svd: DCHKBD type 16 returns NoConvergence at n = 127-129 since the dqds path (#52) #110

Problem

Since #52 (the dqds path for singular values, merged as 5e45c57), the LAPACK SVD suite fails on DCHKBD type 16. The solver returns NoConvergence instead of the singular values.

Failing tests

linalg::svd::tests::lapack_svd_{f32,f64,c32,c64}::lapack::dchkbd_15_to_19 and ::bidiagonal_family. All four dtypes fail. The failing cases are all:

• DCHKBD type 16, seed 0x4c415041434b;
• n = 127, 128 and 129;
• recursion threshold 8 and 128;
• values only (U=false, V=false);
• input either a direct upper bidiagonal or one reached by reduction.

When it started

Both checks used cargo test -p t4a-faer --lib -- --include-ignored "lapack_svd_f64::lapack::dchkbd_15_to_19":

Why it went unnoticed

• scripts/run-lapack-validation.py did not reach the end of the svd family until tests: name the self-adjoint QR accuracy test so the LAPACK runner classifies it (#100) #101.
• In the tests: name the self-adjoint QR accuracy test so the LAPACK runner classifies it (#100) #101 run, the family's parallel tests timed out on four cores.
• The failures showed up in the full LAPACK run for par: every region at the widest width that pays, on a sub-team of that width #109 (並列ゲートの dispatch cost が幅 6 で頭打ち、通れば常に全幅: p=32〜64 で floor 付近の region が過剰に開く #91), where the svd family completes. par: every region at the widest width that pays, on a sub-team of that width #109 does not touch the bidiagonal SVD; the same tests fail on its base.

Next steps (not started)

• Read DCHKBD type 16's matrix class.
• Check the dqds convergence and fallback path that perf(svd): blocked bidiagonalisation, dqds shift, padded work copy, caller-held worker group; values-only SVD at or below the vendor #52 added for values-only calls at n of about 128.

The evidence is in the run dir of the #109 LAPACK run (svd.log), kept outside the repo.