Refactor HSolver to remove global runtime dependencies

[Critsium-xy]

Summary

• remove all GlobalC, GlobalV, and PARAM references from source/source_hsolver
• pass communicator/rank, process-count, and logging dependencies explicitly from ESolver and other orchestration boundaries
• update HSolver unit and MPI tests to use local configuration and explicit communication contexts
• remove the unused cuSolverMP outputParameters() helper

The baseline scan contained 103 matching lines in source/source_hsolver (50 GlobalV occurrences, 56 PARAM occurrences, and no GlobalC occurrences; three lines contained both symbols). The same scan now returns zero matches.

Design

HSolver is treated as a numerical solver layer. Runtime ownership remains at workflow/orchestration boundaries, while solver APIs receive only the context they need:

• DiagoIterAssist receives diag_comm_info for subspace reductions
• BPCG uses the rank already owned by its parallel linear-transform context
• HSolverLCAO and PEXSI receive world rank/process count explicitly
• PW, SDFT, and LCAO-in-PW solvers receive an output stream explicitly
• dense solver implementations no longer write through the global log stream

The governance checker reports migration warnings where existing globals are read at ESolver/LCAO/PSI/PW call boundaries. Those are deliberate boundary reads: this PR removes solver-layer coupling without broadening the refactor into the workflow/configuration layers. The PR-level global dependency budget is non-increasing (added=31, removed=117, net_delta=-86).

Verification

Passed:

cmake -S . -B build -G Ninja \
  -DBUILD_TESTING=ON -DENABLE_MPI=OFF -DENABLE_ELPA=OFF \
  -DMKLROOT=/tmp/abacus-mkl
cmake --build build -j2

Full serial build: 855/855 build steps passed before final formatting. After the final include cleanup, the same build was reconfigured with -DFETCHCONTENT_FULLY_DISCONNECTED=ON and its 29 affected targets rebuilt successfully.

cmake -S . -B /tmp/abacus-build-mpi-openblas -G Ninja \
  -DBUILD_TESTING=ON -DENABLE_MPI=ON -DENABLE_ELPA=OFF \
  -DBLA_VENDOR=OpenBLAS \
  -DCMAKE_CXX_COMPILER=/usr/bin/mpicxx \
  -DCMAKE_C_COMPILER=/usr/bin/mpicc \
  -DFETCHCONTENT_SOURCE_DIR_GOOGLETEST=/tmp/abacus-build-mpi/_deps/googletest-src

cmake --build /tmp/abacus-build-mpi-openblas \
  --target hsolver esolver \
  MODULE_HSOLVER_bpcg MODULE_HSOLVER_cg MODULE_HSOLVER_cg_float \
  MODULE_HSOLVER_cg_real MODULE_HSOLVER_dav MODULE_HSOLVER_dav_float \
  MODULE_HSOLVER_dav_real MODULE_HSOLVER_pw MODULE_HSOLVER_sdft \
  MODULE_HSOLVER_LCAO MODULE_HSOLVER_linear_trans -j2

Focused MPI/OpenBLAS targets built successfully.

OMP_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 \
ctest --test-dir /tmp/abacus-build-mpi-openblas --output-on-failure \
  -R '^MODULE_HSOLVER_(bpcg|cg|cg_float|dav|dav_float|cg_real|dav_real|pw|sdft|LCAO|linear_trans)$'

Result: 11/11 passed.

OMP_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 \
ctest --test-dir /tmp/abacus-build-mpi-openblas --output-on-failure \
  -R '^MODULE_HSOLVER_(para_linear_trans|cg_parallel|parak2d_test_parallel|dav_parallel|LCAO_parallel)$'

Result: 5/5 passed outside the restricted sandbox.

python3 tools/03_code_analysis/agent_governance_check.py \
  --base upstream/develop --head HEAD --format text

Result: passed with review warnings described above.

Also passed: git diff --check and the zero-hit global dependency scan.

CI follow-up

The first CI run exposed a missing direct include in the ELPA-only build path: diago_elpa.cpp still calls ModuleBase::TITLE after dropping the transitive global_variable.h include. Commit 89a0d509c adds the required source_base/tool_title.h include.

The CI failure was reproduced and the fix was verified with:

cmake -S . -B /tmp/abacus-hsolver-elpa-build -G Ninja \
  -DBUILD_TESTING=ON -DENABLE_MPI=ON -DENABLE_ELPA=ON \
  -DBLA_VENDOR=OpenBLAS \
  -DCMAKE_CXX_COMPILER=/usr/bin/mpicxx \
  -DCMAKE_C_COMPILER=/usr/bin/mpicc \
  -DFETCHCONTENT_SOURCE_DIR_GOOGLETEST=/tmp/abacus-build-mpi/_deps/googletest-src \
  -DFETCHCONTENT_FULLY_DISCONNECTED=ON
cmake --build /tmp/abacus-hsolver-elpa-build --target hsolver -j2
cmake --build /tmp/abacus-hsolver-elpa-build \
  --target MODULE_HSOLVER_LCAO MODULE_HSOLVER_dav_real MODULE_HSOLVER_cg_real -j2

Results: ELPA-enabled hsolver build 20/20 passed; MODULE_HSOLVER_LCAO passed; MODULE_HSOLVER_LCAO_parallel passed outside the restricted sandbox. diago_elpa.cpp scores 93/100 in code_quality_score.py.

Notes

• INPUT behavior is unchanged, so no parameter documentation update or regeneration is required.
• CUDA/cuSolverMP and PEXSI interface paths were updated, but those optional backends were not enabled in the local build environment. ELPA was enabled separately for the CI follow-up verification above.
• Sandboxed MPI-linked compilation emitted the documented OpenMPI opal_ifinit: socket() failed errno=1 warning; runtime/MPI tests were rerun outside the sandbox and passed.