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.

Ensure that at least PyTorch 1.1.0 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__)" >>> 1.1.0 $ 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.

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

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

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

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

import torch 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([[6.0, 8.0], [7.0, 9.0], [3.0, 4.0], [5.0, 6.0]]) 

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

Transposes dimensions 0 and 1 of a sparse matrix.

• index (LongTensor) - The index tensor of sparse matrix.
• value (Tensor) - The value tensor of sparse matrix.
• m (int) - The first dimension of corresponding dense matrix.
• n (int) - The second dimension of corresponding dense matrix.
• coalesced (bool, optional) - If set to False, will not coalesce the output. (default: True)

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

import torch 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([[7.0, 9.0], [5.0, 6.0], [6.0, 8.0], [3.0, 4.0]]) 

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

Matrix product of a sparse matrix with a dense matrix.

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

• out (Tensor) - The dense output matrix.

import torch 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]) matrix = torch.Tensor([[1, 4], [2, 5], [3, 6]]) out = spmm(index, value, 3, 3, matrix)

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

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 (use the coalesced attribute to force).

• 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 corresponding dense matrix.
• k (int) - The second dimension of first corresponding dense matrix and first dimension of second corresponding dense matrix.
• n (int) - The second dimension of second corresponding dense matrix.
• coalesced (bool, optional): If set to True, will coalesce both input sparse matrices. (default: False)

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

import torch 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]) indexB = torch.tensor([[0, 2], [1, 0]]) valueB = torch.Tensor([2, 4]) indexC, valueC = spspmm(indexA, valueA, indexB, valueB, 3, 3, 2)

print(indexC) tensor([[0, 1, 2], [0, 1, 1]]) print(valueC) tensor([8.0, 6.0, 8.0]) 

python setup.py test