lapack/testlapack: add implementation comments to Dgebd2 test

lapack/testlapack/dgebd2.go

@@ -30,26 +30,31 @@ func Dgebd2Test(t *testing.T, impl Dgebd2er) {
 		if lda == 0 {
 			lda = n
 		}
-		nb := min(m, n) // 'nb' name parallel with Dlabrd code.
+		// Allocate m×n matrix A and fill it with random numbers.
 		a := make([]float64, m*lda)
 		for i := range a {
 			a[i] = rnd.NormFloat64()
 		}
+		// Store a copy of A for later comparison.
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+		// Allocate slices for the main and off diagonal.
+		nb := min(m, n)
 		d := nanSlice(nb)
 		e := nanSlice(nb - 1)
+		// Allocate slices for scalar factors of elementary reflectors
+		// and fill them with NaNs.
 		tauP := nanSlice(nb)
 		tauQ := nanSlice(nb)
+		// Allocate workspace.
 		work := nanSlice(max(m, n))
-		aCopy := make([]float64, len(a))
-		copy(aCopy, a)
+
+		// Reduce A to upper or lower bidiagonal form by an orthogonal
+		// transformation.
 		impl.Dgebd2(m, n, a, lda, d, e, tauQ, tauP, work)
-		if m >= n && nb == n {
-			tauP[n-1] = 0
-		}
-		if m < n && nb == m {
-			tauQ[m-1] = 0
-		}
 
+		// Check that it holds Q^T * A * P = B where B is represented by
+		// d and e.
 		checkBidiagonal(t, m, n, nb, a, lda, d, e, tauP, tauQ, aCopy)
 	}
 }