Avoid host-device synchronization in Gram-Schmidt CGS2

[kakeueda]

Description

While working on #452, I noticed CGS2 was performing an extra device-to-host copy and synchronization in every orthogonalization step on GPU backends.

The coefficients from the first CGS pass were copied to the host and later added to those from the second pass on the host. Instead, we can keep both coefficient vectors in the active memory space and combine them using VectorHandler::axpy().

Proposed changes

• Removed an unnecessary device-to-host synchronization from CGS2.
• Added vec_Hcolumn_aux_ to store the coefficients from the first CGS pass, then accumulated them with the second coefficients in the active memory space using VectorHandler::axpy() (the additional allocation is small, only restart + 1 elements).

Timed solver.solve() in sysGmres using matrix_ACTIVSg200_AC_renumbered_add9_01.mtx.

Average over five runs

• Before: 0.852530 s
• After: 0.699054 s

The impact of this is easier to observe on smaller matrices.

Test environment:

• NVIDIA GeForce RTX 5050 Laptop GPU
• CUDA 12.9

Checklist

• All tests pass (make test and make test_install per testing instructions). Code tested on
  • CPU backend
  • CUDA backend
  • HIP backend
• I have manually run the non-experimental examples and verified that residuals are close to machine precision. (In your build directory run: ./examples/<your_example>.exe -h to get instructions how to run examples). 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.
• [N/A] There are unit tests for the new code.
• The new code is documented.
• [N/A] 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.

[shakedregev]

Testing this.

[shakedregev]

Tested and ran the Gmres examples on all platforms. Looks good, merging.