SpGEMM for HyKKT

[adhamsi]

Description

This implements the Sparse General Matrix-Matrix multiplication (SpGEMM) module for the HyKKT solver. This provides the class SpGEMM.cpp with functions

• addProductMatrices(matrix::Csr* A, matrix::Csr* B)
• addSumMatrix(matrix::Csr* D)
• addResultMatrix(matrix::Csr** E)
• compute()

where compute will store the result of alpha * A * B + beta * D into E. The scalars are passed to the constructor.

Closes #308.

Proposed changes

The class is intended for efficient reuse. After an initial computation, the product and sum matrices can be reloaded with new values (and the same sparsity pattern) and compute() function called again. The addResultMatrix need only be called once.

On CPU, this is implemented with the CHOLMOD package in SuiteSparse. On CUDA, the cusparseSpGEMM and cusparseXcsrgeam functions for multiplication and addition respectively are used. On HIP, the rocsparse_spgemm function is called.

Checklist

Put an x in the boxes that apply. You can also fill these out after creating
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merging your code.

• All tests pass. Code tested on
  • CPU backend
  • CUDA backend
  • HIP backend
• Code compiles cleanly with flags -Wall -Wpedantic -Wconversion -Wextra.
• The new code follows Re::Solve style guidelines.
• There are unit tests for the new code.
• The new code is documented.
• The feature branch is rebased with respect to the target branch.

Further comments

[shakedregev]

The tests should check if this can add a matrix with a differing sparsity structure (that is not a subset of the product).
I think this is doing $E=A*B+D$. The skipping of $C$ aside, we should put this equation in the documentation as it will be worth 1000 words.

[shakedregev]

I would add a README to HyKKT explaining different rocm requirement.

[adhamsi]

The tests should check if this can add a matrix with a differing sparsity structure (that is not a subset of the product). I think this is doing E = A ∗ B + D . The skipping of C aside, we should put this equation in the documentation as it will be worth 1000 words.

The test was modified so that the nonzero entries of D are no longer a subset of the nonzero entries of A * B. The test passes.

[shakedregev]

The tests pass and this looks good. There is a little bit more work on documentation, readme, and fixing these merge conflicts, which I can get to at some point.

[shakedregev]

Added documentation and fixed the merge conflict (which was not a conflict at all, took both changes).