# The Tensor classes are added to this module by python_tensor.cpp
from typing import Optional, Tuple
import torch
from torch import Tensor
# A workaround to support both TorchScript and MyPy:
from typing import TYPE_CHECKING
if TYPE_CHECKING:
from torch import dtype as DType
else:
DType = int
# TODO: replace the above with
# from torch.types import _dtype as DType
__all__ = [
'addmm',
'mm',
'sum',
'softmax',
'log_softmax',
]
[docs]def addmm(mat, mat1, mat2, beta=1, alpha=1):
# type: (Tensor, Tensor, Tensor, float, float) -> 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 (SparseTensor): a sparse matrix to be multiplied
mat2 (Tensor): a dense matrix be multiplied
beta (Number, optional): multiplier for :attr:`mat` (:math:`\beta`)
alpha (Number, optional): multiplier for :math:`mat1 @ mat2` (:math:`\alpha`)
"""
return torch._sparse_addmm(mat, mat1, mat2, beta=beta, alpha=alpha)
[docs]def mm(mat1, mat2):
r"""
Performs a matrix multiplication of the sparse matrix :attr:`mat1`
and dense 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)` dense 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 dense matrix to be multiplied
Example::
>>> a = torch.randn(2, 3).to_sparse().requires_grad_(True)
>>> 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]),
size=(2, 3), nnz=6, layout=torch.sparse_coo, requires_grad=True)
>>> b = torch.randn(3, 2, requires_grad=True)
>>> b
tensor([[-0.6479, 0.7874],
[-1.2056, 0.5641],
[-1.1716, -0.9923]], requires_grad=True)
>>> y = torch.sparse.mm(a, b)
>>> y
tensor([[-0.3323, 1.8723],
[-1.8951, 0.7904]], grad_fn=<SparseAddmmBackward>)
>>> y.sum().backward()
>>> a.grad
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)
"""
return torch._sparse_mm(mat1, mat2)
[docs]def sum(input, dim=None, dtype=None):
# type: (Tensor, Optional[Tuple[int]], Optional[int]) -> Tensor
r"""
Returns the sum of each row of SparseTensor :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 Tensor instead of SparseTensor.
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 SparseTensor
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 SparseTensor
>>> 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:
return torch._sparse_sum(input, dim)
else:
return torch._sparse_sum(input)
else:
if dim is not None:
return torch._sparse_sum(input, dim, dtype=dtype)
else:
return torch._sparse_sum(input, dtype=dtype)
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 indicies and unspecified
entries are ignores. This is equivalent to defining unspecifed
entries as negative infinity so that :max:`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.
Arguments:
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
"""
return torch._sparse_softmax(input, dim, dtype=dtype)
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.
Arguments:
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
"""
return torch._sparse_log_softmax(input, dim, dtype=dtype)
