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# Source code for torch.sparse

# The Tensor classes are added to this module by python_tensor.cpp
from typing import Optional, Tuple, List, Union

import torch
from torch import Tensor

# A workaround to support both TorchScript and MyPy:
from typing import TYPE_CHECKING
if TYPE_CHECKING:
from torch.types import _dtype as DType
DimOrDims = Optional[Union[int, Tuple[int], List[int]]]
else:
# The JIT doesn't understand Union, nor torch.dtype here
DType = int
DimOrDims = Optional[Tuple[int]]

__all__ = [
'mm',
'sum',
'softmax',
'log_softmax',
]

[docs]def addmm(mat: Tensor, mat1: Tensor, mat2: Tensor,
beta: float = 1., alpha: float = 1.) -> Tensor:
r"""
This function does exact same thing as :func:torch.addmm in the forward,
except that it supports backward for sparse matrix :attr:mat1. :attr:mat1
need to have sparse_dim = 2. Note that the gradients of :attr:mat1 is a
coalesced sparse tensor.

Args:
mat (Tensor): a dense matrix to be added
mat1 (Tensor): a sparse matrix to be multiplied
mat2 (Tensor): a dense matrix to be multiplied
beta (Number, optional): multiplier for :attr:mat (:math:\beta)
alpha (Number, optional): multiplier for :math:mat1 @ mat2 (:math:\alpha)
"""

[docs]def mm(mat1: Tensor, mat2: Tensor) -> Tensor:
r"""
Performs a matrix multiplication of the sparse matrix :attr:mat1
and the (sparse or strided) matrix :attr:mat2. Similar to :func:torch.mm, If :attr:mat1 is a
:math:(n \times m) tensor, :attr:mat2 is a :math:(m \times p) tensor, out will be a
:math:(n \times p) tensor. :attr:mat1 need to have sparse_dim = 2.
This function also supports backward for both matrices. Note that the gradients of
:attr:mat1 is a coalesced sparse tensor.

Args:
mat1 (SparseTensor): the first sparse matrix to be multiplied
mat2 (Tensor): the second matrix to be multiplied, which could be sparse or dense

Shape:
The format of the output tensor of this function follows:
- sparse x sparse -> sparse
- sparse x dense -> dense

Example::

>>> a
tensor(indices=tensor([[0, 0, 0, 1, 1, 1],
[0, 1, 2, 0, 1, 2]]),
values=tensor([ 1.5901,  0.0183, -0.6146,  1.8061, -0.0112,  0.6302]),

>>> b = torch.randn(3, 2, requires_grad=True)
>>> b
tensor([[-0.6479,  0.7874],
[-1.2056,  0.5641],

>>> y = torch.sparse.mm(a, b)
>>> y
tensor([[-0.3323,  1.8723],
>>> y.sum().backward()
tensor(indices=tensor([[0, 0, 0, 1, 1, 1],
[0, 1, 2, 0, 1, 2]]),
values=tensor([ 0.1394, -0.6415, -2.1639,  0.1394, -0.6415, -2.1639]),
size=(2, 3), nnz=6, layout=torch.sparse_coo)
"""
if mat1.is_sparse and mat2.is_sparse:

[docs]def sum(input: Tensor, dim: DimOrDims = None,
dtype: Optional[DType] = None) -> Tensor:
r"""
Returns the sum of each row of the sparse tensor :attr:input in the given
dimensions :attr:dim. If :attr:dim is a list of dimensions,
reduce over all of them. When sum over all sparse_dim, this method
returns a dense tensor instead of a sparse tensor.

All summed :attr:dim are squeezed (see :func:torch.squeeze), resulting an output
tensor having :attr:dim fewer dimensions than :attr:input.

During backward, only gradients at nnz locations of :attr:input
will propagate back. Note that the gradients of :attr:input is coalesced.

Args:
input (Tensor): the input sparse tensor
dim (int or tuple of ints): a dimension or a list of dimensions to reduce. Default: reduce
over all dims.
dtype (:class:torch.dtype, optional): the desired data type of returned Tensor.
Default: dtype of :attr:input.

Example::

>>> nnz = 3
>>> dims = [5, 5, 2, 3]
>>> I = torch.cat([torch.randint(0, dims[0], size=(nnz,)),
torch.randint(0, dims[1], size=(nnz,))], 0).reshape(2, nnz)
>>> V = torch.randn(nnz, dims[2], dims[3])
>>> size = torch.Size(dims)
>>> S = torch.sparse_coo_tensor(I, V, size)
>>> S
tensor(indices=tensor([[2, 0, 3],
[2, 4, 1]]),
values=tensor([[[-0.6438, -1.6467,  1.4004],
[ 0.3411,  0.0918, -0.2312]],

[[ 0.5348,  0.0634, -2.0494],
[-0.7125, -1.0646,  2.1844]],

[[ 0.1276,  0.1874, -0.6334],
[-1.9682, -0.5340,  0.7483]]]),
size=(5, 5, 2, 3), nnz=3, layout=torch.sparse_coo)

# when sum over only part of sparse_dims, return a sparse tensor
>>> torch.sparse.sum(S, [1, 3])
tensor(indices=tensor([[0, 2, 3]]),
values=tensor([[-1.4512,  0.4073],
[-0.8901,  0.2017],
[-0.3183, -1.7539]]),
size=(5, 2), nnz=3, layout=torch.sparse_coo)

# when sum over all sparse dim, return a dense tensor
# with summed dims squeezed
>>> torch.sparse.sum(S, [0, 1, 3])
tensor([-2.6596, -1.1450])
"""
if dtype is None:
if dim is not None:
else:
else:
if dim is not None:
else:

[docs]def softmax(input: Tensor, dim: int, dtype: Optional[DType] = None) -> Tensor:
r"""Applies a softmax function.

Softmax is defined as:

:math:\text{Softmax}(x_{i}) = \frac{exp(x_i)}{\sum_j exp(x_j)}

where :math:i, j run over sparse tensor indices and unspecified
entries are ignores. This is equivalent to defining unspecified
entries as negative infinity so that :math:exp(x_k) = 0 when the
entry with index :math:k has not specified.

It is applied to all slices along dim, and will re-scale them so
that the elements lie in the range [0, 1] and sum to 1.

Args:
input (Tensor): input
dim (int): A dimension along which softmax will be computed.
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
"""

[docs]def log_softmax(input: Tensor, dim: int, dtype: Optional[DType] = None) -> Tensor:
r"""Applies a softmax function followed by logarithm.

See :class:~torch.sparse.softmax for more details.

Args:
input (Tensor): input
dim (int): A dimension along which softmax will be computed.
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
"""


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