PyTorch Sparse

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PyTorch completely lacks autograd support and operations such as sparse sparse matrix multiplication, but is heavily working on improvement (cf. this issue). In the meantime, this package consists of a small extension library of optimized sparse matrix operations with autograd support. This package currently consists of the following methods:

• Coalesce
• Transpose
• Sparse Dense Matrix Multiplication
• Sparse Sparse Matrix Multiplication

All included operations work on varying data types and are implemented both for CPU and GPU. To avoid the hazzle of creating torch.sparse_coo_tensor, this package defines operations on sparse tensors by simply passing index and value tensors as arguments (with same shapes as defined in PyTorch). Note that only value comes with autograd support, as index is discrete and therefore not differentiable.

Installation

Ensure that at least PyTorch 0.4.1 is installed and verify that cuda/bin and cuda/include are in your $PATH and $CPATH respectively, e.g.:

$ python -c "import torch; print(torch.__version__)"
>>> 0.4.1

$ echo $PATH
>>> /usr/local/cuda/bin:...

$ echo $CPATH
>>> /usr/local/cuda/include:...

Then run:

pip install torch-scatter torch-sparse

If you are running into any installation problems, please create an issue. Be sure to import torch first before using this package to resolve symbols the dynamic linker must see.

Coalesce

torch_sparse.coalesce(index, value, m, n, op="add", fill_value=0) -> (torch.LongTensor, torch.Tensor)

Row-wise sorts value and removes duplicate entries. Duplicate entries are removed by scattering them together. For scattering, any operation of torch_scatter can be used.

Parameters

• index (LongTensor) - The index tensor of sparse matrix.
• value (Tensor) - The value tensor of sparse matrix.
• m (int) - The first dimension of sparse matrix.
• n (int) - The second dimension of sparse matrix.
• op (string, optional) - The scatter operation to use. (default: "add")
• fill_value (int, optional) - The initial fill value of scatter operation. (default: 0)

Returns

• index (LongTensor) - The coalesced index tensor of sparse matrix.
• value (Tensor) - The coalesced value tensor of sparse matrix.

Example

from torch_sparse import coalesce

index = torch.tensor([[1, 0, 1, 0, 2, 1],
                      [0, 1, 1, 1, 0, 0]])
value = torch.tensor([[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7]])

index, value = coalesce(index, value, m=3, n=2)

print(index)
tensor([[0, 1, 1, 2],
        [1, 0, 1, 0]])
print(value)
tensor([[6, 8], [7, 9], [3, 4], [5, 6]])

Transpose

torch_sparse.transpose(index, value, m, n) -> (torch.LongTensor, torch.Tensor)

Transposes dimensions 0 and 1 of a sparse matrix.

Parameters

• index (LongTensor) - The index tensor of sparse matrix.
• value (Tensor) - The value tensor of sparse matrix.
• m (int) - The first dimension of sparse matrix.
• n (int) - The second dimension of sparse matrix.

Returns

• index (LongTensor) - The transposed index tensor of sparse matrix.
• value (Tensor) - The transposed value tensor of sparse matrix.

Example

from torch_sparse import transpose

index = torch.tensor([[1, 0, 1, 0, 2, 1],
                      [0, 1, 1, 1, 0, 0]])
value = torch.tensor([[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7]])

index, value = transpose(index, value, 3, 2)

print(index)
tensor([[0, 0, 1, 1],
        [1, 2, 0, 1]])
print(value)
tensor([[7, 9],
        [5, 6],
        [6, 8],
        [3, 4]])

Sparse Dense Matrix Multiplication

torch_sparse.spmm(index, value, m, matrix) -> torch.Tensor

Matrix product of a sparse matrix with a dense matrix.

Parameters

• index (LongTensor) - The index tensor of sparse matrix.
• value (Tensor) - The value tensor of sparse matrix.
• m (int) - The first dimension of sparse matrix.
• matrix (Tensor) - The dense matrix.

Returns

• out (Tensor) - The dense output matrix.

Example

from torch_sparse import spmm

index = torch.tensor([[0, 0, 1, 2, 2],
                      [0, 2, 1, 0, 1]])
value = torch.tensor([1, 2, 4, 1, 3], dtype=torch.float)
matrix = torch.tensor([[1, 4], [2, 5], [3, 6]], dtype=torch.float)

out = spmm(index, value, 3, matrix)

print(out)
tensor([[7.0, 16.0],
        [8.0, 20.0],
        [7.0, 19.0]])

Sparse Sparse Matrix Multiplication

torch_sparse.spspmm(indexA, valueA, indexB, valueB, m, k, n) -> (torch.LongTensor, torch.Tensor)

Matrix product of two sparse tensors. Both input sparse matrices need to be coalesced.

Parameters

• indexA (LongTensor) - The index tensor of first sparse matrix.
• valueA (Tensor) - The value tensor of first sparse matrix.
• indexB (LongTensor) - The index tensor of second sparse matrix.
• valueB (Tensor) - The value tensor of second sparse matrix.
• m (int) - The first dimension of first sparse matrix.
• k (int) - The second dimension of first sparse matrix and first dimension of second sparse matrix.
• n (int) - The second dimension of second sparse matrix.

Returns

• index (LongTensor) - The output index tensor of sparse matrix.
• value (Tensor) - The output value tensor of sparse matrix.

Example

from torch_sparse import spspmm

indexA = torch.tensor([[0, 0, 1, 2, 2], [1, 2, 0, 0, 1]])
valueA = torch.tensor([1, 2, 3, 4, 5], dtype=torch.float)

indexB = torch.tensor([[0, 2], [1, 0]])
valueB = torch.tensor([2, 4], dtype=torch.float)

indexC, valueC = spspmm(indexA, valueA, indexB, valueB, 3, 3, 2)

print(index)
tensor([[0, 1, 2],
        [0, 1, 1]])
print(value)
tensor([8.0, 6.0, 8.0])

Running tests

python setup.py test