tensor

Returns a new tensor with the elements of :attr:`input` at the given indices.
The input tensor is treated as if it were viewed as a 1-D tensor. The result
takes the same shape as the indices.

Args:
    {input}
    index (LongTensor): the indices into tensor

Example::

    >>> src = torch.tensor([[4, 3, 5],
    ...                     [6, 7, 8]])
    >>> torch.take(src, torch.tensor([0, 2, 5]))
    tensor([ 4,  5,  8])
""".format(**common_args))

add_docstr(torch.take_along_dim,
           r"""
take_along_dim(input, indices, dim, *, out=None) -> Tensor

Selects values from :attr:`input` at the 1-dimensional indices from :attr:`indices` along the given :attr:`dim`.

Functions that return indices along a dimension, like :func:`torch.argmax` and :func:`torch.argsort`,
are designed to work with this function. See the examples below.

.. note::
    This function is similar to NumPy's `take_along_axis`.
    See also :func:`torch.gather`.

Args:
    {input}
    indices (tensor): the indices into :attr:`input`. Must have long dtype.
    dim (int): dimension to select along.

Keyword args:
    {out}

Example::

    >>> t = torch.tensor([[10, 30, 20], [60, 40, 50]])
    >>> max_idx = torch.argmax(t)
    >>> torch.take_along_dim(t, max_idx)
    tensor([60])
    >>> sorted_idx = torch.argsort(t, dim=1)
    >>> torch.take_along_dim(t, sorted_idx, dim=1)
    tensor([[10, 20, 30],
            [40, 50, 60]])
""".format(**common_args))

add_docstr(torch.tan,
           r"""
tan(input, *, out=None) -> Tensor

Returns a new tensor with the tangent of the elements of :attr:`input`.

.. math::
    \text{out}_{i} = \tan(\text{input}_{i})
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([-1.2027, -1.7687,  0.4412, -1.3856])
    >>> torch.tan(a)
    tensor([-2.5930,  4.9859,  0.4722, -5.3366])
""".format(**common_args))

add_docstr(torch.tanh,
           r"""
tanh(input, *, out=None) -> Tensor

Returns a new tensor with the hyperbolic tangent of the elements
of :attr:`input`.

.. math::
    \text{out}_{i} = \tanh(\text{input}_{i})
""" + r"""
Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([ 0.8986, -0.7279,  1.1745,  0.2611])
    >>> torch.tanh(a)
    tensor([ 0.7156, -0.6218,  0.8257,  0.2553])
""".format(**common_args))

add_docstr(torch.topk,
           r"""
topk(input, k, dim=None, largest=True, sorted=True, *, out=None) -> (Tensor, LongTensor)

Returns the :attr:`k` largest elements of the given :attr:`input` tensor along
a given dimension.

If :attr:`dim` is not given, the last dimension of the `input` is chosen.

If :attr:`largest` is ``False`` then the `k` smallest elements are returned.

A namedtuple of `(values, indices)` is returned with the `values` and
`indices` of the largest `k` elements of each row of the `input` tensor in the
given dimension `dim`.

The boolean option :attr:`sorted` if ``True``, will make sure that the returned
`k` elements are themselves sorted

Args:
    {input}
    k (int): the k in "top-k"
    dim (int, optional): the dimension to sort along
    largest (bool, optional): controls whether to return largest or
           smallest elements
    sorted (bool, optional): controls whether to return the elements
           in sorted order

Keyword args:
    out (tuple, optional): the output tuple of (Tensor, LongTensor) that can be
        optionally given to be used as output buffers

Example::

    >>> x = torch.arange(1., 6.)
    >>> x
    tensor([ 1.,  2.,  3.,  4.,  5.])
    >>> torch.topk(x, 3)
    torch.return_types.topk(values=tensor([5., 4., 3.]), indices=tensor([4, 3, 2]))
""".format(**common_args))

add_docstr(torch.trace,
           r"""
trace(input) -> Tensor

Returns the sum of the elements of the diagonal of the input 2-D matrix.

Example::

    >>> x = torch.arange(1., 10.).view(3, 3)
    >>> x
    tensor([[ 1.,  2.,  3.],
            [ 4.,  5.,  6.],
            [ 7.,  8.,  9.]])
    >>> torch.trace(x)
    tensor(15.)
""")

add_docstr(torch.transpose,
           r"""
transpose(input, dim0, dim1) -> Tensor

Returns a tensor that is a transposed version of :attr:`input`.
The given dimensions :attr:`dim0` and :attr:`dim1` are swapped.

If :attr:`input` is a strided tensor then the resulting :attr:`out`
tensor shares its underlying storage with the :attr:`input` tensor, so
changing the content of one would change the content of the other.

If :attr:`input` is a :ref:`sparse tensor <sparse-docs>` then the
resulting :attr:`out` tensor *does not* share the underlying storage
with the :attr:`input` tensor.

Args:
    {input}
    dim0 (int): the first dimension to be transposed
    dim1 (int): the second dimension to be transposed

Example::

    >>> x = torch.randn(2, 3)
    >>> x
    tensor([[ 1.0028, -0.9893,  0.5809],
            [-0.1669,  0.7299,  0.4942]])
    >>> torch.transpose(x, 0, 1)
    tensor([[ 1.0028, -0.1669],
            [-0.9893,  0.7299],
            [ 0.5809,  0.4942]])

See also :func:`torch.t`.
""".format(**common_args))

add_docstr(torch.triangular_solve,
           r"""
triangular_solve(b, A, upper=True, transpose=False, unitriangular=False, *, out=None) -> (Tensor, Tensor)

Solves a system of equations with a square upper or lower triangular invertible matrix :math:`A`
and multiple right-hand sides :math:`b`.

In symbols, it solves :math:`AX = b` and assumes :math:`A` is square upper-triangular
(or lower-triangular if :attr:`upper`\ `= False`) and does not have zeros on the diagonal.

`torch.triangular_solve(b, A)` can take in 2D inputs `b, A` or inputs that are
batches of 2D matrices. If the inputs are batches, then returns
batched outputs `X`

If the diagonal of :attr:`A` contains zeros or elements that are very close to zero and
:attr:`unitriangular`\ `= False` (default) or if the input matrix is badly conditioned,
the result may contain `NaN` s.

Supports input of float, double, cfloat and cdouble data types.

.. warning::

    :func:`torch.triangular_solve` is deprecated in favor of :func:`torch.linalg.solve_triangular`
    and will be removed in a future PyTorch release.
    :func:`torch.linalg.solve_triangular` has its arguments reversed and does not return a
    copy of one of the inputs.

    ``X = torch.triangular_solve(B, A).solution`` should be replaced with

    .. code:: python

        X = torch.linalg.solve_triangular(A, B)

Args:
    b (Tensor): multiple right-hand sides of size :math:`(*, m, k)` where
                :math:`*` is zero of more batch dimensions
    A (Tensor): the input triangular coefficient matrix of size :math:`(*, m, m)`
                where :math:`*` is zero or more batch dimensions
    upper (bool, optional): whether :math:`A` is upper or lower triangular. Default: ``True``.
    transpose (bool, optional): solves `op(A)X = b` where `op(A) = A^T` if this flag is ``True``,
                                and `op(A) = A` if it is ``False``. Default: ``False``.
    unitriangular (bool, optional): whether :math:`A` is unit triangular.
        If True, the diagonal elements of :math:`A` are assumed to be
        1 and not referenced from :math:`A`. Default: ``False``.

Keyword args:
    out ((Tensor, Tensor), optional): tuple of two tensors to write
        the output to. Ignored if `None`. Default: `None`.

Returns:
    A namedtuple `(solution, cloned_coefficient)` where `cloned_coefficient`
    is a clone of :math:`A` and `solution` is the solution :math:`X` to :math:`AX = b`
    (or whatever variant of the system of equations, depending on the keyword arguments.)

Examples::

    >>> A = torch.randn(2, 2).triu()
    >>> A
    tensor([[ 1.1527, -1.0753],
            [ 0.0000,  0.7986]])
    >>> b = torch.randn(2, 3)
    >>> b
    tensor([[-0.0210,  2.3513, -1.5492],
            [ 1.5429,  0.7403, -1.0243]])
    >>> torch.triangular_solve(b, A)
    torch.return_types.triangular_solve(
    solution=tensor([[ 1.7841,  2.9046, -2.5405],
            [ 1.9320,  0.9270, -1.2826]]),
    cloned_coefficient=tensor([[ 1.1527, -1.0753],
            [ 0.0000,  0.7986]]))
""")

add_docstr(torch.tril,
           r"""
tril(input, diagonal=0, *, out=None) -> Tensor

Returns the lower triangular part of the matrix (2-D tensor) or batch of matrices
:attr:`input`, the other elements of the result tensor :attr:`out` are set to 0.

The lower triangular part of the matrix is defined as the elements on and
below the diagonal.

The argument :attr:`diagonal` controls which diagonal to consider. If
:attr:`diagonal` = 0, all elements on and below the main diagonal are
retained. A positive value includes just as many diagonals above the main
diagonal, and similarly a negative value excludes just as many diagonals below
the main diagonal. The main diagonal are the set of indices
:math:`\lbrace (i, i) \rbrace` for :math:`i \in [0, \min\{d_{1}, d_{2}\} - 1]` where
:math:`d_{1}, d_{2}` are the dimensions of the matrix.
""" + r"""
Args:
    {input}
    diagonal (int, optional): the diagonal to consider

Keyword args:
    {out}

Example::

    >>> a = torch.randn(3, 3)
    >>> a
    tensor([[-1.0813, -0.8619,  0.7105],
            [ 0.0935,  0.1380,  2.2112],
            [-0.3409, -0.9828,  0.0289]])
    >>> torch.tril(a)
    tensor([[-1.0813,  0.0000,  0.0000],
            [ 0.0935,  0.1380,  0.0000],
            [-0.3409, -0.9828,  0.0289]])

    >>> b = torch.randn(4, 6)
    >>> b
    tensor([[ 1.2219,  0.5653, -0.2521, -0.2345,  1.2544,  0.3461],
            [ 0.4785, -0.4477,  0.6049,  0.6368,  0.8775,  0.7145],
            [ 1.1502,  3.2716, -1.1243, -0.5413,  0.3615,  0.6864],
            [-0.0614, -0.7344, -1.3164, -0.7648, -1.4024,  0.0978]])
    >>> torch.tril(b, diagonal=1)
    tensor([[ 1.2219,  0.5653,  0.0000,  0.0000,  0.0000,  0.0000],
            [ 0.4785, -0.4477,  0.6049,  0.0000,  0.0000,  0.0000],
            [ 1.1502,  3.2716, -1.1243, -0.5413,  0.0000,  0.0000],
            [-0.0614, -0.7344, -1.3164, -0.7648, -1.4024,  0.0000]])
    >>> torch.tril(b, diagonal=-1)
    tensor([[ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000],
            [ 0.4785,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000],
            [ 1.1502,  3.2716,  0.0000,  0.0000,  0.0000,  0.0000],
            [-0.0614, -0.7344, -1.3164,  0.0000,  0.0000,  0.0000]])
""".format(**common_args))

# docstr is split in two parts to avoid format mis-captureing :math: braces '{}'
# as common args.
add_docstr(torch.tril_indices,
           r"""
tril_indices(row, col, offset=0, *, dtype=torch.long, device='cpu', layout=torch.strided) -> Tensor

Returns the indices of the lower triangular part of a :attr:`row`-by-
:attr:`col` matrix in a 2-by-N Tensor, where the first row contains row
coordinates of all indices and the second row contains column coordinates.
Indices are ordered based on rows and then columns.

The lower triangular part of the matrix is defined as the elements on and
below the diagonal.

The argument :attr:`offset` controls which diagonal to consider. If
:attr:`offset` = 0, all elements on and below the main diagonal are
retained. A positive value includes just as many diagonals above the main
diagonal, and similarly a negative value excludes just as many diagonals below
the main diagonal. The main diagonal are the set of indices
:math:`\lbrace (i, i) \rbrace` for :math:`i \in [0, \min\{d_{1}, d_{2}\} - 1]`
where :math:`d_{1}, d_{2}` are the dimensions of the matrix.

.. note::
    When running on CUDA, ``row * col`` must be less than :math:`2^{59}` to
    prevent overflow during calculation.
""" + r"""
Args:
    row (``int``): number of rows in the 2-D matrix.
    col (``int``): number of columns in the 2-D matrix.
    offset (``int``): diagonal offset from the main diagonal.
        Default: if not provided, 0.

Keyword args:
    dtype (:class:`torch.dtype`, optional): the desired data type of returned tensor.
        Default: if ``None``, ``torch.long``.
    {device}
    layout (:class:`torch.layout`, optional): currently only support ``torch.strided``.

Example::

    >>> a = torch.tril_indices(3, 3)
    >>> a
    tensor([[0, 1, 1, 2, 2, 2],
            [0, 0, 1, 0, 1, 2]])

    >>> a = torch.tril_indices(4, 3, -1)
    >>> a
    tensor([[1, 2, 2, 3, 3, 3],
            [0, 0, 1, 0, 1, 2]])

    >>> a = torch.tril_indices(4, 3, 1)
    >>> a
    tensor([[0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3],
            [0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 2]])
""".format(**factory_common_args))

add_docstr(torch.triu,
           r"""
triu(input, diagonal=0, *, out=None) -> Tensor

Returns the upper triangular part of a matrix (2-D tensor) or batch of matrices
:attr:`input`, the other elements of the result tensor :attr:`out` are set to 0.

The upper triangular part of the matrix is defined as the elements on and
above the diagonal.

The argument :attr:`diagonal` controls which diagonal to consider. If
:attr:`diagonal` = 0, all elements on and above the main diagonal are
retained. A positive value excludes just as many diagonals above the main
diagonal, and similarly a negative value includes just as many diagonals below
the main diagonal. The main diagonal are the set of indices
:math:`\lbrace (i, i) \rbrace` for :math:`i \in [0, \min\{d_{1}, d_{2}\} - 1]` where
:math:`d_{1}, d_{2}` are the dimensions of the matrix.
""" + r"""
Args:
    {input}
    diagonal (int, optional): the diagonal to consider

Keyword args:
    {out}

Example::

    >>> a = torch.randn(3, 3)
    >>> a
    tensor([[ 0.2309,  0.5207,  2.0049],
            [ 0.2072, -1.0680,  0.6602],
            [ 0.3480, -0.5211, -0.4573]])
    >>> torch.triu(a)
    tensor([[ 0.2309,  0.5207,  2.0049],
            [ 0.0000, -1.0680,  0.6602],
            [ 0.0000,  0.0000, -0.4573]])
    >>> torch.triu(a, diagonal=1)
    tensor([[ 0.0000,  0.5207,  2.0049],
            [ 0.0000,  0.0000,  0.6602],
            [ 0.0000,  0.0000,  0.0000]])
    >>> torch.triu(a, diagonal=-1)
    tensor([[ 0.2309,  0.5207,  2.0049],
            [ 0.2072, -1.0680,  0.6602],
            [ 0.0000, -0.5211, -0.4573]])

    >>> b = torch.randn(4, 6)
    >>> b
    tensor([[ 0.5876, -0.0794, -1.8373,  0.6654,  0.2604,  1.5235],
            [-0.2447,  0.9556, -1.2919,  1.3378, -0.1768, -1.0857],
            [ 0.4333,  0.3146,  0.6576, -1.0432,  0.9348, -0.4410],
            [-0.9888,  1.0679, -1.3337, -1.6556,  0.4798,  0.2830]])
    >>> torch.triu(b, diagonal=1)
    tensor([[ 0.0000, -0.0794, -1.8373,  0.6654,  0.2604,  1.5235],
            [ 0.0000,  0.0000, -1.2919,  1.3378, -0.1768, -1.0857],
            [ 0.0000,  0.0000,  0.0000, -1.0432,  0.9348, -0.4410],
            [ 0.0000,  0.0000,  0.0000,  0.0000,  0.4798,  0.2830]])
    >>> torch.triu(b, diagonal=-1)
    tensor([[ 0.5876, -0.0794, -1.8373,  0.6654,  0.2604,  1.5235],
            [-0.2447,  0.9556, -1.2919,  1.3378, -0.1768, -1.0857],
            [ 0.0000,  0.3146,  0.6576, -1.0432,  0.9348, -0.4410],
            [ 0.0000,  0.0000, -1.3337, -1.6556,  0.4798,  0.2830]])
""".format(**common_args))

# docstr is split in two parts to avoid format mis-capturing :math: braces '{}'
# as common args.
add_docstr(torch.triu_indices,
           r"""
triu_indices(row, col, offset=0, *, dtype=torch.long, device='cpu', layout=torch.strided) -> Tensor

Returns the indices of the upper triangular part of a :attr:`row` by
:attr:`col` matrix in a 2-by-N Tensor, where the first row contains row
coordinates of all indices and the second row contains column coordinates.
Indices are ordered based on rows and then columns.

The upper triangular part of the matrix is defined as the elements on and
above the diagonal.

The argument :attr:`offset` controls which diagonal to consider. If
:attr:`offset` = 0, all elements on and above the main diagonal are
retained. A positive value excludes just as many diagonals above the main
diagonal, and similarly a negative value includes just as many diagonals below
the main diagonal. The main diagonal are the set of indices
:math:`\lbrace (i, i) \rbrace` for :math:`i \in [0, \min\{d_{1}, d_{2}\} - 1]`
where :math:`d_{1}, d_{2}` are the dimensions of the matrix.

.. note::
    When running on CUDA, ``row * col`` must be less than :math:`2^{59}` to
    prevent overflow during calculation.
""" + r"""
Args:
    row (``int``): number of rows in the 2-D matrix.
    col (``int``): number of columns in the 2-D matrix.
    offset (``int``): diagonal offset from the main diagonal.
        Default: if not provided, 0.

Keyword args:
    dtype (:class:`torch.dtype`, optional): the desired data type of returned tensor.
        Default: if ``None``, ``torch.long``.
    {device}
    layout (:class:`torch.layout`, optional): currently only support ``torch.strided``.

Example::

    >>> a = torch.triu_indices(3, 3)
    >>> a
    tensor([[0, 0, 0, 1, 1, 2],
            [0, 1, 2, 1, 2, 2]])

    >>> a = torch.triu_indices(4, 3, -1)
    >>> a
    tensor([[0, 0, 0, 1, 1, 1, 2, 2, 3],
            [0, 1, 2, 0, 1, 2, 1, 2, 2]])

    >>> a = torch.triu_indices(4, 3, 1)
    >>> a
    tensor([[0, 0, 1],
            [1, 2, 2]])
""".format(**factory_common_args))

add_docstr(torch.true_divide, r"""
true_divide(dividend, divisor, *, out) -> Tensor

Alias for :func:`torch.div` with ``rounding_mode=None``.
""")

add_docstr(torch.trunc,
           r"""
trunc(input, *, out=None) -> Tensor

Returns a new tensor with the truncated integer values of
the elements of :attr:`input`.

Args:
    {input}

Keyword args:
    {out}

Example::

    >>> a = torch.randn(4)
    >>> a
    tensor([ 3.4742,  0.5466, -0.8008, -0.9079])
    >>> torch.trunc(a)
    tensor([ 3.,  0., -0., -0.])
""".format(**common_args))

add_docstr(torch.fake_quantize_per_tensor_affine,
           r"""
fake_quantize_per_tensor_affine(input, scale, zero_point, quant_min, quant_max) -> Tensor

Returns a new tensor with the data in :attr:`input` fake quantized using :attr:`scale`,
:attr:`zero_point`, :attr:`quant_min` and :attr:`quant_max`.

.. math::
    \text{output} = min(
        \text{quant\_max},
        max(
            \text{quant\_min},
            \text{std::nearby\_int}(\text{input} / \text{scale}) + \text{zero\_point}
        )
    )

Args:
    input (Tensor): the input value(s), in ``torch.float32``.
    scale (double or Tensor): quantization scale
    zero_point (int64 or Tensor): quantization zero_point
    quant_min (int64): lower bound of the quantized domain
    quant_max (int64): upper bound of the quantized domain

Returns:
    Tensor: A newly fake_quantized tensor

Example::

    >>> x = torch.randn(4)
    >>> x
    tensor([ 0.0552,  0.9730,  0.3973, -1.0780])
    >>> torch.fake_quantize_per_tensor_affine(x, 0.1, 0, 0, 255)
    tensor([0.1000, 1.0000, 0.4000, 0.0000])
    >>> torch.fake_quantize_per_tensor_affine(x, torch.tensor(0.1), torch.tensor(0), 0, 255)
    tensor([0.6000, 0.4000, 0.0000, 0.0000])
""")

add_docstr(torch.fake_quantize_per_channel_affine,
           r"""
fake_quantize_per_channel_affine(input, scale, zero_point, quant_min, quant_max) -> Tensor

Returns a new tensor with the data in :attr:`input` fake quantized per channel using :attr:`scale`,
:attr:`zero_point`, :attr:`quant_min` and :attr:`quant_max`, across the channel specified by :attr:`axis`.

.. math::
    \text{output} = min(
        \text{quant\_max},
        max(
            \text{quant\_min},
            \text{std::nearby\_int}(\text{input} / \text{scale}) + \text{zero\_point}
        )
    )

Args:
    input (Tensor): the input value(s), in ``torch.float32``.
    scale (Tensor): quantization scale, per channel
    zero_point (Tensor): quantization zero_point, per channel
    axis (int32): channel axis
    quant_min (int64): lower bound of the quantized domain
    quant_max (int64): upper bound of the quantized domain

Returns:
    Tensor: A newly fake_quantized per channel tensor

Example::

    >>> x = torch.randn(2, 2, 2)
    >>> x
    tensor([[[-0.2525, -0.0466],
             [ 0.3491, -0.2168]],

            [[-0.5906,  1.6258],
             [ 0.6444, -0.0542]]])
    >>> scales = (torch.randn(2) + 1) * 0.05
    >>> scales
    tensor([0.0475, 0.0486])
    >>> zero_points = torch.zeros(2).to(torch.long)
    >>> zero_points
    tensor([0, 0])
    >>> torch.fake_quantize_per_channel_affine(x, scales, zero_points, 1, 0, 255)
    tensor([[[0.0000, 0.0000],
             [0.3405, 0.0000]],

            [[0.0000, 1.6134],
            [0.6323, 0.0000]]])
""")

add_docstr(torch.fix,
           r"""
fix(input, *, out=None) -> Tensor

Alias for :func:`torch.trunc`
""")

add_docstr(torch.unsqueeze,
           r"""
unsqueeze(input, dim) -> Tensor

Returns a new tensor with a dimension of size one inserted at the
specified position.

The returned tensor shares the same underlying data with this tensor.

A :attr:`dim` value within the range ``[-input.dim() - 1, input.dim() + 1)``
can be used. Negative :attr:`dim` will correspond to :meth:`unsqueeze`
applied at :attr:`dim` = ``dim + input.dim() + 1``.

Args:
    {input}
    dim (int): the index at which to insert the singleton dimension

Example::

    >>> x = torch.tensor([1, 2, 3, 4])
    >>> torch.unsqueeze(x, 0)
    tensor([[ 1,  2,  3,  4]])
    >>> torch.unsqueeze(x, 1)
    tensor([[ 1],
            [ 2],
            [ 3],
            [ 4]])
""".format(**common_args))

add_docstr(torch.var, r"""
var(input, dim, unbiased, keepdim=False, *, out=None) -> Tensor

If :attr:`unbiased` is ``True``, Bessel's correction will be used.
Otherwise, the sample variance is calculated, without any correction.

Args:
    {input}
    {dim}

Keyword args:
    unbiased (bool): whether to use Bessel's correction (:math:`\delta N = 1`).
    {keepdim}
    {out}

.. function:: var(input, unbiased) -> Tensor
   :noindex:

Calculates the variance of all elements in the :attr:`input` tensor.

If :attr:`unbiased` is ``True``, Bessel's correction will be used.
Otherwise, the sample deviation is calculated, without any correction.

Args:
    {input}
    unbiased (bool): whether to use Bessel's correction (:math:`\delta N = 1`).

Example::

    >>> a = torch.tensor([[-0.8166, -1.3802, -0.3560]])
    >>> torch.var(a, unbiased=False)
    tensor(0.1754)
""".format(**multi_dim_common))

add_docstr(torch.var_mean,
           r"""
var_mean(input, dim, unbiased, keepdim=False, *, out=None) -> (Tensor, Tensor)

If :attr:`unbiased` is ``True``, Bessel's correction will be used to calculate
the variance. Otherwise, the sample variance is calculated, without any
correction.

Args:
    {input}
    {dim}

Keyword args:
    unbiased (bool): whether to use Bessel's correction (:math:`\delta N = 1`).
    {keepdim}
    {out}

Returns:
    A tuple (var, mean) containing the variance and mean.

.. function:: var_mean(input, unbiased) -> (Tensor, Tensor)
   :noindex:

Calculates the variance and mean of all elements in the :attr:`input`
tensor.

If :attr:`unbiased` is ``True``, Bessel's correction will be used.
Otherwise, the sample deviation is calculated, without any correction.

Args:
    {input}
    unbiased (bool): whether to use Bessel's correction (:math:`\delta N = 1`).

Returns:
    A tuple (var, mean) containing the variance and mean.

Example::

    >>> a = torch.tensor([[-0.8166, -1.3802, -0.3560]])
    >>> torch.var_mean(a, unbiased=False)
    (tensor(0.1754), tensor(-0.8509))
""".format(**multi_dim_common))

add_docstr(torch.zeros,
           r"""
zeros(*size, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) -> Tensor

Returns a tensor filled with the scalar value `0`, with the shape defined
by the variable argument :attr:`size`.

Args:
    size (int...): a sequence of integers defining the shape of the output tensor.
        Can be a variable number of arguments or a collection like a list or tuple.

Keyword args:
    {out}
    {dtype}
    {layout}
    {device}
    {requires_grad}

Example::

    >>> torch.zeros(2, 3)
    tensor([[ 0.,  0.,  0.],
            [ 0.,  0.,  0.]])

    >>> torch.zeros(5)
    tensor([ 0.,  0.,  0.,  0.,  0.])
""".format(**factory_common_args))

add_docstr(torch.zeros_like,
           r"""
zeros_like(input, *, dtype=None, layout=None, device=None, requires_grad=False, memory_format=torch.preserve_format) -> Tensor

Returns a tensor filled with the scalar value `0`, with the same size as
:attr:`input`. ``torch.zeros_like(input)`` is equivalent to
``torch.zeros(input.size(), dtype=input.dtype, layout=input.layout, device=input.device)``.

.. warning::
    As of 0.4, this function does not support an :attr:`out` keyword. As an alternative,
    the old ``torch.zeros_like(input, out=output)`` is equivalent to
    ``torch.zeros(input.size(), out=output)``.

Args:
    {input}

Keyword args:
    {dtype}
    {layout}
    {device}
    {requires_grad}
    {memory_format}

Example::

    >>> input = torch.empty(2, 3)
    >>> torch.zeros_like(input)
    tensor([[ 0.,  0.,  0.],
            [ 0.,  0.,  0.]])
""".format(**factory_like_common_args))

add_docstr(torch.empty,
           """
empty(*size, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False, pin_memory=False, \
memory_format=torch.contiguous_format) -> Tensor

Returns a tensor filled with uninitialized data. The shape of the tensor is
defined by the variable argument :attr:`size`.

Args:
    size (int...): a sequence of integers defining the shape of the output tensor.
        Can be a variable number of arguments or a collection like a list or tuple.

Keyword args:
    {out}
    {dtype}
    {layout}
    {device}
    {requires_grad}
    {pin_memory}
    {memory_format}

Example::

    >>> torch.empty((2,3), dtype=torch.int64)
    tensor([[ 9.4064e+13,  2.8000e+01,  9.3493e+13],
            [ 7.5751e+18,  7.1428e+18,  7.5955e+18]])
""".format(**factory_common_args))

add_docstr(torch.empty_like,
           r"""
empty_like(input, *, dtype=None, layout=None, device=None, requires_grad=False, memory_format=torch.preserve_format) -> Tensor

Returns an uninitialized tensor with the same size as :attr:`input`.
``torch.empty_like(input)`` is equivalent to
``torch.empty(input.size(), dtype=input.dtype, layout=input.layout, device=input.device)``.

Args:
    {input}

Keyword args:
    {dtype}
    {layout}
    {device}
    {requires_grad}
    {memory_format}

Example::

    >>> a=torch.empty((2,3), dtype=torch.int32, device = 'cuda')
    >>> torch.empty_like(a)
    tensor([[0, 0, 0],
            [0, 0, 0]], device='cuda:0', dtype=torch.int32)
""".format(**factory_like_common_args))

add_docstr(torch.empty_strided,
           r"""
empty_strided(size, stride, *, dtype=None, layout=None, device=None, requires_grad=False, pin_memory=False) -> Tensor

Creates a tensor with the specified :attr:`size` and :attr:`stride` and filled with undefined data.

.. warning::
    If the constructed tensor is "overlapped" (with multiple indices referring to the same element
    in memory) its behavior is undefined.

Args:
    size (tuple of ints): the shape of the output tensor
    stride (tuple of ints): the strides of the output tensor

Keyword args:
    {dtype}
    {layout}
    {device}
    {requires_grad}
    {pin_memory}

Example::

    >>> a = torch.empty_strided((2, 3), (1, 2))
    >>> a
    tensor([[8.9683e-44, 4.4842e-44, 5.1239e+07],
            [0.0000e+00, 0.0000e+00, 3.0705e-41]])
    >>> a.stride()
    (1, 2)
    >>> a.size()
    torch.Size([2, 3])
""".format(**factory_common_args))

add_docstr(torch.full, r"""
full(size, fill_value, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) -> Tensor

Creates a tensor of size :attr:`size` filled with :attr:`fill_value`. The
tensor's dtype is inferred from :attr:`fill_value`.

Args:
    size (int...): a list, tuple, or :class:`torch.Size` of integers defining the
        shape of the output tensor.
    fill_value (Scalar): the value to fill the output tensor with.

Keyword args:
    {out}
    {dtype}
    {layout}
    {device}
    {requires_grad}

Example::

    >>> torch.full((2, 3), 3.141592)
    tensor([[ 3.1416,  3.1416,  3.1416],
            [ 3.1416,  3.1416,  3.1416]])
""".format(**factory_common_args))

add_docstr(torch.full_like,
           """
full_like(input, fill_value, \\*, dtype=None, layout=torch.strided, device=None, requires_grad=False, \
memory_format=torch.preserve_format) -> Tensor

Returns a tensor with the same size as :attr:`input` filled with :attr:`fill_value`.
``torch.full_like(input, fill_value)`` is equivalent to
``torch.full(input.size(), fill_value, dtype=input.dtype, layout=input.layout, device=input.device)``.

Args:
    {input}
    fill_value: the number to fill the output tensor with.

Keyword args:
    {dtype}
    {layout}
    {device}
    {requires_grad}
    {memory_format}
""".format(**factory_like_common_args))

add_docstr(torch.det, r"""
det(input) -> Tensor

Alias for :func:`torch.linalg.det`
""")

add_docstr(torch.where,
           r"""
where(condition, x, y) -> Tensor

Return a tensor of elements selected from either :attr:`x` or :attr:`y`, depending on :attr:`condition`.

The operation is defined as:

.. math::
    \text{out}_i = \begin{cases}
        \text{x}_i & \text{if } \text{condition}_i \\
        \text{y}_i & \text{otherwise} \\
    \end{cases}

.. note::
    The tensors :attr:`condition`, :attr:`x`, :attr:`y` must be :ref:`broadcastable <broadcasting-semantics>`.

.. note::
    Currently valid scalar and tensor combination are
    1. Scalar of floating dtype and torch.double
    2. Scalar of integral dtype and torch.long
    3. Scalar of complex dtype and torch.complex128

Arguments:
    condition (BoolTensor): When True (nonzero), yield x, otherwise yield y
    x (Tensor or Scalar): value (if :attr:`x` is a scalar) or values selected at indices
                          where :attr:`condition` is ``True``
    y (Tensor or Scalar): value (if :attr:`y` is a scalar) or values selected at indices
                          where :attr:`condition` is ``False``

Returns:
    Tensor: A tensor of shape equal to the broadcasted shape of :attr:`condition`, :attr:`x`, :attr:`y`

Example::

    >>> x = torch.randn(3, 2)
    >>> y = torch.ones(3, 2)
    >>> x
    tensor([[-0.4620,  0.3139],
            [ 0.3898, -0.7197],
            [ 0.0478, -0.1657]])
    >>> torch.where(x > 0, x, y)
    tensor([[ 1.0000,  0.3139],
            [ 0.3898,  1.0000],
            [ 0.0478,  1.0000]])
    >>> x = torch.randn(2, 2, dtype=torch.double)
    >>> x
    tensor([[ 1.0779,  0.0383],
            [-0.8785, -1.1089]], dtype=torch.float64)
    >>> torch.where(x > 0, x, 0.)
    tensor([[1.0779, 0.0383],
            [0.0000, 0.0000]], dtype=torch.float64)

.. function:: where(condition) -> tuple of LongTensor
   :noindex:

``torch.where(condition)`` is identical to
``torch.nonzero(condition, as_tuple=True)``.

.. note::
    See also :func:`torch.nonzero`.
""")

add_docstr(torch.logdet,
           r"""
logdet(input) -> Tensor

Calculates log determinant of a square matrix or batches of square matrices.

.. note::
    Result is ``-inf`` if :attr:`input` has zero log determinant, and is ``nan`` if
    :attr:`input` has negative determinant.

.. note::
    Backward through :meth:`logdet` internally uses SVD results when :attr:`input`
    is not invertible. In this case, double backward through :meth:`logdet` will
    be unstable in when :attr:`input` doesn't have distinct singular values. See
    :func:`torch.linalg.svd` for details.

Arguments:
    input (Tensor): the input tensor of size ``(*, n, n)`` where ``*`` is zero or more
                batch dimensions.

Example::

    >>> A = torch.randn(3, 3)
    >>> torch.det(A)
    tensor(0.2611)
    >>> torch.logdet(A)
    tensor(-1.3430)
    >>> A
    tensor([[[ 0.9254, -0.6213],
             [-0.5787,  1.6843]],

            [[ 0.3242, -0.9665],
             [ 0.4539, -0.0887]],

            [[ 1.1336, -0.4025],
             [-0.7089,  0.9032]]])
    >>> A.det()
    tensor([1.1990, 0.4099, 0.7386])
    >>> A.det().log()
    tensor([ 0.1815, -0.8917, -0.3031])
""")

add_docstr(torch.slogdet, r"""
slogdet(input) -> (Tensor, Tensor)

Alias for :func:`torch.linalg.slogdet`
""")

add_docstr(torch.pinverse, r"""
pinverse(input, rcond=1e-15) -> Tensor

Alias for :func:`torch.linalg.pinv`
""")

add_docstr(torch.hann_window,
           """
hann_window(window_length, periodic=True, *, dtype=None, \
layout=torch.strided, device=None, requires_grad=False) -> Tensor
""" + r"""
Hann window function.

.. math::
    w[n] = \frac{1}{2}\ \left[1 - \cos \left( \frac{2 \pi n}{N - 1} \right)\right] =
            \sin^2 \left( \frac{\pi n}{N - 1} \right),

where :math:`N` is the full window size.

The input :attr:`window_length` is a positive integer controlling the
returned window size. :attr:`periodic` flag determines whether the returned
window trims off the last duplicate value from the symmetric window and is
ready to be used as a periodic window with functions like
:meth:`torch.stft`. Therefore, if :attr:`periodic` is true, the :math:`N` in
above formula is in fact :math:`\text{window\_length} + 1`. Also, we always have
``torch.hann_window(L, periodic=True)`` equal to
``torch.hann_window(L + 1, periodic=False)[:-1])``.

.. note::
    If :attr:`window_length` :math:`=1`, the returned window contains a single value 1.
""" + r"""
Arguments:
    window_length (int): the size of returned window
    periodic (bool, optional): If True, returns a window to be used as periodic
        function. If False, return a symmetric window.

Keyword args:
    {dtype} Only floating point types are supported.
    layout (:class:`torch.layout`, optional): the desired layout of returned window tensor. Only
          ``torch.strided`` (dense layout) is supported.
    {device}
    {requires_grad}

Returns:
    Tensor: A 1-D tensor of size :math:`(\text{{window\_length}},)` containing the window

""".format(**factory_common_args))


add_docstr(torch.hamming_window,
           """
hamming_window(window_length, periodic=True, alpha=0.54, beta=0.46, *, dtype=None, \
layout=torch.strided, device=None, requires_grad=False) -> Tensor
""" + r"""
Hamming window function.

.. math::
    w[n] = \alpha - \beta\ \cos \left( \frac{2 \pi n}{N - 1} \right),

where :math:`N` is the full window size.

The input :attr:`window_length` is a positive integer controlling the
returned window size. :attr:`periodic` flag determines whether the returned
window trims off the last duplicate value from the symmetric window and is
ready to be used as a periodic window with functions like
:meth:`torch.stft`. Therefore, if :attr:`periodic` is true, the :math:`N` in
above formula is in fact :math:`\text{window\_length} + 1`. Also, we always have
``torch.hamming_window(L, periodic=True)`` equal to
``torch.hamming_window(L + 1, periodic=False)[:-1])``.

.. note::
    If :attr:`window_length` :math:`=1`, the returned window contains a single value 1.

.. note::
    This is a generalized version of :meth:`torch.hann_window`.
""" + r"""
Arguments:
    window_length (int): the size of returned window
    periodic (bool, optional): If True, returns a window to be used as periodic
        function. If False, return a symmetric window.
    alpha (float, optional): The coefficient :math:`\alpha` in the equation above
    beta (float, optional): The coefficient :math:`\beta` in the equation above

Keyword args:
    {dtype} Only floating point types are supported.
    layout (:class:`torch.layout`, optional): the desired layout of returned window tensor. Only
          ``torch.strided`` (dense layout) is supported.
    {device}
    {requires_grad}

Returns:
    Tensor: A 1-D tensor of size :math:`(\text{{window\_length}},)` containing the window

""".format(**factory_common_args))


add_docstr(torch.bartlett_window,
           """
bartlett_window(window_length, periodic=True, *, dtype=None, \
layout=torch.strided, device=None, requires_grad=False) -> Tensor
""" + r"""
Bartlett window function.

.. math::
    w[n] = 1 - \left| \frac{2n}{N-1} - 1 \right| = \begin{cases}
        \frac{2n}{N - 1} & \text{if } 0 \leq n \leq \frac{N - 1}{2} \\
        2 - \frac{2n}{N - 1} & \text{if } \frac{N - 1}{2} < n < N \\
    \end{cases},

where :math:`N` is the full window size.

The input :attr:`window_length` is a positive integer controlling the
returned window size. :attr:`periodic` flag determines whether the returned
window trims off the last duplicate value from the symmetric window and is
ready to be used as a periodic window with functions like
:meth:`torch.stft`. Therefore, if :attr:`periodic` is true, the :math:`N` in
above formula is in fact :math:`\text{window\_length} + 1`. Also, we always have
``torch.bartlett_window(L, periodic=True)`` equal to
``torch.bartlett_window(L + 1, periodic=False)[:-1])``.

.. note::
    If :attr:`window_length` :math:`=1`, the returned window contains a single value 1.
""" + r"""
Arguments:
    window_length (int): the size of returned window
    periodic (bool, optional): If True, returns a window to be used as periodic
        function. If False, return a symmetric window.

Keyword args:
    {dtype} Only floating point types are supported.
    layout (:class:`torch.layout`, optional): the desired layout of returned window tensor. Only
          ``torch.strided`` (dense layout) is supported.
    {device}
    {requires_grad}

Returns:
    Tensor: A 1-D tensor of size :math:`(\text{{window\_length}},)` containing the window

""".format(**factory_common_args))


add_docstr(torch.blackman_window,
           """
blackman_window(window_length, periodic=True, *, dtype=None, \
layout=torch.strided, device=None, requires_grad=False) -> Tensor
""" + r"""
Blackman window function.

.. math::
    w[n] = 0.42 - 0.5 \cos \left( \frac{2 \pi n}{N - 1} \right) + 0.08 \cos \left( \frac{4 \pi n}{N - 1} \right)

where :math:`N` is the full window size.

The input :attr:`window_length` is a positive integer controlling the
returned window size. :attr:`periodic` flag determines whether the returned
window trims off the last duplicate value from the symmetric window and is
ready to be used as a periodic window with functions like
:meth:`torch.stft`. Therefore, if :attr:`periodic` is true, the :math:`N` in
above formula is in fact :math:`\text{window\_length} + 1`. Also, we always have
``torch.blackman_window(L, periodic=True)`` equal to
``torch.blackman_window(L + 1, periodic=False)[:-1])``.

.. note::
    If :attr:`window_length` :math:`=1`, the returned window contains a single value 1.
""" + r"""
Arguments:
    window_length (int): the size of returned window
    periodic (bool, optional): If True, returns a window to be used as periodic
        function. If False, return a symmetric window.

Keyword args:
    {dtype} Only floating point types are supported.
    layout (:class:`torch.layout`, optional): the desired layout of returned window tensor. Only
          ``torch.strided`` (dense layout) is supported.
    {device}
    {requires_grad}

Returns:
    Tensor: A 1-D tensor of size :math:`(\text{{window\_length}},)` containing the window

""".format(**factory_common_args))


add_docstr(torch.kaiser_window, """
kaiser_window(window_length, periodic=True, beta=12.0, *, dtype=None, \
layout=torch.strided, device=None, requires_grad=False) -> Tensor
""" + r"""
Computes the Kaiser window with window length :attr:`window_length` and shape parameter :attr:`beta`.

Let I_0 be the zeroth order modified Bessel function of the first kind (see :func:`torch.i0`) and
``N = L - 1`` if :attr:`periodic` is False and ``L`` if :attr:`periodic` is True,
where ``L`` is the :attr:`window_length`. This function computes:

.. math::
    out_i = I_0 \left( \beta \sqrt{1 - \left( {\frac{i - N/2}{N/2}} \right) ^2 } \right) / I_0( \beta )

Calling ``torch.kaiser_window(L, B, periodic=True)`` is equivalent to calling
``torch.kaiser_window(L + 1, B, periodic=False)[:-1])``.
The :attr:`periodic` argument is intended as a helpful shorthand
to produce a periodic window as input to functions like :func:`torch.stft`.

.. note::
    If :attr:`window_length` is one, then the returned window is a single element tensor containing a one.

""" + r"""
Args:
    window_length (int): length of the window.
    periodic (bool, optional): If True, returns a periodic window suitable for use in spectral analysis.
        If False, returns a symmetric window suitable for use in filter design.
    beta (float, optional): shape parameter for the window.

Keyword args:
    {dtype}
    layout (:class:`torch.layout`, optional): the desired layout of returned window tensor. Only
          ``torch.strided`` (dense layout) is supported.
    {device}
    {requires_grad}

""".format(**factory_common_args))


add_docstr(torch.vander,
           """
vander(x, N=None, increasing=False) -> Tensor
""" + r"""
Generates a Vandermonde matrix.

The columns of the output matrix are elementwise powers of the input vector :math:`x^{{(N-1)}}, x^{{(N-2)}}, ..., x^0`.
If increasing is True, the order of the columns is reversed :math:`x^0, x^1, ..., x^{{(N-1)}}`. Such a
matrix with a geometric progression in each row is named for Alexandre-Theophile Vandermonde.

Arguments:
    x (Tensor): 1-D input tensor.
    N (int, optional): Number of columns in the output. If N is not specified,
        a square array is returned :math:`(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.

Returns:
    Tensor: Vandermonde matrix. If increasing is False, the first column is :math:`x^{{(N-1)}}`,
    the second :math:`x^{{(N-2)}}` and so forth. If increasing is True, the columns
    are :math:`x^0, x^1, ..., x^{{(N-1)}}`.

Example::

    >>> x = torch.tensor([1, 2, 3, 5])
    >>> torch.vander(x)
    tensor([[  1,   1,   1,   1],
            [  8,   4,   2,   1],
            [ 27,   9,   3,   1],
            [125,  25,   5,   1]])
    >>> torch.vander(x, N=3)
    tensor([[ 1,  1,  1],
            [ 4,  2,  1],
            [ 9,  3,  1],
            [25,  5,  1]])
    >>> torch.vander(x, N=3, increasing=True)
    tensor([[ 1,  1,  1],
            [ 1,  2,  4],
            [ 1,  3,  9],
            [ 1,  5, 25]])

""".format(**factory_common_args))


add_docstr(torch.unbind,
           r"""
unbind(input, dim=0) -> seq

Removes a tensor dimension.

Returns a tuple of all slices along a given dimension, already without it.

Arguments:
    input (Tensor): the tensor to unbind
    dim (int): dimension to remove

Example::

    >>> torch.unbind(torch.tensor([[1, 2, 3],
    >>>                            [4, 5, 6],
    >>>                            [7, 8, 9]]))
    (tensor([1, 2, 3]), tensor([4, 5, 6]), tensor([7, 8, 9]))
""")


add_docstr(torch.combinations,
           r"""
combinations(input, r=2, with_replacement=False) -> seq

Compute combinations of length :math:`r` of the given tensor. The behavior is similar to
python's `itertools.combinations` when `with_replacement` is set to `False`, and
`itertools.combinations_with_replacement` when `with_replacement` is set to `True`.

Arguments:
    input (Tensor): 1D vector.
    r (int, optional): number of elements to combine
    with_replacement (boolean, optional): whether to allow duplication in combination

Returns:
    Tensor: A tensor equivalent to converting all the input tensors into lists, do
    `itertools.combinations` or `itertools.combinations_with_replacement` on these
    lists, and finally convert the resulting list into tensor.

Example::

    >>> a = [1, 2, 3]
    >>> list(itertools.combinations(a, r=2))
    [(1, 2), (1, 3), (2, 3)]
    >>> list(itertools.combinations(a, r=3))
    [(1, 2, 3)]
    >>> list(itertools.combinations_with_replacement(a, r=2))
    [(1, 1), (1, 2), (1, 3), (2, 2), (2, 3), (3, 3)]
    >>> tensor_a = torch.tensor(a)
    >>> torch.combinations(tensor_a)
    tensor([[1, 2],
            [1, 3],
            [2, 3]])
    >>> torch.combinations(tensor_a, r=3)
    tensor([[1, 2, 3]])
    >>> torch.combinations(tensor_a, with_replacement=True)
    tensor([[1, 1],
            [1, 2],
            [1, 3],
            [2, 2],
            [2, 3],
            [3, 3]])

""")

add_docstr(torch.trapezoid,
           r"""
trapezoid(y, x=None, *, dx=None, dim=-1) -> Tensor

Computes the `trapezoidal rule <https://en.wikipedia.org/wiki/Trapezoidal_rule>`_ along
:attr:`dim`. By default the spacing between elements is assumed to be 1, but
:attr:`dx` can be used to specify a different constant spacing, and :attr:`x` can be
used to specify arbitrary spacing along :attr:`dim`.


Assuming :attr:`y` is a one-dimensional tensor with elements :math:`{y_0, y_1, ..., y_n}`,
the default computation is

.. math::
    \begin{aligned}
        \sum_{i = 1}^{n-1} \frac{1}{2} (y_i + y_{i-1})
    \end{aligned}

When :attr:`dx` is specified the computation becomes

.. math::
    \begin{aligned}
        \sum_{i = 1}^{n-1} \frac{\Delta x}{2} (y_i + y_{i-1})
    \end{aligned}

effectively multiplying the result by :attr:`dx`. When :attr:`x` is specified,
assuming :attr:`x` is also a one-dimensional tensor with
elements :math:`{x_0, x_1, ..., x_n}`, the computation becomes

.. math::
    \begin{aligned}
        \sum_{i = 1}^{n-1} \frac{(x_i - x_{i-1})}{2} (y_i + y_{i-1})
    \end{aligned}

When :attr:`x` and :attr:`y` have the same size, the computation is as described above and no broadcasting is needed.
The broadcasting behavior of this function is as follows when their sizes are different. For both :attr:`x`
and :attr:`y`, the function computes the difference between consecutive elements along
dimension :attr:`dim`. This effectively creates two tensors, `x_diff` and `y_diff`, that have
the same shape as the original tensors except their lengths along the dimension :attr:`dim` is reduced by 1.
After that, those two tensors are broadcast together to compute final output as part of the trapezoidal rule.
See the examples below for details.

.. note::
    The trapezoidal rule is a technique for approximating the definite integral of a function
    by averaging its left and right Riemann sums. The approximation becomes more accurate as
    the resolution of the partition increases.

Arguments:
    y (Tensor): Values to use when computing the trapezoidal rule.
    x (Tensor): If specified, defines spacing between values as specified above.

Keyword arguments:
    dx (float): constant spacing between values. If neither :attr:`x` or :attr:`dx`
        are specified then this defaults to 1. Effectively multiplies the result by its value.
    dim (int): The dimension along which to compute the trapezoidal rule.
        The last (inner-most) dimension by default.

Examples::

    >>> # Computes the trapezoidal rule in 1D, spacing is implicitly 1
    >>> y = torch.tensor([1, 5, 10])
    >>> torch.trapezoid(y)
    tensor(10.5)

    >>> # Computes the same trapezoidal rule directly to verify
    >>> (1 + 10 + 10) / 2
    10.5

    >>> # Computes the trapezoidal rule in 1D with constant spacing of 2
    >>> # NOTE: the result is the same as before, but multiplied by 2
    >>> torch.trapezoid(y, dx=2)
    21.0

    >>> # Computes the trapezoidal rule in 1D with arbitrary spacing
    >>> x = torch.tensor([1, 3, 6])
    >>> torch.trapezoid(y, x)
    28.5

    >>> # Computes the same trapezoidal rule directly to verify
    >>> ((3 - 1) * (1 + 5) + (6 - 3) * (5 + 10)) / 2
    28.5

    >>> # Computes the trapezoidal rule for each row of a 3x3 matrix
    >>> y = torch.arange(9).reshape(3, 3)
    tensor([[0, 1, 2],
            [3, 4, 5],
            [6, 7, 8]])
    >>> torch.trapezoid(y)
    tensor([ 2., 8., 14.])

    >>> # Computes the trapezoidal rule for each column of the matrix
    >>> torch.trapezoid(y, dim=0)
    tensor([ 6., 8., 10.])

    >>> # Computes the trapezoidal rule for each row of a 3x3 ones matrix
    >>> #   with the same arbitrary spacing
    >>> y = torch.ones(3, 3)
    >>> x = torch.tensor([1, 3, 6])
    >>> torch.trapezoid(y, x)
    array([5., 5., 5.])

    >>> # Computes the trapezoidal rule for each row of a 3x3 ones matrix
    >>> #   with different arbitrary spacing per row
    >>> y = torch.ones(3, 3)
    >>> x = torch.tensor([[1, 2, 3], [1, 3, 5], [1, 4, 7]])
    >>> torch.trapezoid(y, x)
    array([2., 4., 6.])
""")

add_docstr(torch.trapz,
           r"""
trapz(y, x, *, dim=-1) -> Tensor

Alias for :func:`torch.trapezoid`.
""")

add_docstr(torch.cumulative_trapezoid,
           r"""
cumulative_trapezoid(y, x=None, *, dx=None, dim=-1) -> Tensor

Cumulatively computes the `trapezoidal rule <https://en.wikipedia.org/wiki/Trapezoidal_rule>`_
along :attr:`dim`. By default the spacing between elements is assumed to be 1, but
:attr:`dx` can be used to specify a different constant spacing, and :attr:`x` can be
used to specify arbitrary spacing along :attr:`dim`.

For more details, please read :func:`torch.trapezoid`. The difference between :func:`torch.trapezoid`
and this function is that, :func:`torch.trapezoid` returns a value for each integration,
where as this function returns a cumulative value for every spacing within the integration. This
is analogous to how `.sum` returns a value and `.cumsum` returns a cumulative sum.

Arguments:
    y (Tensor): Values to use when computing the trapezoidal rule.
    x (Tensor): If specified, defines spacing between values as specified above.

Keyword arguments:
    dx (float): constant spacing between values. If neither :attr:`x` or :attr:`dx`
        are specified then this defaults to 1. Effectively multiplies the result by its value.
    dim (int): The dimension along which to compute the trapezoidal rule.
        The last (inner-most) dimension by default.

Examples::

    >>> # Cumulatively computes the trapezoidal rule in 1D, spacing is implicitly 1.
    >>> y = torch.tensor([1, 5, 10])
    >>> torch.cumulative_trapezoid(y)
    tensor([3., 10.5])

    >>> # Computes the same trapezoidal rule directly up to each element to verify
    >>> (1 + 5) / 2
    3.0
    >>> (1 + 10 + 10) / 2
    10.5

    >>> # Cumulatively computes the trapezoidal rule in 1D with constant spacing of 2
    >>> # NOTE: the result is the same as before, but multiplied by 2
    >>> torch.cumulative_trapezoid(y, dx=2)
    tensor([6., 21.])

    >>> # Cumulatively computes the trapezoidal rule in 1D with arbitrary spacing
    >>> x = torch.tensor([1, 3, 6])
    >>> torch.cumulative_trapezoid(y, x)
    tensor([6., 28.5])

    >>> # Computes the same trapezoidal rule directly up to each element to verify
    >>> ((3 - 1) * (1 + 5)) / 2
    6.0
    >>> ((3 - 1) * (1 + 5) + (6 - 3) * (5 + 10)) / 2
    28.5

    >>> # Cumulatively computes the trapezoidal rule for each row of a 3x3 matrix
    >>> y = torch.arange(9).reshape(3, 3)
    tensor([[0, 1, 2],
            [3, 4, 5],
            [6, 7, 8]])
    >>> torch.cumulative_trapezoid(y)
    tensor([[ 0.5,  2.],
            [ 3.5,  8.],
            [ 6.5, 14.]])

    >>> # Cumulatively computes the trapezoidal rule for each column of the matrix
    >>> torch.cumulative_trapezoid(y, dim=0)
    tensor([[ 1.5,  2.5,  3.5],
            [ 6.0,  8.0, 10.0]])

    >>> # Cumulatively computes the trapezoidal rule for each row of a 3x3 ones matrix
    >>> #   with the same arbitrary spacing
    >>> y = torch.ones(3, 3)
    >>> x = torch.tensor([1, 3, 6])
    >>> torch.cumulative_trapezoid(y, x)
    tensor([[2., 5.],
            [2., 5.],
            [2., 5.]])

    >>> # Cumulatively computes the trapezoidal rule for each row of a 3x3 ones matrix
    >>> #   with different arbitrary spacing per row
    >>> y = torch.ones(3, 3)
    >>> x = torch.tensor([[1, 2, 3], [1, 3, 5], [1, 4, 7]])
    >>> torch.cumulative_trapezoid(y, x)
    tensor([[1., 2.],
            [2., 4.],
            [3., 6.]])
""")

add_docstr(torch.repeat_interleave,
           r"""
repeat_interleave(input, repeats, dim=None, *, output_size=None) -> Tensor

Repeat elements of a tensor.

.. warning::

    This is different from :meth:`torch.Tensor.repeat` but similar to ``numpy.repeat``.

Args:
    {input}
    repeats (Tensor or int): The number of repetitions for each element.
        repeats is broadcasted to fit the shape of the given axis.
    dim (int, optional): The dimension along which to repeat values.
        By default, use the flattened input array, and return a flat output
        array.

Keyword args:
    output_size (int, optional): Total output size for the given axis
        ( e.g. sum of repeats). If given, it will avoid stream syncronization
        needed to calculate output shape of the tensor.

Returns:
    Tensor: Repeated tensor which has the same shape as input, except along the given axis.

Example::

    >>> x = torch.tensor([1, 2, 3])
    >>> x.repeat_interleave(2)
    tensor([1, 1, 2, 2, 3, 3])
    >>> y = torch.tensor([[1, 2], [3, 4]])
    >>> torch.repeat_interleave(y, 2)
    tensor([1, 1, 2, 2, 3, 3, 4, 4])
    >>> torch.repeat_interleave(y, 3, dim=1)
    tensor([[1, 1, 1, 2, 2, 2],
            [3, 3, 3, 4, 4, 4]])
    >>> torch.repeat_interleave(y, torch.tensor([1, 2]), dim=0)
    tensor([[1, 2],
            [3, 4],
            [3, 4]])
    >>> torch.repeat_interleave(y, torch.tensor([1, 2]), dim=0, output_size=3)
    tensor([[1, 2],
            [3, 4],
            [3, 4]])

.. function:: repeat_interleave(repeats, *, output_size=None) -> Tensor
   :noindex:

If the `repeats` is `tensor([n1, n2, n3, ...])`, then the output will be
`tensor([0, 0, ..., 1, 1, ..., 2, 2, ..., ...])` where `0` appears `n1` times,
`1` appears `n2` times, `2` appears `n3` times, etc.
""".format(**common_args))

add_docstr(torch.tile, r"""
tile(input, dims) -> Tensor

Constructs a tensor by repeating the elements of :attr:`input`.
The :attr:`dims` argument specifies the number of repetitions
in each dimension.

If :attr:`dims` specifies fewer dimensions than :attr:`input` has, then
ones are prepended to :attr:`dims` until all dimensions are specified.
For example, if :attr:`input` has shape (8, 6, 4, 2) and :attr:`dims`
is (2, 2), then :attr:`dims` is treated as (1, 1, 2, 2).

Analogously, if :attr:`input` has fewer dimensions than :attr:`dims`
specifies, then :attr:`input` is treated as if it were unsqueezed at
dimension zero until it has as many dimensions as :attr:`dims` specifies.
For example, if :attr:`input` has shape (4, 2) and :attr:`dims`
is (3, 3, 2, 2), then :attr:`input` is treated as if it had the
shape (1, 1, 4, 2).

.. note::

    This function is similar to NumPy's tile function.

Args:
    input (Tensor): the tensor whose elements to repeat.
    dims (tuple): the number of repetitions per dimension.

Example::

    >>> x = torch.tensor([1, 2, 3])
    >>> x.tile((2,))
    tensor([1, 2, 3, 1, 2, 3])
    >>> y = torch.tensor([[1, 2], [3, 4]])
    >>> torch.tile(y, (2, 2))
    tensor([[1, 2, 1, 2],
            [3, 4, 3, 4],
            [1, 2, 1, 2],
            [3, 4, 3, 4]])
""")

add_docstr(torch.quantize_per_tensor,
           r"""
quantize_per_tensor(input, scale, zero_point, dtype) -> Tensor

Converts a float tensor to a quantized tensor with given scale and zero point.

Arguments:
    input (Tensor): float tensor or list of tensors to quantize
    scale (float or Tensor): scale to apply in quantization formula
    zero_point (int or Tensor): offset in integer value that maps to float zero
    dtype (:class:`torch.dtype`): the desired data type of returned tensor.
        Has to be one of the quantized dtypes: ``torch.quint8``, ``torch.qint8``, ``torch.qint32``

Returns:
    Tensor: A newly quantized tensor or list of quantized tensors.

Example::

    >>> torch.quantize_per_tensor(torch.tensor([-1.0, 0.0, 1.0, 2.0]), 0.1, 10, torch.quint8)
    tensor([-1.,  0.,  1.,  2.], size=(4,), dtype=torch.quint8,
           quantization_scheme=torch.per_tensor_affine, scale=0.1, zero_point=10)
    >>> torch.quantize_per_tensor(torch.tensor([-1.0, 0.0, 1.0, 2.0]), 0.1, 10, torch.quint8).int_repr()
    tensor([ 0, 10, 20, 30], dtype=torch.uint8)
    >>> torch.quantize_per_tensor([torch.tensor([-1.0, 0.0]), torch.tensor([-2.0, 2.0])],
    >>> torch.tensor([0.1, 0.2]), torch.tensor([10, 20]), torch.quint8)
    (tensor([-1.,  0.], size=(2,), dtype=torch.quint8,
        quantization_scheme=torch.per_tensor_affine, scale=0.1, zero_point=10),
        tensor([-2.,  2.], size=(2,), dtype=torch.quint8,
        quantization_scheme=torch.per_tensor_affine, scale=0.2, zero_point=20))
    >>> torch.quantize_per_tensor(torch.tensor([-1.0, 0.0, 1.0, 2.0]), torch.tensor(0.1), torch.tensor(10), torch.quint8)
    tensor([-1.,  0.,  1.,  2.], size=(4,), dtype=torch.quint8,
       quantization_scheme=torch.per_tensor_affine, scale=0.10, zero_point=10)
""")

add_docstr(torch.quantize_per_tensor_dynamic,
           r"""
quantize_per_tensor_dynamic(input, dtype, reduce_range) -> Tensor

Converts a float tensor to a quantized tensor with scale and zero_point calculated
dynamically based on the input.

Arguments:
    input (Tensor): float tensor or list of tensors to quantize
    dtype (:class:`torch.dtype`): the desired data type of returned tensor.
        Has to be one of the quantized dtypes: ``torch.quint8``, ``torch.qint8``
    reduce_range (bool): a flag to indicate whether to reduce the range of quantized
    data by 1 bit, it's required to avoid instruction overflow for some hardwares

Returns:
    Tensor: A newly (dynamically) quantized tensor

Example::

    >>> t = torch.quantize_per_tensor_dynamic(torch.tensor([-1.0, 0.0, 1.0, 2.0]), torch.quint8, False)
    >>> print(t)
    tensor([-1.,  0.,  1.,  2.], size=(4,), dtype=torch.quint8,
           quantization_scheme=torch.per_tensor_affine, scale=0.011764705882352941,
           zero_point=85)
    >>> t.int_repr()
    tensor([  0,  85, 170, 255], dtype=torch.uint8)
""")

add_docstr(torch.quantize_per_channel,
           r"""
quantize_per_channel(input, scales, zero_points, axis, dtype) -> Tensor

Converts a float tensor to a per-channel quantized tensor with given scales and zero points.

Arguments:
    input (Tensor): float tensor to quantize
    scales (Tensor): float 1D tensor of scales to use, size should match ``input.size(axis)``
    zero_points (int): integer 1D tensor of offset to use, size should match ``input.size(axis)``
    axis (int): dimension on which apply per-channel quantization
    dtype (:class:`torch.dtype`): the desired data type of returned tensor.
        Has to be one of the quantized dtypes: ``torch.quint8``, ``torch.qint8``, ``torch.qint32``

Returns:
    Tensor: A newly quantized tensor

Example::

    >>> x = torch.tensor([[-1.0, 0.0], [1.0, 2.0]])
    >>> torch.quantize_per_channel(x, torch.tensor([0.1, 0.01]), torch.tensor([10, 0]), 0, torch.quint8)
    tensor([[-1.,  0.],
            [ 1.,  2.]], size=(2, 2), dtype=torch.quint8,
           quantization_scheme=torch.per_channel_affine,
           scale=tensor([0.1000, 0.0100], dtype=torch.float64),
           zero_point=tensor([10,  0]), axis=0)
    >>> torch.quantize_per_channel(x, torch.tensor([0.1, 0.01]), torch.tensor([10, 0]), 0, torch.quint8).int_repr()
    tensor([[  0,  10],
            [100, 200]], dtype=torch.uint8)
""")


add_docstr(torch.quantized_batch_norm,
           r"""
quantized_batch_norm(input, weight=None, bias=None, mean, var, eps, output_scale, output_zero_point) -> Tensor

Applies batch normalization on a 4D (NCHW) quantized tensor.

.. math::

        y = \frac{x - \mathrm{E}[x]}{\sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta

Arguments:
    input (Tensor): quantized tensor
    weight (Tensor): float tensor that corresponds to the gamma, size C
    bias (Tensor):  float tensor that corresponds to the beta, size C
    mean (Tensor): float mean value in batch normalization, size C
    var (Tensor): float tensor for variance, size C
    eps (float): a value added to the denominator for numerical stability.
    output_scale (float): output quantized tensor scale
    output_zero_point (int): output quantized tensor zero_point

Returns:
    Tensor: A quantized tensor with batch normalization applied.

Example::

    >>> qx = torch.quantize_per_tensor(torch.rand(2, 2, 2, 2), 1.5, 3, torch.quint8)
    >>> torch.quantized_batch_norm(qx, torch.ones(2), torch.zeros(2), torch.rand(2), torch.rand(2), 0.00001, 0.2, 2)
    tensor([[[[-0.2000, -0.2000],
          [ 1.6000, -0.2000]],

         [[-0.4000, -0.4000],
          [-0.4000,  0.6000]]],


        [[[-0.2000, -0.2000],
          [-0.2000, -0.2000]],

         [[ 0.6000, -0.4000],
          [ 0.6000, -0.4000]]]], size=(2, 2, 2, 2), dtype=torch.quint8,
       quantization_scheme=torch.per_tensor_affine, scale=0.2, zero_point=2)
""")


add_docstr(torch.quantized_max_pool1d,
           r"""
quantized_max_pool1d(input, kernel_size, stride=[], padding=0, dilation=1, ceil_mode=False) -> Tensor

Applies a 1D max pooling over an input quantized tensor composed of several input planes.

Arguments:
    input (Tensor): quantized tensor
    kernel_size (list of int): the size of the sliding window
    stride (``list of int``, optional): the stride of the sliding window
    padding (``list of int``, opttional): padding to be added on both sides, must be >= 0 and <= kernel_size / 2
    dilation (``list of int``, optional): The stride between elements within a sliding window, must be > 0. Default 1
    ceil_mode (bool, optional):  If True, will use ceil instead of floor to compute the output shape.
        Defaults to False.


Returns:
    Tensor: A quantized tensor with max_pool1d applied.

Example::

    >>> qx = torch.quantize_per_tensor(torch.rand(2, 2), 1.5, 3, torch.quint8)
    >>> torch.quantized_max_pool1d(qx, [2])
    tensor([[0.0000],
            [1.5000]], size=(2, 1), dtype=torch.quint8,
        quantization_scheme=torch.per_tensor_affine, scale=1.5, zero_point=3)
""")


add_docstr(torch.quantized_max_pool2d,
           r"""
quantized_max_pool2d(input, kernel_size, stride=[], padding=0, dilation=1, ceil_mode=False) -> Tensor

Applies a 2D max pooling over an input quantized tensor composed of several input planes.

Arguments:
    input (Tensor): quantized tensor
    kernel_size (``list of int``): the size of the sliding window
    stride (``list of int``, optional): the stride of the sliding window
    padding (``list of int``, optional): padding to be added on both sides, must be >= 0 and <= kernel_size / 2
    dilation (``list of int``, optional): The stride between elements within a sliding window, must be > 0. Default 1
    ceil_mode (bool, optional):  If True, will use ceil instead of floor to compute the output shape.
        Defaults to False.


Returns:
    Tensor: A quantized tensor with max_pool2d applied.

Example::

    >>> qx = torch.quantize_per_tensor(torch.rand(2, 2, 2, 2), 1.5, 3, torch.quint8)
    >>> torch.quantized_max_pool2d(qx, [2,2])
    tensor([[[[1.5000]],

            [[1.5000]]],


            [[[0.0000]],

            [[0.0000]]]], size=(2, 2, 1, 1), dtype=torch.quint8,
        quantization_scheme=torch.per_tensor_affine, scale=1.5, zero_point=3)
""")


add_docstr(torch.Generator,
           r"""
Generator(device='cpu') -> Generator

Creates and returns a generator object that manages the state of the algorithm which
produces pseudo random numbers. Used as a keyword argument in many :ref:`inplace-random-sampling`
functions.

Arguments:
    device (:class:`torch.device`, optional): the desired device for the generator.

Returns:
    Generator: An torch.Generator object.

Example::

    >>> g_cpu = torch.Generator()
    >>> g_cuda = torch.Generator(device='cuda')
""")


add_docstr(torch.Generator.set_state,
           r"""
Generator.set_state(new_state) -> void

Sets the Generator state.

Arguments:
    new_state (torch.ByteTensor): The desired state.

Example::

    >>> g_cpu = torch.Generator()
    >>> g_cpu_other = torch.Generator()
    >>> g_cpu.set_state(g_cpu_other.get_state())
""")


add_docstr(torch.Generator.get_state,
           r"""
Generator.get_state() -> Tensor

Returns the Generator state as a ``torch.ByteTensor``.

Returns:
    Tensor: A ``torch.ByteTensor`` which contains all the necessary bits
    to restore a Generator to a specific point in time.

Example::

    >>> g_cpu = torch.Generator()
    >>> g_cpu.get_state()
""")


add_docstr(torch.Generator.manual_seed,
           r"""
Generator.manual_seed(seed) -> Generator

Sets the seed for generating random numbers. Returns a `torch.Generator` object.
It is recommended to set a large seed, i.e. a number that has a good balance of 0
and 1 bits. Avoid having many 0 bits in the seed.

Arguments:
    seed (int): The desired seed. Value must be within the inclusive range
        `[-0x8000_0000_0000_0000, 0xffff_ffff_ffff_ffff]`. Otherwise, a RuntimeError
        is raised. Negative inputs are remapped to positive values with the formula
        `0xffff_ffff_ffff_ffff + seed`.

Returns:
    Generator: An torch.Generator object.

Example::

    >>> g_cpu = torch.Generator()
    >>> g_cpu.manual_seed(2147483647)
""")


add_docstr(torch.Generator.initial_seed,
           r"""
Generator.initial_seed() -> int

Returns the initial seed for generating random numbers.

Example::

    >>> g_cpu = torch.Generator()
    >>> g_cpu.initial_seed()
    2147483647
""")


add_docstr(torch.Generator.seed,
           r"""
Generator.seed() -> int

Gets a non-deterministic random number from std::random_device or the current
time and uses it to seed a Generator.

Example::

    >>> g_cpu = torch.Generator()
    >>> g_cpu.seed()
    1516516984916
""")


add_docstr(torch.Generator.device,
           r"""
Generator.device -> device

Gets the current device of the generator.

Example::

    >>> g_cpu = torch.Generator()
    >>> g_cpu.device
    device(type='cpu')
""")

add_docstr(torch._assert_async,
           r"""
_assert_async(tensor) -> void

Asynchronously assert that the contents of tensor are nonzero.  For CPU tensors,
this is equivalent to ``assert tensor`` or ``assert tensor.is_nonzero()``; for
CUDA tensors, we DO NOT synchronize and you may only find out the assertion
failed at a later CUDA kernel launch.  Asynchronous assertion can be helpful for
testing invariants in CUDA tensors without giving up performance.  This function
is NOT intended to be used for regular error checking, as it will trash your CUDA
context if the assert fails (forcing you to restart your PyTorch process.)

Args:
    tensor (Tensor): a one element tensor to test to see if it is nonzero.  Zero
        elements (including False for boolean tensors) cause an assertion failure
        to be raised.
""")

add_docstr(torch.searchsorted,
           r"""
searchsorted(sorted_sequence, values, *, out_int32=False, right=False, side='left', out=None, sorter=None) -> Tensor

Find the indices from the *innermost* dimension of :attr:`sorted_sequence` such that, if the
corresponding values in :attr:`values` were inserted before the indices, when sorted, the order
of the corresponding *innermost* dimension within :attr:`sorted_sequence` would be preserved.
Return a new tensor with the same size as :attr:`values`. If :attr:`right` is False or side is
'left (default), then the left boundary of :attr:`sorted_sequence` is closed. More formally,
the returned index satisfies the following rules:

.. list-table::
   :widths: 12 10 78
   :header-rows: 1

   * - :attr:`sorted_sequence`
     - :attr:`right`
     - *returned index satisfies*
   * - 1-D
     - False
     - ``sorted_sequence[i-1] < values[m][n]...[l][x] <= sorted_sequence[i]``
   * - 1-D
     - True
     - ``sorted_sequence[i-1] <= values[m][n]...[l][x] < sorted_sequence[i]``
   * - N-D
     - False
     - ``sorted_sequence[m][n]...[l][i-1] < values[m][n]...[l][x] <= sorted_sequence[m][n]...[l][i]``
   * - N-D
     - True
     - ``sorted_sequence[m][n]...[l][i-1] <= values[m][n]...[l][x] < sorted_sequence[m][n]...[l][i]``

Args:
    sorted_sequence (Tensor): N-D or 1-D tensor, containing monotonically increasing sequence on the *innermost*
                              dimension unless :attr:`sorter` is provided, in which case the sequence does not
                              need to be sorted
    values (Tensor or Scalar): N-D tensor or a Scalar containing the search value(s).

Keyword args:
    out_int32 (bool, optional): indicate the output data type. torch.int32 if True, torch.int64 otherwise.
                                Default value is False, i.e. default output data type is torch.int64.
    right (bool, optional): if False, return the first suitable location that is found. If True, return the
                            last such index. If no suitable index found, return 0 for non-numerical value
                            (eg. nan, inf) or the size of *innermost* dimension within :attr:`sorted_sequence`
                            (one pass the last index of the *innermost* dimension). In other words, if False,
                            gets the lower bound index for each value in :attr:`values` on the corresponding
                            *innermost* dimension of the :attr:`sorted_sequence`. If True, gets the upper
                            bound index instead. Default value is False. :attr:`side` does the same and is
                            preferred. It will error if :attr:`side` is set to "left" while this is True.
    side (str, optional): the same as :attr:`right` but preferred. "left" corresponds to False for :attr:`right`
                            and "right" corresponds to True for :attr:`right`. It will error if this is set to
                            "left" while :attr:`right` is True.
    out (Tensor, optional): the output tensor, must be the same size as :attr:`values` if provided.
    sorter (LongTensor, optional): if provided, a tensor matching the shape of the unsorted
                            :attr:`sorted_sequence` containing a sequence of indices that sort it in the
                            ascending order on the innermost dimension


Example::

    >>> sorted_sequence = torch.tensor([[1, 3, 5, 7, 9], [2, 4, 6, 8, 10]])
    >>> sorted_sequence
    tensor([[ 1,  3,  5,  7,  9],
            [ 2,  4,  6,  8, 10]])
    >>> values = torch.tensor([[3, 6, 9], [3, 6, 9]])
    >>> values
    tensor([[3, 6, 9],
            [3, 6, 9]])
    >>> torch.searchsorted(sorted_sequence, values)
    tensor([[1, 3, 4],
            [1, 2, 4]])
    >>> torch.searchsorted(sorted_sequence, values, side='right')
    tensor([[2, 3, 5],
            [1, 3, 4]])

    >>> sorted_sequence_1d = torch.tensor([1, 3, 5, 7, 9])
    >>> sorted_sequence_1d
    tensor([1, 3, 5, 7, 9])
    >>> torch.searchsorted(sorted_sequence_1d, values)
    tensor([[1, 3, 4],
            [1, 3, 4]])
""")

add_docstr(torch.bucketize,
           r"""
bucketize(input, boundaries, *, out_int32=False, right=False, out=None) -> Tensor

Returns the indices of the buckets to which each value in the :attr:`input` belongs, where the
boundaries of the buckets are set by :attr:`boundaries`. Return a new tensor with the same size
as :attr:`input`. If :attr:`right` is False (default), then the left boundary is closed. More
formally, the returned index satisfies the following rules:

.. list-table::
   :widths: 15 85
   :header-rows: 1

   * - :attr:`right`
     - *returned index satisfies*
   * - False
     - ``boundaries[i-1] < input[m][n]...[l][x] <= boundaries[i]``
   * - True
     - ``boundaries[i-1] <= input[m][n]...[l][x] < boundaries[i]``

Args:
    input (Tensor or Scalar): N-D tensor or a Scalar containing the search value(s).
    boundaries (Tensor): 1-D tensor, must contain a monotonically increasing sequence.

Keyword args:
    out_int32 (bool, optional): indicate the output data type. torch.int32 if True, torch.int64 otherwise.
                                Default value is False, i.e. default output data type is torch.int64.
    right (bool, optional): if False, return the first suitable location that is found. If True, return the
                            last such index. If no suitable index found, return 0 for non-numerical value
                            (eg. nan, inf) or the size of :attr:`boundaries` (one pass the last index).
                            In other words, if False, gets the lower bound index for each value in :attr:`input`
                            from :attr:`boundaries`. If True, gets the upper bound index instead.
                            Default value is False.
    out (Tensor, optional): the output tensor, must be the same size as :attr:`input` if provided.


Example::

    >>> boundaries = torch.tensor([1, 3, 5, 7, 9])
    >>> boundaries
    tensor([1, 3, 5, 7, 9])
    >>> v = torch.tensor([[3, 6, 9], [3, 6, 9]])
    >>> v
    tensor([[3, 6, 9],
            [3, 6, 9]])
    >>> torch.bucketize(v, boundaries)
    tensor([[1, 3, 4],
            [1, 3, 4]])
    >>> torch.bucketize(v, boundaries, right=True)
    tensor([[2, 3, 5],
            [2, 3, 5]])
""")