[shinaoka]

Closes #144.

Problem

aggressive_early_deflation sorts the deflation window's eigenvalues with a bubble sort ported from LAPACK dlaqr3. The port had two faults:

• It sorted the deflated part ns..jw. dlaqr3's initial I = NS + 1 only sets the first pass's end, and the port read it as the start of the sort.
• It set each next window from the position of the last swap.

schur_swap reports success even when schur_swap_22 rejects an ill-conditioned 2 x 2 swap, so the pass recorded the same position every time and compared the same pair forever. Mat::eigen of the f32 matrix J_n + 1e-6 G, scaled to 2^-100, did not return at n = 128 and 257.

Fix

The sort follows dlaqr3 line by line:

• It sorts the undeflated part infqr..ns.
• Each pass ends at kend, one before where the previous pass stopped, so the sort ends after at most ns passes whatever the swaps do.
• It swaps with schur_swap_checked (the dlaexc ports for 1 x 2 and 2 x 1), and a rejected swap leaves the pair in place, as dlaqr3 does after DTREXC fails.

After a successful swap, the next position i + n2 equals DTREXC's adjusted ILST for all four block-size pairs.

Tests

• New tests::aed_sort_terminates_when_a_swap_fails: runs the reproducer at n = 128 and 257 through hessenberg_schur_real, each under a 120 s timeout. On origin/main it times out at n = 128; here it finishes in about 2 s. Both factors must be finite, and:
  • at 2^-100, the residual must be within LAPACK's smlnum = safmin * n / eps;
  • the same matrix at 2^-80 must have residual within 10 n eps |H|;
  • orthogonality must be within 10 n eps.
• Separate observation, not changed here: at 2^-90 and below, the residual relative to |H| is large on origin/main too, and also with the sort disabled. The input there lies below smlnum, and ?HSEQR likewise does not scale its input. Mat::eigen scales its input since LAPACK validation: the nonsymmetric EVD fixtures exceed the GET22-style residual threshold (4 dtypes) #112.
• cargo test --release -p t4a-faer --lib: 553 passed, 0 failed.
• Ignored LAPACK validation under linalg::evd: 51 of 52 pass. The failure is the known c32 entry in scripts/lapack-known-failures.json (LAPACK validation: the nonsymmetric EVD fixtures exceed the GET22-style residual threshold (4 dtypes) #112); it goes through the complex Schur, which this PR does not touch.
• Timing: none. This is a correctness fix; the sort now runs over the undeflated window and terminates.

Records

• PATCHSET.md: new row (KEEP).
• Upstream report: upstream-reports/faer-029-real-schur-aed-sort-hang. It reproduces on faer 0.24.4 (neither size returns within 60 s), and upstream main 0ecd846 has the same code.
• Review: an independent review (gpt-6.1-sol) found no correctness defect in the rewrite. It flagged a duplicate report number and an overstated accuracy claim; both are fixed.

🤖 Generated with Claude Code

[shinaoka]

Combined into #154 together with the other two nonsymmetric EVD fixes (#148, #151, #152), as the maintainer directed on 2026-10-29. The commits are carried over with their authorship; the upstream reports are renumbered faer-029 (#112), faer-030 (#144) and faer-031 (#145).