Fix Issue #135

[nathanielpritchard]

Description

Changes the kaczmarz solver to work for sparse matrices and vectors when Sampling compressor is used.
Fixes #135

Motivation and Context

Currently, using Kaczmarz with a sparse matrix and Sampling compressor it returns an error about being unable to convert a SparseArray to an Array. This is because in the initial allocations, only dense arrays were allocated. To fix this a few changes needed to be made.

1. I needed to add a condition in the complete_solver function that performed preallocations of sparse arrays if a Sampling compressor is used with a sparse matrix.
2. I needed to add a check to ensure that if the row or block of rows was all zeros no update would be run.
3. I needed to change the * implementation for the Sampling compressor to preallocate SparseArrays when being applied to sparse objects.
4. I have added tests for the Sampling and Kaczmarz structures that check the code on sparse matrices.

How has this been tested

The following code should now work.

using RLinearAlgebra
using SparseArrays
using LinearAlgebra
using Random

Random.seed!(42)

# Create a sparse linear system
m, n = 100, 50
A = sprand(m, n, 0.1)  # 10% density sparse matrix
b = rand(m)
x = zeros(n)

# Configure Kaczmarz solver with Sampling compressor
compressor = Sampling(
    cardinality=Left(),
    compression_dim=5,
    distribution=Uniform()
)

solver = Kaczmarz(
    compressor=compressor,
    log=BasicLogger(max_it=10),
    error=FullResidual(),
    sub_solver=LQSolver()
)

# This fails with sparse matrix
x_sol, recipe = rsolve!(solver, x, A, b)

Additionally, the new tests now incorporate sparse matrices in the completion of the solver and in the block update steps, which should be sufficient for ensuring that everything works as expected for sparse matrices in the future.

Types of changes

• CI
• Docs
• Feature
• Fix
• Performance
• Refactor
• Style
• Test
• Other (use sparingly):

Checklists:

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