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# torch.sparse.mm¶

torch.sparse.mm(mat1, mat2)[source]

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. mat1 need to have sparse_dim = 2. This function also supports backward for both matrices. Note that the gradients of mat1 is a coalesced sparse tensor.

Parameters
• 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 = 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]),

>>> 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)


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