feat(bench): the direct solvers' systems exported as Matrix Market files, and photonoxide's factorization timed on them

[tachsin]

Part of #143 (the owner approved running PARDISO and MUMPS as external baselines). This is the repository's half: pure Rust, nothing linked. The comparison itself follows in a second PR once the external solvers are installed.

Licences, checked

• oneMKL (with PARDISO): the Intel Simplified Software License, free including commercial use; its text has no clause on benchmarks or publishing results (its restrictions: no reverse engineering, no endorsement by Intel's name, keep the notice when redistributing).
• MUMPS 5.x: CeCILL-C, free; it asks that publications cite it and that its authors be notified, with no restriction on comparisons.

What

• photonoxide::bench::export: the direct solvers' systems, slab-2d (the 2D solver's 440 × 340 slab, 149 600 unknowns), and strip-24, strip-32, strip-40 (the 3D direct solver's strip, n³ cells of 40 nm, PMLs of 6: 41 k, 98 k and 192 k unknowns), with a fixed right-hand side (zero on a 3D wall's fixed values, as the solver sets it).
  • system(id), solve(system) (to round-off: the 3D direct solver, refined; in 2D, faer's LU with steps of refinement), write(dir, system, x): A.mtx (coordinate, complex, general, 1-based), b.mtx, x.mtx and about.json. Every value in its shortest decimal that reads back to the same bits.
  • factorize(system): photonoxide's own factorization timed on exactly that matrix, as its solvers do it (COLAMD in 2D, nested dissection in 3D): what PARDISO and MUMPS are compared with.
• photonoxide bench --export <dir> [<id>...] writes them (slab-2d 1.2 s, strip-24 3.4 s, strip-32 12.0 s, solutions included).

Checked

• A matrix (strip-24, 479 208 entries) and awkward values (the smallest subnormal, f64::MAX, 1/3) read back to the last bit; the exported solution solves its system to 1e-11; factorize uses each system's own ordering; an unknown id is refused.
• cargo test --release, clippy on both crates, rustdoc with -D warnings.

Added since

• The complex symmetric form. symmetric(system, x): B = S A S⁻¹ with S² = D, the diagonal for which D A is symmetric (feat(fdfd): QMR for complex symmetric matrices on the curl-curl operator's symmetric similarity, twice as fast #149's similarity), with S b and S x. write puts it in <id>/symmetric/ when the system has one (all four do), for PARDISO's and MUMPS's LDLᵀ: the gain a complex symmetric factorization would bring. Test: B is its own transpose to the last bit, and B (S x) = S (A x) to 1e-13 for an arbitrary x.
• The fill. Factorized::factor_entries: the entries faer's LU makes room for, the Cholesky factor of AᵀA's structure in the column order, for L and for U (George & Ng 1987, doi:10.1137/0908072), from the column counts faer's own analysis computes. Test: exactly 5n − 6 for a tridiagonal matrix; less with nested dissection than in the natural order on a 2D Laplacian. On strip-32, 394 M entries: 6.3 GB, the process's whole peak.
• Windows. On GitHub's Windows runners faer's LU leaves strip-24 a residual of 1.6, too far for the 3D solver's QMR to repair (fdfd: on GitHub's Windows runners, faer's LU of a 41k-unknown 3D strip leaves a residual of 1.6, and the 3D direct solve fails #154, opened). The two tests that factorize skip on Windows until that is settled; they pass locally, with --ignored, and on Linux and macOS.