Eigen中稠密-稀疏矩阵乘积是否支持多线程？已知稀疏-稠密乘积支持

Great question! Let me share what I know about this from working with Eigen and digging into its implementation details:

• First, to recap: As you noted, Eigen does support multithreading for sparse-dense matrix products (SparseMatrix * DenseMatrix), which is covered in the official documentation.
• For the reverse case—dense-sparse products (DenseMatrix * SparseMatrix)—the short answer is: Eigen does NOT have built-in multithreading support for this operation by default.

Why the difference? #

The core reason lies in how parallelization can be efficiently applied to each operation:

• Sparse-dense multiplication can be easily split by rows of the sparse matrix. Each row's computation is independent, making it straightforward to distribute work across threads.
• Dense-sparse multiplication, however, involves multiplying dense rows with sparse columns. The irregular structure of sparse columns makes it much harder to split the work into balanced, independent chunks that would benefit from parallelization. Eigen's developers haven't implemented a robust multithreaded path for this scenario yet.

A workaround to enable multithreading for dense-sparse products #

If you need parallelism for Dense * Sparse, you can leverage the supported sparse-dense path using transposition:

// Instead of doing:
result = dense_mat * sparse_mat;

// Do this to use multithreading:
result = (sparse_mat.transpose() * dense_mat.transpose()).transpose();

This converts the operation into a Sparse^T * Dense^T product (a sparse-dense type that supports multithreading), then transposes the result back to get the original dense-sparse product.

Quick note on enabling Eigen multithreading #

Make sure you have Eigen's multithreading enabled in your build:

• If using OpenMP, compile with OpenMP flags (e.g., -fopenmp for GCC/Clang) and ensure Eigen is configured to use OpenMP.
• You can also set the number of threads explicitly with:

Eigen::setNbThreads(4); // Adjust to your desired thread count

内容的提问来源于stack exchange，提问作者avgn