LAPACK validation: the nonsymmetric EVD fixtures exceed the GET22-style residual threshold (4 dtypes)

Known failure in the bounded LAPACK validation (docs/lapack-validation.md, family nonsymmetric_evd). Tracked so the nightly run can treat it as known instead of a new failure.

What fails

cargo test -p t4a-faer --lib -- --include-ignored --exact linalg::evd::lapack::f64::lapack_nonsymmetric_evd_cases and its parallel sibling, at all four dtypes:

linalg::evd::lapack::{f32,f64,c32,c64}::lapack_nonsymmetric_evd_cases
linalg::evd::lapack::{f32,f64,c32,c64}::lapack_nonsymmetric_evd_parallel

Run on main 1ac38c6 (evo, CARGO_PROFILE_DEV_DEBUG=0, CARGO_INCREMENTAL=0, 4 cores, scripts/run-lapack-validation.sh):

dtype	principal calls	diagnostics
`f32`	1776 (+24 parallel)	282 (+24)
`f64`	1776 (+24 parallel)	306 (+24)
`c32`	1776 (+24 parallel)	220 (+24)
`c64`	1776 (+24 parallel)	216 (+24)

Every call returns; the failures are GET22-style right/left eigenvector residual violations above the recorded threshold of 20, which is why the family exits non-zero. A size-129 tightly clustered f64 fixture was confirmed against an 80-decimal-digit computation (docs/lapack-validation.md, phase 2): native residual ratio 39.81 against a reference 39.76, so the residual is the library's, not the reference's.

What would close it

Either the residual comes down for those fixtures, or the family documents why the threshold should differ for them. Until then it is listed in scripts/lapack-known-failures.json under this issue, and a nightly run that fails there is not news.

Record: docs/lapack-validation.md (phases 2 and "Reproduction and scheduled operation").

ci: run the LAPACK validation nightly, with known failures carrying t…

evd: clamp the eigenvector back substitution relative to the eigenval…

upstream-reports: faer-003, the nonsymmetric EVD eigenvector residual…

upstream-reports: three defects that reproduce on upstream faer and p…

evd tests: the GET22 threshold grows like sqrt(n) (#112)

evd tests: the GET22 threshold grows like sqrt(n) (#112) (#127)

Stage-by-stage comparison with LAPACK cgeev, as asked (2026-10-29).

Where the c32 gap comes from. On kinds 6/7 at n = 63-65, the Hessenberg backward error is the same with and without first scaling the matrix to unit size: 16-20. The complex Schur backward error is not: 226-258 as is, 67-93 scaled. ?GEEV scales its input into [smlnum, bignum] (smlnum = sqrt(safmin) / eps) before the reduction; faer's evd_imp did not.

Where the gap is more serious. I ran a 372-matrix sweep against LAPACK ?geev, over f32/f64/c32/c64, n = 16-257, and random, Grcar, near-Jordan and graded families, with scales up to the range limits.

Below the bound, the eigenvectors lost every digit. The ratio grew from about 2^-90 (32-bit), and at 2^-100 (32-bit) and 2^-960 (64-bit) and below it was 1e4 to 2e15, where LAPACK gives 2 to 70.
Upstream faer 0.24.4 returns NaN/inf eigenvectors with Ok there.
After the fix in evd: scale the input into range as ?GEEV does (#112) #148, every non-graded series is at most 1.74× LAPACK. The two cells above 1.5× are at n = 16 with small absolute values.

Fix: #148. evd_imp scales the input as ?GEEV does, by a power of two. The c32 LAPACK group now passes, so the known-failures entry is removed. The upstream record is upstream-reports/faer-028; nothing was posted upstream.

Separate defects found by the sweep, both also present in upstream 0.24.4:

real Schur: the deflation-window sort never terminates when a 2 x 2 swap fails #144: the real Schur deflation-window sort never terminates when a 2×2 swap fails.
real EVD: eigenvectors of strongly graded matrices have GET22 residuals up to 2.6e9 #145: the real EVD of strongly graded matrices has GET22 residuals up to 2.6e9, against LAPACK below 5e-4 and complex faer at about 1. The error is in the real Schur eigenvector back substitution.