fix(linalg): converge the Hermitian Jacobi sweep on near-diagonal matrices

Assisted-by: GLM 5.3 Flash

linalg/decomp3.go

@@ -122,6 +122,17 @@ func hermitianJacobi(h []complex128, v []complex128, n int) error {
 	// the floor already diagonal and return its raw diagonal, identity
 	// eigenvectors included.
 	threshold := 1e-13 * norm
+	// The per-entry skip must sit where a matrix whose every
+	// off-diagonal entry is skippable also passes the aggregate
+	// convergence test: with P pairs the off-norm of all-skipped entries
+	// reaches skip·√P, so a skip at the plain threshold leaves a matrix
+	// whose entries are uniformly just under it frozen above the test,
+	// and the sweep exhausts its passes without turning a single
+	// rotation.
+	skip := threshold
+	if pairs := float64(n * (n - 1) / 2); pairs > 1 {
+		skip = threshold / math.Sqrt(pairs)
+	}
 	offMass := func() float64 {
 		off := 0.0
 		for p := range n {
@@ -139,7 +150,7 @@ func hermitianJacobi(h []complex128, v []complex128, n int) error {
 		for p := range n {
 			for q := p + 1; q < n; q++ {
 				z := h[p*n+q]
-				if base.AbsComplex(z) <= threshold {
+				if base.AbsComplex(z) <= skip {
 					continue
 				}
 				// Step 1: a diagonal phase turn makes the pair entry