Description

This pull request adds sparse solvers to xobjects via the xo.sparse module. This functionality is important for extending xfields to include Finite Difference solvers.

The xo.sparse module can be used to solve sparse linear systems of equations:
A*x = b
where A is a sparse matrix.

Currently only CPU and Cupy contexts are supported. This module contains a variety of solvers for different contexts, with consistent APIs. The intended use is to reuse the same LHS for many solves, so the solvers work as follows:

solver(A) # Performs decomposition/factorization
solver.solve(b) # Solves Ax = b using precomputed factors

For optimal performance across backends b should be a column-major (F Contiguous) array or vector.

The intended interface for this module is:

xo.sparse.factorized_sparse_solver()

The above function includes detailed documentation for usage, but in short, it returns the best performing solver object based on the context and available modules. If the context is not explicitly defined, it is inferred based on the input matrix.

For development and convenience purposes the xo.sparse.solvers module is present, which provides the following aliases:

• xo.sparse.solvers.CPU.
  • scipysplu : Alias for scipy SuperLU
  • KLUSuperLU : Alias for PyKLU
• xo.sparse.solvers.CPU.
  • cuDSS : nvmath.sparse.advanced.DirectSolver Wrapper with a SuperLU-like interface
  • cachedSpSM : Rewrite of cupy's SuperLU to cache the SpSM analysis step offering massive speedups compared to cupy splu when the only available backend is SpSM
  • cupysplu : Alias for scipy SuperLU

This pull request introduces new optional dependencies for xobjects:
nvmath-python: Provides the cuDSS bindings for fast solves on GPU
PyKLU: For fast LU solves on CPU (now published in pypi)
cuDSS needs to be installed in the conda environment and to be supported by the driver version (CUDA 12.0+)

Additional changes:

• Added ModuleNotAvailableError class
• Raise ModuleNotAvailableError when OpenCL/Cupy is not installed and an instance of the context is initiated

Checklist

Mandatory:

• I have added tests to cover my changes
• All the tests are passing, including my new ones
• I described my changes in this PR description

Optional:

• The code I wrote follows good style practices (see PEP 8 and PEP 20).
• I have updated the docs in relation to my changes, if applicable (added examples)
• I have tested also GPU contexts