torch/sparse/__init__.py - platform/external/pytorch - Git at Google

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

 import torch
 from torch._C import _add_docstr, _sparse  # type: ignore[attr-defined]
 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__ = [
     'addmm',
     'mm',
     'sum',
     'softmax',
     'log_softmax',
 ]


 addmm = _add_docstr(_sparse._sparse_addmm, r"""
 sparse.addmm(mat, mat1, mat2, *, beta=1., alpha=1.) -> Tensor

 This function does exact same thing as :func:`torch.addmm` in the forward,
 except that it supports backward for sparse COO matrix :attr:`mat1`.
 When :attr:`mat1` is a COO tensor it must have `sparse_dim = 2`.
 When inputs are COO tensors, this function also supports backward for both inputs.

 Supports both CSR and COO storage formats.

 .. note::
     This function doesn't support computing derivaties with respect to CSR matrices.

 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`)
 """)


 mm = _add_docstr(_sparse._sparse_mm, 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.
     When :attr:`mat1` is a COO tensor it must have `sparse_dim = 2`.
     When inputs are COO tensors, this function also supports backward for both inputs.

     Supports both CSR and COO storage formats.

 .. note::
     This function doesn't support computing derivaties with respect to CSR matrices.

     Args:
         mat1 (Tensor): 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 = 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)
     """)


 sampled_addmm = _add_docstr(_sparse.sparse_sampled_addmm, r"""
 sparse.sampled_addmm(input, mat1, mat2, *, beta=1., alpha=1., out=None) -> Tensor

 Performs a matrix multiplication of the dense matrices :attr:`mat1` and :attr:`mat2` at the locations
 specified by the sparsity pattern of :attr:`input`. The matrix :attr:`input` is added to the final result.

 Mathematically this performs the following operation:

 .. math::

     \text{out} = \alpha\ (\text{mat1} \mathbin{@} \text{mat2})*\text{spy}(\text{input}) + \beta\ \text{input}

 where :math:`\text{spy}(\text{input})` is the sparsity pattern matrix of :attr:`input`, :attr:`alpha`
 and :attr:`beta` are the scaling factors.
 :math:`\text{spy}(\text{input})` has value 1 at the positions where :attr:`input` has non-zero values, and 0 elsewhere.

 .. note::
     :attr:`input` must be a sparse CSR tensor. :attr:`mat1` and :attr:`mat2` must be dense tensors.
     This function is implemented only for tensors on CUDA devices.

 Args:
     input (Tensor): a sparse CSR matrix of shape `(m, n)` to be added and used to compute
         the sampled matrix multiplication
     mat1 (Tensor): a dense matrix of shape `(m, k)` to be multiplied
     mat2 (Tensor): a dense matrix of shape `(k, n)` to be multiplied

 Keyword args:
     beta (Number, optional): multiplier for :attr:`input` (:math:`\beta`)
     alpha (Number, optional): multiplier for :math:`mat1 @ mat2` (:math:`\alpha`)
     out (Tensor, optional): output tensor. Ignored if `None`. Default: `None`.

 Examples::

     >>> input = torch.eye(3, device='cuda').to_sparse_csr()
     >>> mat1 = torch.randn(3, 5, device='cuda')
     >>> mat2 = torch.randn(5, 3, device='cuda')
     >>> torch.sparse.sampled_addmm(input, mat1, mat2)
     tensor(crow_indices=tensor([0, 1, 2, 3]),
         col_indices=tensor([0, 1, 2]),
         values=tensor([ 0.2847, -0.7805, -0.1900]), device='cuda:0',
         size=(3, 3), nnz=3, layout=torch.sparse_csr)
     >>> torch.sparse.sampled_addmm(input, mat1, mat2).to_dense()
     tensor([[ 0.2847,  0.0000,  0.0000],
         [ 0.0000, -0.7805,  0.0000],
         [ 0.0000,  0.0000, -0.1900]], device='cuda:0')
     >>> torch.sparse.sampled_addmm(input, mat1, mat2, beta=0.5, alpha=0.5)
     tensor(crow_indices=tensor([0, 1, 2, 3]),
         col_indices=tensor([0, 1, 2]),
         values=tensor([ 0.1423, -0.3903, -0.0950]), device='cuda:0',
         size=(3, 3), nnz=3, layout=torch.sparse_csr)
 """)


 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:
             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)


 softmax = _add_docstr(_sparse._sparse_softmax, r"""
 sparse.softmax(input, dim, *, dtype=None) -> Tensor

 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
 """)


 log_softmax = _add_docstr(_sparse._sparse_log_softmax, r"""
 sparse.log_softmax(input, dim, *, dtype=None) -> Tensor

 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
 """)


 spdiags = _add_docstr(
     _sparse._spdiags,
     r"""
 sparse.spdiags(diagonals, offsets, shape, layout=None) -> Tensor

 Creates a sparse 2D tensor by placing the values from rows of
 :attr:`diagonals` along specified diagonals of the output

 The :attr:`offsets` tensor controls which diagonals are set.

 - If :attr:`offsets[i]` = 0, it is the main diagonal
 - If :attr:`offsets[i]` < 0, it is below the main diagonal
 - If :attr:`offsets[i]` > 0, it is above the main diagonal

 The number of rows in :attr:`diagonals` must match the length of :attr:`offsets`,
 and an offset may not be repeated.

 Args:
     diagonals (Tensor): Matrix storing diagonals row-wise
     offsets (Tensor): The diagonals to be set, stored as a vector
     shape (2-tuple of ints): The desired shape of the result
 Keyword args:
     layout (:class:`torch.layout`, optional): The desired layout of the
         returned tensor. ``torch.sparse_coo``, ``torch.sparse_csc`` and ``torch.sparse_csr``
         are supported. Default: ``torch.sparse_coo``

 Examples:

 Set the main and first two lower diagonals of a matrix::

     >>> diags = torch.arange(9).reshape(3, 3)
     >>> diags
     tensor([[0, 1, 2],
             [3, 4, 5],
             [6, 7, 8]])
     >>> s = torch.sparse.spdiags(diags, torch.tensor([0, -1, -2]), (3, 3))
     >>> s
     tensor(indices=tensor([[0, 1, 2, 1, 2, 2],
                            [0, 1, 2, 0, 1, 0]]),
            values=tensor([0, 1, 2, 3, 4, 6]),
            size=(3, 3), nnz=6, layout=torch.sparse_coo)
     >>> s.to_dense()
     tensor([[0, 0, 0],
             [3, 1, 0],
             [6, 4, 2]])


 Change the output layout::

     >>> diags = torch.arange(9).reshape(3, 3)
     >>> diags
     tensor([[0, 1, 2],[3, 4, 5], [6, 7, 8])
     >>> s = torch.sparse.spdiags(diags, torch.tensor([0, -1, -2]), (3, 3), layout=torch.sparse_csr)
     >>> s
     tensor(crow_indices=tensor([0, 1, 3, 6]),
            col_indices=tensor([0, 0, 1, 0, 1, 2]),
            values=tensor([0, 3, 1, 6, 4, 2]), size=(3, 3), nnz=6,
            layout=torch.sparse_csr)
     >>> s.to_dense()
     tensor([[0, 0, 0],
             [3, 1, 0],
             [6, 4, 2]])

 Set partial diagonals of a large output::

     >>> diags = torch.tensor([[1, 2], [3, 4]])
     >>> offsets = torch.tensor([0, -1])
     >>> torch.sparse.spdiags(diags, offsets, (5, 5)).to_dense()
     tensor([[1, 0, 0, 0, 0],
             [3, 2, 0, 0, 0],
             [0, 4, 0, 0, 0],
             [0, 0, 0, 0, 0],
             [0, 0, 0, 0, 0]])

 .. note::

     When setting the values along a given diagonal the index into the diagonal
     and the index into the row of :attr:`diagonals` is taken as the
     column index in the output. This has the effect that when setting a diagonal
     with a positive offset `k` the first value along that diagonal will be
     the value in position `k` of the row of :attr:`diagonals`

 Specifying a positive offset::

     >>> diags = torch.tensor([[1, 2, 3], [1, 2, 3], [1, 2, 3]])
     >>> torch.sparse.spdiags(diags, torch.tensor([0, 1, 2]), (5, 5)).to_dense()
     tensor([[1, 2, 3, 0, 0],
             [0, 2, 3, 0, 0],
             [0, 0, 3, 0, 0],
             [0, 0, 0, 0, 0],
             [0, 0, 0, 0, 0]])
 """)
	# The Tensor classes are added to this module by python_tensor.cpp
	from typing import Optional, Tuple, List, Union

	import torch
	from torch._C import _add_docstr, _sparse # type: ignore[attr-defined]
	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__ = [
	'addmm',
	'mm',
	'sum',
	'softmax',
	'log_softmax',
	]


	addmm = _add_docstr(_sparse._sparse_addmm, r"""
	sparse.addmm(mat, mat1, mat2, *, beta=1., alpha=1.) -> Tensor

	This function does exact same thing as :func:`torch.addmm` in the forward,
	except that it supports backward for sparse COO matrix :attr:`mat1`.
	When :attr:`mat1` is a COO tensor it must have `sparse_dim = 2`.
	When inputs are COO tensors, this function also supports backward for both inputs.

	Supports both CSR and COO storage formats.

	.. note::
	This function doesn't support computing derivaties with respect to CSR matrices.

	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`)
	""")


	mm = _add_docstr(_sparse._sparse_mm, 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.
	When :attr:`mat1` is a COO tensor it must have `sparse_dim = 2`.
	When inputs are COO tensors, this function also supports backward for both inputs.

	Supports both CSR and COO storage formats.

	.. note::
	This function doesn't support computing derivaties with respect to CSR matrices.

	Args:
	mat1 (Tensor): 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 = 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)
	""")


	sampled_addmm = _add_docstr(_sparse.sparse_sampled_addmm, r"""
	sparse.sampled_addmm(input, mat1, mat2, *, beta=1., alpha=1., out=None) -> Tensor

	Performs a matrix multiplication of the dense matrices :attr:`mat1` and :attr:`mat2` at the locations
	specified by the sparsity pattern of :attr:`input`. The matrix :attr:`input` is added to the final result.

	Mathematically this performs the following operation:

	.. math::

	\text{out} = \alpha\ (\text{mat1} \mathbin{@} \text{mat2})*\text{spy}(\text{input}) + \beta\ \text{input}

	where :math:`\text{spy}(\text{input})` is the sparsity pattern matrix of :attr:`input`, :attr:`alpha`
	and :attr:`beta` are the scaling factors.
	:math:`\text{spy}(\text{input})` has value 1 at the positions where :attr:`input` has non-zero values, and 0 elsewhere.

	.. note::
	:attr:`input` must be a sparse CSR tensor. :attr:`mat1` and :attr:`mat2` must be dense tensors.
	This function is implemented only for tensors on CUDA devices.

	Args:
	input (Tensor): a sparse CSR matrix of shape `(m, n)` to be added and used to compute
	the sampled matrix multiplication
	mat1 (Tensor): a dense matrix of shape `(m, k)` to be multiplied
	mat2 (Tensor): a dense matrix of shape `(k, n)` to be multiplied

	Keyword args:
	beta (Number, optional): multiplier for :attr:`input` (:math:`\beta`)
	alpha (Number, optional): multiplier for :math:`mat1 @ mat2` (:math:`\alpha`)
	out (Tensor, optional): output tensor. Ignored if `None`. Default: `None`.

	Examples::

	>>> input = torch.eye(3, device='cuda').to_sparse_csr()
	>>> mat1 = torch.randn(3, 5, device='cuda')
	>>> mat2 = torch.randn(5, 3, device='cuda')
	>>> torch.sparse.sampled_addmm(input, mat1, mat2)
	tensor(crow_indices=tensor([0, 1, 2, 3]),
	col_indices=tensor([0, 1, 2]),
	values=tensor([ 0.2847, -0.7805, -0.1900]), device='cuda:0',
	size=(3, 3), nnz=3, layout=torch.sparse_csr)
	>>> torch.sparse.sampled_addmm(input, mat1, mat2).to_dense()
	tensor([[ 0.2847, 0.0000, 0.0000],
	[ 0.0000, -0.7805, 0.0000],
	[ 0.0000, 0.0000, -0.1900]], device='cuda:0')
	>>> torch.sparse.sampled_addmm(input, mat1, mat2, beta=0.5, alpha=0.5)
	tensor(crow_indices=tensor([0, 1, 2, 3]),
	col_indices=tensor([0, 1, 2]),
	values=tensor([ 0.1423, -0.3903, -0.0950]), device='cuda:0',
	size=(3, 3), nnz=3, layout=torch.sparse_csr)
	""")


	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:
	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)


	softmax = _add_docstr(_sparse._sparse_softmax, r"""
	sparse.softmax(input, dim, *, dtype=None) -> Tensor

	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
	""")


	log_softmax = _add_docstr(_sparse._sparse_log_softmax, r"""
	sparse.log_softmax(input, dim, *, dtype=None) -> Tensor

	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
	""")


	spdiags = _add_docstr(
	_sparse._spdiags,
	r"""
	sparse.spdiags(diagonals, offsets, shape, layout=None) -> Tensor

	Creates a sparse 2D tensor by placing the values from rows of
	:attr:`diagonals` along specified diagonals of the output

	The :attr:`offsets` tensor controls which diagonals are set.

	- If :attr:`offsets[i]` = 0, it is the main diagonal
	- If :attr:`offsets[i]` < 0, it is below the main diagonal
	- If :attr:`offsets[i]` > 0, it is above the main diagonal

	The number of rows in :attr:`diagonals` must match the length of :attr:`offsets`,
	and an offset may not be repeated.

	Args:
	diagonals (Tensor): Matrix storing diagonals row-wise
	offsets (Tensor): The diagonals to be set, stored as a vector
	shape (2-tuple of ints): The desired shape of the result
	Keyword args:
	layout (:class:`torch.layout`, optional): The desired layout of the
	returned tensor. ``torch.sparse_coo``, ``torch.sparse_csc`` and ``torch.sparse_csr``
	are supported. Default: ``torch.sparse_coo``

	Examples:

	Set the main and first two lower diagonals of a matrix::

	>>> diags = torch.arange(9).reshape(3, 3)
	>>> diags
	tensor([[0, 1, 2],
	[3, 4, 5],
	[6, 7, 8]])
	>>> s = torch.sparse.spdiags(diags, torch.tensor([0, -1, -2]), (3, 3))
	>>> s
	tensor(indices=tensor([[0, 1, 2, 1, 2, 2],
	[0, 1, 2, 0, 1, 0]]),
	values=tensor([0, 1, 2, 3, 4, 6]),
	size=(3, 3), nnz=6, layout=torch.sparse_coo)
	>>> s.to_dense()
	tensor([[0, 0, 0],
	[3, 1, 0],
	[6, 4, 2]])


	Change the output layout::

	>>> diags = torch.arange(9).reshape(3, 3)
	>>> diags
	tensor([[0, 1, 2],[3, 4, 5], [6, 7, 8])
	>>> s = torch.sparse.spdiags(diags, torch.tensor([0, -1, -2]), (3, 3), layout=torch.sparse_csr)
	>>> s
	tensor(crow_indices=tensor([0, 1, 3, 6]),
	col_indices=tensor([0, 0, 1, 0, 1, 2]),
	values=tensor([0, 3, 1, 6, 4, 2]), size=(3, 3), nnz=6,
	layout=torch.sparse_csr)
	>>> s.to_dense()
	tensor([[0, 0, 0],
	[3, 1, 0],
	[6, 4, 2]])

	Set partial diagonals of a large output::

	>>> diags = torch.tensor([[1, 2], [3, 4]])
	>>> offsets = torch.tensor([0, -1])
	>>> torch.sparse.spdiags(diags, offsets, (5, 5)).to_dense()
	tensor([[1, 0, 0, 0, 0],
	[3, 2, 0, 0, 0],
	[0, 4, 0, 0, 0],
	[0, 0, 0, 0, 0],
	[0, 0, 0, 0, 0]])

	.. note::

	When setting the values along a given diagonal the index into the diagonal
	and the index into the row of :attr:`diagonals` is taken as the
	column index in the output. This has the effect that when setting a diagonal
	with a positive offset `k` the first value along that diagonal will be
	the value in position `k` of the row of :attr:`diagonals`

	Specifying a positive offset::

	>>> diags = torch.tensor([[1, 2, 3], [1, 2, 3], [1, 2, 3]])
	>>> torch.sparse.spdiags(diags, torch.tensor([0, 1, 2]), (5, 5)).to_dense()
	tensor([[1, 2, 3, 0, 0],
	[0, 2, 3, 0, 0],
	[0, 0, 3, 0, 0],
	[0, 0, 0, 0, 0],
	[0, 0, 0, 0, 0]])
	""")