testlapack: add test for Dlacn2

Resolves #200

cgo/lapack_test.go

@@ -44,6 +44,10 @@ func (bl blockedTranslate) Dorgl2(m, n, k int, a []float64, lda int, tau, work [
 	impl.Dorglq(m, n, k, a, lda, tau, work, len(work))
 }
 
+func TestDlacn2(t *testing.T) {
+	testlapack.Dlacn2Test(t, impl)
+}
+
 func TestDlacpy(t *testing.T) {
 	testlapack.DlacpyTest(t, impl)
 }

native/lapack_test.go

@@ -100,6 +100,10 @@ func TestDlabrd(t *testing.T) {
 	testlapack.DlabrdTest(t, impl)
 }
 
+func TestDlacn2(t *testing.T) {
+	testlapack.Dlacn2Test(t, impl)
+}
+
 func TestDlacpy(t *testing.T) {
 	testlapack.DlacpyTest(t, impl)
 }

testlapack/dlacn2.go

@@ -0,0 +1,72 @@
+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"github.com/gonum/blas"
+	"github.com/gonum/blas/blas64"
+)
+
+type Dlacn2er interface {
+	Dlacn2(n int, v, x []float64, isgn []int, est float64, kase int, isave *[3]int) (float64, int)
+}
+
+func Dlacn2Test(t *testing.T, impl Dlacn2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, n := range []int{1, 2, 3, 4, 5, 7, 10, 15, 20, 100} {
+		for cas := 0; cas < 10; cas++ {
+			a := randomGeneral(n, n, n, rnd)
+
+			// Compute the 1-norm of A explicitly.
+			var norm1 float64
+			for j := 0; j < n; j++ {
+				var sum float64
+				for i := 0; i < n; i++ {
+					sum += math.Abs(a.Data[i*a.Stride+j])
+				}
+				if sum > norm1 {
+					norm1 = sum
+				}
+			}
+
+			// Compute the estimate of 1-norm using Dlanc2.
+			x := make([]float64, n)
+			work := make([]float64, n)
+			v := make([]float64, n)
+			isgn := make([]int, n)
+			var (
+				kase  int
+				isave [3]int
+				got   float64
+			)
+		loop:
+			for {
+				got, kase = impl.Dlacn2(n, v, x, isgn, got, kase, &isave)
+				switch kase {
+				default:
+					panic("Dlacn2 returned invalid value of kase")
+				case 0:
+					break loop
+				case 1:
+					blas64.Gemv(blas.NoTrans, 1, a, blas64.Vector{1, x}, 0, blas64.Vector{1, work})
+					copy(x, work)
+				case 2:
+					blas64.Gemv(blas.Trans, 1, a, blas64.Vector{1, x}, 0, blas64.Vector{1, work})
+					copy(x, work)
+				}
+			}
+
+			// Check that got is either accurate enough or a
+			// lower estimate of the 1-norm of A.
+			if math.Abs(got-norm1) > 1e-8 && got > norm1 {
+				t.Errorf("Case n=%v: not lower estimate. 1-norm %v, estimate %v", n, norm1, got)
+			}
+		}
+	}
+}