[Stardust0831]

What's changed?

LCAO EXX initialization builds radial tables with many small quadrature operations and repeated product-orbital transforms. For CUDA calculations, batch the existing Simpson quadrature into FP64 GEMM using ABACUS's tensor/BLAS interfaces. The quadrature grids, weights, derivative recurrence and analytic origin values are preserved.

The existing resolved device selection is passed explicitly through initialization and Coulomb refresh. CPU full-table construction retains individual quadrature. Product orbitals are shared during batched and selective construction, and their unused origin derivative is omitted. Required integral gradients remain calculated.

GPU batching uses device gpu in a CUDA build. It works with the default LibRI revision b0eff7a and requires no DDLA, LibRI GPU backend, or new build/INPUT option. Other RI consumers retain CPU execution.

Performance

System	Stage	Baseline (s)	This PR (s)	Paired speedup
Si32	RI initialization	6.52–7.15	1.34–1.41	4.86–5.09x
Si32	Complete SCF + forces + stress	182.22–203.71	181.38–187.34	1.00–1.09x
CsPbI3	RI initialization	343.48–344.15	14.73–15.38	22.33–23.37x
CsPbI3	Complete SCF + forces + stress	424.48–426.14	95.52–96.23	4.43–4.44x

LCAO HSE calculations on displaced Si32 and CsPbI3 (5 atoms), using one V100, one MPI rank, four physical CPU cores/OpenMP threads and serial BLAS on SAI. Both versions use cuSOLVER diagonalization and CPU LibRI contractions. The baseline is unmodified d20090cc137f.

Ranges cover two paired runs in separate allocations on shared nodes, with reversed execution order. Ratios are calculated within each pair; SCF iteration counts match. Complete time includes process startup. The Exx_LRI::init speedup includes GPU batching and product preparation reuse.

Explicit GPU workspace and corresponding host staging are each bounded at 160 MiB per MPI rank and released before SCF. CUDA context/library allocations and existing host tables are outside this bound. Sampled process GPU peaks were 442–450 / 460–462 MiB for Si32 and 438 / 530 MiB for CsPbI3 (baseline / this PR; 0.5 s sampling).

Unit Tests and/or Case Tests for my changes

The full CUDA executable build and CPU/CUDA radial-table tests passed with one and four OpenMP threads, including execution of the GPU test. Tests cover individual versus batched tables, product sharing, high angular momenta, origin/cutoff behavior, radial tiling and gradients.

cmake --build build --target abacus_std_gpu MODULE_LCAO_radial_tables MODULE_LCAO_radial_tables_gpu --parallel 24
OMP_NUM_THREADS=1 ctest --test-dir build -V -R '^(MODULE_LCAO_radial_tables|MODULE_LCAO_radial_tables_gpu)$'
OMP_NUM_THREADS=4 ctest --test-dir build -V -R '^(MODULE_LCAO_radial_tables|MODULE_LCAO_radial_tables_gpu)$'

The benchmark cases, a CPU execution control, and complex-tensor Si32 on a regular 2x1x1 k mesh with two MPI ranks/GPUs all converged with matching iteration counts. Maximum differences were 2.2e-11 eV/atom, 2.3e-9 eV/Angstrom and 9.6e-9 kbar. These comparisons establish agreement with the baseline. The combined changes also passed a build and regression checks with CUDA disabled.

Inputs, timings, numerical comparisons and test logs. Benchmark executables enable identical existing timer JSON output; this instrumentation is excluded from the change.

Linked Issue

Supersedes the radial-table preparation part of #8193 and can be merged independently of the integral-evaluation and Libxc optimizations. LibRI/DDLA GPU contractions remain separate in #8169.

Governance Notes

Core impact is limited to RI table construction and explicit device propagation. No documentation update required: the existing device option and its metadata are unchanged. <memory> is required for the owning std::shared_ptr<const ProductOrbitals> member.

[AsTonyshment]

I haven't looked into the implementation in detail (as I'm not particularly familiar with the RI code), but it seems that the newly added GPU unit test hasn't been included in the CI workflow in .github/workflows/cuda.yml, has it?

[Stardust0831]

Yes, that was missing. Added MODULE_LCAO_radial_tables_gpu to the CUDA workflow's CTest selection in 026ea36. That commit's CI log confirms that BatchedGpuMatchesIndividualTables executed and passed.

[ABACUS-PR-BOT]

No confirmed correctness defect found in the current in-tree paths. The inline comments ask to clarify selective-table reuse and name the workspace-limit calculations.

Static review of dfc71eb1 against d20090cc: whitespace passed and governance checks completed with no blockers. No builds or runtime tests were performed; the reported numerical and performance results remain author-reported.

[ABACUS-PR-BOT]

Non-blocking: Please make the selective-initialization contract explicit and add a test that calls it twice with different radius sets. orb11s.clear() discards previously populated rows, while the prior implementation retained them; the current in-tree subset callers initialize once.

[Stardust0831]

Thanks for catching this behavior change. Restored and documented accumulation across selective calls in a853060, retaining existing entries and the product orbitals they reference. The new regression covers repeated individual calls and mixed batches of initialized and new objects, checking overlaps and gradients against full tables. It fails before the fix. After the fix, both CPU and CUDA radial-table test targets pass with one and four OpenMP threads on SAI.

[ABACUS-PR-BOT]

Non-blocking: Please assign the per-buffer capacity calculations and inner batch cap to named locals before these std::min calls. This follows AGENTS.md rule 14 and makes each part of the workspace bound directly inspectable.

[Stardust0831]

Thanks for the suggestion. The three device-buffer budgets already have named constants. I would prefer to retain the remaining capacity expressions in this revision.