torch.sparse.mm

torch.sparse.mm()

Performs a matrix multiplication of the sparse matrix mat1 and the (sparse or strided) matrix mat2. Similar to torch.mm(), if mat1 is a $(n \times m)$ tensor, mat2 is a $(m \times p)$ tensor, out will be a $(n \times p)$ tensor. When mat1 is a COO tensor it must have sparse_dim = 2.

Supports both CSR and COO storage formats.

Note

Gradient support:

• COO @ Dense: Backward is supported for both inputs. The gradient for the sparse input is returned as a sparse COO tensor.

• CSR @ Dense: Backward is supported for both inputs. The gradient for the sparse input is returned as a sparse CSR tensor.

• CSC/BSR/BSC @ Dense: Not supported.

• Sparse @ Sparse (COO @ COO, CSR @ CSR): Forward works, but backward is not supported.

• Mixed formats (COO @ CSR, CSR @ COO): Not supported.

This function also additionally accepts an optional reduce argument that allows specification of an optional reduction operation, mathematically performs the following operation:

$$z_{ij} = \bigoplus_{k = 0}^{K - 1} x_{ik} y_{kj}$$

where $\bigoplus$ defines the reduce operator. reduce is implemented only for CSR storage format on CPU device.

Parameters:

• mat1 (Tensor) – the first sparse matrix to be multiplied

• mat2 (Tensor) – the second matrix to be multiplied, which could be sparse or dense

• reduce (str, optional) – the reduction operation to apply for non-unique indices ("sum", "mean", "amax", "amin"). Default "sum".

Shape:

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

Example:

>>> a = torch.tensor([[1., 0, 2], [0, 3, 0]]).to_sparse().requires_grad_()
>>> a
tensor(indices=tensor([[0, 0, 1],
                       [0, 2, 1]]),
       values=tensor([1., 2., 3.]),
       size=(2, 3), nnz=3, layout=torch.sparse_coo, requires_grad=True)
>>> b = torch.tensor([[0, 1.], [2, 0], [0, 0]], requires_grad=True)
>>> b
tensor([[0., 1.],
        [2., 0.],
        [0., 0.]], requires_grad=True)
>>> y = torch.sparse.mm(a, b)
>>> y
tensor([[0., 1.],
        [6., 0.]], grad_fn=<SparseAddmmBackward0>)
>>> y.sum().backward()
>>> a.grad
tensor(indices=tensor([[0, 0, 1],
                       [0, 2, 1]]),
       values=tensor([1., 0., 2.]),
       size=(2, 3), nnz=3, layout=torch.sparse_coo)
>>> c = a.detach().to_sparse_csr()
>>> c
tensor(crow_indices=tensor([0, 2, 3]),
       col_indices=tensor([0, 2, 1]),
       values=tensor([1., 2., 3.]), size=(2, 3), nnz=3,
       layout=torch.sparse_csr)
>>> y1 = torch.sparse.mm(c, b, 'sum')
>>> y1
tensor([[0., 1.],
        [6., 0.]], grad_fn=<SparseMmReduceImplBackward0>)
>>> y2 = torch.sparse.mm(c, b, 'max')
>>> y2
tensor([[0., 1.],
        [6., 0.]], grad_fn=<SparseMmReduceImplBackward0>)