# Source code for dgl.sparse.sddmm

```"""Sampled Dense-Dense Matrix Multiplication (SDDMM) operator module."""
import torch

from .sparse_matrix import SparseMatrix

__all__ = ["sddmm", "bsddmm"]

# pylint: disable=invalid-name
[docs]def sddmm(A: SparseMatrix, X1: torch.Tensor, X2: torch.Tensor) -> SparseMatrix:
r"""Sampled-Dense-Dense Matrix Multiplication (SDDMM).

``sddmm`` matrix-multiplies two dense matrices :attr:`X1` and :attr:`X2`,
then elementwise-multiplies the result with sparse matrix :attr:`A` at the
nonzero locations.

Mathematically ``sddmm`` is formulated as:

.. math::
out = (X1 @ X2) * A

In particular, :attr:`X1` and :attr:`X2` can be 1-D, then ``X1 @ X2``
becomes the out-product of the two vectors (which results in a matrix).

Parameters
----------
A : SparseMatrix
Sparse matrix of shape ``(L, N)``
X1 : torch.Tensor
Dense matrix of shape ``(L, M)`` or ``(L,)``
X2 : torch.Tensor
Dense matrix of shape ``(M, N)`` or ``(N,)``

Returns
-------
SparseMatrix
Sparse matrix of shape ``(L, N)``

Examples
--------

>>> indices = torch.tensor([[1, 1, 2], [2, 3, 3]])
>>> val = torch.arange(1, 4).float()
>>> A = dglsp.spmatrix(indices, val, (3, 4))
>>> X1 = torch.randn(3, 5)
>>> X2 = torch.randn(5, 4)
>>> dglsp.sddmm(A, X1, X2)
SparseMatrix(indices=tensor([[1, 1, 2],
[2, 3, 3]]),
values=tensor([-1.6585, -3.9714, -0.5406]),
shape=(3, 4), nnz=3)
"""
return SparseMatrix(torch.ops.dgl_sparse.sddmm(A.c_sparse_matrix, X1, X2))

# pylint: disable=invalid-name
[docs]def bsddmm(A: SparseMatrix, X1: torch.Tensor, X2: torch.Tensor) -> SparseMatrix:
r"""Sampled-Dense-Dense Matrix Multiplication (SDDMM) by batches.

``sddmm`` matrix-multiplies two dense matrices :attr:`X1` and :attr:`X2`,
then elementwise-multiplies the result with sparse matrix :attr:`A` at the
nonzero locations.

Mathematically ``sddmm`` is formulated as:

.. math::
out = (X1 @ X2) * A

The batch dimension is the last dimension for input dense matrices. In
particular, if the sparse matrix has scalar non-zero values, it will be

Parameters
----------
A : SparseMatrix
Sparse matrix of shape ``(L, N)`` with scalar values or vector values of
length ``K``
X1 : Tensor
Dense matrix of shape ``(L, M, K)``
X2 : Tensor
Dense matrix of shape ``(M, N, K)``

Returns
-------
SparseMatrix
Sparse matrix of shape ``(L, N)`` with vector values of length ``K``

Examples
--------

>>> indices = torch.tensor([[1, 1, 2], [2, 3, 3]])
>>> val = torch.arange(1, 4).float()
>>> A = dglsp.spmatrix(indices, val, (3, 4))
>>> X1 = torch.arange(0, 3 * 5 * 2).view(3, 5, 2).float()
>>> X2 = torch.arange(0, 5 * 4 * 2).view(5, 4, 2).float()
>>> dglsp.bsddmm(A, X1, X2)
SparseMatrix(indices=tensor([[1, 1, 2],
[2, 3, 3]]),
values=tensor([[1560., 1735.],
[3400., 3770.],
[8400., 9105.]]),
shape=(3, 4), nnz=3, val_size=(2,))
"""
return sddmm(A, X1, X2)
```