Source code for torch.functional
from typing import (
Tuple, Optional, Union, Any, Sequence, TYPE_CHECKING
)
import torch
import torch.nn.functional as F
from torch.types import _size
from ._lowrank import svd_lowrank, pca_lowrank
from .overrides import (
has_torch_function, has_torch_function_unary, has_torch_function_variadic,
handle_torch_function)
from ._jit_internal import boolean_dispatch, List
from ._jit_internal import _overload as overload
from torch._autograd_functions import _LU
Tensor = torch.Tensor
from torch import _VF
__all__ = [
'atleast_1d',
'atleast_2d',
'atleast_3d',
'align_tensors',
'broadcast_shapes',
'broadcast_tensors',
'cartesian_prod',
'block_diag',
'cdist',
'chain_matmul',
'einsum',
'istft',
'lu',
'lu_unpack',
'norm',
'meshgrid',
'pca_lowrank',
'split',
'stft',
'svd_lowrank',
'tensordot',
'unique',
'unique_consecutive',
]
[docs]def broadcast_tensors(*tensors):
r"""broadcast_tensors(*tensors) -> List of Tensors
Broadcasts the given tensors according to :ref:`broadcasting-semantics`.
Args:
*tensors: any number of tensors of the same type
.. warning::
More than one element of a broadcasted 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.
Example::
>>> x = torch.arange(3).view(1, 3)
>>> y = torch.arange(2).view(2, 1)
>>> a, b = torch.broadcast_tensors(x, y)
>>> a.size()
torch.Size([2, 3])
>>> a
tensor([[0, 1, 2],
[0, 1, 2]])
"""
if has_torch_function(tensors):
return handle_torch_function(broadcast_tensors, tensors, *tensors)
return _VF.broadcast_tensors(tensors) # type: ignore
[docs]def broadcast_shapes(*shapes):
r"""broadcast_shapes(*shapes) -> Size
Similar to :func:`broadcast_tensors` but for shapes.
This is equivalent to
``torch.broadcast_tensors(*map(torch.empty, shapes))[0].shape``
but avoids the need create to intermediate tensors. This is useful for
broadcasting tensors of common batch shape but different rightmost shape,
e.g. to broadcast mean vectors with covariance matrices.
Example::
>>> torch.broadcast_shapes((2,), (3, 1), (1, 1, 1))
torch.Size([1, 3, 2])
Args:
\*shapes (torch.Size): Shapes of tensors.
Returns:
shape (torch.Size): A shape compatible with all input shapes.
Raises:
RuntimeError: If shapes are incompatible.
"""
# TODO Movie this to C++ once the jit has better support for torch.Size.
with torch.no_grad():
scalar = torch.zeros((), device="cpu")
tensors = [scalar.expand(shape) for shape in shapes]
tensors = broadcast_tensors(*tensors)
return tensors[0].shape
def split(tensor, split_size_or_sections, dim=0):
r"""Splits the tensor into chunks. Each chunk is a view of the original tensor.
If :attr:`split_size_or_sections` is an integer type, then :attr:`tensor` will
be split into equally sized chunks (if possible). Last chunk will be smaller if
the tensor size along the given dimension :attr:`dim` is not divisible by
:attr:`split_size`.
If :attr:`split_size_or_sections` is a list, then :attr:`tensor` will be split
into ``len(split_size_or_sections)`` chunks with sizes in :attr:`dim` according
to :attr:`split_size_or_sections`.
Args:
tensor (Tensor): tensor to split.
split_size_or_sections (int) or (list(int)): size of a single chunk or
list of sizes for each chunk
dim (int): dimension along which to split the tensor.
Example::
>>> a = torch.arange(10).reshape(5,2)
>>> a
tensor([[0, 1],
[2, 3],
[4, 5],
[6, 7],
[8, 9]])
>>> torch.split(a, 2)
(tensor([[0, 1],
[2, 3]]),
tensor([[4, 5],
[6, 7]]),
tensor([[8, 9]]))
>>> torch.split(a, [1,4])
(tensor([[0, 1]]),
tensor([[2, 3],
[4, 5],
[6, 7],
[8, 9]]))
"""
if has_torch_function_unary(tensor):
return handle_torch_function(
split, (tensor,), tensor, split_size_or_sections, dim=dim)
# Overwriting reason:
# This dispatches to two ATen functions depending on the type of
# split_size_or_sections. The branching code is in tensor.py, which we
# call here.
return tensor.split(split_size_or_sections, dim)
if TYPE_CHECKING:
_Indices = _size
else:
_Indices = List[int]
# equivalent to itertools.product(indices)
def _indices_product(indices: _Indices) -> List[List[int]]:
empty_list = torch.jit.annotate(List[int], [])
result = [empty_list]
for idx in indices:
result_temp = torch.jit.annotate(List[List[int]], [])
for res in result:
for i in range(idx):
result_temp.append(res + [i])
result = result_temp
return result
def _index_tensor_with_indices_list(tensor, indices):
# type: (Tensor, List[int]) -> Tensor
out = tensor
for index in indices:
out = out[index]
return out
def lu_unpack(LU_data, LU_pivots, unpack_data=True, unpack_pivots=True):
# type: (Tensor, Tensor, bool, bool) -> (Tuple[Optional[Tensor], Optional[Tensor], Optional[Tensor]])
r"""Unpacks the data and pivots from a LU factorization of a tensor.
Returns a tuple of tensors as ``(the pivots, the L tensor, the U tensor)``.
Args:
LU_data (Tensor): the packed LU factorization data
LU_pivots (Tensor): the packed LU factorization pivots
unpack_data (bool): flag indicating if the data should be unpacked
unpack_pivots (bool): flag indicating if the pivots should be unpacked
Examples::
>>> A = torch.randn(2, 3, 3)
>>> A_LU, pivots = A.lu()
>>> P, A_L, A_U = torch.lu_unpack(A_LU, pivots)
>>>
>>> # can recover A from factorization
>>> A_ = torch.bmm(P, torch.bmm(A_L, A_U))
>>> # LU factorization of a rectangular matrix:
>>> A = torch.randn(2, 3, 2)
>>> A_LU, pivots = A.lu()
>>> P, A_L, A_U = torch.lu_unpack(A_LU, pivots)
>>> P
tensor([[[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]],
[[0., 0., 1.],
[0., 1., 0.],
[1., 0., 0.]]])
>>> A_L
tensor([[[ 1.0000, 0.0000],
[ 0.4763, 1.0000],
[ 0.3683, 0.1135]],
[[ 1.0000, 0.0000],
[ 0.2957, 1.0000],
[-0.9668, -0.3335]]])
>>> A_U
tensor([[[ 2.1962, 1.0881],
[ 0.0000, -0.8681]],
[[-1.0947, 0.3736],
[ 0.0000, 0.5718]]])
>>> A_ = torch.bmm(P, torch.bmm(A_L, A_U))
>>> torch.norm(A_ - A)
tensor(2.9802e-08)
"""
if has_torch_function_variadic(LU_data, LU_pivots):
return handle_torch_function(
lu_unpack, (LU_data, LU_pivots), LU_data, LU_pivots,
unpack_data=unpack_data,
unpack_pivots=unpack_pivots)
shape = LU_data.shape
# In generalized LU factorization, the following shape relations hold:
# A.shape[-2:] == (m, n)
# P.shape[-2:] == (m, m)
# L.shape[-2:] == (m, k)
# U.shape[-2:] == (k, n)
# where k = min(m, n)
m, n = shape[-2:]
k = min(m, n)
if unpack_data:
U: Optional[Tensor] = LU_data.triu()
assert U is not None
if m != k:
U = U.narrow(-2, 0, k)
L: Optional[Tensor] = LU_data.tril()
assert L is not None
if k != n:
L = L.narrow(-1, 0, k)
L.diagonal(dim1=-2, dim2=-1).fill_(1)
else:
L = U = None
if unpack_pivots:
LU_pivots_zero_idx = LU_pivots - 1
if LU_data.dim() > 2:
P: Optional[Tensor] = torch.eye(m, device=LU_data.device,
dtype=LU_data.dtype) \
.expand(shape[:-1] + (m,)) \
.clone(memory_format=torch.contiguous_format)
assert P is not None
# TODO: rewrite when TorchScript supports product and map as
# product(*map(lambda x: list(range(x)), shape[:-2])) when issue 33781 is fixed
indices = _indices_product(shape[:-2])
for idx in indices:
final_order = list(range(m))
for k, j in enumerate(_index_tensor_with_indices_list(LU_pivots_zero_idx, idx)):
final_order[k], final_order[j] = final_order[j], final_order[k]
# TODO: remove _index_tensor_with_indices_list when TorchScript supports indexing Tensor with list
p_idx = _index_tensor_with_indices_list(P, idx)
p_idx.copy_(p_idx.index_select(1, torch.as_tensor(final_order, device=LU_pivots.device)))
else:
P = torch.eye(m, device=LU_data.device, dtype=LU_data.dtype)
final_order = list(range(m))
for k, j, in enumerate(LU_pivots_zero_idx):
final_order[k], final_order[j] = final_order[j], final_order[k]
P = P.index_select(1, torch.as_tensor(final_order, device=LU_pivots.device))
else:
P = None
return P, L, U
def einsum(equation, *operands):
r"""einsum(equation, *operands) -> Tensor
Sums the product of the elements of the input :attr:`operands` along dimensions specified using a notation
based on the Einstein summation convention.
Einsum allows computing many common multi-dimensional linear algebraic array operations by representing them
in a short-hand format based on the Einstein summation convention, given by :attr:`equation`. The details of
this format are described below, but the general idea is to label every dimension of the input :attr:`operands`
with some subscript and define which subscripts are part of the output. The output is then computed by summing
the product of the elements of the :attr:`operands` along the dimensions whose subscripts are not part of the
output. For example, matrix multiplication can be computed using einsum as `torch.einsum("ij,jk->ik", A, B)`.
Here, j is the summation subscript and i and k the output subscripts (see section below for more details on why).
Equation:
The :attr:`equation` string specifies the subscripts (lower case letters `['a', 'z']`) for each dimension of
the input :attr:`operands` in the same order as the dimensions, separating subcripts for each operand by a
comma (','), e.g. `'ij,jk'` specify subscripts for two 2D operands. The dimensions labeled with the same subscript
must be broadcastable, that is, their size must either match or be `1`. The exception is if a subscript is
repeated for the same input operand, in which case the dimensions labeled with this subscript for this operand
must match in size and the operand will be replaced by its diagonal along these dimensions. The subscripts that
appear exactly once in the :attr:`equation` will be part of the output, sorted in increasing alphabetical order.
The output is computed by multiplying the input :attr:`operands` element-wise, with their dimensions aligned based
on the subscripts, and then summing out the dimensions whose subscripts are not part of the output.
Optionally, the output subscripts can be explicitly defined by adding an arrow ('->') at the end of the equation
followed by the subscripts for the output. For instance, the following equation computes the transpose of a
matrix multiplication: 'ij,jk->ki'. The output subscripts must appear at least once for some input operand and
at most once for the output.
Ellipsis ('...') can be used in place of subscripts to broadcast the dimensions covered by the ellipsis.
Each input operand may contain at most one ellipsis which will cover the dimensions not covered by subscripts,
e.g. for an input operand with 5 dimensions, the ellipsis in the equation `'ab...c'` cover the third and fourth
dimensions. The ellipsis does not need to cover the same number of dimensions across the :attr:`operands` but the
'shape' of the ellipsis (the size of the dimensions covered by them) must broadcast together. If the output is not
explicitly defined with the arrow ('->') notation, the ellipsis will come first in the output (left-most dimensions),
before the subscript labels that appear exactly once for the input operands. e.g. the following equation implements
batch matrix multiplication `'...ij,...jk'`.
A few final notes: the equation may contain whitespaces between the different elements (subscripts, ellipsis,
arrow and comma) but something like `'. . .'` is not valid. An empty string `''` is valid for scalar operands.
.. note::
``torch.einsum`` handles ellipsis ('...') differently from NumPy in that it allows dimensions
covered by the ellipsis to be summed over, that is, ellipsis are not required to be part of the output.
.. note::
This function does not optimize the given expression, so a different formula for the same computation may
run faster or consume less memory. Projects like opt_einsum (https://optimized-einsum.readthedocs.io/en/stable/)
can optimize the formula for you.
Args:
equation (string): The subscripts for the Einstein summation.
operands (Tensor): The operands to compute the Einstein sum of.
Examples::
# trace
>>> torch.einsum('ii', torch.randn(4, 4))
tensor(-1.2104)
# diagonal
>>> torch.einsum('ii->i', torch.randn(4, 4))
tensor([-0.1034, 0.7952, -0.2433, 0.4545])
# outer product
>>> x = torch.randn(5)
>>> y = torch.randn(4)
>>> torch.einsum('i,j->ij', x, y)
tensor([[ 0.1156, -0.2897, -0.3918, 0.4963],
[-0.3744, 0.9381, 1.2685, -1.6070],
[ 0.7208, -1.8058, -2.4419, 3.0936],
[ 0.1713, -0.4291, -0.5802, 0.7350],
[ 0.5704, -1.4290, -1.9323, 2.4480]])
# batch matrix multiplication
>>> As = torch.randn(3,2,5)
>>> Bs = torch.randn(3,5,4)
>>> torch.einsum('bij,bjk->bik', As, Bs)
tensor([[[-1.0564, -1.5904, 3.2023, 3.1271],
[-1.6706, -0.8097, -0.8025, -2.1183]],
[[ 4.2239, 0.3107, -0.5756, -0.2354],
[-1.4558, -0.3460, 1.5087, -0.8530]],
[[ 2.8153, 1.8787, -4.3839, -1.2112],
[ 0.3728, -2.1131, 0.0921, 0.8305]]])
# batch permute
>>> A = torch.randn(2, 3, 4, 5)
>>> torch.einsum('...ij->...ji', A).shape
torch.Size([2, 3, 5, 4])
# equivalent to torch.nn.functional.bilinear
>>> A = torch.randn(3,5,4)
>>> l = torch.randn(2,5)
>>> r = torch.randn(2,4)
>>> torch.einsum('bn,anm,bm->ba', l, A, r)
tensor([[-0.3430, -5.2405, 0.4494],
[ 0.3311, 5.5201, -3.0356]])
"""
if has_torch_function(operands):
return handle_torch_function(einsum, operands, equation, *operands)
if len(operands) == 1 and isinstance(operands[0], (list, tuple)):
# the old interface of passing the operands as one list argument
_operands = operands[0]
# recurse incase operands contains value that has torch function
# in the original implementation this line is omitted
return einsum(equation, *_operands)
return _VF.einsum(equation, operands) # type: ignore
if TYPE_CHECKING:
# The JIT doesn't understand Union, so only add type annotation for mypy
def meshgrid(*tensors: Union[Tensor, List[Tensor]]) -> Tuple[Tensor, ...]:
return _meshgrid(*tensors)
else:
def meshgrid(*tensors):
r"""Take :math:`N` tensors, each of which can be either scalar or 1-dimensional
vector, and create :math:`N` N-dimensional grids, where the :math:`i` :sup:`th` grid is defined by
expanding the :math:`i` :sup:`th` input over dimensions defined by other inputs.
Args:
tensors (list of Tensor): list of scalars or 1 dimensional tensors. Scalars will be
treated as tensors of size :math:`(1,)` automatically
Returns:
seq (sequence of Tensors): If the input has :math:`k` tensors of size
:math:`(N_1,), (N_2,), \ldots , (N_k,)`, then the output would also have :math:`k` tensors,
where all tensors are of size :math:`(N_1, N_2, \ldots , N_k)`.
Example::
>>> x = torch.tensor([1, 2, 3])
>>> y = torch.tensor([4, 5, 6])
>>> grid_x, grid_y = torch.meshgrid(x, y)
>>> grid_x
tensor([[1, 1, 1],
[2, 2, 2],
[3, 3, 3]])
>>> grid_y
tensor([[4, 5, 6],
[4, 5, 6],
[4, 5, 6]])
"""
return _meshgrid(*tensors)
def _meshgrid(*tensors):
if has_torch_function(tensors):
return handle_torch_function(meshgrid, tensors, *tensors)
if len(tensors) == 1 and isinstance(tensors[0], (list, tuple)):
# the old interface of passing the operands as one list argument
tensors = tensors[0] # type: ignore
return _VF.meshgrid(tensors) # type: ignore
def stft(input: Tensor, n_fft: int, hop_length: Optional[int] = None,
win_length: Optional[int] = None, window: Optional[Tensor] = None,
center: bool = True, pad_mode: str = 'reflect', normalized: bool = False,
onesided: Optional[bool] = None,
return_complex: Optional[bool] = None) -> Tensor:
r"""Short-time Fourier transform (STFT).
.. warning::
From version 1.8.0, :attr:`return_complex` must always be given
explicitly for real inputs and `return_complex=False` has been
deprecated. Strongly prefer `return_complex=True` as in a future
pytorch release, this function will only return complex tensors.
Note that :func:`torch.view_as_real` can be used to recover a real
tensor with an extra last dimension for real and imaginary components.
The STFT computes the Fourier transform of short overlapping windows of the
input. This giving frequency components of the signal as they change over
time. The interface of this function is modeled after the librosa_ stft function.
.. _librosa: https://librosa.org/doc/latest/generated/librosa.stft.html
Ignoring the optional batch dimension, this method computes the following
expression:
.. math::
X[m, \omega] = \sum_{k = 0}^{\text{win\_length-1}}%
\text{window}[k]\ \text{input}[m \times \text{hop\_length} + k]\ %
\exp\left(- j \frac{2 \pi \cdot \omega k}{\text{win\_length}}\right),
where :math:`m` is the index of the sliding window, and :math:`\omega` is
the frequency that :math:`0 \leq \omega < \text{n\_fft}`. When
:attr:`onesided` is the default value ``True``,
* :attr:`input` must be either a 1-D time sequence or a 2-D batch of time
sequences.
* If :attr:`hop_length` is ``None`` (default), it is treated as equal to
``floor(n_fft / 4)``.
* If :attr:`win_length` is ``None`` (default), it is treated as equal to
:attr:`n_fft`.
* :attr:`window` can be a 1-D tensor of size :attr:`win_length`, e.g., from
:meth:`torch.hann_window`. If :attr:`window` is ``None`` (default), it is
treated as if having :math:`1` everywhere in the window. If
:math:`\text{win\_length} < \text{n\_fft}`, :attr:`window` will be padded on
both sides to length :attr:`n_fft` before being applied.
* If :attr:`center` is ``True`` (default), :attr:`input` will be padded on
both sides so that the :math:`t`-th frame is centered at time
:math:`t \times \text{hop\_length}`. Otherwise, the :math:`t`-th frame
begins at time :math:`t \times \text{hop\_length}`.
* :attr:`pad_mode` determines the padding method used on :attr:`input` when
:attr:`center` is ``True``. See :meth:`torch.nn.functional.pad` for
all available options. Default is ``"reflect"``.
* If :attr:`onesided` is ``True`` (default for real input), only values for
:math:`\omega` in :math:`\left[0, 1, 2, \dots, \left\lfloor
\frac{\text{n\_fft}}{2} \right\rfloor + 1\right]` are returned because
the real-to-complex Fourier transform satisfies the conjugate symmetry,
i.e., :math:`X[m, \omega] = X[m, \text{n\_fft} - \omega]^*`.
Note if the input or window tensors are complex, then :attr:`onesided`
output is not possible.
* If :attr:`normalized` is ``True`` (default is ``False``), the function
returns the normalized STFT results, i.e., multiplied by :math:`(\text{frame\_length})^{-0.5}`.
* If :attr:`return_complex` is ``True`` (default if input is complex), the
return is a ``input.dim() + 1`` dimensional complex tensor. If ``False``,
the output is a ``input.dim() + 2`` dimensional real tensor where the last
dimension represents the real and imaginary components.
Returns either a complex tensor of size :math:`(* \times N \times T)` if
:attr:`return_complex` is true, or a real tensor of size :math:`(* \times N
\times T \times 2)`. Where :math:`*` is the optional batch size of
:attr:`input`, :math:`N` is the number of frequencies where STFT is applied
and :math:`T` is the total number of frames used.
.. warning::
This function changed signature at version 0.4.1. Calling with the
previous signature may cause error or return incorrect result.
Args:
input (Tensor): the input tensor
n_fft (int): size of Fourier transform
hop_length (int, optional): the distance between neighboring sliding window
frames. Default: ``None`` (treated as equal to ``floor(n_fft / 4)``)
win_length (int, optional): the size of window frame and STFT filter.
Default: ``None`` (treated as equal to :attr:`n_fft`)
window (Tensor, optional): the optional window function.
Default: ``None`` (treated as window of all :math:`1` s)
center (bool, optional): whether to pad :attr:`input` on both sides so
that the :math:`t`-th frame is centered at time :math:`t \times \text{hop\_length}`.
Default: ``True``
pad_mode (string, optional): controls the padding method used when
:attr:`center` is ``True``. Default: ``"reflect"``
normalized (bool, optional): controls whether to return the normalized STFT results
Default: ``False``
onesided (bool, optional): controls whether to return half of results to
avoid redundancy for real inputs.
Default: ``True`` for real :attr:`input` and :attr:`window`, ``False`` otherwise.
return_complex (bool, optional): whether to return a complex tensor, or
a real tensor with an extra last dimension for the real and
imaginary components.
Returns:
Tensor: A tensor containing the STFT result with shape described above
"""
if has_torch_function_unary(input):
return handle_torch_function(
stft, (input,), input, n_fft, hop_length=hop_length, win_length=win_length,
window=window, center=center, pad_mode=pad_mode, normalized=normalized,
onesided=onesided, return_complex=return_complex)
# TODO: after having proper ways to map Python strings to ATen Enum, move
# this and F.pad to ATen.
if center:
signal_dim = input.dim()
extended_shape = [1] * (3 - signal_dim) + list(input.size())
pad = int(n_fft // 2)
input = F.pad(input.view(extended_shape), [pad, pad], pad_mode)
input = input.view(input.shape[-signal_dim:])
return _VF.stft(input, n_fft, hop_length, win_length, window, # type: ignore
normalized, onesided, return_complex)
def istft(input: Tensor, n_fft: int, hop_length: Optional[int] = None,
win_length: Optional[int] = None, window: Optional[Tensor] = None,
center: bool = True, normalized: bool = False,
onesided: Optional[bool] = None, length: Optional[int] = None,
return_complex: bool = False) -> Tensor:
r"""Inverse short time Fourier Transform. This is expected to be the inverse of :func:`~torch.stft`.
It has the same parameters (+ additional optional parameter of :attr:`length`) and it should return the
least squares estimation of the original signal. The algorithm will check using the NOLA condition (
nonzero overlap).
Important consideration in the parameters :attr:`window` and :attr:`center` so that the envelop
created by the summation of all the windows is never zero at certain point in time. Specifically,
:math:`\sum_{t=-\infty}^{\infty} |w|^2[n-t\times hop\_length] \cancel{=} 0`.
Since :func:`~torch.stft` discards elements at the end of the signal if they do not fit in a frame,
``istft`` may return a shorter signal than the original signal (can occur if :attr:`center` is False
since the signal isn't padded).
If :attr:`center` is ``True``, then there will be padding e.g. ``'constant'``, ``'reflect'``, etc.
Left padding can be trimmed off exactly because they can be calculated but right padding cannot be
calculated without additional information.
Example: Suppose the last window is:
``[17, 18, 0, 0, 0]`` vs ``[18, 0, 0, 0, 0]``
The :attr:`n_fft`, :attr:`hop_length`, :attr:`win_length` are all the same which prevents the calculation
of right padding. These additional values could be zeros or a reflection of the signal so providing
:attr:`length` could be useful. If :attr:`length` is ``None`` then padding will be aggressively removed
(some loss of signal).
[1] D. W. Griffin and J. S. Lim, "Signal estimation from modified short-time Fourier transform,"
IEEE Trans. ASSP, vol.32, no.2, pp.236-243, Apr. 1984.
Args:
input (Tensor): The input tensor. Expected to be output of :func:`~torch.stft`,
can either be complex (``channel``, ``fft_size``, ``n_frame``), or real
(``channel``, ``fft_size``, ``n_frame``, 2) where the ``channel``
dimension is optional.
.. deprecated:: 1.8.0
Real input is deprecated, use complex inputs as returned by
``stft(..., return_complex=True)`` instead.
n_fft (int): Size of Fourier transform
hop_length (Optional[int]): The distance between neighboring sliding window frames.
(Default: ``n_fft // 4``)
win_length (Optional[int]): The size of window frame and STFT filter. (Default: ``n_fft``)
window (Optional[torch.Tensor]): The optional window function.
(Default: ``torch.ones(win_length)``)
center (bool): Whether :attr:`input` was padded on both sides so that the :math:`t`-th frame is
centered at time :math:`t \times \text{hop\_length}`.
(Default: ``True``)
normalized (bool): Whether the STFT was normalized. (Default: ``False``)
onesided (Optional[bool]): Whether the STFT was onesided.
(Default: ``True`` if ``n_fft != fft_size`` in the input size)
length (Optional[int]): The amount to trim the signal by (i.e. the
original signal length). (Default: whole signal)
return_complex (Optional[bool]):
Whether the output should be complex, or if the input should be
assumed to derive from a real signal and window.
Note that this is incompatible with ``onesided=True``.
(Default: ``False``)
Returns:
Tensor: Least squares estimation of the original signal of size (..., signal_length)
"""
if has_torch_function_unary(input):
return handle_torch_function(
istft, (input,), input, n_fft, hop_length=hop_length, win_length=win_length,
window=window, center=center, normalized=normalized, onesided=onesided,
length=length, return_complex=return_complex)
return _VF.istft(input, n_fft, hop_length, win_length, window, center, # type: ignore
normalized, onesided, length, return_complex)
del torch.unique_dim
if TYPE_CHECKING:
# These _impl functions return a variable number of tensors as output with
# __torch_function__; tuple unpacking is done already rather than being
# done by the caller of the _impl function
_unique_impl_out = Any
else:
_unique_impl_out = Tuple[Tensor, Tensor, Tensor]
def _unique_impl(input: Tensor, sorted: bool = True,
return_inverse: bool = False, return_counts: bool = False,
dim: Optional[int] = None) -> _unique_impl_out:
r"""Returns the unique elements of the input tensor.
.. note:: This function is different from :func:`torch.unique_consecutive` in the sense that
this function also eliminates non-consecutive duplicate values.
.. note:: Currently in the CUDA implementation and the CPU implementation when dim is specified,
`torch.unique` always sort the tensor at the beginning regardless of the `sort` argument.
Sorting could be slow, so if your input tensor is already sorted, it is recommended to use
:func:`torch.unique_consecutive` which avoids the sorting.
Args:
input (Tensor): the input tensor
sorted (bool): Whether to sort the unique elements in ascending order
before returning as output.
return_inverse (bool): Whether to also return the indices for where
elements in the original input ended up in the returned unique list.
return_counts (bool): Whether to also return the counts for each unique
element.
dim (int): the dimension to apply unique. If ``None``, the unique of the
flattened input is returned. default: ``None``
Returns:
(Tensor, Tensor (optional), Tensor (optional)): A tensor or a tuple of tensors containing
- **output** (*Tensor*): the output list of unique scalar elements.
- **inverse_indices** (*Tensor*): (optional) if
:attr:`return_inverse` is True, there will be an additional
returned tensor (same shape as input) representing the indices
for where elements in the original input map to in the output;
otherwise, this function will only return a single tensor.
- **counts** (*Tensor*): (optional) if
:attr:`return_counts` is True, there will be an additional
returned tensor (same shape as output or output.size(dim),
if dim was specified) representing the number of occurrences
for each unique value or tensor.
Example::
>>> output = torch.unique(torch.tensor([1, 3, 2, 3], dtype=torch.long))
>>> output
tensor([ 2, 3, 1])
>>> output, inverse_indices = torch.unique(
... torch.tensor([1, 3, 2, 3], dtype=torch.long), sorted=True, return_inverse=True)
>>> output
tensor([ 1, 2, 3])
>>> inverse_indices
tensor([ 0, 2, 1, 2])
>>> output, inverse_indices = torch.unique(
... torch.tensor([[1, 3], [2, 3]], dtype=torch.long), sorted=True, return_inverse=True)
>>> output
tensor([ 1, 2, 3])
>>> inverse_indices
tensor([[ 0, 2],
[ 1, 2]])
"""
if has_torch_function_unary(input):
return handle_torch_function(
unique, (input,), input, sorted=sorted, return_inverse=return_inverse,
return_counts=return_counts, dim=dim)
if dim is not None:
output, inverse_indices, counts = _VF.unique_dim( # type: ignore
input,
dim,
sorted=sorted,
return_inverse=return_inverse,
return_counts=return_counts,
)
else:
output, inverse_indices, counts = torch._unique2(
input,
sorted=sorted,
return_inverse=return_inverse,
return_counts=return_counts,
)
return output, inverse_indices, counts
def _unique_consecutive_impl(input: Tensor, return_inverse: bool = False,
return_counts: bool = False,
dim: Optional[int] = None) -> _unique_impl_out:
r"""Eliminates all but the first element from every consecutive group of equivalent elements.
.. note:: This function is different from :func:`torch.unique` in the sense that this function
only eliminates consecutive duplicate values. This semantics is similar to `std::unique`
in C++.
Args:
input (Tensor): the input tensor
return_inverse (bool): Whether to also return the indices for where
elements in the original input ended up in the returned unique list.
return_counts (bool): Whether to also return the counts for each unique
element.
dim (int): the dimension to apply unique. If ``None``, the unique of the
flattened input is returned. default: ``None``
Returns:
(Tensor, Tensor (optional), Tensor (optional)): A tensor or a tuple of tensors containing
- **output** (*Tensor*): the output list of unique scalar elements.
- **inverse_indices** (*Tensor*): (optional) if
:attr:`return_inverse` is True, there will be an additional
returned tensor (same shape as input) representing the indices
for where elements in the original input map to in the output;
otherwise, this function will only return a single tensor.
- **counts** (*Tensor*): (optional) if
:attr:`return_counts` is True, there will be an additional
returned tensor (same shape as output or output.size(dim),
if dim was specified) representing the number of occurrences
for each unique value or tensor.
Example::
>>> x = torch.tensor([1, 1, 2, 2, 3, 1, 1, 2])
>>> output = torch.unique_consecutive(x)
>>> output
tensor([1, 2, 3, 1, 2])
>>> output, inverse_indices = torch.unique_consecutive(x, return_inverse=True)
>>> output
tensor([1, 2, 3, 1, 2])
>>> inverse_indices
tensor([0, 0, 1, 1, 2, 3, 3, 4])
>>> output, counts = torch.unique_consecutive(x, return_counts=True)
>>> output
tensor([1, 2, 3, 1, 2])
>>> counts
tensor([2, 2, 1, 2, 1])
"""
if has_torch_function_unary(input):
return handle_torch_function(
unique_consecutive, (input,), input, return_inverse=return_inverse,
return_counts=return_counts, dim=dim)
output, inverse_indices, counts = _VF.unique_consecutive( # type: ignore
input, return_inverse=return_inverse, return_counts=return_counts, dim=dim)
return output, inverse_indices, counts
def _return_counts(input, sorted=True, return_inverse=False, return_counts=False, dim=None):
# type: (Tensor, bool, bool, bool, Optional[int]) -> Tuple[Tensor, Tensor]
if has_torch_function_unary(input):
return _unique_impl(input, sorted, return_inverse, return_counts, dim)
output, _, counts = _unique_impl(input, sorted, return_inverse, return_counts, dim)
return output, counts
def _return_output(input, sorted=True, return_inverse=False, return_counts=False, dim=None):
# type: (Tensor, bool, bool, bool, Optional[int]) -> Tensor
if has_torch_function_unary(input):
return _unique_impl(input, sorted, return_inverse, return_counts, dim)
output, _, _ = _unique_impl(input, sorted, return_inverse, return_counts, dim)
return output
def _return_inverse(input, sorted=True, return_inverse=False, return_counts=False, dim=None):
# type: (Tensor, bool, bool, bool, Optional[int]) -> Tuple[Tensor, Tensor]
if has_torch_function_unary(input):
return _unique_impl(input, sorted, return_inverse, return_counts, dim)
output, inverse_indices, _ = _unique_impl(input, sorted, return_inverse, return_counts, dim)
return output, inverse_indices
_return_inverse_false = boolean_dispatch(
arg_name='return_counts',
arg_index=3,
default=False,
if_true=_return_counts,
if_false=_return_output,
module_name=__name__,
func_name='unique')
_return_inverse_true = boolean_dispatch(
arg_name='return_counts',
arg_index=3,
default=False,
if_true=_unique_impl,
if_false=_return_inverse,
module_name=__name__,
func_name='unique')
# The return type of unique depends on `return_inverse`, and `return_counts` so in order to
# resolve the output type in TorchScript we need to statically know the value of both parameters
unique = boolean_dispatch(
arg_name='return_inverse',
arg_index=2,
default=False,
if_true=_return_inverse_true,
if_false=_return_inverse_false,
module_name=__name__,
func_name='unique')
unique.__doc__ = _unique_impl.__doc__
def _consecutive_return_counts(input, return_inverse=False, return_counts=False, dim=None):
# type: (Tensor, bool, bool, Optional[int]) -> Tuple[Tensor, Tensor]
if has_torch_function_unary(input):
return _unique_consecutive_impl(input, return_inverse, return_counts, dim)
output, _, counts = _unique_consecutive_impl(input, return_inverse, return_counts, dim)
return output, counts
def _consecutive_return_output(input, return_inverse=False, return_counts=False, dim=None):
# type: (Tensor, bool, bool, Optional[int]) -> Tensor
if has_torch_function_unary(input):
return _unique_consecutive_impl(input, return_inverse, return_counts, dim)
output, _, _ = _unique_consecutive_impl(input, return_inverse, return_counts, dim)
return output
def _consecutive_return_inverse(input, return_inverse=False, return_counts=False, dim=None):
# type: (Tensor, bool, bool, Optional[int]) -> Tuple[Tensor, Tensor]
if has_torch_function_unary(input):
return _unique_consecutive_impl(input, return_inverse, return_counts, dim)
output, inverse_indices, _ = _unique_consecutive_impl(input, return_inverse, return_counts, dim)
return output, inverse_indices
_consecutive_return_inverse_false = boolean_dispatch(
arg_name='return_counts',
arg_index=1,
default=False,
if_true=_consecutive_return_counts,
if_false=_consecutive_return_output,
module_name=__name__,
func_name='unique_consecutive')
_consecutive_return_inverse_true = boolean_dispatch(
arg_name='return_counts',
arg_index=1,
default=False,
if_true=_unique_consecutive_impl,
if_false=_consecutive_return_inverse,
module_name=__name__,
func_name='unique_consecutive')
# The return type of unique depends on `return_inverse`, and `return_counts` so in order to
# resolve the output type in TorchScript we need to statically know the value of both parameters
unique_consecutive = boolean_dispatch(
arg_name='return_inverse',
arg_index=2,
default=False,
if_true=_consecutive_return_inverse_true,
if_false=_consecutive_return_inverse_false,
module_name=__name__,
func_name='unique_consecutive')
unique_consecutive.__doc__ = _unique_consecutive_impl.__doc__
def tensordot(a, b, dims=2, out=None):
r"""Returns a contraction of a and b over multiple dimensions.
:attr:`tensordot` implements a generalized matrix product.
Args:
a (Tensor): Left tensor to contract
b (Tensor): Right tensor to contract
dims (int or Tuple[List[int]] containing two lists): number of dimensions to
contract or explicit lists of dimensions for :attr:`a` and
:attr:`b` respectively
When called with a non-negative integer argument :attr:`dims` = :math:`d`, and
the number of dimensions of :attr:`a` and :attr:`b` is :math:`m` and :math:`n`,
respectively, :func:`~torch.tensordot` computes
.. math::
r_{i_0,...,i_{m-d}, i_d,...,i_n}
= \sum_{k_0,...,k_{d-1}} a_{i_0,...,i_{m-d},k_0,...,k_{d-1}} \times b_{k_0,...,k_{d-1}, i_d,...,i_n}.
When called with :attr:`dims` of the list form, the given dimensions will be contracted
in place of the last :math:`d` of :attr:`a` and the first :math:`d` of :math:`b`. The sizes
in these dimensions must match, but :func:`~torch.tensordot` will deal with broadcasted
dimensions.
Examples::
>>> a = torch.arange(60.).reshape(3, 4, 5)
>>> b = torch.arange(24.).reshape(4, 3, 2)
>>> torch.tensordot(a, b, dims=([1, 0], [0, 1]))
tensor([[4400., 4730.],
[4532., 4874.],
[4664., 5018.],
[4796., 5162.],
[4928., 5306.]])
>>> a = torch.randn(3, 4, 5, device='cuda')
>>> b = torch.randn(4, 5, 6, device='cuda')
>>> c = torch.tensordot(a, b, dims=2).cpu()
tensor([[ 8.3504, -2.5436, 6.2922, 2.7556, -1.0732, 3.2741],
[ 3.3161, 0.0704, 5.0187, -0.4079, -4.3126, 4.8744],
[ 0.8223, 3.9445, 3.2168, -0.2400, 3.4117, 1.7780]])
>>> a = torch.randn(3, 5, 4, 6)
>>> b = torch.randn(6, 4, 5, 3)
>>> torch.tensordot(a, b, dims=([2, 1, 3], [1, 2, 0]))
tensor([[ 7.7193, -2.4867, -10.3204],
[ 1.5513, -14.4737, -6.5113],
[ -0.2850, 4.2573, -3.5997]])
"""
if has_torch_function_variadic(a, b):
return handle_torch_function(tensordot, (a, b), a, b, dims=dims)
if isinstance(dims, (list, tuple)) or \
(isinstance(dims, torch.Tensor) and dims.numel() > 1):
dims_a, dims_b = dims
else:
if isinstance(dims, torch.Tensor):
dims = dims.item()
if dims < 0:
raise RuntimeError(f"tensordot expects dims >= 0, but got dims={dims}")
dims_a = list(range(-dims, 0))
dims_b = list(range(dims))
if out is None:
return _VF.tensordot(a, b, dims_a, dims_b) # type: ignore
else:
return _VF.tensordot(a, b, dims_a, dims_b, out=out) # type: ignore
[docs]def cartesian_prod(*tensors):
"""Do cartesian product of the given sequence of tensors. The behavior is similar to
python's `itertools.product`.
Args:
*tensors: any number of 1 dimensional tensors.
Returns:
Tensor: A tensor equivalent to converting all the input tensors into lists,
do `itertools.product` on these lists, and finally convert the resulting list
into tensor.
Example::
>>> a = [1, 2, 3]
>>> b = [4, 5]
>>> list(itertools.product(a, b))
[(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)]
>>> tensor_a = torch.tensor(a)
>>> tensor_b = torch.tensor(b)
>>> torch.cartesian_prod(tensor_a, tensor_b)
tensor([[1, 4],
[1, 5],
[2, 4],
[2, 5],
[3, 4],
[3, 5]])
"""
if has_torch_function(tensors):
return handle_torch_function(cartesian_prod, tensors, *tensors)
return _VF.cartesian_prod(tensors) # type: ignore
[docs]def block_diag(*tensors):
"""Create a block diagonal matrix from provided tensors.
Args:
*tensors: One or more tensors with 0, 1, or 2 dimensions.
Returns:
Tensor: A 2 dimensional tensor with all the input tensors arranged in
order such that their upper left and lower right corners are
diagonally adjacent. All other elements are set to 0.
Example::
>>> import torch
>>> A = torch.tensor([[0, 1], [1, 0]])
>>> B = torch.tensor([[3, 4, 5], [6, 7, 8]])
>>> C = torch.tensor(7)
>>> D = torch.tensor([1, 2, 3])
>>> E = torch.tensor([[4], [5], [6]])
>>> torch.block_diag(A, B, C, D, E)
tensor([[0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 3, 4, 5, 0, 0, 0, 0, 0],
[0, 0, 6, 7, 8, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 7, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 1, 2, 3, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 4],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 5],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 6]])
"""
if has_torch_function(tensors):
return handle_torch_function(block_diag, tensors, *tensors)
return torch._C._VariableFunctions.block_diag(tensors) # type: ignore
[docs]def cdist(x1, x2, p=2., compute_mode='use_mm_for_euclid_dist_if_necessary'):
# type: (Tensor, Tensor, float, str) -> (Tensor)
r"""Computes batched the p-norm distance between each pair of the two collections of row vectors.
Args:
x1 (Tensor): input tensor of shape :math:`B \times P \times M`.
x2 (Tensor): input tensor of shape :math:`B \times R \times M`.
p: p value for the p-norm distance to calculate between each vector pair
:math:`\in [0, \infty]`.
compute_mode:
'use_mm_for_euclid_dist_if_necessary' - will use matrix multiplication approach to calculate
euclidean distance (p = 2) if P > 25 or R > 25
'use_mm_for_euclid_dist' - will always use matrix multiplication approach to calculate
euclidean distance (p = 2)
'donot_use_mm_for_euclid_dist' - will never use matrix multiplication approach to calculate
euclidean distance (p = 2)
Default: use_mm_for_euclid_dist_if_necessary.
If x1 has shape :math:`B \times P \times M` and x2 has shape :math:`B \times R \times M` then the
output will have shape :math:`B \times P \times R`.
This function is equivalent to `scipy.spatial.distance.cdist(input,'minkowski', p=p)`
if :math:`p \in (0, \infty)`. When :math:`p = 0` it is equivalent to
`scipy.spatial.distance.cdist(input, 'hamming') * M`. When :math:`p = \infty`, the closest
scipy function is `scipy.spatial.distance.cdist(xn, lambda x, y: np.abs(x - y).max())`.
Example:
>>> a = torch.tensor([[0.9041, 0.0196], [-0.3108, -2.4423], [-0.4821, 1.059]])
>>> a
tensor([[ 0.9041, 0.0196],
[-0.3108, -2.4423],
[-0.4821, 1.0590]])
>>> b = torch.tensor([[-2.1763, -0.4713], [-0.6986, 1.3702]])
>>> b
tensor([[-2.1763, -0.4713],
[-0.6986, 1.3702]])
>>> torch.cdist(a, b, p=2)
tensor([[3.1193, 2.0959],
[2.7138, 3.8322],
[2.2830, 0.3791]])
"""
if has_torch_function_variadic(x1, x2):
return handle_torch_function(
cdist, (x1, x2), x1, x2, p=p, compute_mode=compute_mode)
if compute_mode == 'use_mm_for_euclid_dist_if_necessary':
return _VF.cdist(x1, x2, p, None) # type: ignore
elif compute_mode == 'use_mm_for_euclid_dist':
return _VF.cdist(x1, x2, p, 1) # type: ignore
elif compute_mode == 'donot_use_mm_for_euclid_dist':
return _VF.cdist(x1, x2, p, 2) # type: ignore
else:
raise ValueError(f"{compute_mode} is not a valid value for compute_mode")
def atleast_1d(*tensors):
r"""
Returns a 1-dimensional view of each input tensor with zero dimensions.
Input tensors with one or more dimensions are returned as-is.
Args:
input (Tensor or list of Tensors)
Returns:
output (Tensor or tuple of Tensors)
Example::
>>> x = torch.randn(2)
>>> x
tensor([1.4584, 0.7583])
>>> torch.atleast_1d(x)
tensor([1.4584, 0.7583])
>>> x = torch.tensor(1.)
>>> x
tensor(1.)
>>> torch.atleast_1d(x)
tensor([1.])
>>> x = torch.tensor(0.5)
>>> y = torch.tensor(1.)
>>> torch.atleast_1d((x,y))
(tensor([0.5000]), tensor([1.]))
"""
if has_torch_function(tensors):
return handle_torch_function(atleast_1d, tensors, *tensors)
if len(tensors) == 1:
tensors = tensors[0]
return _VF.atleast_1d(tensors) # type: ignore
def atleast_2d(*tensors):
r"""
Returns a 2-dimensional view of each input tensor with zero dimensions.
Input tensors with two or more dimensions are returned as-is.
Args:
input (Tensor or list of Tensors)
Returns:
output (Tensor or tuple of Tensors)
Example::
>>> x = torch.tensor(1.)
>>> x
tensor(1.)
>>> torch.atleast_2d(x)
tensor([[1.]])
>>> x = torch.randn(2,2)
>>> x
tensor([[2.2086, 2.5165],
[0.1757, 0.5194]])
>>> torch.atleast_2d(x)
tensor([[2.2086, 2.5165],
[0.1757, 0.5194]])
>>> x = torch.tensor(0.5)
>>> y = torch.tensor(1.)
>>> torch.atleast_2d((x,y))
(tensor([[0.5000]]), tensor([[1.]]))
"""
if has_torch_function(tensors):
return handle_torch_function(atleast_2d, tensors, *tensors)
if len(tensors) == 1:
tensors = tensors[0]
return _VF.atleast_2d(tensors) # type: ignore
def atleast_3d(*tensors):
r"""
Returns a 3-dimensional view of each input tensor with zero dimensions.
Input tensors with three or more dimensions are returned as-is.
Args:
input (Tensor or list of Tensors)
Returns:
output (Tensor or tuple of Tensors)
Example:
>>> x = torch.tensor(0.5)
>>> x
tensor(0.5000)
>>> torch.atleast_3d(x)
tensor([[[0.5000]]])
>>> y = torch.randn(2,2)
>>> y
tensor([[-0.8079, 0.7460],
[-1.1647, 1.4734]])
>>> torch.atleast_3d(y)
tensor([[[-0.8079],
[ 0.7460]],
<BLANKLINE>
[[-1.1647],
[ 1.4734]]])
>>> x = torch.randn(1,1,1)
>>> x
tensor([[[-1.5689]]])
>>> torch.atleast_3d(x)
tensor([[[-1.5689]]])
>>> x = torch.tensor(0.5)
>>> y = torch.tensor(1.)
>>> torch.atleast_3d((x,y))
(tensor([[[0.5000]]]), tensor([[[1.]]]))
"""
if has_torch_function(tensors):
return handle_torch_function(atleast_3d, tensors, *tensors)
if len(tensors) == 1:
tensors = tensors[0]
return _VF.atleast_3d(tensors) # type: ignore
if TYPE_CHECKING:
pass
# There's no good way to use this type annotation; cannot rename norm() to
# _norm_impl() in a way that doesn't break JIT overloads. So leave untyped
# for mypy for now.
# def norm(input: Tensor,
# p: Optional[Union[str, Number]] = "fro",
# dim: Optional[Union[int, List[int]]] = None,
# keepdim: bool = False,
# out: Optional[Tensor] = None,
# dtype: _dtype = None) -> Tensor:
# return _norm_impl(input, p, dim, keepdim, out, dtype)
else:
# TODO: type dim as BroadcastingList when
# https://github.com/pytorch/pytorch/issues/33782 is fixed
@overload # noqa: 749
def norm(input, p="fro", dim=None, keepdim=False, out=None, dtype=None): # noqa: 749
# type: (Tensor, str, Optional[List[int]], bool, Optional[Tensor], Optional[int]) -> Tensor
pass
@overload # noqa: 749
def norm(input, p="fro", dim=None, keepdim=False, out=None, dtype=None): # noqa: 749
# type: (Tensor, Optional[number], Optional[List[int]], bool, Optional[Tensor], Optional[int]) -> Tensor
pass
@overload # noqa: 749
def norm(input, p="fro", dim=None, keepdim=False, out=None, dtype=None): # noqa: 749
# type: (Tensor, Optional[number], Optional[int], bool, Optional[Tensor], Optional[int]) -> Tensor
pass
@overload # noqa: 749
def norm(input, p="fro", dim=None, keepdim=False, out=None, dtype=None): # noqa: 749
# type: (Tensor, str, Optional[int], bool, Optional[Tensor], Optional[int]) -> Tensor
pass
def norm(input, p="fro", dim=None, keepdim=False, out=None, dtype=None): # noqa: 749
r"""Returns the matrix norm or vector norm of a given tensor.
.. warning::
torch.norm is deprecated and may be removed in a future PyTorch release.
Use :func:`torch.linalg.norm` instead, but note that :func:`torch.linalg.norm`
has a different signature and slightly different behavior that is
more consistent with NumPy's numpy.linalg.norm.
Args:
input (Tensor): The input tensor. Its data type must be either a floating
point or complex type. For complex inputs, the norm is calculated using the
absolute value of each element. If the input is complex and neither
:attr:`dtype` nor :attr:`out` is specified, the result's data type will
be the corresponding floating point type (e.g. float if :attr:`input` is
complexfloat).
p (int, float, inf, -inf, 'fro', 'nuc', optional): the order of norm. Default: ``'fro'``
The following norms can be calculated:
====== ============== ==========================
ord matrix norm vector norm
====== ============== ==========================
'fro' Frobenius norm --
'nuc' nuclear norm --
Number -- sum(abs(x)**ord)**(1./ord)
====== ============== ==========================
The vector norm can be calculated across any number of dimensions.
The corresponding dimensions of :attr:`input` are flattened into
one dimension, and the norm is calculated on the flattened
dimension.
Frobenius norm produces the same result as ``p=2`` in all cases
except when :attr:`dim` is a list of three or more dims, in which
case Frobenius norm throws an error.
Nuclear norm can only be calculated across exactly two dimensions.
dim (int, tuple of ints, list of ints, optional):
Specifies which dimension or dimensions of :attr:`input` to
calculate the norm across. If :attr:`dim` is ``None``, the norm will
be calculated across all dimensions of :attr:`input`. If the norm
type indicated by :attr:`p` does not support the specified number of
dimensions, an error will occur.
keepdim (bool, optional): whether the output tensors have :attr:`dim`
retained or not. Ignored if :attr:`dim` = ``None`` and
:attr:`out` = ``None``. Default: ``False``
out (Tensor, optional): the output tensor. Ignored if
:attr:`dim` = ``None`` and :attr:`out` = ``None``.
dtype (:class:`torch.dtype`, optional): the desired data type of
returned tensor. If specified, the input tensor is casted to
:attr:'dtype' while performing the operation. Default: None.
.. note::
Even though ``p='fro'`` supports any number of dimensions, the true
mathematical definition of Frobenius norm only applies to tensors with
exactly two dimensions. :func:`torch.linalg.norm` with ``ord='fro'`` aligns
with the mathematical definition, since it can only be applied across
exactly two dimensions.
Example::
>>> import torch
>>> a = torch.arange(9, dtype= torch.float) - 4
>>> b = a.reshape((3, 3))
>>> torch.norm(a)
tensor(7.7460)
>>> torch.norm(b)
tensor(7.7460)
>>> torch.norm(a, float('inf'))
tensor(4.)
>>> torch.norm(b, float('inf'))
tensor(4.)
>>> c = torch.tensor([[ 1, 2, 3],[-1, 1, 4]] , dtype= torch.float)
>>> torch.norm(c, dim=0)
tensor([1.4142, 2.2361, 5.0000])
>>> torch.norm(c, dim=1)
tensor([3.7417, 4.2426])
>>> torch.norm(c, p=1, dim=1)
tensor([6., 6.])
>>> d = torch.arange(8, dtype= torch.float).reshape(2,2,2)
>>> torch.norm(d, dim=(1,2))
tensor([ 3.7417, 11.2250])
>>> torch.norm(d[0, :, :]), torch.norm(d[1, :, :])
(tensor(3.7417), tensor(11.2250))
"""
if has_torch_function_unary(input):
return handle_torch_function(
norm, (input,), input, p=p, dim=dim, keepdim=keepdim, out=out, dtype=dtype)
ndim = input.dim()
# catch default case
if dim is None and out is None and dtype is None and p is not None:
if isinstance(p, str):
if p == "fro":
return _VF.frobenius_norm(input, dim=(), keepdim=keepdim) # type: ignore
if not isinstance(p, str):
_dim = [i for i in range(ndim)] # noqa: C416 TODO: rewrite as list(range(m))
return _VF.norm(input, p, dim=_dim, keepdim=keepdim) # type: ignore
# TODO: when https://github.com/pytorch/pytorch/issues/33782 is fixed
# remove the overloads where dim is an int and replace with BraodcastingList1
# and remove next four lines, replace _dim with dim
if dim is not None:
if isinstance(dim, int):
_dim = [dim]
else:
_dim = dim
else:
_dim = None # type: ignore
if isinstance(p, str):
if p == "fro":
if dtype is not None:
raise ValueError("dtype argument is not supported in frobenius norm")
if _dim is None:
_dim = list(range(ndim))
if out is None:
return _VF.frobenius_norm(input, _dim, keepdim=keepdim) # type: ignore
else:
return _VF.frobenius_norm(input, _dim, keepdim=keepdim, out=out) # type: ignore
elif p == "nuc":
if dtype is not None:
raise ValueError("dtype argument is not supported in nuclear norm")
if _dim is None:
if out is None:
return _VF.nuclear_norm(input, keepdim=keepdim) # type: ignore
else:
return _VF.nuclear_norm(input, keepdim=keepdim, out=out) # type: ignore
else:
if out is None:
return _VF.nuclear_norm(input, _dim, keepdim=keepdim) # type: ignore
else:
return _VF.nuclear_norm(input, _dim, keepdim=keepdim, out=out) # type: ignore
raise RuntimeError(f"only valid string values are 'fro' and 'nuc', found {p}")
else:
if _dim is None:
_dim = list(range(ndim))
if out is None:
if dtype is None:
return _VF.norm(input, p, _dim, keepdim=keepdim) # type: ignore
else:
return _VF.norm(input, p, _dim, keepdim=keepdim, dtype=dtype) # type: ignore
else:
if dtype is None:
return _VF.norm(input, p, _dim, keepdim=keepdim, out=out) # type: ignore
else:
return _VF.norm(input, p, _dim, keepdim=keepdim, dtype=dtype, out=out) # type: ignore
[docs]def chain_matmul(*matrices):
r"""Returns the matrix product of the :math:`N` 2-D tensors. This product is efficiently computed
using the matrix chain order algorithm which selects the order in which incurs the lowest cost in terms
of arithmetic operations (`[CLRS]`_). Note that since this is a function to compute the product, :math:`N`
needs to be greater than or equal to 2; if equal to 2 then a trivial matrix-matrix product is returned.
If :math:`N` is 1, then this is a no-op - the original matrix is returned as is.
Args:
matrices (Tensors...): a sequence of 2 or more 2-D tensors whose product is to be determined.
Returns:
Tensor: if the :math:`i^{th}` tensor was of dimensions :math:`p_{i} \times p_{i + 1}`, then the product
would be of dimensions :math:`p_{1} \times p_{N + 1}`.
Example::
>>> a = torch.randn(3, 4)
>>> b = torch.randn(4, 5)
>>> c = torch.randn(5, 6)
>>> d = torch.randn(6, 7)
>>> torch.chain_matmul(a, b, c, d)
tensor([[ -2.3375, -3.9790, -4.1119, -6.6577, 9.5609, -11.5095, -3.2614],
[ 21.4038, 3.3378, -8.4982, -5.2457, -10.2561, -2.4684, 2.7163],
[ -0.9647, -5.8917, -2.3213, -5.2284, 12.8615, -12.2816, -2.5095]])
.. _`[CLRS]`: https://mitpress.mit.edu/books/introduction-algorithms-third-edition
"""
if has_torch_function(matrices):
return handle_torch_function(chain_matmul, matrices, *matrices)
return _VF.chain_matmul(matrices) # type: ignore
def _lu_impl(A, pivot=True, get_infos=False, out=None):
# type: (Tensor, bool, bool, Any) -> Tuple[Tensor, Tensor, Tensor]
r"""Computes the LU factorization of a matrix or batches of matrices
:attr:`A`. Returns a tuple containing the LU factorization and
pivots of :attr:`A`. Pivoting is done if :attr:`pivot` is set to
``True``.
.. note::
The pivots returned by the function are 1-indexed. If :attr:`pivot` is ``False``,
then the returned pivots is a tensor filled with zeros of the appropriate size.
.. note::
LU factorization with :attr:`pivot` = ``False`` is not available for CPU, and attempting
to do so will throw an error. However, LU factorization with :attr:`pivot` = ``False`` is
available for CUDA.
.. note::
This function does not check if the factorization was successful or not if
:attr:`get_infos` is ``True`` since the status of the factorization is present in the
third element of the return tuple.
.. note::
In the case of batches of square matrices with size less or
equal to 32 on a CUDA device, the LU factorization is repeated
for singular matrices due to the bug in the MAGMA library (see
magma issue 13).
.. note::
``L``, ``U``, and ``P`` can be derived using :func:`torch.lu_unpack`.
.. warning::
The LU factorization does have backward support,
but only for square inputs of full rank.
Args:
A (Tensor): the tensor to factor of size :math:`(*, m, n)`
pivot (bool, optional): controls whether pivoting is done. Default: ``True``
get_infos (bool, optional): if set to ``True``, returns an info IntTensor.
Default: ``False``
out (tuple, optional): optional output tuple. If :attr:`get_infos` is ``True``,
then the elements in the tuple are Tensor, IntTensor,
and IntTensor. If :attr:`get_infos` is ``False``, then the
elements in the tuple are Tensor, IntTensor. Default: ``None``
Returns:
(Tensor, IntTensor, IntTensor (optional)): A tuple of tensors containing
- **factorization** (*Tensor*): the factorization of size :math:`(*, m, n)`
- **pivots** (*IntTensor*): the pivots of size :math:`(*, \text{min}(m, n))`.
``pivots`` stores all the intermediate transpositions of rows.
The final permutation ``perm`` could be reconstructed by
applying ``swap(perm[i], perm[pivots[i] - 1])`` for ``i = 0, ..., pivots.size(-1) - 1``,
where ``perm`` is initially the identity permutation of :math:`m` elements
(essentially this is what :func:`torch.lu_unpack` is doing).
- **infos** (*IntTensor*, *optional*): if :attr:`get_infos` is ``True``, this is a tensor of
size :math:`(*)` where non-zero values indicate whether factorization for the matrix or
each minibatch has succeeded or failed
Example::
>>> A = torch.randn(2, 3, 3)
>>> A_LU, pivots = torch.lu(A)
>>> A_LU
tensor([[[ 1.3506, 2.5558, -0.0816],
[ 0.1684, 1.1551, 0.1940],
[ 0.1193, 0.6189, -0.5497]],
[[ 0.4526, 1.2526, -0.3285],
[-0.7988, 0.7175, -0.9701],
[ 0.2634, -0.9255, -0.3459]]])
>>> pivots
tensor([[ 3, 3, 3],
[ 3, 3, 3]], dtype=torch.int32)
>>> A_LU, pivots, info = torch.lu(A, get_infos=True)
>>> if info.nonzero().size(0) == 0:
... print('LU factorization succeeded for all samples!')
LU factorization succeeded for all samples!
"""
if not torch._jit_internal.is_scripting():
if A.requires_grad:
if not (A.size(-2) == A.size(-1) and A.dtype.is_floating_point):
raise ValueError(
'lu.backward works only with batches of squared full-rank matrices'
' of floating types.'
)
return _LU.apply(A, pivot, get_infos)
else:
if A.requires_grad:
raise RuntimeError(
'Script and require gradients is not supported at the moment.'
'If you just want to do the forward, use .detach()'
'on the input before calling the function.'
)
# If get_infos is True, then we don't need to check for errors and vice versa
return torch._lu_with_info(A, pivot=pivot, check_errors=(not get_infos))
if TYPE_CHECKING:
_ListOrSeq = Sequence[Tensor]
else:
_ListOrSeq = List[Tensor]
def _check_list_size(out_len: int, get_infos: bool, out: _ListOrSeq) -> None:
get_infos_int = 1 if get_infos else 0
if out_len - get_infos_int != 2:
raise TypeError(f"expected tuple of {2 + int(get_infos)} elements but got {out_len}")
if not isinstance(out, (tuple, list)):
raise TypeError(f"argument 'out' must be tuple of Tensors, not {type(out).__name__}")
def _lu_with_infos(A, pivot=True, get_infos=False, out=None):
# type: (Tensor, bool, bool, Optional[Tuple[Tensor, Tensor, Tensor]]) -> Tuple[Tensor, Tensor, Tensor]
if has_torch_function_unary(A):
return handle_torch_function(
lu, (A,), A, pivot=pivot, get_infos=get_infos, out=out)
result = _lu_impl(A, pivot, get_infos, out)
if out is not None:
_check_list_size(len(out), get_infos, out)
for i in range(len(out)):
out[i].resize_as_(result[i]).copy_(result[i])
return out
else:
return result # A_LU, pivots, infos
def _lu_no_infos(A, pivot=True, get_infos=False, out=None):
# type: (Tensor, bool, bool, Optional[Tuple[Tensor, Tensor]]) -> Tuple[Tensor, Tensor]
# need to check for torch_function here so that we exit if
if has_torch_function_unary(A):
return handle_torch_function(
lu, (A,), A, pivot=pivot, get_infos=get_infos, out=out)
result = _lu_impl(A, pivot, get_infos, out)
if out is not None:
_check_list_size(len(out), get_infos, out)
for i in range(len(out)):
out[i].resize_as_(result[i]).copy_(result[i])
return out
else:
return result[0], result[1] # A_LU, pivots
# The return type of lu depends on `get_infos`, so in order to resolve the output type
# of lu in TorchScript we need to statically know the value of `get_infos`
lu = boolean_dispatch(
arg_name='get_infos',
arg_index=2,
default=False,
if_true=_lu_with_infos,
if_false=_lu_no_infos,
module_name=__name__,
func_name='lu')
lu.__doc__ = _lu_impl.__doc__
def align_tensors(*tensors):
raise RuntimeError('`align_tensors` not yet implemented.')
