testlapack: add isIdentity helper

lapack/testlapack/dgetri.go

@@ -5,7 +5,6 @@
 package testlapack
 
 import (
-	"math"
 	"testing"
 
 	"golang.org/x/exp/rand"
@@ -67,23 +66,8 @@ func DgetriTest(t *testing.T, impl Dgetrier) {
 		// Check that A(inv) * A = I.
 		ans := make([]float64, len(a))
 		bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, aCopy, lda, a, lda, 0, ans, lda)
-		isEye := true
+		// The tolerance is so high because computing matrix inverses is very unstable.
-		for i := 0; i < n; i++ {
+		if !isIdentity(n, ans, lda, 5e-2) {
-			for j := 0; j < n; j++ {
-				if i == j {
-					// This tolerance is so high because computing matrix inverses
-					// is very unstable.
-					if math.Abs(ans[i*lda+j]-1) > 5e-2 {
-						isEye = false
-					}
-				} else {
-					if math.Abs(ans[i*lda+j]) > 5e-2 {
-						isEye = false
-					}
-				}
-			}
-		}
-		if !isEye {
 			t.Errorf("Inv(A) * A != I. n = %v, lda = %v", n, lda)
 		}
 	}

lapack/testlapack/dlarfg.go

@@ -104,21 +104,7 @@ func DlarfgTest(t *testing.T, impl Dlarfger) {
 			Data:   make([]float64, n*n),
 		}
 		blas64.Gemm(blas.Trans, blas.NoTrans, 1, hmat, hmat, 0, eye)
-		iseye := true
+		if !isIdentity(n, eye.Data, n, 1e-14) {
-		for i := 0; i < n; i++ {
-			for j := 0; j < n; j++ {
-				if i == j {
-					if math.Abs(eye.Data[i*n+j]-1) > 1e-14 {
-						iseye = false
-					}
-				} else {
-					if math.Abs(eye.Data[i*n+j]) > 1e-14 {
-						iseye = false
-					}
-				}
-			}
-		}
-		if !iseye {
 			t.Errorf("H^T * H is not I %v", eye)
 		}
 

lapack/testlapack/dtrti2.go

@@ -5,7 +5,6 @@
 package testlapack
 
 import (
-	"math"
 	"testing"
 
 	"golang.org/x/exp/rand"
@@ -149,23 +148,7 @@ func Dtrti2Test(t *testing.T, impl Dtrti2er) {
 				ans := make([]float64, len(a))
 				bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, a, lda, aCopy, lda, 0, ans, lda)
 				// Check that ans is the identity matrix.
-				iseye := true
+				if !isIdentity(n, ans, lda, tol) {
-				for i := 0; i < n; i++ {
-					for j := 0; j < n; j++ {
-						if i == j {
-							if math.Abs(ans[i*lda+i]-1) > tol {
-								iseye = false
-								break
-							}
-						} else {
-							if math.Abs(ans[i*lda+j]) > tol {
-								iseye = false
-								break
-							}
-						}
-					}
-				}
-				if !iseye {
 					t.Errorf("inv(A) * A != I. Upper = %v, unit = %v, ans = %v", uplo == blas.Upper, diag == blas.Unit, ans)
 				}
 			}

lapack/testlapack/dtrtri.go

@@ -5,7 +5,6 @@
 package testlapack
 
 import (
-	"math"
 	"testing"
 
 	"golang.org/x/exp/rand"
@@ -80,23 +79,7 @@ func DtrtriTest(t *testing.T, impl Dtrtrier) {
 				ans := make([]float64, len(a))
 				bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, a, lda, aCopy, lda, 0, ans, lda)
 				// Check that ans is the identity matrix.
-				iseye := true
+				if !isIdentity(n, ans, lda, tol) {
-				for i := 0; i < n; i++ {
-					for j := 0; j < n; j++ {
-						if i == j {
-							if math.Abs(ans[i*lda+i]-1) > tol {
-								iseye = false
-								break
-							}
-						} else {
-							if math.Abs(ans[i*lda+j]) > tol {
-								iseye = false
-								break
-							}
-						}
-					}
-				}
-				if !iseye {
 					t.Errorf("inv(A) * A != I. Upper = %v, unit = %v, n = %v, lda = %v",
 						uplo == blas.Upper, diag == blas.Unit, n, lda)
 				}

lapack/testlapack/general.go

@@ -1464,3 +1464,28 @@ func constructGSVPresults(n, p, m, k, l int, a, b blas64.General) (zeroA, zeroB
 
 	return zeroA, zeroB
 }
+
+// isIdentity returns whether an n×n matrix A is approximately equal to the
+// identity matrix.
+func isIdentity(n int, a []float64, lda int, tol float64) bool {
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			aij := a[i*lda+j]
+			if math.IsNaN(aij) {
+				return false
+			}
+			if i == j {
+				if math.Abs(aij-1) > tol {
+					fmt.Println(i, j, aij)
+					return false
+				}
+			} else {
+				if math.Abs(aij) > tol {
+					fmt.Println(i, j, aij)
+					return false
+				}
+			}
+		}
+	}
+	return true
+}

lapack/testlapack/matgen_test.go

@@ -5,7 +5,6 @@
 package testlapack
 
 import (
-	"math"
 	"testing"
 
 	"golang.org/x/exp/rand"
@@ -21,40 +20,19 @@ func TestDlagsy(t *testing.T) {
 			if lda == 0 {
 				lda = max(1, n)
 			}
+			// D is the identity matrix I.
 			d := make([]float64, n)
 			for i := range d {
 				d[i] = 1
 			}
-			a := blas64.General{
+			// Allocate an n×n symmetric matrix A and fill it with NaNs.
-				Rows:   n,
+			a := nanSlice(n * lda)
-				Cols:   n,
+			work := make([]float64, 2*n)
-				Stride: lda,
+			// Compute A = U * D * U^T where U is a random orthogonal matrix.
-				Data:   nanSlice(n * lda),
+			Dlagsy(n, 0, d, a, lda, rnd, work)
-			}
+			// A should be the identity matrix because
-			work := make([]float64, a.Rows+a.Cols)
+			//  A = U * D * U^T = U * I * U^T = U * U^T = I.
-
+			if !isIdentity(n, a, lda, tol) {
-			Dlagsy(a.Rows, 0, d, a.Data, a.Stride, rnd, work)
-
-			isIdentity := true
-		identityLoop:
-			for i := 0; i < n; i++ {
-				for j := 0; j < n; j++ {
-					aij := a.Data[i*a.Stride+j]
-					if math.IsNaN(aij) {
-						isIdentity = false
-					}
-					if i == j && math.Abs(aij-1) > tol {
-						isIdentity = false
-					}
-					if i != j && math.Abs(aij) > tol {
-						isIdentity = false
-					}
-					if !isIdentity {
-						break identityLoop
-					}
-				}
-			}
-			if !isIdentity {
 				t.Errorf("Case n=%v,lda=%v: unexpected result", n, lda)
 			}
 		}