fix(linalg): refuse non-finite input in dense Cholesky, Eigen and rank-one updates

Assisted-by: GLM 5.3 Flash

linalg/cholupdate.go

@@ -71,14 +71,25 @@ func cholRankOne(l, x *core.Array, name string, sign int) (*core.Array, error) {
 	}
 	// The rotations below assume a lower triangular factor; a nonzero
 	// strict upper triangle would silently corrupt the sweep, so it is
-	// refused up front.
+	// refused up front, and so is a non-finite entry anywhere: the
+	// diagonal test cannot see a NaN, and the hyperbolic square of an
+	// Inf overflows mid-sweep. The sparse twin refuses the same input.
 	for i := range n {
-		for j := i + 1; j < n; j++ {
-			if out.RawFloats()[i*n+j] != 0 {
+		for j := range n {
+			w := out.RawFloats()[i*n+j]
+			if math.IsNaN(w) || math.IsInf(w, 0) {
+				return nil, base.Errf("%s: factor entry [%d,%d] is not finite", name, i, j)
+			}
+			if j > i && w != 0 {
 				return nil, base.Errf("%s: the factor must be lower triangular (nonzero entry at row %d, column %d)", name, i, j)
 			}
 		}
 	}
+	for i := range n {
+		if math.IsNaN(v[i]) || math.IsInf(v[i], 0) {
+			return nil, base.Errf("%s: entry %d is not finite", name, i)
+		}
+	}
 	// The modified matrix reads [L, x]·J·[L, x]ᵀ with J = diag(I, ±1):
 	// one sweep of (hyperbolic for −1, orthogonal for +1) rotations
 	// eliminates the vector column, and the surviving columns are the