PyTorch Sparse

---

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

Binaries

We provide pip wheels for all major OS/PyTorch/CUDA combinations, see here.

PyTorch 2.8

To install the binaries for PyTorch 2.8.0, simply run

pip install torch-scatter torch-sparse -f https://data.pyg.org/whl/torch-2.8.0+${CUDA}.html

where ${CUDA} should be replaced by either cpu, cu126, cu128, or cu129 depending on your PyTorch installation.

	cpu	cu126	cu128	cu129
Linux	✅	✅	✅	✅
Windows	✅	✅	✅	✅
macOS	✅

PyTorch 2.7

To install the binaries for PyTorch 2.7.0, simply run

pip install torch-scatter torch-sparse -f https://data.pyg.org/whl/torch-2.7.0+${CUDA}.html

where ${CUDA} should be replaced by either cpu, cu118, cu126, or cu128 depending on your PyTorch installation.

	cpu	cu118	cu126	cu128
Linux	✅	✅	✅	✅
Windows	✅	✅	✅	✅
macOS	✅

PyTorch 2.6

To install the binaries for PyTorch 2.6.0, simply run

pip install torch-scatter torch-sparse -f https://data.pyg.org/whl/torch-2.6.0+${CUDA}.html

where ${CUDA} should be replaced by either cpu, cu118, cu124, or cu126 depending on your PyTorch installation.

	cpu	cu118	cu124	cu126
Linux	✅	✅	✅	✅
Windows	✅	✅	✅	✅
macOS	✅

Note: Binaries of older versions are also provided for PyTorch 1.4.0, PyTorch 1.5.0, PyTorch 1.6.0, PyTorch 1.7.0/1.7.1, PyTorch 1.8.0/1.8.1, PyTorch 1.9.0, PyTorch 1.10.0/1.10.1/1.10.2, PyTorch 1.11.0, PyTorch 1.12.0/1.12.1, PyTorch 1.13.0/1.13.1, PyTorch 2.0.0/2.0.1, PyTorch 2.1.0/2.1.1/2.1.2, PyTorch 2.2.0/2.2.1/2.2.2, PyTorch 2.3.0/2.3.1, PyTorch 2.4.0/2.4.1, and PyTorch 2.5.0/2.5.1 (following the same procedure). For older versions, you need to explicitly specify the latest supported version number or install via pip install --no-index in order to prevent a manual installation from source. You can look up the latest supported version number here.

From source

Ensure that at least PyTorch 1.7.0 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__)"
>>> 1.7.0

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

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

If you want to additionally build torch-sparse with METIS support, e.g. for partioning, please download and install the METIS library by following the instructions in the Install.txt file. Note that METIS needs to be installed with 64 bit IDXTYPEWIDTH by changing include/metis.h. Afterwards, set the environment variable WITH_METIS=1.

Then run:

pip install torch-scatter torch-sparse

When running in a docker container without NVIDIA driver, PyTorch needs to evaluate the compute capabilities and may fail. In this case, ensure that the compute capabilities are set via TORCH_CUDA_ARCH_LIST, e.g.:

export TORCH_CUDA_ARCH_LIST="6.0 6.1 7.2+PTX 7.5+PTX"

Functions

Coalesce

torch_sparse.coalesce(index, value, m, n, op="add") -> (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.

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")

Returns

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

Example

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]])

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.
• coalesced (bool, optional) - If set to False, will not coalesce the output. (default: True)

Returns

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

Example

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]])

Sparse Dense Matrix Multiplication

torch_sparse.spmm(index, value, m, n, 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.
• n (int) - The second dimension of sparse matrix.
• matrix (Tensor) - The dense matrix.

Returns

• out (Tensor) - The dense output matrix.

Example

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]])

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 (use the coalesced attribute to force).

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.
• coalesced (bool, optional): If set to True, will coalesce both input sparse matrices. (default: False)

Returns

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

Example

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])

Running tests

pytest

C++ API

torch-sparse also offers a C++ API that contains C++ equivalent of python models. For this, we need to add TorchLib to the -DCMAKE_PREFIX_PATH (run import torch; print(torch.utils.cmake_prefix_path) to obtain it).

mkdir build
cd build
# Add -DWITH_CUDA=on support for CUDA support
cmake -DCMAKE_PREFIX_PATH="..." ..
make
make install