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

Assisted-by: GLM 5.3 Flash

linalg/decomp3_test.go

@@ -294,6 +294,39 @@ func subComplex(a, b []complex128) []complex128 {
 	return out
 }
 
+// TestEigenComplexNearDiagonalConverges pins the Jacobi sweep against a
+// matrix whose every off-diagonal entry sits just under the per-entry
+// skip level while the aggregate off-norm stays above the convergence
+// threshold: the skip must not freeze the sweep above its own
+// convergence test, which used to exhaust the passes and report the
+// nearly diagonal matrix as unconverged.
+func TestEigenComplexNearDiagonalConverges(t *testing.T) {
+	const n = 30
+	cv := make([]complex128, n*n)
+	for i := range n {
+		cv[i*n+i] = 1
+	}
+	for i := range n {
+		for j := i + 1; j < n; j++ {
+			cv[i*n+j] = complex(0.9e-13, 0)
+			cv[j*n+i] = complex(0.9e-13, 0)
+		}
+	}
+	a, err := core.FromComplexes(cv, n, n)
+	if err != nil {
+		t.Fatalf("FromComplexes: %v", err)
+	}
+	vals, _, err := EigenComplex(a)
+	if err != nil {
+		t.Fatalf("EigenComplex: %v", err)
+	}
+	for i := range n {
+		if math.Abs(vals.FloatAt(i)-1) > 1e-11 {
+			t.Fatalf("eigenvalue %d is %.12g, want 1", i, vals.FloatAt(i))
+		}
+	}
+}
+
 // TestEigenComplexRefusesNonFinite pins that a poisoned matrix never
 // reads as Hermitian: the mirror comparison cannot see a NaN
 // difference, so the entry is refused outright, the way the sparse