Implement A := c*A+I and A := c*A+B methods in MatrixHandler

[quantumsteve]

Description

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documentation, enhancement, etc.). Please also include relevant motivation and
context. List any dependencies that are required for this change.

This is part of #393. CUDA and HIP functions are not implemented.

Proposed changes

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should be accepted.

This adds a new member function MatrixHandler::scaleAddI to compute A := c*A+I. The sparsity pattern (row pointers and column indices) are stored in LinAlgWorkspaceCpu and reused by future calculations. On each column one must check if the diagonal element is already nonzero and add 1 or add a new nonzero element to the matrix.

The test verifies that the sum of rows is 1 larger than the sum of the original row scaled by c.

This adds a new member function MatrixHandler::scaleAddB to compute A := c*A+B. The sparsity pattern (row pointers and column indices) are stored in LinAlgWorkspaceCpu and reused by future calculations. On each column one must increment column indices such that the resulting indices and values are sorted.

Checklist

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• 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.
• I have updated CHANGELOG.md to reflect the changes in this PR. If this is a minor PR that is part of a larger fix already included in the file, state so.

Further comments

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