dgl.sparse.softmax

dgl.sparse.softmax(input: SparseMatrix, dim: int = 1) → SparseMatrix

Applies softmax to the non-zero elements of the sparse matrix on the dimension :attr:dim. dim = 0 or 1 indicates column-wise or row-wise softmax respectively.

If input.val takes shape (nnz, D), then the output matrix output and output.val take the same shape as input and input.val. output.val[:, i] is calculated based on input.val[:, i].

Parameters:

input (SparseMatrix) – The input sparse matrix

Returns:

The output sparse matrix

Return type:

SparseMatrix

Examples

Case1: row-wise softmax on matrix with values of shape (nnz)

>>> indices = torch.tensor([[0, 0, 1, 2], [1, 2, 2, 0]])
>>> val = torch.tensor([0., 1., 2., 3.])
>>> A = dglsp.spmatrix(indices, val)
>>> dglsp.softmax(A)
SparseMatrix(indices=tensor([[0, 0, 1, 2],
                             [1, 2, 2, 0]]),
             values=tensor([0.2689, 0.7311, 1.0000, 1.0000]),
             shape=(3, 3), nnz=4)

Case2: row-wise softmax on matrix with values of shape (nnz, D)

>>> indices = torch.tensor([[0, 0, 1, 2], [1, 2, 2, 0]])
>>> val = torch.tensor([[0., 7.], [1., 3.], [2., 2.], [3., 1.]])
>>> A = dglsp.spmatrix(indices, val)
>>> dglsp.softmax(A)
SparseMatrix(indices=tensor([[0, 0, 1, 2],
                             [1, 2, 2, 0]]),
             values=tensor([[0.2689, 0.9820],
                            [0.7311, 0.0180],
                            [1.0000, 1.0000],
                            [1.0000, 1.0000]]),
             shape=(3, 3), nnz=4, val_size=(2,))

Case3: column-wise softmax on matrix with values of shape (nnz)

>>> indices = torch.tensor([[0, 0, 1, 2], [1, 2, 2, 0]])
>>> val = torch.tensor([0., 1., 2., 3.])
>>> A = dglsp.spmatrix(indices, val)
>>> dglsp.softmax(A, 0)
SparseMatrix(indices=tensor([[0, 0, 1, 2],
                             [1, 2, 2, 0]]),
             values=tensor([1.0000, 0.2689, 0.7311, 1.0000]),
             shape=(3, 3), nnz=4)