lapack/testlapack: fix comments and error messages about orthogonality

lapack/testlapack/dgeql2.go

@@ -72,7 +72,7 @@ func Dgeql2Test(t *testing.T, impl Dgeql2er) {
 			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, h, qTmp, 0, q)
 		}
 		if !isOrthogonal(q) {
-			t.Errorf("Q is not orthonormal")
+			t.Errorf("Q is not orthogonal")
 		}
 		l := blas64.General{
 			Rows:   m,

lapack/testlapack/dlatrd.go

@@ -134,7 +134,7 @@ func DlatrdTest(t *testing.T, impl Dlatrder) {
 			}
 			errStr := fmt.Sprintf("isUpper = %v, n = %v, nb = %v", uplo == blas.Upper, n, nb)
 			if !isOrthogonal(q) {
-				t.Errorf("Q not orthonormal. %s", errStr)
+				t.Errorf("Q not orthogonal. %s", errStr)
 			}
 			aGen := genFromSym(blas64.Symmetric{N: n, Stride: lda, Uplo: uplo, Data: aCopy})
 			if !dlatrdCheckDecomposition(t, uplo, n, nb, e, tau, a, lda, aGen, q) {

lapack/testlapack/dorg2l.go

@@ -48,12 +48,12 @@ func Dorg2lTest(t *testing.T, impl Dorg2ler) {
 		copy(aCopy, a)
 		impl.Dorg2l(m, n, k, a, lda, tau[n-k:], work)
 		if !hasOrthonormalColumns(m, n, a, lda) {
-			t.Errorf("Q is not orthonormal. m = %v, n = %v, k = %v", m, n, k)
+			t.Errorf("Case m=%v, n=%v, k=%v: columns of Q not orthonormal", m, n, k)
 		}
 	}
 }
 
-// hasOrthornormalColumns checks that the columns of a are orthonormal.
+// hasOrthonormalColumns returns whether the columns of A are orthonormal.
 func hasOrthonormalColumns(m, n int, a []float64, lda int) bool {
 	for i := 0; i < n; i++ {
 		for j := i; j < n; j++ {

lapack/testlapack/dsteqr.go

@@ -60,13 +60,14 @@ func DsteqrTest(t *testing.T, impl Dsteqrer) {
 				aCopy := make([]float64, len(a))
 				copy(aCopy, a)
 				if compz == lapack.OriginalEV {
-					// Compute triangular decomposition and orthonormal matrix.
 					uplo := blas.Upper
 					tau := make([]float64, n)
 					work := make([]float64, 1)
 					impl.Dsytrd(blas.Upper, n, a, lda, d, e, tau, work, -1)
 					work = make([]float64, int(work[0]))
+					// Reduce A to symmetric tridiagonal form.
 					impl.Dsytrd(uplo, n, a, lda, d, e, tau, work, len(work))
+					// Compute the orthogonal matrix Q.
 					impl.Dorgtr(uplo, n, a, lda, tau, work, len(work))
 				} else {
 					for i := 0; i < n; i++ {