Make the ISVD test robust against ill-conditioning and sign ambiguity

[timholy]

Problem

The @testset "ISVD" fails intermittently — it failed on the Julia min CI job of #26, at test/runtests.jl's U2 ≈ U comparison.

The test built its target as M = A*B with A = rand(20, 5), B = rand(5, 30). Two independent issues made it flaky:

1. No headroom in the target. rand entries are all positive, so M is dominated by a rank-one "mean" component and has a lopsided spectrum — σ₅/σ₁ frequently lands at 0.02–0.06. The trailing singular vector is then only weakly determined, and the two incremental SVD paths the test compares (update! from a nothing start vs. isvd from a zero-filled start) disagree on it by more than the default isapprox tolerance. Measured rate: ~0.7% of random draws.

2. Sign ambiguity. Left singular vectors are determined only up to sign, and the two paths occasionally pick opposite signs for a column. @test U2 ≈ U ignores this — even with a well-conditioned target, ~0.03% of draws fail on a clean sign flip. The test already handles this correctly for its unequal-block comparisons (col1 ≈ col2 || col1 ≈ -col2) but not here.

Fix

• Build M from orthonormal factors with an explicit, well-separated set of singular values (5, 4, 3, 2, 1), so every singular vector is pinned down to full precision. No seeded RNG — the stream is not stable across Julia versions; the headroom is structural instead.
• Compare U columnwise allowing a sign flip (matching the idiom already used elsewhere in the file). The sign-coupled rows of Vt are compared by magnitude.

Verification

• Core comparisons (pA ≈ A, sign-aware U2 ≈ U, s2 ≈ s): 0 failures over 80,000 random trials on both Julia 1.10 and 1.12 — vs. ~206/30,000 with the old construction.
• Full edited testset: 0 failures over 500 runs.
• Pkg.test() passes (37/37).

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.71%. Comparing base (48603f5) to head (e048e41).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master      #28   +/-   ##
=======================================
  Coverage   98.71%   98.71%           
=======================================
  Files           1        1           
  Lines          78       78           
=======================================
  Hits           77       77           
  Misses          1        1           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.