Add Cholesky factorization benchmark (bench_potrf_compact) - #28
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Add the potrf analogue of bench_geqrf_compact: a throughput benchmark of the batched Cholesky factorization on symmetric positive-definite matrices, comparing three implementations of the same ?potrf math -- cqr-compact cqr_mkl_dpotrf_compact (this project's batched SIMD kernel) mkl-compact mkl_dpotrf_compact (Intel MKL's batched compact kernel) per-matrix LAPACKE_dpotrf (conventional one-matrix-at-a-time) over pools of small SPD matrices across the target size range, on the tuned column-major lower path (A = L L^T). It reports per-size throughput (matrices/s, GFLOP/s from the n^3/3 + n^2/2 + n/6 Cholesky flop count) and a geometric-mean speedup, and -- since the SPD factor is unique -- gates the compact factor elementwise against LAPACKE_dpotrf, so it doubles as an integration test. Unlike geqrf, potrf needs no workspace, so there is no lwork query and no per-thread work array. The SPD pool uses the cheap diagonally dominant A_ii = 2n form (SPD without an O(n^3) M^T M). The --size-sweep and --simdlen flags mirror bench_geqrf_compact. Wire it into CMakeLists.txt as the bench_potrf_compact target plus a small CTest integration run (33 1, exercising a padded final group). Document it in the README (Examples bullets/table, CTest list), flip the potrf benchmark note in PLANS.md from Deferred to Benchmarked, and add a section 9 (Benchmark) to the potrf design doc mirroring geqrf's. Verified: full ctest suite passes on both GCC and Clang (12/12), the accuracy gate holds at machine precision, and a -march=native run shows the expected story -- the compact path beats per-matrix LAPACK and is competitive with mkl_dpotrf_compact on the small-size range, LAPACK's blocked algorithm crossing ahead only at larger orders. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01GKgcv8eoffP2gWrED44KqH
Per the project's convention to stop documenting benchmarks in the routine design documents, consolidate all benchmark documentation into a single examples/BENCHMARKS.md next to the programs it describes. - Add examples/BENCHMARKS.md documenting all three benchmarks (bench_geqrf_compact, bench_potrf_compact, bench_qr_compact): what each measures, the three-way comparison, how to run them, the -march=native fairness caveat, the OpenMP outer loop, the optional --size-sweep/--simdlen flags, how to read the output, and the CTest integration gating. - Remove the "9. Benchmark" section from both the geqrf and potrf design docs (it was the last section in each), replacing it with a one-line pointer to examples/BENCHMARKS.md. - Fix every stale "section 9" cross-reference: the two benchmark source-file header comments, both PLANS.md "Benchmarked" bullets, and the CMakeLists.txt target comments now point to examples/BENCHMARKS.md. - Link the new doc from the root README's Examples section. No functional change: the benchmarks build and their CTest integration runs still pass on GCC (bench_qr/geqrf/potrf_compact_integration, 3/3). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01GKgcv8eoffP2gWrED44KqH
Address review feedback on the benchmark work: - Deduplicate the two compact-format helpers that were copied across the benchmark files. compact_format_name (3 copies) and format_for_vlen (2 copies) now live once in cqr::detail (cqr_mkl_ext.h), next to their sibling vlen_for_format; the benchmarks pull them in with using-declarations. format_for_vlen is now the type-correct inverse of vlen_for_format (templated on the scalar type, keyed on v*sizeof(T) register bytes) instead of a double-only mapping; call sites pass <double>. Behavior is unchanged for the double benchmarks. - Drop the two "documented in examples/BENCHMARKS.md" pointer lines from the geqrf and potrf design docs, per the convention to keep benchmark docs out of the design documents entirely. - Trim examples/BENCHMARKS.md (148 -> 108 lines): fold the per-benchmark three-way lists into the overview table, state the shared "pack once, time only the factorization" methodology once, and drop the standalone Threading section. Verified: full ctest passes on both GCC and Clang (12/12), including the three benchmark integration runs. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01GKgcv8eoffP2gWrED44KqH
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Summary
This PR adds a comprehensive throughput benchmark for the batched Cholesky factorization (
cqr_mkl_dpotrf_compact), mirroring the existing QR factorization benchmark (bench_geqrf_compact). The benchmark compares three implementations: the project's compact SIMD kernel, Intel MKL's compact kernel, and conventional per-matrix LAPACK, over pools of small symmetric positive-definite (SPD) matrices.Key Changes
New benchmark executable (
bench_potrf_compact):A = L L^T)cqr_mkl_dpotrf_compactvsmkl_dpotrf_compactvs per-matrixLAPACKE_dpotrfBenchmark features:
--size-sweep=nmin:nmax[:stride]for cqr-only throughput scans--simdlen=2|4|8to force narrower interleave widths than the host defaultIntegration testing:
bench_potrf_compact_integration) with 33 matrices and 1 repBuild integration:
cqr_mkl_extandMKL::CompactDocumentation:
Implementation Details
A_ii = 2n) rather than expensiveM^T Mproductsgeqrf,potrfrequires no workspace, so no per-thread work arrays are neededstd::chrono::steady_clockwith best-of-multiple-passes methodologyhttps://claude.ai/code/session_01GKgcv8eoffP2gWrED44KqH