testlapack: add isIdentity helper

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{
-				Rows:   n,
-				Cols:   n,
-				Stride: lda,
-				Data:   nanSlice(n * lda),
-			}
-			work := make([]float64, a.Rows+a.Cols)
-
-			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 {
+			// Allocate an n×n symmetric matrix A and fill it with NaNs.
+			a := nanSlice(n * lda)
+			work := make([]float64, 2*n)
+			// Compute A = U * D * U^T where U is a random orthogonal matrix.
+			Dlagsy(n, 0, d, a, lda, rnd, work)
+			// A should be the identity matrix because
+			//  A = U * D * U^T = U * I * U^T = U * U^T = I.
+			if !isIdentity(n, a, lda, tol) {
 				t.Errorf("Case n=%v,lda=%v: unexpected result", n, lda)
 			}
 		}