OSSForks/pytorch
1
0
Fork 0
mirror of https://github.com/zebrajr/pytorch.git synced 2025-12-06 12:20:52 +01:00
Code Issues Actions 38 Packages Projects Releases Wiki Activity
91b090ceaf
pytorch/torch/_torch_docs.py
ita 91b090ceaf Add polygamma where n >= 2 (#42499) 
Summary:
https://github.com/pytorch/pytorch/issues/40980

I have a few questions during implementing Polygamma function...
so, I made PR prior to complete it.

1. some code blocks brought from cephes library(and I did too)
```
/*
 * The following function comes with the following copyright notice.
 * It has been released under the BSD license.
 *
 * Cephes Math Library Release 2.8:  June, 2000
 * Copyright 1984, 1987, 1992, 2000 by Stephen L. Moshier
 */
```
is it okay for me to use cephes code with this same copyright notice(already in the Pytorch codebases)

2. There is no linting in internal Aten library. (as far as I know, I read https://github.com/pytorch/pytorch/blob/master/CONTRIBUTING.md)
How do I'm sure my code will follow appropriate guidelines of this library..?

3. Actually, there's a digamma, trigamma function already
digamma is needed, however, trigamma function becomes redundant if  polygamma function is added.
it is okay for trigamma to be there or should be removed?

btw, CPU version works fine with 3-rd order polygamma(it's what we need to play with variational inference with beta/gamma distribution) now and I'm going to finish GPU version soon.

Pull Request resolved: https://github.com/pytorch/pytorch/pull/42499

Reviewed By: gchanan

Differential Revision: D23110016

Pulled By: albanD

fbshipit-source-id: 246f4c2b755a99d9e18a15fcd1a24e3df5e0b53e
2020-08-14 17:00:24 -07:00

8779 lines
271 KiB
Python
Raw Blame History

"""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.
""")
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``.
""")
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`
""".format(**common_args))
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.acosh,
r"""
acosh(input, out=None) -> Tensor
Returns a new tensor with the inverse hyperbolic cosine of the elements of :attr:`input`.
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`.
.. math::
\text{out}_{i} = \cosh^{-1}(\text{input}_{i})
""" + 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.add,
r"""
add(input, other, out=None)
Adds the scalar :attr:`other` to each element of the input :attr:`input`
and returns a new resulting tensor.
.. math::
\text{{out}} = \text{{input}} + \text{{other}}
If :attr:`input` is of type FloatTensor or DoubleTensor, :attr:`other` must be
a real number, otherwise it should be an integer.
Args:
{input}
value (Number): the number to be added to each element of :attr:`input`
Keyword arguments:
{out}
Example::
>>> 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])
.. function:: add(input, other, *, alpha=1, out=None)
Each element of the tensor :attr:`other` is multiplied by the scalar
:attr:`alpha` and added to each element of the tensor :attr:`input`.
The resulting tensor is returned.
The shapes of :attr:`input` and :attr:`other` must be
:ref:`broadcastable <broadcasting-semantics>`.
.. math::
\text{{out}} = \text{{input}} + \text{{alpha}} \times \text{{other}}
If :attr:`other` is of type FloatTensor or DoubleTensor, :attr:`alpha` must be
a real number, otherwise it should be an integer.
Args:
input (Tensor): the first input tensor
other (Tensor): the second input tensor
alpha (Number): the scalar multiplier for :attr:`other`
Keyword arguments:
{out}
Example::
>>> a = torch.randn(4)
>>> a
tensor([-0.9732, -0.3497, 0.6245, 0.4022])
>>> b = torch.randn(4, 1)
>>> b
tensor([[ 0.3743],
[-1.7724],
[-0.5811],
[-0.8017]])
>>> torch.add(a, b, 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)
""" + r"""
For inputs of type `FloatTensor` or `DoubleTensor`, arguments :attr:`beta` and :attr:`alpha`
must be real numbers, otherwise they should be integers.
Args:
batch1 (Tensor): the first batch of matrices to be multiplied
batch2 (Tensor): the second batch of matrices to be multiplied
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))
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 :attr:`tensor1` and :attr:`tensor2`.
The historic addcdiv behavior can be implemented using :func:`floor_divide`
for integral inputs
(:attr:`input` + :attr:`value` * :attr:`tensor1` // :attr:`tensor2`)
and :func:`div` for float inputs
(:attr:`input` + :attr:`value` * :attr:`tensor1` / :attr:`tensor2`).
The future addcdiv behavior can be implemented with :func:`true_divide`
(:attr:`input` + :attr:`value` * torch.true_divide(:attr:`tensor1`,
:attr:`tensor2`).
.. 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
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
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)
""" + 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): matrix to be added
mat1 (Tensor): the first matrix to be multiplied
mat2 (Tensor): the second matrix to be multiplied
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))
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})
""" + 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 multiplied
vec (Tensor): vector to be multiplied
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})
""" + 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)`.
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): matrix to be added
vec1 (Tensor): the first vector of the outer product
vec2 (Tensor): the second vector of the outer product
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.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}
{out}
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::
More than one element of a created tensor may refer to a single memory
location. As a result, in-place operations (especially ones that are
vectorized) may result in incorrect behavior. If you need to write to
the tensors, please clone them first.
Many PyTorch functions, which return a view of a tensor, are internally
implemented with this function. Those functions, like
:meth:`torch.Tensor.expand`, are easier to read and are therefore more
advisable to use.
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
Convert the data into a `torch.Tensor`. If the data is already a `Tensor` with the same `dtype` and `device`,
no copy will be performed, otherwise a new `Tensor` will be returned with computational graph retained if data
`Tensor` has ``requires_grad=True``. Similarly, if the data is an ``ndarray`` of the corresponding `dtype` and
the `device` is the cpu, no copy will be performed.
Args:
{data}
{dtype}
{device}
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}
{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.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.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}
{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.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
{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.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.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)
""" + 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): 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
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))
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
{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:
In some circumstances when using the CUDA backend with 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``.
Please see the notes on :doc:`/notes/randomness` for background.
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])
""")
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}
{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, deterministic=False, 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"""
.. 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
deterministic (bool, optional): flag to choose between a faster non-deterministic
calculation, or a slower deterministic calculation.
This argument is only available for sparse-dense CUDA bmm.
Default: ``False``
{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))
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
{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
{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
{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.stack,
r"""
stack(tensors, dim=0, out=None) -> Tensor
Concatenates 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)
{out}
""".format(**common_args))
add_docstr(torch.chunk,
r"""
chunk(input, chunks, dim=0) -> List of Tensors
Splits a tensor into a specific number of chunks. Each chunk is a view of
the input tensor.
Last chunk will be smaller if the tensor size along the given dimension
:attr:`dim` is not divisible by :attr:`chunks`.
Arguments:
input (Tensor): the tensor to split
chunks (int): number of chunks to return
dim (int): dimension along which to split the tensor
""")
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.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.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
{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.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 = \left\lfloor \text{input}_{i} \right\rfloor + 1
""" + r"""
Args:
{input}
{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}}
""" + r"""
Args:
{input}
{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.
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``
out (Tensor, optional): the output matrix
Example::
>>> a = torch.randn(3, 3)
>>> a = torch.mm(a, a.t()) # 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]])
>>> torch.mm(l, l.t())
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)
>>> a = torch.matmul(a, a.transpose(-1, -2)) + 1e-03 # make symmetric positive-definite
>>> l = torch.cholesky(a)
>>> z = torch.matmul(l, l.transpose(-1, -2))
>>> torch.max(torch.abs(z - a)) # Max non-zero
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`
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``.
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.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}}
Args:
input (Tensor): the input 2-D tensor :math:`u`, a upper or lower triangular
Cholesky factor
upper (bool, optional): whether to return a lower (default) or upper triangular matrix
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.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]])
""")
add_docstr(torch.clamp, r"""
clamp(input, min, max, out=None) -> Tensor
Clamp all elements in :attr:`input` into the range `[` :attr:`min`, :attr:`max` `]` and return
a resulting tensor:
.. math::
y_i = \begin{cases}
\text{min} & \text{if } x_i < \text{min} \\
x_i & \text{if } \text{min} \leq x_i \leq \text{max} \\
\text{max} & \text{if } x_i > \text{max}
\end{cases}
""" + r"""
If :attr:`input` is of type `FloatTensor` or `DoubleTensor`, args :attr:`min`
and :attr:`max` must be real numbers, otherwise they should be integers.
Args:
{input}
min (Number): lower-bound of the range to be clamped to
max (Number): upper-bound of the range to be clamped to
{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])
.. function:: clamp(input, *, min, out=None) -> Tensor
Clamps all elements in :attr:`input` to be larger or equal :attr:`min`.
If :attr:`input` is of type `FloatTensor` or `DoubleTensor`, :attr:`value`
should be a real number, otherwise it should be an integer.
Args:
{input}
value (Number): minimal value of each element in the output
{out}
Example::
>>> a = torch.randn(4)
>>> a
tensor([-0.0299, -2.3184, 2.1593, -0.8883])
>>> torch.clamp(a, min=0.5)
tensor([ 0.5000, 0.5000, 2.1593, 0.5000])
.. function:: clamp(input, *, max, out=None) -> Tensor
Clamps all elements in :attr:`input` to be smaller or equal :attr:`max`.
If :attr:`input` is of type `FloatTensor` or `DoubleTensor`, :attr:`value`
should be a real number, otherwise it should be an integer.
Args:
{input}
value (Number): maximal value of each element in the output
{out}
Example::
>>> a = torch.randn(4)
>>> a
tensor([ 0.7753, -0.4702, -0.4599, 1.1899])
>>> torch.clamp(a, max=0.5)
tensor([ 0.5000, -0.4702, -0.4599, 0.5000])
""".format(**common_args))
add_docstr(torch.clip, r"""
clip(input, min, max, *, out=None) -> Tensor
Alias for :func:`torch.clamp`.
""".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
""" + 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,
r"""
conj(input, out=None) -> Tensor
Computes the element-wise conjugate of the given :attr:`input` tensor.
.. math::
\text{out}_{i} = conj(\text{input}_{i})
""" + r"""
Args:
{input}
{out}
Example::
>>> torch.conj(torch.tensor([-1 + 1j, -2 + 2j, 3 - 3j]))
tensor([-1 - 1j, -2 - 2j, 3 + 3j])
""".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}
{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}
{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])
""".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`.
:attr:`input` and :attr:`other` must have the same size, and the size of their
:attr:`dim` dimension should be 3.
If :attr:`dim` is not given, it defaults to the first dimension found with the
size 3. Note that this might be unexpected.
Args:
{input}
other (Tensor): the second input tensor
dim (int, optional): the dimension to take the cross-product in.
{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
{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
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
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, out=None, dtype=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
{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, out=None, dtype=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
{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
Given a quantized Tensor, dequantize it and return an fp32 Tensor
Args:
tensor (Tensor): A quantized Tensor
.. function:: dequantize(tensors) -> sequence of Tensors
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
{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.digamma,
r"""
digamma(input, out=None) -> Tensor
Computes the logarithmic derivative of the gamma function on `input`.
.. math::
\psi(x) = \frac{d}{dx} \ln\left(\Gamma\left(x\right)\right) = \frac{\Gamma'(x)}{\Gamma(x)}
Args:
input (Tensor): the tensor to compute the digamma function on
Example::
>>> a = torch.tensor([1, 0.5])
>>> torch.digamma(a)
tensor([-0.5772, -1.9635])
""")
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, out=None) -> Tensor
Divides each element of the input ``input`` with the scalar ``other`` and
returns a new resulting tensor.
.. warning::
Integer division using div is no longer supported, and in a future release
div will perform true division as in Python 3. Use :func:`torch.true_divide`
or :func:`torch.floor_divide` (// in Python), instead.
.. math::
\text{{out}}_i = \frac{{\text{{input}}_i}}{{\text{{other}}}}
If the :class:`torch.dtype` of ``input`` and ``other`` differ, the
:class:`torch.dtype` of the result tensor is determined following rules
described in the type promotion :ref:`documentation <type-promotion-doc>`. If
``out`` is specified, the result must be :ref:`castable <type-promotion-doc>`
to the :class:`torch.dtype` of the specified output tensor. Integral division
by zero leads to undefined behavior.
Args:
{input}
other (Number): the number to be divided to each element of ``input``
Keyword args:
{out}
Example::
>>> a = torch.randn(5)
>>> a
tensor([ 0.3810, 1.2774, -0.2972, -0.3719, 0.4637])
>>> torch.div(a, 0.5)
tensor([ 0.7620, 2.5548, -0.5944, -0.7439, 0.9275])
.. function:: div(input, other, out=None) -> Tensor
Each element of the tensor ``input`` is divided by each element of the tensor
``other``. The resulting tensor is returned.
.. math::
\text{{out}}_i = \frac{{\text{{input}}_i}}{{\text{{other}}_i}}
The shapes of ``input`` and ``other`` must be :ref:`broadcastable
<broadcasting-semantics>`. If the :class:`torch.dtype` of ``input`` and
``other`` differ, the :class:`torch.dtype` of the result tensor is determined
following rules described in the type promotion :ref:`documentation
<type-promotion-doc>`. If ``out`` is specified, the result must be
:ref:`castable <type-promotion-doc>` to the :class:`torch.dtype` of the
specified output tensor. Integral division by zero leads to undefined behavior.
Args:
input (Tensor): the numerator tensor
other (Tensor): the denominator tensor
Keyword args:
{out}
Example::
>>> a = torch.randn(4, 4)
>>> a
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.randn(4)
>>> b
tensor([ 0.8032, 0.2930, -0.8113, -0.2308])
>>> torch.div(a, b)
tensor([[-0.4620, -6.6051, 0.5676, 1.2637],
[ 0.2260, -3.4507, -1.2086, 6.8988],
[ 0.1322, 4.9764, -0.9564, 5.3480],
[-0.2278, -0.1068, -1.4678, 6.3936]])
""".format(**common_args))
add_docstr(torch.dot,
r"""
dot(input, tensor) -> Tensor
Computes the dot product (inner product) of two tensors.
.. note:: This function does not :ref:`broadcast <broadcasting-semantics>`.
Example::
>>> torch.dot(torch.tensor([2, 3]), torch.tensor([2, 1]))
tensor(7)
""")
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
for :func:`torch.symeig`
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
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]`.
""")
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
Computes the error function of each element. The error function is defined as follows:
.. math::
\mathrm{erf}(x) = \frac{2}{\sqrt{\pi}} \int_{0}^{x} e^{-t^2} dt
""" + r"""
Args:
{input}
{out}
Example::
>>> torch.erf(torch.tensor([0, -1., 10.]))
tensor([ 0.0000, -0.8427, 1.0000])
""".format(**common_args))
add_docstr(torch.erfc,
r"""
erfc(input, out=None) -> Tensor
Computes the complementary error function of each element of :attr:`input`.
The complementary error function is defined as follows:
.. math::
\mathrm{erfc}(x) = 1 - \frac{2}{\sqrt{\pi}} \int_{0}^{x} e^{-t^2} dt
""" + r"""
Args:
{input}
{out}
Example::
>>> torch.erfc(torch.tensor([0, -1., 10.]))
tensor([ 1.0000, 1.8427, 0.0000])
""".format(**common_args))
add_docstr(torch.erfinv,
r"""
erfinv(input, out=None) -> Tensor
Computes the inverse error function of each element of :attr:`input`.
The inverse error function is defined in the range :math:`(-1, 1)` as:
.. math::
\mathrm{erfinv}(\mathrm{erf}(x)) = x
""" + r"""
Args:
{input}
{out}
Example::
>>> torch.erfinv(torch.tensor([0, 0.5, -1.]))
tensor([ 0.0000, 0.4769, -inf])
""".format(**common_args))
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}
{out}
Example::
>>> torch.exp(torch.tensor([0, math.log(2.)]))
tensor([ 1., 2.])
""".format(**common_args))
add_docstr(torch.expm1,
r"""
expm1(input, out=None) -> Tensor
Returns a new tensor with the exponential of the elements minus 1
of :attr:`input`.
.. math::
y_{i} = e^{x_{i}} - 1
""" + r"""
Args:
{input}
{out}
Example::
>>> torch.expm1(torch.tensor([0, math.log(2.)]))
tensor([ 0., 1.])
""".format(**common_args))
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`
{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}
{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
Return the division of the inputs rounded down to the nearest integer. See :func:`torch.div`
for type promotion and broadcasting rules.
.. math::
\text{{out}}_i = \left\lfloor \frac{{\text{{input}}_i}}{{\text{{other}}_i}} \right\rfloor
""" + r"""
Args:
input (Tensor): the numerator tensor
other (Tensor or Scalar): the denominator
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
Computes the element-wise remainder of division.
The dividend and divisor may contain both for integer and floating point
numbers. The remainder has the same sign as the dividend :attr:`input`.
When :attr:`other` is a tensor, the shapes of :attr:`input` and
:attr:`other` must be :ref:`broadcastable <broadcasting-semantics>`.
Args:
input (Tensor): the dividend
other (Tensor or float): the divisor, which may be either a number or a tensor of the same shape as the dividend
{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.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``.
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.flatten,
r"""
flatten(input, start_dim=0, end_dim=-1) -> Tensor
Flattens a contiguous range of dims in a tensor.
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, out=None, sparse_grad=False) -> 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
If :attr:`input` is an n-dimensional tensor with size
:math:`(x_0, x_1..., x_{i-1}, x_i, x_{i+1}, ..., x_{n-1})`
and ``dim = i``, then :attr:`index` must be an :math:`n`-dimensional tensor with
size :math:`(x_0, x_1, ..., x_{i-1}, y, x_{i+1}, ..., x_{n-1})` where :math:`y \geq 1`
and :attr:`out` will have the same size as :attr:`index`.
""" + r"""
Args:
input (Tensor): the source tensor
dim (int): the axis along which to index
index (LongTensor): the indices of elements to gather
out (Tensor, optional): the destination tensor
sparse_grad(bool,optional): If ``True``, gradient w.r.t. :attr:`input` will be a sparse 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.geqrf,
r"""
geqrf(input, out=None) -> (Tensor, Tensor)
This is a low-level function for calling LAPACK directly. This function
returns a namedtuple (a, tau) as defined in `LAPACK documentation for geqrf`_ .
You'll generally want to use :func:`torch.qr` instead.
Computes a QR decomposition of :attr:`input`, but without constructing
:math:`Q` and :math:`R` as explicit separate matrices.
Rather, this directly calls the underlying LAPACK function `?geqrf`
which produces a sequence of 'elementary reflectors'.
See `LAPACK documentation for geqrf`_ for further details.
Args:
input (Tensor): the input matrix
out (tuple, optional): the output tuple of (Tensor, Tensor)
.. _LAPACK documentation for geqrf:
https://software.intel.com/en-us/node/521004
""")
add_docstr(torch.outer, r"""
outer(input, vec2, *, out=None) -> Tensor
Alias of :func:`torch.ger`.
""")
add_docstr(torch.ger,
r"""
ger(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
out (Tensor, optional): optional output matrix
Example::
>>> v1 = torch.arange(1., 5.)
>>> v2 = torch.arange(1., 4.)
>>> torch.ger(v1, v2)
tensor([[ 1., 2., 3.],
[ 2., 4., 6.],
[ 3., 6., 9.],
[ 4., 8., 12.]])
""")
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`.
.. note::
Irrespective of the original strides, the returned matrices
`solution` and `LU` will be transposed, i.e. with strides like
`B.contiguous().transpose(-1, -2).stride()` and
`A.contiguous().transpose(-1, -2).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.
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.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 (int): lower end of the range (inclusive)
max (int): upper end of the range (inclusive)
{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.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.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 (LongTensor): the 1-D tensor containing the indices to index
{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
Takes the inverse of the square matrix :attr:`input`. :attr:`input` can be batches
of 2D square tensors, in which case this function would return a tensor composed of
individual inverses.
.. note::
Irrespective of the original strides, the returned tensors will be
transposed, i.e. with strides like `input.contiguous().transpose(-2, -1).stride()`
Args:
input (Tensor): the input tensor of size :math:`(*, n, n)` where `*` is zero or more
batch dimensions
{out}
Example::
>>> x = torch.rand(4, 4)
>>> y = torch.inverse(x)
>>> z = torch.mm(x, y)
>>> z
tensor([[ 1.0000, -0.0000, -0.0000, 0.0000],
[ 0.0000, 1.0000, 0.0000, 0.0000],
[ 0.0000, 0.0000, 1.0000, 0.0000],
[ 0.0000, -0.0000, -0.0000, 1.0000]])
>>> torch.max(torch.abs(z - torch.eye(4))) # Max non-zero
tensor(1.1921e-07)
>>> # Batched inverse example
>>> x = torch.randn(2, 3, 4, 4)
>>> y = torch.inverse(x)
>>> z = torch.matmul(x, y)
>>> torch.max(torch.abs(z - torch.eye(4).expand_as(x))) # Max non-zero
tensor(1.9073e-06)
""".format(**common_args))
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.
Arguments:
{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])
""")
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.
Arguments:
{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`` and ``torch.float16``.
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_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.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.
Args:
{input}
k (int): k for the k-th smallest element
dim (int, optional): the dimension to find the kth value along
{keepdim}
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.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.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
{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 logarithm of the gamma function on :attr:`input`.
.. math::
\text{out}_{i} = \log \Gamma(\text{input}_{i})
""" + """
Args:
{input}
{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=100, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) -> Tensor
Returns a one-dimensional tensor of :attr:`steps`
equally spaced points between :attr:`start` and :attr:`end`.
The output tensor is 1-D of size :attr:`steps`.
Args:
start (float): the starting value for the set of points
end (float): the ending value for the set of points
steps (int): number of points to sample between :attr:`start`
and :attr:`end`. Default: ``100``.
{out}
{dtype}
{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}
{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}
{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}
{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}
{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.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
{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}
{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
{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
{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,
r"""
logspace(start, end, steps=100, base=10.0, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) -> Tensor
Returns a one-dimensional tensor of :attr:`steps` points
logarithmically spaced with base :attr:`base` between
:math:`{{\text{{base}}}}^{{\text{{start}}}}` and :math:`{{\text{{base}}}}^{{\text{{end}}}}`.
The output tensor is 1-D of size :attr:`steps`.
Args:
start (float): the starting value for the set of points
end (float): the ending value for the set of points
steps (int): number of points to sample between :attr:`start`
and :attr:`end`. Default: ``100``.
base (float): base of the logarithm function. Default: ``10.0``.
{out}
{dtype}
{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}
{out}
Example::
>>> a = torch.randn(3, 3)
>>> torch.logsumexp(a, 1)
tensor([ 0.8442, 1.4322, 0.8711])
""".format(**multi_dim_common))
add_docstr(torch.lstsq,
r"""
lstsq(input, A, out=None) -> 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}{ll}
\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.
.. 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`
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_solve,
r"""
lu_solve(input, 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`.
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`.
{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
{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) -> 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`.
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``
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)
""")
add_docstr(torch.matrix_power,
r"""
matrix_power(input, n) -> Tensor
Returns the matrix raised to the power :attr:`n` for square matrices.
For batch of matrices, each individual matrix is raised to the power :attr:`n`.
If :attr:`n` is negative, then the inverse of the matrix (if invertible) is
raised to the power :attr:`n`. For a batch of matrices, the batched inverse
(if invertible) is raised to the power :attr:`n`. If :attr:`n` is 0, then an identity matrix
is returned.
Args:
{input}
n (int): the power to raise the matrix to
Example::
>>> a = torch.randn(2, 2, 2)
>>> a
tensor([[[-1.9975, -1.9610],
[ 0.9592, -2.3364]],
[[-1.2534, -1.3429],
[ 0.4153, -1.4664]]])
>>> torch.matrix_power(a, 3)
tensor([[[ 3.9392, -23.9916],
[ 11.7357, -0.2070]],
[[ 0.2468, -6.7168],
[ 2.0774, -0.8187]]])
""".format(**common_args))
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)
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).
.. warning::
``indices`` does not necessarily contain the first occurrence of each
maximal 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.
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``.
Args:
{input}
{dim}
{keepdim} Default: ``False``.
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
Each element of the tensor ``input`` is compared with the corresponding
element of the tensor ``other`` and an element-wise maximum is taken.
The shapes of ``input`` and ``other`` don't need to match,
but they must be :ref:`broadcastable <broadcasting-semantics>`.
.. math::
\text{{out}}_i = \max(\text{{tensor}}_i, \text{{other}}_i)
.. note:: When the shapes do not match, the shape of the returned output tensor
follows the :ref:`broadcasting rules <broadcasting-semantics>`.
Args:
{input}
other (Tensor): the second input tensor
{out}
Example::
>>> a = torch.randn(4)
>>> a
tensor([ 0.2942, -0.7416, 0.2653, -0.1584])
>>> b = torch.randn(4)
>>> b
tensor([ 0.8722, -1.7421, -0.4141, -0.5055])
>>> torch.max(a, b)
tensor([ 0.8722, -0.7416, 0.2653, -0.1584])
""".format(**single_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.
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
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.mean,
r"""
mean(input) -> Tensor
Returns the mean value of all elements in the :attr:`input` tensor.
Args:
{input}
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, out=None) -> Tensor
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}
{out}
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.median,
r"""
median(input) -> Tensor
Returns the median value of all elements in the :attr:`input` tensor.
.. 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)
Returns a namedtuple ``(values, indices)`` where ``values`` is the median
value of each row of the :attr:`input` tensor in the given dimension
:attr:`dim`. And ``indices`` is the index location of each median 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 outputs tensor having 1 fewer dimension than :attr:`input`.
.. 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}
out (tuple, optional): the result tuple of two output tensors (max, max_indices)
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.quantile,
r"""
quantile(input, q) -> Tensor
Returns the q-th quantiles of all elements in the :attr:`input` tensor, doing a linear
interpolation when the q-th quantile lies between two data.
Args:
{input}
q (float or Tensor): a scalar or 1D tensor of quantile values in the range [0, 1]
Example::
>>> a = torch.randn(1, 3)
>>> a
tensor([[ 0.0700, -0.5446, 0.9214]])
>>> q = torch.tensor([0, 0.5, 1])
>>> torch.quantile(a, q)
tensor([-0.5446, 0.0700, 0.9214])
.. function:: quantile(input, q, dim=None, keepdim=False, *, out=None) -> Tensor
Returns the q-th quantiles of each row of the :attr:`input` tensor along the dimension
:attr:`dim`, doing a linear interpolation when the q-th quantile lies between two
data points. By default, :attr:`dim` is `None` resulting in the :attr:`input` tensor
beign flattened before computation.
If :attr:`q` is a 1D tensor, the first dimension of the result corresponds to the quantiles
and the remaining dimensions are what remains from the reduction of the :attr:`input` tensor.
If :attr:`q` is a scalar or scalar tensor, the result is placed in the reduced dimension.
If :attr:`keepdim` is ``True``, the remaining dimensions are of the same size as
:attr:`input` except in the dimension :attr:`dim` where it is size 1. Otherwise,
the dimension :attr:`dim` is squeezed (see :func:`torch.squeeze`).
Args:
{input}
q (float or Tensor): a scalar or 1D tensor of quantile values in the range [0, 1]
{dim}
{keepdim}
Keyword arguments:
{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])
""".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)
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).
.. warning::
``indices`` does not necessarily contain the first occurrence of each
minimal 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.
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`.
Args:
{input}
{dim}
{keepdim}
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
Each element of the tensor :attr:`input` is compared with the corresponding
element of the tensor :attr:`other` and an element-wise minimum is taken.
The resulting tensor is returned.
The shapes of :attr:`input` and :attr:`other` don't need to match,
but they must be :ref:`broadcastable <broadcasting-semantics>`.
.. math::
\text{{out}}_i = \min(\text{{tensor}}_i, \text{{other}}_i)
.. note:: When the shapes do not match, the shape of the returned output tensor
follows the :ref:`broadcasting rules <broadcasting-semantics>`.
Args:
{input}
other (Tensor): the second input tensor
{out}
Example::
>>> a = torch.randn(4)
>>> a
tensor([ 0.8137, -1.1740, -0.6460, 0.6308])
>>> b = torch.randn(4)
>>> b
tensor([-0.1369, 0.1555, 0.4019, -0.1929])
>>> torch.min(a, b)
tensor([-0.1369, -1.1740, -0.6460, -0.1929])
""".format(**single_dim_common))
add_docstr(torch.argmin,
r"""
argmin(input) -> LongTensor
Returns the indices of the minimum value of all elements in the :attr:`input` tensor.
This is the second value returned by :meth:`torch.min`. See its
documentation for the exact semantics of this method.
Args:
{input}
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)
.. function:: argmin(input, dim, keepdim=False, out=None) -> LongTensor
Returns the indices of the minimum values of a tensor across a dimension.
This is the second value returned by :meth:`torch.min`. See its
documentation for the exact semantics of this method.
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, dim=1)
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`.
Args:
input (Tensor): the first matrix to be multiplied
mat2 (Tensor): the second matrix to be multiplied
{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))
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 m)` tensor and :attr:`other` is a :math:`(k \times m \times p)`
tensor, :attr:`out` will be an :math:`(j \times k \times n \times p)` tensor.
.. 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
{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))
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}
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)
Multiplies each element of the input :attr:`input` with the scalar
:attr:`other` and returns a new resulting tensor.
.. math::
\text{out}_i = \text{other} \times \text{input}_i
""" + r"""
If :attr:`input` is of type `FloatTensor` or `DoubleTensor`, :attr:`other`
should be a real number, otherwise it should be an integer
Args:
{input}
value (Number): the number to be multiplied to each element of :attr:`input`
{out}
Example::
>>> a = torch.randn(3)
>>> a
tensor([ 0.2015, -0.4255, 2.6087])
>>> torch.mul(a, 100)
tensor([ 20.1494, -42.5491, 260.8663])
.. function:: mul(input, other, out=None)
Each element of the tensor :attr:`input` is multiplied by the corresponding
element of the Tensor :attr:`other`. The resulting tensor is returned.
The shapes of :attr:`input` and :attr:`other` must be
:ref:`broadcastable <broadcasting-semantics>`.
.. math::
\text{out}_i = \text{input}_i \times \text{other}_i
""" + r"""
Args:
input (Tensor): the first multiplicand tensor
other (Tensor): the second multiplicand tensor
{out}
Example::
>>> a = torch.randn(4, 1)
>>> a
tensor([[ 1.1207],
[-0.3137],
[ 0.0700],
[ 0.8378]])
>>> b = torch.randn(1, 4)
>>> b
tensor([[ 0.5146, 0.1216, -0.5244, 2.2382]])
>>> torch.mul(a, b)
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.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
{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
{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) -> Tensor
Computes the `multivariate log-gamma function
<https://en.wikipedia.org/wiki/Multivariate_gamma_function>`_) with dimension
:math:`p` element-wise, given by
.. math::
\log(\Gamma_{p}(a)) = C + \displaystyle \sum_{i=1}^{p} \log\left(\Gamma\left(a - \frac{i - 1}{2}\right)\right)
where :math:`C = \log(\pi) \times \frac{p (p - 1)}{4}` and :math:`\Gamma(\cdot)` is the Gamma function.
All elements must be greater than :math:`\frac{p - 1}{2}`, otherwise an error would be thrown.
Args:
input (Tensor): the tensor to compute the multivariate log-gamma function
p (int): the number of dimensions
Example::
>>> a = torch.empty(2, 3).uniform_(1, 2)
>>> a
tensor([[1.6835, 1.8474, 1.1929],
[1.0475, 1.7162, 1.4180]])
>>> torch.mvlgamma(a, 2)
tensor([[0.3928, 0.4007, 0.7586],
[1.0311, 0.3901, 0.5049]])
""")
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.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 :attr:`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.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.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}
{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.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, 2]), torch.Tensor([2, 1])) == 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:`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}
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
Args:
mean (Tensor): the tensor of per-element means
std (Tensor): the tensor of per-element standard deviations
{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
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
{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
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
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
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.
{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.
{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}
{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, input2) -> Tensor
Computes the orthogonal matrix `Q` of a QR factorization, from the `(input, input2)`
tuple returned by :func:`torch.geqrf`.
This directly calls the underlying LAPACK function `?orgqr`.
See `LAPACK documentation for orgqr`_ for further details.
Args:
input (Tensor): the `a` from :func:`torch.geqrf`.
input2 (Tensor): the `tau` from :func:`torch.geqrf`.
.. _LAPACK documentation for orgqr:
https://software.intel.com/en-us/mkl-developer-reference-c-orgqr
""")
add_docstr(torch.ormqr,
r"""
ormqr(input, input2, input3, left=True, transpose=False) -> Tensor
Multiplies `mat` (given by :attr:`input3`) by the orthogonal `Q` matrix of the QR factorization
formed by :func:`torch.geqrf` that is represented by `(a, tau)` (given by (:attr:`input`, :attr:`input2`)).
This directly calls the underlying LAPACK function `?ormqr`.
See `LAPACK documentation for ormqr`_ for further details.
Args:
input (Tensor): the `a` from :func:`torch.geqrf`.
input2 (Tensor): the `tau` from :func:`torch.geqrf`.
input3 (Tensor): the matrix to be multiplied.
.. _LAPACK documentation for ormqr:
https://software.intel.com/en-us/mkl-developer-reference-c-ormqr
""")
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
{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
Computes the :math:`n^{th}` derivative of the digamma function on :attr:`input`.
:math:`n \geq 0` is called the order of the polygamma function.
.. math::
\psi^{(n)}(x) = \frac{d^{(n)}}{dx^{(n)}} \psi(x)
.. note::
This function is implemented only for nonnegative integers :math:`n \geq 0`.
""" + """
Args:
n (int): the order of the polygamma function
{input}
{out}
Example::
>>> a = torch.tensor([1, 0.5])
>>> torch.polygamma(1, a)
tensor([1.64493, 4.9348])
>>> torch.polygamma(2, a)
tensor([ -2.4041, -16.8288])
>>> torch.polygamma(3, a)
tensor([ 6.4939, 97.4091])
>>> torch.polygamma(4, a)
tensor([ -24.8863, -771.4742])
""".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
{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
: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
{out}
Example::
>>> exp = torch.arange(1., 5.)
>>> base = 2
>>> torch.pow(base, exp)
tensor([ 2., 4., 8., 16.])
""".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}
{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
Returns the product of each row of the :attr:`input` tensor in the given
dimension :attr:`dim`.
{keepdim_details}
Args:
{input}
{dim}
{keepdim}
{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.
.. note:: precision may be lost if the magnitudes of the elements of :attr:`input`
are large
.. note:: While it should always give you a valid decomposition, it may not
give you the same one across platforms - it will depend on your
LAPACK implementation.
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.
out (tuple, optional): tuple of `Q` and `R` tensors
satisfying :code:`input = torch.matmul(Q, R)`.
The dimensions of `Q` and `R` are :math:`(*, m, k)` and :math:`(*, k, n)`
respectively, where :math:`k = \min(m, n)` if :attr:`some:` is ``True`` and
:math:`k = m` otherwise.
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.transpose(-2, -1), 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.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.
{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}
{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.
{generator}
{out}
{dtype}
{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.
{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.
{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}
{dtype}
{layout}
{device}
{requires_grad}
{memory_format}
""".format(**factory_like_common_args))
add_docstr(torch.randperm,
r"""
randperm(n, out=None, dtype=torch.int64, layout=torch.strided, device=None, requires_grad=False) -> LongTensor
Returns a random permutation of integers from ``0`` to ``n - 1``.
Args:
n (int): the upper bound (exclusive)
{out}
dtype (:class:`torch.dtype`, optional): the desired data type of returned tensor.
Default: ``torch.int64``.
{layout}
{device}
{requires_grad}
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 :attr:`data`.
.. warning::
:func:`torch.tensor` always copies :attr:`data`. If you have a Tensor
``data`` and want to avoid a copy, use :func:`torch.Tensor.requires_grad_`
or :func:`torch.Tensor.detach`.
If you have a NumPy ``ndarray`` and want to avoid a copy, use
:func:`torch.as_tensor`.
.. warning::
When data is a tensor `x`, :func:`torch.tensor` reads out 'the data' from whatever it is passed,
and constructs a leaf variable. Therefore ``torch.tensor(x)`` is equivalent to ``x.clone().detach()``
and ``torch.tensor(x, requires_grad=True)`` is equivalent to ``x.clone().detach().requires_grad_(True)``.
The equivalents using ``clone()`` and ``detach()`` are recommended.
Args:
{data}
{dtype}
{device}
{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 torch.cuda.DoubleTensor
tensor([[ 0.1111, 0.2222, 0.3333]], dtype=torch.float64, device='cuda:0')
>>> torch.tensor(3.14159) # Create a scalar (zero-dimensional 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 in favor of :func:`torch.arange`.
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``.
{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``.
{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.remainder,
r"""
remainder(input, other, out=None) -> Tensor
Computes the element-wise remainder of division.
The dividend and divisor may contain both for integer and floating point
numbers. The remainder has the same sign as the divisor :attr:`other`.
When :attr:`other` is a tensor, the shapes of :attr:`input` and
:attr:`other` must be :ref:`broadcastable <broadcasting-semantics>`.
Args:
input (Tensor): the dividend
other (Tensor or float): the divisor that may be either a number or a
Tensor of the same shape as the dividend
{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([ 1.0000, 0.5000, 0.0000, 1.0000, 0.5000])
.. seealso::
:func:`torch.fmod`, which computes the element-wise remainder of
division equivalently to the C library function ``fmod()``.
""".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
{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.round,
r"""
round(input, out=None) -> Tensor
Returns a new tensor with each of the elements of :attr:`input` rounded
to the closest integer.
Args:
{input}
{out}
Example::
>>> a = torch.randn(4)
>>> a
tensor([ 0.9920, 0.6077, 0.9734, -1.0362])
>>> torch.round(a)
tensor([ 1., 1., 1., -1.])
""".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}
{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.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
Returns a new tensor with the sigmoid of the elements of :attr:`input`.
.. math::
\text{out}_{i} = \frac{1}{1 + e^{-\text{input}_{i}}}
""" + r"""
Args:
{input}
Keyword args:
{out}
Example::
>>> a = torch.randn(4)
>>> a
tensor([ 0.9213, 1.0887, -0.8858, -1.7683])
>>> torch.sigmoid(a)
tensor([ 0.7153, 0.7481, 0.2920, 0.1458])
""".format(**common_args))
add_docstr(torch.logit,
r"""
logit(input, eps=None, out=None) -> Tensor
Returns a new tensor with the logit of the elements of :attr:`input`.
:attr:`input` is clamped to [eps, 1 - eps] when eps is not None.
When eps is None and :attr:`input` < 0 or :attr:`input` > 1, the function will yields NaN.
.. math::
y_{i} = \ln(\frac{z_{i}}{1 - z_{i}}) \\
z_{i} = \begin{cases}
x_{i} & \text{if eps is None} \\
\text{eps} & \text{if } x_{i} < \text{eps} \\
x_{i} & \text{if } \text{eps} \leq x_{i} \leq 1 - \text{eps} \\
1 - \text{eps} & \text{if } x_{i} > 1 - \text{eps}
\end{cases}
""" + r"""
Args:
{input}
eps (float, optional): the epsilon for input clamp bound. Default: ``None``
{out}
Example::
>>> a = torch.rand(5)
>>> a
tensor([0.2796, 0.9331, 0.6486, 0.1523, 0.6516])
>>> torch.logit(a, eps=1e-6)
tensor([-0.9466, 2.6352, 0.6131, -1.7169, 0.6261])
""".format(**common_args))
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}
{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.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}
{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.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}
{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])
""".format(**common_args))
add_docstr(torch.sort,
r"""
sort(input, dim=-1, descending=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.
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)
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]])
""".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.sparse_coo_tensor,
r"""
sparse_coo_tensor(indices, values, size=None, dtype=None, device=None, requires_grad=False) -> Tensor
Constructs a sparse tensors in COO(rdinate) format with non-zero elements at the given :attr:`indices`
with the given :attr:`values`. A sparse tensor can be `uncoalesced`, in that case, there are duplicate
coordinates in the indices, and the value at that index is the sum of all duplicate value entries:
`torch.sparse`_.
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.
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}
{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}
{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
{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, unbiased=True) -> Tensor
Returns the standard-deviation of all elements in the :attr:`input` tensor.
If :attr:`unbiased` is ``False``, then the standard-deviation will be calculated
via the biased estimator. Otherwise, Bessel's correction will be used.
Args:
{input}
unbiased (bool): whether to use the unbiased estimation or not
Example::
>>> a = torch.randn(1, 3)
>>> a
tensor([[-0.8166, -1.3802, -0.3560]])
>>> torch.std(a)
tensor(0.5130)
.. function:: std(input, dim, unbiased=True, keepdim=False, out=None) -> Tensor
Returns the standard-deviation of each row of the :attr:`input` tensor in the
dimension :attr:`dim`. If :attr:`dim` is a list of dimensions,
reduce over all of them.
{keepdim_details}
If :attr:`unbiased` is ``False``, then the standard-deviation will be calculated
via the biased estimator. Otherwise, Bessel's correction will be used.
Args:
{input}
{dim}
unbiased (bool): whether to use the unbiased estimation or not
{keepdim}
{out}
Example::
>>> a = torch.randn(4, 4)
>>> a
tensor([[ 0.2035, 1.2959, 1.8101, -0.4644],
[ 1.5027, -0.3270, 0.5905, 0.6538],
[-1.5745, 1.3330, -0.5596, -0.6548],
[ 0.1264, -0.5080, 1.6420, 0.1992]])
>>> torch.std(a, dim=1)
tensor([ 1.0311, 0.7477, 1.2204, 0.9087])
""".format(**multi_dim_common))
add_docstr(torch.std_mean,
r"""
std_mean(input, unbiased=True) -> (Tensor, Tensor)
Returns the standard-deviation and mean of all elements in the :attr:`input` tensor.
If :attr:`unbiased` is ``False``, then the standard-deviation will be calculated
via the biased estimator. Otherwise, Bessel's correction will be used.
Args:
{input}
unbiased (bool): whether to use the unbiased estimation or not
Example::
>>> a = torch.randn(1, 3)
>>> a
tensor([[0.3364, 0.3591, 0.9462]])
>>> torch.std_mean(a)
(tensor(0.3457), tensor(0.5472))
.. function:: std_mean(input, dim, unbiased=True, keepdim=False) -> (Tensor, Tensor)
Returns the standard-deviation and mean of each row of the :attr:`input` tensor in the
dimension :attr:`dim`. If :attr:`dim` is a list of dimensions,
reduce over all of them.
{keepdim_details}
If :attr:`unbiased` is ``False``, then the standard-deviation will be calculated
via the biased estimator. Otherwise, Bessel's correction will be used.
Args:
{input}
{dim}
unbiased (bool): whether to use the unbiased estimation or not
{keepdim}
Example::
>>> a = torch.randn(4, 4)
>>> a
tensor([[ 0.5648, -0.5984, -1.2676, -1.4471],
[ 0.9267, 1.0612, 1.1050, -0.6014],
[ 0.0154, 1.9301, 0.0125, -1.0904],
[-1.9711, -0.7748, -1.3840, 0.5067]])
>>> torch.std_mean(a, 1)
(tensor([0.9110, 0.8197, 1.2552, 1.0608]), tensor([-0.6871, 0.6229, 0.2169, -0.9058]))
""".format(**multi_dim_common))
add_docstr(torch.sum,
r"""
sum(input, dtype=None) -> Tensor
Returns the sum of all elements in the :attr:`input` tensor.
Args:
{input}
{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
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}
{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
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)
This function returns a namedtuple ``(U, S, V)`` which is the singular value
decomposition of a input real matrix or batches of real matrices :attr:`input` such that
:math:`input = U \times diag(S) \times V^T`.
If :attr:`some` is ``True`` (default), the method returns the reduced singular value decomposition
i.e., if the last two dimensions of :attr:`input` are ``m`` and ``n``, then the returned
`U` and `V` matrices will contain only :math:`min(n, m)` orthonormal columns.
If :attr:`compute_uv` is ``False``, the returned `U` and `V` matrices will be zero matrices
of shape :math:`(m \times m)` and :math:`(n \times n)` respectively. :attr:`some` will be ignored here.
.. 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 is returned in descending order.
.. note:: The implementation of SVD on CPU uses the LAPACK routine `?gesdd` (a divide-and-conquer
algorithm) instead of `?gesvd` for speed. Analogously, the SVD on GPU uses the MAGMA routine
`gesdd` as well.
.. note:: Irrespective of the original strides, the returned matrix `U`
will be transposed, i.e. with strides :code:`U.contiguous().transpose(-2, -1).stride()`
.. note:: Extra care needs to be taken when backward through `U` and `V`
outputs. Such operation is really only stable when :attr:`input` is
full rank with all distinct singular values. Otherwise, ``NaN`` can
appear as the gradients are not properly defined. Also, notice that
double backward will usually do an additional backward through `U` and
`V` even if the original backward is only on `S`.
.. note:: When :attr:`some` = ``False``, the gradients on :code:`U[..., :, min(m, n):]`
and :code:`V[..., :, min(m, n):]` will be ignored in backward as those vectors
can be arbitrary bases of the subspaces.
.. note:: When :attr:`compute_uv` = ``False``, backward cannot be performed since `U` and `V`
from the forward pass is required for the backward operation.
Args:
input (Tensor): the input tensor of size :math:`(*, m, n)` where `*` is zero or more
batch dimensions consisting of :math:`m \times n` matrices.
some (bool, optional): controls the shape of returned `U` and `V`
compute_uv (bool, optional): option whether to compute `U` and `V` or not
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.transpose(-2, -1)))
tensor(2.6503e-06)
""")
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 matrix :attr:`input` or a batch of real symmetric matrices,
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,
only the upper triangular portion is used by default.
If :attr:`upper` is ``False``, then lower triangular portion is used.
.. 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().transpose(-1, -2).stride()`.
.. note:: Extra care needs to be taken when backward through outputs. Such
operation is really only stable when all eigenvalues are distinct.
Otherwise, ``NaN`` can appear as the gradients are not properly defined.
Args:
input (Tensor): the input tensor of size :math:`(*, n, n)` where `*` is zero or more
batch dimensions consisting of symmetric matrices.
eigenvectors(boolean, optional): controls whether eigenvectors have to be computed
upper(boolean, optional): controls whether to consider upper-triangular or lower-triangular region
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.transpose(-2, -1) # To make a_big symmetric
>>> e, v = a_big.symeig(eigenvectors=True)
>>> torch.allclose(torch.matmul(v, torch.matmul(e.diag_embed(), v.transpose(-2, -1))), 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]])
""".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.
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 array 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:
Equivalent to input[:,::-1]. Requires the array to be at least 2-D.
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 array 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:
Equivalent to input[::-1,...]. Requires the array to be at least 1-D.
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 along the given dimension(s). Elements that are shifted beyond the
last position are re-introduced at the first position. If a dimension is not
specified, 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, 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}
indices (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.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}
{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}
{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, where the `indices` are the indices
of the elements in the original `input` tensor.
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
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.
The resulting :attr:`out` tensor shares it's underlying storage with the
:attr:`input` tensor, so changing the content of one would change the content
of the other.
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]])
""".format(**common_args))
add_docstr(torch.triangular_solve,
r"""
triangular_solve(input, A, upper=True, transpose=False, unitriangular=False) -> (Tensor, Tensor)
Solves a system of equations with a triangular coefficient matrix :math:`A`
and multiple right-hand sides :math:`b`.
In particular, solves :math:`AX = b` and assumes :math:`A` is upper-triangular
with the default keyword arguments.
`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`
Args:
input (Tensor): multiple right-hand sides of size :math:`(*, m, k)` where
:math:`*` is zero of more batch dimensions (:math:`b`)
A (Tensor): the input triangular coefficient matrix of size :math:`(*, m, m)`
where :math:`*` is zero or more batch dimensions
upper (bool, optional): whether to solve the upper-triangular system
of equations (default) or the lower-triangular system of equations. Default: ``True``.
transpose (bool, optional): whether :math:`A` should be transposed before
being sent into the solver. 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``.
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
{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.
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
{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.
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
Performs "true division" that always computes the division
in floating point. Analogous to division in Python 3 and equivalent to
:func:`torch.div` except when both inputs have bool or integer scalar types,
in which case they are cast to the default (floating) scalar type before the division.
.. math::
\text{{out}}_i = \frac{{\text{{dividend}}_i}}{{\text{{divisor}}}}
Args:
dividend (Tensor): the dividend
divisor (Tensor or Scalar): the divisor
Keyword args:
{out}
Example::
>>> dividend = torch.tensor([5, 3], dtype=torch.int)
>>> divisor = torch.tensor([3, 2], dtype=torch.int)
>>> torch.true_divide(dividend, divisor)
tensor([1.6667, 1.5000])
>>> torch.true_divide(dividend, 2)
tensor([2.5000, 1.5000])
""".format(**common_args))
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}
{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.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, unbiased=True) -> Tensor
Returns the variance of all elements in the :attr:`input` tensor.
If :attr:`unbiased` is ``False``, then the variance will be calculated via the
biased estimator. Otherwise, Bessel's correction will be used.
Args:
{input}
unbiased (bool): whether to use the unbiased estimation or not
Example::
>>> a = torch.randn(1, 3)
>>> a
tensor([[-0.3425, -1.2636, -0.4864]])
>>> torch.var(a)
tensor(0.2455)
.. function:: var(input, dim, keepdim=False, unbiased=True, out=None) -> Tensor
Returns the variance of each row of the :attr:`input` tensor in the given
dimension :attr:`dim`.
{keepdim_details}
If :attr:`unbiased` is ``False``, then the variance will be calculated via the
biased estimator. Otherwise, Bessel's correction will be used.
Args:
{input}
{dim}
{keepdim}
unbiased (bool): whether to use the unbiased estimation or not
{out}
Example::
>>> a = torch.randn(4, 4)
>>> a
tensor([[-0.3567, 1.7385, -1.3042, 0.7423],
[ 1.3436, -0.1015, -0.9834, -0.8438],
[ 0.6056, 0.1089, -0.3112, -1.4085],
[-0.7700, 0.6074, -0.1469, 0.7777]])
>>> torch.var(a, 1)
tensor([ 1.7444, 1.1363, 0.7356, 0.5112])
""".format(**multi_dim_common))
add_docstr(torch.var_mean,
r"""
var_mean(input, unbiased=True) -> (Tensor, Tensor)
Returns the variance and mean of all elements in the :attr:`input` tensor.
If :attr:`unbiased` is ``False``, then the variance will be calculated via the
biased estimator. Otherwise, Bessel's correction will be used.
Args:
{input}
unbiased (bool): whether to use the unbiased estimation or not
Example::
>>> a = torch.randn(1, 3)
>>> a
tensor([[0.0146, 0.4258, 0.2211]])
>>> torch.var_mean(a)
(tensor(0.0423), tensor(0.2205))
.. function:: var_mean(input, dim, keepdim=False, unbiased=True) -> (Tensor, Tensor)
Returns the variance and mean of each row of the :attr:`input` tensor in the given
dimension :attr:`dim`.
{keepdim_details}
If :attr:`unbiased` is ``False``, then the variance will be calculated via the
biased estimator. Otherwise, Bessel's correction will be used.
Args:
{input}
{dim}
{keepdim}
unbiased (bool): whether to use the unbiased estimation or not
Example::
>>> a = torch.randn(4, 4)
>>> a
tensor([[-1.5650, 2.0415, -0.1024, -0.5790],
[ 0.2325, -2.6145, -1.6428, -0.3537],
[-0.2159, -1.1069, 1.2882, -1.3265],
[-0.6706, -1.5893, 0.6827, 1.6727]])
>>> torch.var_mean(a, 1)
(tensor([2.3174, 1.6403, 1.4092, 2.0791]), tensor([-0.0512, -1.0946, -0.3403, 0.0239]))
""".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.
{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}
{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,
r"""
empty(*size, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False, pin_memory=False) -> 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.
{out}
{dtype}
{layout}
{device}
{requires_grad}
{pin_memory}
{memory_format}
Example::
>>> torch.empty(2, 3)
tensor(1.00000e-08 *
[[ 6.3984, 0.0000, 0.0000],
[ 0.0000, 0.0000, 0.0000]])
""".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}
{dtype}
{layout}
{device}
{requires_grad}
{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_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
Returns a tensor filled with uninitialized data. The shape and strides of the tensor is
defined by the variable argument :attr:`size` and :attr:`stride` respectively.
``torch.empty_strided(size, stride)`` is equivalent to
``torch.empty(size).as_strided(size, stride)``.
.. warning::
More than one element of the created tensor may refer to a single memory
location. As a result, in-place operations (especially ones that are
vectorized) may result in incorrect behavior. If you need to write to
the tensors, please clone them first.
Args:
size (tuple of ints): the shape of the output tensor
stride (tuple of ints): the strides of the output tensor
{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.
{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, out=None, 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.
{dtype}
{layout}
{device}
{requires_grad}
{memory_format}
""".format(**factory_like_common_args))
add_docstr(torch.det,
r"""
det(input) -> Tensor
Calculates determinant of a square matrix or batches of square matrices.
.. note::
Backward through :meth:`det` internally uses SVD results when :attr:`input` is
not invertible. In this case, double backward through :meth:`det` will be
unstable in when :attr:`input` doesn't have distinct singular values. See
:meth:`~torch.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(3.7641)
>>> A = torch.randn(3, 2, 2)
>>> 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])
""")
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:x 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
``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
:meth:`~torch.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)
Calculates the sign and log absolute value of the determinant(s) of a square matrix or batches of square matrices.
.. note::
If ``input`` has zero determinant, this returns ``(0, -inf)``.
.. note::
Backward through :meth:`slogdet` internally uses SVD results when :attr:`input`
is not invertible. In this case, double backward through :meth:`slogdet`
will be unstable in when :attr:`input` doesn't have distinct singular values.
See :meth:`~torch.svd` for details.
Arguments:
input (Tensor): the input tensor of size ``(*, n, n)`` where ``*`` is zero or more
batch dimensions.
Returns:
A namedtuple (sign, logabsdet) containing the sign of the determinant, and the log
value of the absolute determinant.
Example::
>>> A = torch.randn(3, 3)
>>> A
tensor([[ 0.0032, -0.2239, -1.1219],
[-0.6690, 0.1161, 0.4053],
[-1.6218, -0.9273, -0.0082]])
>>> torch.det(A)
tensor(-0.7576)
>>> torch.logdet(A)
tensor(nan)
>>> torch.slogdet(A)
torch.return_types.slogdet(sign=tensor(-1.), logabsdet=tensor(-0.2776))
""")
add_docstr(torch.pinverse,
r"""
pinverse(input, rcond=1e-15) -> Tensor
Calculates the pseudo-inverse (also known as the Moore-Penrose inverse) of a 2D tensor.
Please look at `Moore-Penrose inverse`_ for more details
.. note::
This method is implemented using the Singular Value Decomposition.
.. note::
The pseudo-inverse is not necessarily a continuous function in the elements of the matrix `[1]`_.
Therefore, derivatives are not always existent, and exist for a constant rank only `[2]`_.
However, this method is backprop-able due to the implementation by using SVD results, and
could be unstable. Double-backward will also be unstable due to the usage of SVD internally.
See :meth:`~torch.svd` for more details.
Arguments:
input (Tensor): The input tensor of size :math:`(*, m, n)` where :math:`*` is zero or more batch dimensions
rcond (float): A floating point value to determine the cutoff for small singular values.
Default: 1e-15
Returns:
The pseudo-inverse of :attr:`input` of dimensions :math:`(*, n, m)`
Example::
>>> input = torch.randn(3, 5)
>>> input
tensor([[ 0.5495, 0.0979, -1.4092, -0.1128, 0.4132],
[-1.1143, -0.3662, 0.3042, 1.6374, -0.9294],
[-0.3269, -0.5745, -0.0382, -0.5922, -0.6759]])
>>> torch.pinverse(input)
tensor([[ 0.0600, -0.1933, -0.2090],
[-0.0903, -0.0817, -0.4752],
[-0.7124, -0.1631, -0.2272],
[ 0.1356, 0.3933, -0.5023],
[-0.0308, -0.1725, -0.5216]])
>>> # Batched pinverse example
>>> a = torch.randn(2,6,3)
>>> b = torch.pinverse(a)
>>> torch.matmul(b, a)
tensor([[[ 1.0000e+00, 1.6391e-07, -1.1548e-07],
[ 8.3121e-08, 1.0000e+00, -2.7567e-07],
[ 3.5390e-08, 1.4901e-08, 1.0000e+00]],
[[ 1.0000e+00, -8.9407e-08, 2.9802e-08],
[-2.2352e-07, 1.0000e+00, 1.1921e-07],
[ 0.0000e+00, 8.9407e-08, 1.0000e+00]]])
.. _Moore-Penrose inverse: https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse
.. _[1]: https://epubs.siam.org/doi/10.1137/0117004
.. _[2]: https://www.jstor.org/stable/2156365
""")
add_docstr(torch.fft, r"""
fft(input, signal_ndim, normalized=False) -> Tensor
Complex-to-complex Discrete Fourier Transform
This method computes the complex-to-complex discrete Fourier transform.
Ignoring the batch dimensions, it computes the following expression:
.. math::
X[\omega_1, \dots, \omega_d] =
\sum_{n_1=0}^{N_1-1} \dots \sum_{n_d=0}^{N_d-1} x[n_1, \dots, n_d]
e^{-j\ 2 \pi \sum_{i=0}^d \frac{\omega_i n_i}{N_i}},
where :math:`d` = :attr:`signal_ndim` is number of dimensions for the
signal, and :math:`N_i` is the size of signal dimension :math:`i`.
This method supports 1D, 2D and 3D complex-to-complex transforms, indicated
by :attr:`signal_ndim`. :attr:`input` must be a tensor with last dimension
of size 2, representing the real and imaginary components of complex
numbers, and should have at least ``signal_ndim + 1`` dimensions with optionally
arbitrary number of leading batch dimensions. If :attr:`normalized` is set to
``True``, this normalizes the result by dividing it with
:math:`\sqrt{\prod_{i=1}^K N_i}` so that the operator is unitary.
Returns the real and the imaginary parts together as one tensor of the same
shape of :attr:`input`.
The inverse of this function is :func:`~torch.ifft`.
.. note::
For CUDA tensors, an LRU cache is used for cuFFT plans to speed up
repeatedly running FFT methods on tensors of same geometry with same
configuration. See :ref:`cufft-plan-cache` for more details on how to
monitor and control the cache.
.. warning::
If the torch.fft module is imported then "torch.fft" will refer to the
module and not this function. Use :meth:`torch.Tensor.fft` instead.
.. warning::
Due to limited dynamic range of half datatype, performing this operation in half
precision may cause the first element of result to overflow for certain inputs.
.. warning::
For CPU tensors, this method is currently only available with MKL. Use
:func:`torch.backends.mkl.is_available` to check if MKL is installed.
Arguments:
input (Tensor): the input tensor of at least :attr:`signal_ndim` ``+ 1``
dimensions
signal_ndim (int): the number of dimensions in each signal.
:attr:`signal_ndim` can only be 1, 2 or 3
normalized (bool, optional): controls whether to return normalized results.
Default: ``False``
Returns:
Tensor: A tensor containing the complex-to-complex Fourier transform result
Example::
>>> # unbatched 2D FFT
>>> x = torch.randn(4, 3, 2)
>>> torch.fft(x, 2)
tensor([[[-0.0876, 1.7835],
[-2.0399, -2.9754],
[ 4.4773, -5.0119]],
[[-1.5716, 2.7631],
[-3.8846, 5.2652],
[ 0.2046, -0.7088]],
[[ 1.9938, -0.5901],
[ 6.5637, 6.4556],
[ 2.9865, 4.9318]],
[[ 7.0193, 1.1742],
[-1.3717, -2.1084],
[ 2.0289, 2.9357]]])
>>> # batched 1D FFT
>>> torch.fft(x, 1)
tensor([[[ 1.8385, 1.2827],
[-0.1831, 1.6593],
[ 2.4243, 0.5367]],
[[-0.9176, -1.5543],
[-3.9943, -2.9860],
[ 1.2838, -2.9420]],
[[-0.8854, -0.6860],
[ 2.4450, 0.0808],
[ 1.3076, -0.5768]],
[[-0.1231, 2.7411],
[-0.3075, -1.7295],
[-0.5384, -2.0299]]])
>>> # arbitrary number of batch dimensions, 2D FFT
>>> x = torch.randn(3, 3, 5, 5, 2)
>>> y = torch.fft(x, 2)
>>> y.shape
torch.Size([3, 3, 5, 5, 2])
""")
add_docstr(torch.ifft,
r"""
ifft(input, signal_ndim, normalized=False) -> Tensor
Complex-to-complex Inverse Discrete Fourier Transform
This method computes the complex-to-complex inverse discrete Fourier
transform. Ignoring the batch dimensions, it computes the following
expression:
.. math::
X[\omega_1, \dots, \omega_d] =
\frac{1}{\prod_{i=1}^d N_i} \sum_{n_1=0}^{N_1-1} \dots \sum_{n_d=0}^{N_d-1} x[n_1, \dots, n_d]
e^{\ j\ 2 \pi \sum_{i=0}^d \frac{\omega_i n_i}{N_i}},
where :math:`d` = :attr:`signal_ndim` is number of dimensions for the
signal, and :math:`N_i` is the size of signal dimension :math:`i`.
The argument specifications are almost identical with :func:`~torch.fft`.
However, if :attr:`normalized` is set to ``True``, this instead returns the
results multiplied by :math:`\sqrt{\prod_{i=1}^d N_i}`, to become a unitary
operator. Therefore, to invert a :func:`~torch.fft`, the :attr:`normalized`
argument should be set identically for :func:`~torch.fft`.
Returns the real and the imaginary parts together as one tensor of the same
shape of :attr:`input`.
The inverse of this function is :func:`~torch.fft`.
.. note::
For CUDA tensors, an LRU cache is used for cuFFT plans to speed up
repeatedly running FFT methods on tensors of same geometry with same
configuration. See :ref:`cufft-plan-cache` for more details on how to
monitor and control the cache.
.. warning::
Due to limited dynamic range of half datatype, performing this operation in half
precision may cause the first element of result to overflow for certain inputs.
.. warning::
For CPU tensors, this method is currently only available with MKL. Use
:func:`torch.backends.mkl.is_available` to check if MKL is installed.
Arguments:
input (Tensor): the input tensor of at least :attr:`signal_ndim` ``+ 1``
dimensions
signal_ndim (int): the number of dimensions in each signal.
:attr:`signal_ndim` can only be 1, 2 or 3
normalized (bool, optional): controls whether to return normalized results.
Default: ``False``
Returns:
Tensor: A tensor containing the complex-to-complex inverse Fourier transform result
Example::
>>> x = torch.randn(3, 3, 2)
>>> x
tensor([[[ 1.2766, 1.3680],
[-0.8337, 2.0251],
[ 0.9465, -1.4390]],
[[-0.1890, 1.6010],
[ 1.1034, -1.9230],
[-0.9482, 1.0775]],
[[-0.7708, -0.8176],
[-0.1843, -0.2287],
[-1.9034, -0.2196]]])
>>> y = torch.fft(x, 2)
>>> torch.ifft(y, 2) # recover x
tensor([[[ 1.2766, 1.3680],
[-0.8337, 2.0251],
[ 0.9465, -1.4390]],
[[-0.1890, 1.6010],
[ 1.1034, -1.9230],
[-0.9482, 1.0775]],
[[-0.7708, -0.8176],
[-0.1843, -0.2287],
[-1.9034, -0.2196]]])
""")
add_docstr(torch.rfft,
r"""
rfft(input, signal_ndim, normalized=False, onesided=True) -> Tensor
Real-to-complex Discrete Fourier Transform
This method computes the real-to-complex discrete Fourier transform. It is
mathematically equivalent with :func:`~torch.fft` with differences only in
formats of the input and output.
This method supports 1D, 2D and 3D real-to-complex transforms, indicated
by :attr:`signal_ndim`. :attr:`input` must be a tensor with at least
``signal_ndim`` dimensions with optionally arbitrary number of leading batch
dimensions. If :attr:`normalized` is set to ``True``, this normalizes the result
by dividing it with :math:`\sqrt{\prod_{i=1}^K N_i}` so that the operator is
unitary, where :math:`N_i` is the size of signal dimension :math:`i`.
The real-to-complex Fourier transform results follow conjugate symmetry:
.. math::
X[\omega_1, \dots, \omega_d] = X^*[N_1 - \omega_1, \dots, N_d - \omega_d],
where the index arithmetic is computed modulus the size of the corresponding
dimension, :math:`\ ^*` is the conjugate operator, and
:math:`d` = :attr:`signal_ndim`. :attr:`onesided` flag controls whether to avoid
redundancy in the output results. If set to ``True`` (default), the output will
not be full complex result of shape :math:`(*, 2)`, where :math:`*` is the shape
of :attr:`input`, but instead the last dimension will be halfed as of size
:math:`\lfloor \frac{N_d}{2} \rfloor + 1`.
The inverse of this function is :func:`~torch.irfft`.
.. note::
For CUDA tensors, an LRU cache is used for cuFFT plans to speed up
repeatedly running FFT methods on tensors of same geometry with same
configuration. See :ref:`cufft-plan-cache` for more details on how to
monitor and control the cache.
.. warning::
Due to limited dynamic range of half datatype, performing this operation in half
precision may cause the first element of result to overflow for certain inputs.
.. warning::
For CPU tensors, this method is currently only available with MKL. Use
:func:`torch.backends.mkl.is_available` to check if MKL is installed.
Arguments:
input (Tensor): the input tensor of at least :attr:`signal_ndim` dimensions
signal_ndim (int): the number of dimensions in each signal.
:attr:`signal_ndim` can only be 1, 2 or 3
normalized (bool, optional): controls whether to return normalized results.
Default: ``False``
onesided (bool, optional): controls whether to return half of results to
avoid redundancy. Default: ``True``
Returns:
Tensor: A tensor containing the real-to-complex Fourier transform result
Example::
>>> x = torch.randn(5, 5)
>>> torch.rfft(x, 2).shape
torch.Size([5, 3, 2])
>>> torch.rfft(x, 2, onesided=False).shape
torch.Size([5, 5, 2])
""")
add_docstr(torch.irfft,
r"""
irfft(input, signal_ndim, normalized=False, onesided=True, signal_sizes=None) -> Tensor
Complex-to-real Inverse Discrete Fourier Transform
This method computes the complex-to-real inverse discrete Fourier transform.
It is mathematically equivalent with :func:`ifft` with differences only in
formats of the input and output.
The argument specifications are almost identical with :func:`~torch.ifft`.
Similar to :func:`~torch.ifft`, if :attr:`normalized` is set to ``True``,
this normalizes the result by multiplying it with
:math:`\sqrt{\prod_{i=1}^K N_i}` so that the operator is unitary, where
:math:`N_i` is the size of signal dimension :math:`i`.
.. note::
Due to the conjugate symmetry, :attr:`input` do not need to contain the full
complex frequency values. Roughly half of the values will be sufficient, as
is the case when :attr:`input` is given by :func:`~torch.rfft` with
``rfft(signal, onesided=True)``. In such case, set the :attr:`onesided`
argument of this method to ``True``. Moreover, the original signal shape
information can sometimes be lost, optionally set :attr:`signal_sizes` to be
the size of the original signal (without the batch dimensions if in batched
mode) to recover it with correct shape.
Therefore, to invert an :func:`~torch.rfft`, the :attr:`normalized` and
:attr:`onesided` arguments should be set identically for :func:`~torch.irfft`,
and preferably a :attr:`signal_sizes` is given to avoid size mismatch. See the
example below for a case of size mismatch.
See :func:`~torch.rfft` for details on conjugate symmetry.
The inverse of this function is :func:`~torch.rfft`.
.. warning::
Generally speaking, input to this function should contain values
following conjugate symmetry. Note that even if :attr:`onesided` is
``True``, often symmetry on some part is still needed. When this
requirement is not satisfied, the behavior of :func:`~torch.irfft` is
undefined. Since :func:`torch.autograd.gradcheck` estimates numerical
Jacobian with point perturbations, :func:`~torch.irfft` will almost
certainly fail the check.
.. note::
For CUDA tensors, an LRU cache is used for cuFFT plans to speed up
repeatedly running FFT methods on tensors of same geometry with same
configuration. See :ref:`cufft-plan-cache` for more details on how to
monitor and control the cache.
.. warning::
Due to limited dynamic range of half datatype, performing this operation in half
precision may cause the first element of result to overflow for certain inputs.
.. warning::
For CPU tensors, this method is currently only available with MKL. Use
:func:`torch.backends.mkl.is_available` to check if MKL is installed.
Arguments:
input (Tensor): the input tensor of at least :attr:`signal_ndim` ``+ 1``
dimensions
signal_ndim (int): the number of dimensions in each signal.
:attr:`signal_ndim` can only be 1, 2 or 3
normalized (bool, optional): controls whether to return normalized results.
Default: ``False``
onesided (bool, optional): controls whether :attr:`input` was halfed to avoid
redundancy, e.g., by :func:`rfft`. Default: ``True``
signal_sizes (list or :class:`torch.Size`, optional): the size of the original
signal (without batch dimension). Default: ``None``
Returns:
Tensor: A tensor containing the complex-to-real inverse Fourier transform result
Example::
>>> x = torch.randn(4, 4)
>>> torch.rfft(x, 2, onesided=True).shape
torch.Size([4, 3, 2])
>>>
>>> # notice that with onesided=True, output size does not determine the original signal size
>>> x = torch.randn(4, 5)
>>> torch.rfft(x, 2, onesided=True).shape
torch.Size([4, 3, 2])
>>>
>>> # now we use the original shape to recover x
>>> x
tensor([[-0.8992, 0.6117, -1.6091, -0.4155, -0.8346],
[-2.1596, -0.0853, 0.7232, 0.1941, -0.0789],
[-2.0329, 1.1031, 0.6869, -0.5042, 0.9895],
[-0.1884, 0.2858, -1.5831, 0.9917, -0.8356]])
>>> y = torch.rfft(x, 2, onesided=True)
>>> torch.irfft(y, 2, onesided=True, signal_sizes=x.shape) # recover x
tensor([[-0.8992, 0.6117, -1.6091, -0.4155, -0.8346],
[-2.1596, -0.0853, 0.7232, 0.1941, -0.0789],
[-2.0329, 1.1031, 0.6869, -0.5042, 0.9895],
[-0.1884, 0.2858, -1.5831, 0.9917, -0.8356]])
""")
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.
{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
{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.
{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.
{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.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.trapz,
r"""
trapz(y, x, *, dim=-1) -> Tensor
Estimate :math:`\int y\,dx` along `dim`, using the trapezoid rule.
Arguments:
y (Tensor): The values of the function to integrate
x (Tensor): The points at which the function `y` is sampled.
If `x` is not in ascending order, intervals on which it is decreasing
contribute negatively to the estimated integral (i.e., the convention
:math:`\int_a^b f = -\int_b^a f` is followed).
dim (int): The dimension along which to integrate.
By default, use the last dimension.
Returns:
A Tensor with the same shape as the input, except with `dim` removed.
Each element of the returned tensor represents the estimated integral
:math:`\int y\,dx` along `dim`.
Example::
>>> y = torch.randn((2, 3))
>>> y
tensor([[-2.1156, 0.6857, -0.2700],
[-1.2145, 0.5540, 2.0431]])
>>> x = torch.tensor([[1, 3, 4], [1, 2, 3]])
>>> torch.trapz(y, x)
tensor([-1.2220, 0.9683])
.. function:: trapz(y, *, dx=1, dim=-1) -> Tensor
As above, but the sample points are spaced uniformly at a distance of `dx`.
Arguments:
y (Tensor): The values of the function to integrate
dx (float): The distance between points at which `y` is sampled.
dim (int): The dimension along which to integrate.
By default, use the last dimension.
Returns:
A Tensor with the same shape as the input, except with `dim` removed.
Each element of the returned tensor represents the estimated integral
:math:`\int y\,dx` along `dim`.
""")
add_docstr(torch.repeat_interleave,
r"""
repeat_interleave(input, repeats, dim=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.
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]])
.. function:: repeat_interleave(repeats) -> Tensor
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.quantize_per_tensor,
r"""
quantize_per_tensor(input, scale, zero_point, dtype) -> Tensor
Converts a float tensor to quantized tensor with given scale and zero point.
Arguments:
input (Tensor): float tensor to quantize
scale (float): scale to apply in quantization formula
zero_point (int): 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
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)
""")
add_docstr(torch.quantize_per_channel,
r"""
quantize_per_channel(input, scales, zero_points, axis, dtype) -> Tensor
Converts a float tensor to 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.Generator,
r"""
Generator(device='cpu') -> Generator
Creates and returns a generator object which manages the state of the algorithm that
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.searchsorted,
r"""
searchsorted(sorted_sequence, values, out_int32=False, right=False, out=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, 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 (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.
values (Tensor or Scalar): N-D tensor or a Scalar containing the search value(s).
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.
out (Tensor, optional): the output tensor, must be the same size as :attr:`values` if provided.
.. note:: If your use case is always 1-D sorted sequence, :func:`torch.bucketize` is preferred,
because it has fewer dimension checks resulting in slightly better performance.
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, right=True)
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.
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]])
""")
Reference in New Issue View Git Blame Copy Permalink