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pytorch/torch/functional.py
Thomas Viehmann d34578026c Various example code fixes (#12707) 
Summary:
- Fix broken sparse_coo_examples, update output
- Tensor(...) to tensor(...)
- Fix arguments to math.log to be floats

While the last might be debateable, mypy currently complains when passing an int to math.log. As it is not essential for our examples, let's be clean w.r.t. other people's expectations.

These popped up while checking examples in the context of  #12500 .
Pull Request resolved: https://github.com/pytorch/pytorch/pull/12707

Differential Revision: D10415256

Pulled By: SsnL

fbshipit-source-id: c907b576b02cb0f89d8f261173dbf4b3175b4b8d
2018-10-16 21:59:40 -07:00

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import torch
import torch.nn.functional as F
from torch._six import inf
from operator import mul
from functools import reduce
import math
__all__ = [
'argmax',
'argmin',
'argsort',
'btrifact',
'btriunpack',
'chain_matmul',
'einsum',
'broadcast_tensors',
'isfinite',
'isinf',
'isnan',
'norm',
'meshgrid',
'split',
'stft',
'tensordot',
'unique',
]
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
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]])
"""
return torch._C._VariableFunctions.broadcast_tensors(tensors)
def split(tensor, split_size_or_sections, dim=0):
r"""Splits the tensor into chunks.
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`.
Arguments:
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.
"""
# 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)
def btrifact(A, info=None, pivot=True):
r"""Batch LU factorization.
Returns a tuple containing the LU factorization and pivots. Pivoting is done if
:attr:`pivot` is set.
The optional argument :attr:`info` stores information if the factorization
succeeded for each minibatch example. The :attr:`info` is provided as an
`IntTensor`, its values will be filled from dgetrf and a non-zero value
indicates an error occurred. Specifically, the values are from cublas if cuda is
being used, otherwise LAPACK.
.. warning::
The :attr:`info` argument is deprecated in favor of :meth:`torch.btrifact_with_info`.
Arguments:
A (Tensor): the tensor to factor
info (IntTensor, optional): (deprecated) an `IntTensor` to store values
indicating whether factorization succeeds
pivot (bool, optional): controls whether pivoting is done
Returns:
A tuple containing factorization and pivots.
Example::
>>> A = torch.randn(2, 3, 3)
>>> A_LU, pivots = torch.btrifact(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)
"""
# Overwriting reason:
# `info` is being deprecated in favor of `btrifact_with_info`. This warning
# is in tensor.py, which we call here.
return A.btrifact(info, pivot)
def btriunpack(LU_data, LU_pivots, unpack_data=True, unpack_pivots=True):
r"""Unpacks the data and pivots from a batched LU factorization (btrifact) of a tensor.
Returns a tuple of tensors as ``(the pivots, the L tensor, the U tensor)``.
Arguments:
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
Example::
>>> A = torch.randn(2, 3, 3)
>>> A_LU, pivots = A.btrifact()
>>> P, A_L, A_U = torch.btriunpack(A_LU, pivots)
>>>
>>> # can recover A from factorization
>>> A_ = torch.bmm(P, torch.bmm(A_L, A_U))
"""
nBatch, sz, _ = LU_data.size()
if unpack_data:
I_U = torch.triu(torch.ones(sz, sz)).type_as(LU_data).byte().unsqueeze(0).expand(nBatch, sz, sz)
I_L = 1 - I_U
L = LU_data.new(LU_data.size()).zero_()
U = LU_data.new(LU_data.size()).zero_()
I_diag = torch.eye(sz).type_as(LU_data).byte().unsqueeze(0).expand(nBatch, sz, sz)
L[I_diag] = 1.0
L[I_L] = LU_data[I_L]
U[I_U] = LU_data[I_U]
else:
L = U = None
if unpack_pivots:
P = torch.eye(sz).type_as(LU_data).unsqueeze(0).repeat(nBatch, 1, 1)
for i in range(nBatch):
for j in range(sz):
k = int(LU_pivots[i, j] - 1)
t = P[i, :, j].clone()
P[i, :, j] = P[i, :, k]
P[i, :, k] = t
else:
P = None
return P, L, U
def einsum(equation, *operands):
r"""einsum(equation, *operands) -> Tensor
This function provides a way of computing multilinear expressions (i.e. sums of products) using the
Einstein summation convention.
Args:
equation (string): The equation is given in terms of lower case letters (indices) to be associated
with each dimension of the operands and result. The left hand side lists the operands
dimensions, separated by commas. There should be one index letter per tensor dimension.
The right hand side follows after `->` and gives the indices for the output.
If the `->` and right hand side are omitted, it implicitly defined as the alphabetically
sorted list of all indices appearing exactly once in the left hand side.
The indices not apprearing in the output are summed over after multiplying the operands
entries.
If an index appears several times for the same operand, a diagonal is taken.
Ellipses `...` represent a fixed number of dimensions. If the right hand side is inferred,
the ellipsis dimensions are at the beginning of the output.
operands (list of Tensors): The operands to compute the Einstein sum of.
Note that the operands are passed as a list, not as individual arguments.
Examples::
>>> x = torch.randn(5)
>>> y = torch.randn(4)
>>> torch.einsum('i,j->ij', x, y) # outer product
tensor([[-0.0570, -0.0286, -0.0231, 0.0197],
[ 1.2616, 0.6335, 0.5113, -0.4351],
[ 1.4452, 0.7257, 0.5857, -0.4984],
[-0.4647, -0.2333, -0.1883, 0.1603],
[-1.1130, -0.5588, -0.4510, 0.3838]])
>>> 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) # compare torch.nn.functional.bilinear
tensor([[-0.3430, -5.2405, 0.4494],
[ 0.3311, 5.5201, -3.0356]])
>>> As = torch.randn(3,2,5)
>>> Bs = torch.randn(3,5,4)
>>> torch.einsum('bij,bjk->bik', As, Bs) # batch matrix multiplication
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]]])
>>> A = torch.randn(3, 3)
>>> torch.einsum('ii->i', A) # diagonal
tensor([-0.7825, 0.8291, -0.1936])
>>> A = torch.randn(4, 3, 3)
>>> torch.einsum('...ii->...i', A) # batch diagonal
tensor([[-1.0864, 0.7292, 0.0569],
[-0.9725, -1.0270, 0.6493],
[ 0.5832, -1.1716, -1.5084],
[ 0.4041, -1.1690, 0.8570]])
>>> A = torch.randn(2, 3, 4, 5)
>>> torch.einsum('...ij->...ji', A).shape # batch permute
torch.Size([2, 3, 5, 4])
"""
if len(operands) == 1 and isinstance(operands[0], (list, tuple)):
# the old interface of passing the operands as one list argument
operands = operands[0]
return torch._C._VariableFunctions.einsum(equation, operands)
def isfinite(tensor):
r"""Returns a new tensor with boolean elements representing if each element is `Finite` or not.
Arguments:
tensor (Tensor): A tensor to check
Returns:
Tensor: A ``torch.ByteTensor`` containing a 1 at each location of finite elements and 0 otherwise
Example::
>>> torch.isfinite(torch.tensor([1, float('inf'), 2, float('-inf'), float('nan')]))
tensor([ 1, 0, 1, 0, 0], dtype=torch.uint8)
"""
if not isinstance(tensor, torch.Tensor):
raise ValueError("The argument is not a tensor", str(tensor))
return (tensor == tensor) & (tensor.abs() != inf)
def isinf(tensor):
r"""Returns a new tensor with boolean elements representing if each element is `+/-INF` or not.
Arguments:
tensor (Tensor): A tensor to check
Returns:
Tensor: A ``torch.ByteTensor`` containing a 1 at each location of `+/-INF` elements and 0 otherwise
Example::
>>> torch.isinf(torch.tensor([1, float('inf'), 2, float('-inf'), float('nan')]))
tensor([ 0, 1, 0, 1, 0], dtype=torch.uint8)
"""
if not isinstance(tensor, torch.Tensor):
raise ValueError("The argument is not a tensor", str(tensor))
return tensor.abs() == inf
def meshgrid(*tensors, **kwargs):
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`th grid is defined by
expanding the :math:`i`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 has :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]])
"""
if kwargs:
raise TypeError("meshgrid() got an unexpected keyword argument '%s'" % (list(kwargs)[0],))
if len(tensors) == 1 and isinstance(tensors[0], (list, tuple)):
# the old interface of passing the operands as one list argument
tensors = tensors[0]
return torch._C._VariableFunctions.meshgrid(tensors)
def stft(input, n_fft, hop_length=None, win_length=None, window=None,
center=True, pad_mode='reflect', normalized=False, onesided=True):
r"""Short-time Fourier transform (STFT).
Ignoring the optional batch dimension, this method computes the following
expression:
.. math::
X[m, \omega] = \sum_{k = 0}^{\text{win\_length}}%
\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 sequenceor 2-D a 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), 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]^*`.
* 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}`.
Returns the real and the imaginary parts together as one 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, :math:`T` is the total number of frames used, and each pair
in the last dimension represents a complex number as the real part and the
imaginary part.
.. warning::
This function changed signature at version 0.4.1. Calling with the
previous signature may cause error or return incorrect result.
Arguments:
input (Tensor): the input tensor
n_fft (int, optional): size of Fourier transform
hop_length (int): the distance between neighboring sliding window
frames. Default: ``None`` (treated as equal to ``floor(n_fft / 4)``)
win_length (int): 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 Default: ``True``
Returns:
Tensor: A tensor containing the STFT result with shape described above
"""
# 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 torch._C._VariableFunctions.stft(input, n_fft, hop_length, win_length, window, normalized, onesided)
def isnan(tensor):
r"""Returns a new tensor with boolean elements representing if each element is `NaN` or not.
Arguments:
tensor (Tensor): A tensor to check
Returns:
Tensor: A ``torch.ByteTensor`` containing a 1 at each location of `NaN` elements.
Example::
>>> torch.isnan(torch.tensor([1, float('nan'), 2]))
tensor([ 0, 1, 0], dtype=torch.uint8)
"""
if not isinstance(tensor, torch.Tensor):
raise ValueError("The argument is not a tensor", str(tensor))
return tensor != tensor
def unique(input, sorted=False, return_inverse=False, dim=None):
r"""Returns the unique scalar elements of the input tensor as a 1-D tensor.
Arguments:
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.
dim (int): the dimension to apply unique. If ``None``, the unique of the
flattened input is returned. default: ``None``
Returns:
(Tensor, 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 a
2nd 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.
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 dim is not None:
output, inverse_indices = torch._unique_dim(
input,
dim,
sorted=sorted,
return_inverse=return_inverse
)
else:
output, inverse_indices = torch._unique(
input,
sorted=sorted,
return_inverse=return_inverse,
)
if return_inverse:
return output, inverse_indices
else:
return output
def argmax(input, dim=None, keepdim=False):
r"""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 (Tensor): the input tensor
dim (int): the dimension to reduce. If ``None``, the argmax of the
flattened input is returned.
keepdim (bool): whether the output tensors have :attr:`dim`
retained or not. 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])
"""
if dim is None:
return torch._argmax(input.contiguous().view(-1), dim=0, keepdim=False)
return torch._argmax(input, dim, keepdim)
def argmin(input, dim=None, keepdim=False):
r"""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 (Tensor): the input tensor
dim (int): the dimension to reduce. If ``None``, the argmin of the
flattened input is returned.
keepdim (bool): whether the output tensors have :attr:`dim`
retained or not. 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])
"""
if dim is None:
return torch._argmin(input.contiguous().view(-1), dim=0, keepdim=False)
return torch._argmin(input, dim, keepdim)
def tensordot(a, b, dims=2):
r"""Returns a contraction of a and b over multiple dimensions.
:attr:`tensordot` implements a generalizes the matrix product.
Args:
a (Tensor): Left tensor to contract
b (Tensor): Right tensor to contract
dims (int or tuple of two lists of integers): number of dimensions to
contract or explicit lists of dimensions for :attr:`a` and
:attr:`b` respectively
When called with an integer argument :attr:`dims` = :math:`d`, and the number of
dimensions of :attr:`a` and :attr:`b` is :math:`m` and :math:`n`, respectively,
it 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 :attr:`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]])
"""
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()
dims_a = list(range(-dims, 0))
dims_b = list(range(dims))
return torch._C._VariableFunctions.tensordot(a, b, dims_a, dims_b)
def argsort(input, dim=None, descending=False):
r"""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 (Tensor): the input tensor
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]])
"""
if dim is None:
return torch.sort(input, -1, descending)[1]
return torch.sort(input, dim, descending)[1]
def norm(input, p="fro", dim=None, keepdim=False, out=None):
r"""Returns the matrix norm or vector norm of a given tensor.
Args:
input (Tensor): the input tensor
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
===== ============================ ==========================
None Frobenius norm 2-norm
'fro' Frobenius norm --
'nuc' nuclear norm --
Other as vec norm when dim is None sum(abs(x)**ord)**(1./ord)
===== ============================ ==========================
dim (int, 2-tuple of ints, 2-list of ints, optional): If it is an int,
vector norm will be calculated, if it is 2-tuple of ints, matrix norm
will be calculated. If the value is None, matrix norm will be calculated
when the input tensor only has two dimensions, vector norm will be
calculated when the input tensor only has one dimension. If the input
tensor has more than two dimensions, the vector norm will be applied to
last dimension.
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``.
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., 3., 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))
"""
ndim = input.dim()
# catch default case
if dim is None and out is None:
if p == "fro":
return torch._C._VariableFunctions.frobenius_norm(input)
elif p != "nuc":
return torch._C._VariableFunctions.norm(input, p)
if p == "fro":
if dim is None:
dim = tuple(range(ndim))
if out is None:
return torch._C._VariableFunctions.frobenius_norm(input, dim, keepdim=keepdim)
return torch._C._VariableFunctions.frobenius_norm(input, dim, keepdim=keepdim, out=out)
elif p == "nuc":
if out is None:
torch._C._VariableFunctions.nuclear_norm(input, keepdim=keepdim)
return torch._C._VariableFunctions.nuclear_norm(input, keepdim=keepdim, out=out)
else:
if out is None:
return torch._C._VariableFunctions.norm(input, p, dim, keepdim=keepdim)
return torch._C._VariableFunctions.norm(input, p, dim, keepdim=keepdim, out=out)
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
"""
return torch._C._VariableFunctions.chain_matmul(matrices)
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