bench: cuDSS vs SparseDirectSolver.jl comparison per planned feature

[michel2323]

No issue: owner-requested benchmark tooling, not a TASKS.md task. No claude:pr label, so the agent review does not run.

Task: none.

What was built:

• bench/features.jl: one comparison feature per capability planned in TASKS.md (Cholesky, 16 right-hand sides, LDLᵀ, refinement, uniform batch, LU, Schur, matching, non-uniform batch, partitioned-inverse solve, hybrid memory, mixed precision). A feature counts as done when its task is marked done in TASKS.md.
• bench/compare.jl: times analysis, factorization, refactorization and solve per feature and matrix with BenchmarkTools. It runs one solver per process (--solver=cudss or --solver=sds) and merges the rows into bench/comparison/<solver>.csv. The SDS run skips pending features, so only those need rerunning when a task lands.
• bench/compare_report.jl: writes bench/comparison/comparison.md (an overview plus a table per feature, with pending features left blank) and comparison.png (SDS/cuDSS ratio per feature and phase). It uses the new bench/report/ environment with CairoMakie.
• The README shows the plot. bench/README.md and AGENTS.md document the commands.

Current results (RTX 4080, cuDSS 0.8.0, rebased on T16; geometric mean of SDS time / cuDSS time):

feature	matrices	analysis	factorization	refactorization	solve
Cholesky, Float64	14	0.60×	5.64×	9.06×	8.93×
Cholesky, 16 right-hand sides	14	0.60×	6.06×	9.52×	7.28×
LDLᵀ, static pivoting (T15)	23	1.12×	20.44×	29.78×	13.42×
LDLᵀ + 2 refinement steps, K2 dumps (T16)	9	2.67×	23.40×	35.99×	33.25×

Cholesky residuals match cuDSS. For LDLᵀ, residuals on the K2 dumps are lower than cuDSS's with default settings. With refinement they reach 1e-9 or better on case14 and case118, and stay large on case1354 for both solvers. The T15 LDLᵀ factorization is slow on large fronts, taking 14.6 s on lap3d_40 and 91 s on apache2, as the T25 owner note expects. Those two rows are timed from a single run (--single-run-above, default 5 s) rather than a BenchmarkTools trial.

Tests: SDS_TEST_ONLY="test_bench_smoke,test_bench_compare" SDS_TEST_GPU=0 julia --project=. -e 'using Pkg; Pkg.test()' gives 123 pass / 0 fail / 0 broken on the KA CPU backend. The new test/test_bench_compare.jl covers the feature table, the TASKS.md gate and the Markdown rendering on synthetic CSVs. It runs on the CPU only and does no plotting. CUDA: pending CI.

Deviations from PLAN.md / TASKS.md:

• Each timed sample spins the GPU for 0.2 s before the phase. Without the spin, the GPU drops to a low clock during the host-side setup, and lap2d_300 factorization varied between 6 and 19 ms. With it the time is a stable 5.9 ms, against 6.05 ms in the T04 baseline.
• Plain Float32 is not compared, because cuDSS fails on every condensed KKT dump in Float32.
• The SDS calls for uniform and non-uniform batches assume APIs that do not exist yet. They need a check when T17 and T22 land.
• New dependencies, all on the bench and test side:
  • bench env: BenchmarkTools for phase timing, Metis for the default ordering, and SparseDirectSolver through [sources].
  • bench/report: CairoMakie for the plot, DelimitedFiles for the CSV, Printf for formatting.
  • test env: DelimitedFiles and Printf for the report test.

Follow-up issues opened: none.

🤖 Generated with Claude Code

https://claude.ai/code/session_01TJrmq7e9jiW4VxBMEVup2E