Add Dgebrd, Dgebd2, and Dlabrd and tests

native/dgebd2.go

@@ -4,6 +4,8 @@
 
 package native
 
+import "github.com/gonum/blas"
+
 // Dgebd2 reduces an m×n matrix A to upper or lower bidiagonal form by an orthogonal
 // transformation.
 //  Q^T * A * P = B
@@ -13,14 +15,58 @@ package native
 func (impl Implementation) Dgebd2(m, n int, a []float64, lda int, d, e, tauQ, tauP, work []float64) {
 	checkMatrix(m, n, a, lda)
 	if len(d) < min(m, n) {
-		panic("lapack: insufficient d")
+		panic(badD)
 	}
 	if len(e) < min(m, n)-1 {
-		panic("lapack: insufficient e")
+		panic(badE)
 	}
-	if m > n {
+	if len(tauQ) < min(m, n) {
+		panic(badTauQ)
+	}
+	if len(tauP) < min(m, n) {
+		panic(badTauP)
+	}
+	if len(work) < max(m, n) {
+		panic(badWork)
+	}
+	if m >= n {
 		for i := 0; i < n; i++ {
-			impl.Dlarfg(m-i, a[i*lda+i], a[min(i+1, m-1)*lda+i:], 1)
+			a[i*lda+i], tauQ[i] = impl.Dlarfg(m-i, a[i*lda+i], a[min(i+1, m-1)*lda+i:], lda)
+			d[i] = a[i*lda+i]
+			a[i*lda+i] = 1
+			// Apply H[i] to A[i:m, i+1:n] from the left.
+			if i < n-1 {
+				impl.Dlarf(blas.Left, m-i, n-i-1, a[i*lda+i:], lda, tauQ[i], a[i*lda+i+1:], lda, work)
+			}
+			a[i*lda+i] = d[i]
+			if i < n-1 {
+				a[i*lda+i+1], tauP[i] = impl.Dlarfg(n-i-1, a[i*lda+i+1], a[i*lda+min(i+2, n-1):], 1)
+				e[i] = a[i*lda+i+1]
+				a[i*lda+i+1] = 1
+				impl.Dlarf(blas.Right, m-i-1, n-i-1, a[i*lda+i+1:], 1, tauP[i], a[(i+1)*lda+i+1:], lda, work)
+				a[i*lda+i+1] = e[i]
+			} else {
+				tauP[i] = 0
+			}
+		}
+		return
+	}
+	for i := 0; i < m; i++ {
+		a[i*lda+i], tauP[i] = impl.Dlarfg(n-i, a[i*lda+i], a[i*lda+min(i+1, n-1):], 1)
+		d[i] = a[i*lda+i]
+		a[i*lda+i] = 1
+		if i < m-1 {
+			impl.Dlarf(blas.Right, m-i-1, n-i, a[i*lda+i:], 1, tauP[i], a[(i+1)*lda+i:], lda, work)
+		}
+		a[i*lda+i] = d[i]
+		if i < m-1 {
+			a[(i+1)*lda+i], tauQ[i] = impl.Dlarfg(m-i-1, a[(i+1)*lda+i], a[min(i+2, m-1)*lda+i:], lda)
+			e[i] = a[(i+1)*lda+i]
+			a[(i+1)*lda+i] = 1
+			impl.Dlarf(blas.Left, m-i-1, n-i-1, a[(i+1)*lda+i:], lda, tauQ[i], a[(i+1)*lda+i+1:], lda, work)
+			a[(i+1)*lda+i] = e[i]
+		} else {
+			tauQ[i] = 0
 		}
 	}
 }