[DanielZhao0432]

Reminder

• I have read AGENTS.md and docs/developers_guide/agent_governance.md.
• I have linked an issue or explained why this PR does not need one.
• I have added adequate unit tests and/or case tests, or explained why not.
• I have listed the exact verification commands run and their results.
• I have described user-visible behavior changes, including INPUT parameter changes.
• I have explained core-module impact for ESolver, HSolver, ElecState, Hamilt, Operator, Psi, or other source/ changes.
• I have requested any needed governance exception below.

Linked Issue

Fix #8247

Unit Tests and/or Case Tests for my changes

• Commands run:
  1. Functional test of the fallback (local, no DSP hardware): compiled
     cpack_zhegvx_fallback.cpp with -D__DSP together with a small driver that
     calls cpack_zhegvx_driver on a 2x2 generalized eigenproblem (workspace
     query + solve, same protocol as diago_lapack.cpp), linked against system
     OpenBLAS/LAPACK → correct eigenvalues, max residual 4.4e-16.
  2. CMake configure matrix with mock vendor prefixes:
     • USE_DSP=ON without MT_CPACK_DIR → configures; prints the fallback
       STATUS message; cpack_zhegvx_fallback.cpp is added to the hsolver target;
     • USE_DSP=ON with valid MT_CPACK_DIR → configures; fallback not added,
       libc_pack.a linked (behavior unchanged from [Feat] Add DSP Lapack support #8097);
     • USE_DSP=ON with a bad MT_CPACK_DIR → FATAL_ERROR with a clear message;
     • reconfiguring the same build directory with and without MT_CPACK_DIR
       switches the provider selection correctly both ways;
     • DSP PW-only build (ENABLE_LCAO=OFF, no MT_CPACK_DIR) → configures, and
       the fallback is correctly not added to any target.
  3. MODULE_HSOLVER_LCAO unit test (ENABLE_ELPA=OFF build), now with a
     registered complex ks_solver=lapack case: 5/5 pass single-rank and on 2 MPI
     ranks. The ELPA variant fails to link on this machine due to a pre-existing
     local ELPA/genelpa version mismatch, unrelated to this PR (diago_elpa.cpp
     is untouched).
  4. python3 tools/03_code_analysis/agent_governance_check.py --staged → exit 0.
• Result summary: all checks above pass (tested revision 073b3ae606).
• Reproducibility record:
  • Fallback driver: g++ -std=c++11 -D__DSP -I source driver.cpp source/source_hsolver/cpack_zhegvx_fallback.cpp -o test -lopenblas -lgfortran;
    the driver calls cpack_zhegvx_driver on a 2x2 generalized eigenproblem
    (workspace query + solve) and checks residuals of H z = lambda S z.
  • Configure matrix: cmake -S . -B <dir> -DUSE_DSP=ON -DENABLE_ELPA=OFF -DMTBLAS_FFT_DIR=<mock> -DMT_HOST_DIR=<mock> [+- -DMT_CPACK_DIR=<mock>] for
    the unset/valid/invalid-prefix, reconfiguration-toggle, and ENABLE_LCAO=OFF
    scenarios; provider selection verified via the generated hsolver build files.
  • Solver tests: build with ENABLE_ELPA=OFF and run
    OMP_NUM_THREADS=1 ./MODULE_HSOLVER_LCAO (1 rank) and
    mpirun -np 2 ./MODULE_HSOLVER_LCAO. Note: the new complex lapack case is
    NOT skipped on 2 ranks because nb2d=1 gives a 1x1 BLACS grid (dsize==1);
    the dsize > 1 skip guard only triggers for larger grids.
• Checks not run, with reason: full DSP compile+run requires Tianhe hardware and
  will be verified there (both configurations: with and without MT_CPACK_DIR)
  and reported; CI has no DSP toolchain.

What's changed?

• Since [Feat] Add DSP Lapack support #8097, every DSP build hard-required C_PACK (MT_CPACK_DIR) because
  DiagoLapack always calls cpack_zhegvx_driver under __DSP. This makes
  C_PACK optional: with MT_CPACK_DIR set, behavior is unchanged; without it,
  the new source/source_hsolver/cpack_zhegvx_fallback.cpp provides
  cpack_zhegvx_driver by forwarding to the configured LAPACK provider's
  zhegvx_.
• Implementation selection is done by CMake source-file selection (the fallback is
  added to the hsolver objects only when USE_DSP is on and MT_CPACK_DIR is
  unset), so no new compile-time macro is introduced and the two implementations
  can never be linked together.
• MODULE_HSOLVER_LCAO compiles diago_lapack.cpp directly, so the fallback is
  wired into that test target as well for DSP builds without C_PACK.
• A complex ks_solver=lapack case is added to the DiagoKPointsTest
  instantiation in test_diago_lcao.cpp; the complex LAPACK path previously had
  no registered coverage there.
• Legacy Makefile and pyabacus build surfaces need no update: neither supports
  DSP builds (no __DSP there).
• User-visible change: DSP builds no longer require C_PACK; MT_CPACK_DIR
  remains the way to enable the DSP-offloaded eigensolver. No INPUT changes.

Governance Notes

• INPUT/docs changes: none.
• Core module impact: hsolver build lists and the DSP link libraries only; no
  runtime code path changes for non-DSP builds.
• Exceptions requested: none.

[ABACUS-PR-BOT]

No confirmed implementation defect found in the inspected forwarding and build-selection paths. The inline comment asks for a reproducible validation record and clearer skip counts.

Static review of 073b3ae6 against d20090cc: whitespace and governance checks completed with no blockers; the documentation warning was assessed against the stated scope. No build or runtime checks were performed. Full DSP validation remains outstanding as noted in the PR.