testlapack: adjust some tolerances (#1224)

lapack/testlapack/dgeev.go

@@ -285,6 +285,7 @@ func DgeevTest(t *testing.T, impl Dgeever) {
 			a:      Gear(4).Matrix(),
 			evWant: Gear(4).Eigenvalues(),
 			valTol: 1e-7,
+			vecTol: 1e-11,
 		},
 		{
 			a:      Gear(5).Matrix(),
@@ -294,6 +295,7 @@ func DgeevTest(t *testing.T, impl Dgeever) {
 			a:      Gear(10).Matrix(),
 			evWant: Gear(10).Eigenvalues(),
 			valTol: 1e-8,
+			vecTol: 1e-11,
 		},
 		{
 			a:      Gear(15).Matrix(),
@@ -303,11 +305,13 @@ func DgeevTest(t *testing.T, impl Dgeever) {
 			a:      Gear(30).Matrix(),
 			evWant: Gear(30).Eigenvalues(),
 			valTol: 1e-8,
+			vecTol: 1e-11,
 		},
 		{
 			a:      Gear(50).Matrix(),
 			evWant: Gear(50).Eigenvalues(),
 			valTol: 1e-8,
+			vecTol: 1e-11,
 		},
 		{
 			a:      Gear(101).Matrix(),
@@ -317,6 +321,7 @@ func DgeevTest(t *testing.T, impl Dgeever) {
 			a:      Gear(150).Matrix(),
 			evWant: Gear(150).Eigenvalues(),
 			valTol: 1e-8,
+			vecTol: 1e-11,
 		},
 
 		{

lapack/testlapack/dlaln2.go

@@ -33,7 +33,7 @@ func Dlaln2Test(t *testing.T, impl Dlaln2er) {
 }
 
 func testDlaln2(t *testing.T, impl Dlaln2er, trans bool, na, nw, extra int, rnd *rand.Rand) {
-	const tol = 1e-12
+	const tol = 1e-11
 
 	// Generate random input scalars.
 	ca := rnd.NormFloat64()

lapack/testlapack/dlansb.go

@@ -121,7 +121,7 @@ func dlansbTest(t *testing.T, impl Dlansber, rnd *rand.Rand, uplo blas.Uplo, n,
 		case lapack.Frobenius:
 			normWant = frobWant
 		}
-		if math.Abs(normGot-normWant) >= tol {
+		if math.Abs(normGot-normWant) > tol*float64(n) {
 			t.Errorf("%v: unexpected result; got %v, want %v", name, normGot, normWant)
 		}
 	}

lapack/testlapack/dlascl.go

@@ -19,7 +19,7 @@ type Dlascler interface {
 }
 
 func DlasclTest(t *testing.T, impl Dlascler) {
-	const tol = 1e-16
+	const tol = 1e-15
 
 	rnd := rand.New(rand.NewSource(1))
 	for ti, test := range []struct {
@@ -56,14 +56,44 @@ func DlasclTest(t *testing.T, impl Dlascler) {
 					t.Errorf("%v: out-of-range write to A", prefix)
 				}
 				switch kind {
+				case lapack.UpperTri:
+					var mod bool
+				loopLower:
+					for i := 0; i < m; i++ {
+						for j := 0; j < min(i, n); j++ {
+							if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
+								mod = true
+								break loopLower
+							}
+						}
+					}
+					if mod {
+						t.Errorf("%v: unexpected modification in lower triangle of A", prefix)
+					}
+				case lapack.LowerTri:
+					var mod bool
+				loopUpper:
+					for i := 0; i < m; i++ {
+						for j := i + 1; j < n; j++ {
+							if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
+								mod = true
+								break loopUpper
+							}
+						}
+					}
+					if mod {
+						t.Errorf("%v: unexpected modification in upper triangle of A", prefix)
+					}
+				}
+
+				var resid float64
+				switch kind {
 				case lapack.General:
 					for i := 0; i < m; i++ {
 						for j := 0; j < n; j++ {
 							want := scale * aCopy.Data[i*aCopy.Stride+j]
 							got := a.Data[i*a.Stride+j]
-							if math.Abs(want-got) > tol {
+							resid = math.Max(resid, math.Abs(want-got))
-								t.Errorf("%v: unexpected A[%v,%v]=%v, want %v", prefix, i, j, got, want)
-							}
 						}
 					}
 				case lapack.UpperTri:
@@ -71,16 +101,7 @@ func DlasclTest(t *testing.T, impl Dlascler) {
 						for j := i; j < n; j++ {
 							want := scale * aCopy.Data[i*aCopy.Stride+j]
 							got := a.Data[i*a.Stride+j]
-							if math.Abs(want-got) > tol {
+							resid = math.Max(resid, math.Abs(want-got))
-								t.Errorf("%v: unexpected A[%v,%v]=%v, want %v", prefix, i, j, got, want)
-							}
-						}
-					}
-					for i := 0; i < m; i++ {
-						for j := 0; j < min(i, n); j++ {
-							if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
-								t.Errorf("%v: unexpected modification in lower triangle of A", prefix)
-							}
 						}
 					}
 				case lapack.LowerTri:
@@ -88,19 +109,13 @@ func DlasclTest(t *testing.T, impl Dlascler) {
 						for j := 0; j <= min(i, n-1); j++ {
 							want := scale * aCopy.Data[i*aCopy.Stride+j]
 							got := a.Data[i*a.Stride+j]
-							if math.Abs(want-got) > tol {
+							resid = math.Max(resid, math.Abs(want-got))
-								t.Errorf("%v: unexpected A[%v,%v]=%v, want %v", prefix, i, j, got, want)
-							}
-						}
-					}
-					for i := 0; i < m; i++ {
-						for j := i + 1; j < n; j++ {
-							if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
-								t.Errorf("%v: unexpected modification in upper triangle of A", prefix)
-							}
 						}
 					}
 				}
+				if resid > tol*float64(max(m, n)) {
+					t.Errorf("%v: unexpected result; residual=%v, want<=%v", prefix, resid, tol*float64(max(m, n)))
+				}
 			}
 		}
 	}