[CUDA-Q] Feature request: need a MGMN version of eigsh

[zohimchandani]

Need a multi gpu, multi node eigenvalue solver for real matrices that are sparse and hermitian.

Only smallest eigenvalue is required.

Ideally MGMN version of eigsh

Thanks

[shriram-jagan]

Based on discussion with Zohim, this is for SKQD. NVIDIA is collaborating with UCL and this API is used in their joint work. The current bottleneck for them is running larger problem sizes, which is where legate-sparse might come in handy. The work is aimed for a GTC 2026 release. cc @dongb

@zohimchandani plans to get an estimate of the problem size or dimension of the csr matrix.

I'll scope out the work required from our end.

[zohimchandani]

Ran some numbers on the size of a sparse matrix as a function of size for various densities/ sparsities - see plot below.

We want functionality to diagonalize as large of a matrix as possible. Assuming a size of N = 10^7, memory = 10^5 GB, which is about 170 Grace Hoppers or 1250 Hoppers.

[zohimchandani]

Note eigsh accepts a sparse matrix or a linear operator and we would need to test with both inputs if possible.

[shriram-jagan]

@zohimchandani, thanks for the follow-up and the update. @fglines-nv will decide by the end of the week if he has time to work on this.

[shriram-jagan]

@zohimchandani , do you want it for real or complex datatype? from your earlier comment "real matrices that are sparse and hermitian." -- I'm under the impression that hermitian matrix is of complex datatype while symmetric matrices are real. Can you please confirm your input datatype?

[zohimchandani]

sorry, we want the feature for sparse & hermitian matrices.