lapack: imported lapack as a subtree

lapack/testlapack/dlanv2.go

@@ -0,0 +1,69 @@
+// 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 (
+	"fmt"
+	"math"
+	"math/rand"
+	"testing"
+)
+
+type Dlanv2er interface {
+	Dlanv2(a, b, c, d float64) (aa, bb, cc, dd float64, rt1r, rt1i, rt2r, rt2i float64, cs, sn float64)
+}
+
+func Dlanv2Test(t *testing.T, impl Dlanv2er) {
+	rnd := rand.New(rand.NewSource(1))
+	for i := 0; i < 1000; i++ {
+		a := rnd.NormFloat64()
+		b := rnd.NormFloat64()
+		c := rnd.NormFloat64()
+		d := rnd.NormFloat64()
+		aa, bb, cc, dd, rt1r, rt1i, rt2r, rt2i, cs, sn := impl.Dlanv2(a, b, c, d)
+
+		mat := fmt.Sprintf("[%v %v; %v %v]", a, b, c, d)
+		if cc == 0 {
+			if rt1i != 0 || rt2i != 0 {
+				t.Errorf("Unexpected complex eigenvalues for %v", mat)
+			}
+		} else {
+			if aa != dd {
+				t.Errorf("Diagonal elements not equal for %v: got [%v %v]", mat, aa, dd)
+			}
+			if bb*cc >= 0 {
+				t.Errorf("Non-diagonal elements have the same sign for %v: got [%v %v]", mat, bb, cc)
+			} else {
+				im := math.Sqrt(-bb * cc)
+				if math.Abs(rt1i-im) > 1e-14 && math.Abs(rt1i+im) > 1e-14 {
+					t.Errorf("Unexpected imaginary part of eigenvalue for %v: got %v, want %v or %v", mat, rt1i, im, -im)
+				}
+				if math.Abs(rt2i-im) > 1e-14 && math.Abs(rt2i+im) > 1e-14 {
+					t.Errorf("Unexpected imaginary part of eigenvalue for %v: got %v, want %v or %v", mat, rt2i, im, -im)
+				}
+			}
+		}
+		if rt1r != aa && rt1r != dd {
+			t.Errorf("Unexpected real part of eigenvalue for %v: got %v, want %v or %v", mat, rt1r, aa, dd)
+		}
+		if rt2r != aa && rt2r != dd {
+			t.Errorf("Unexpected real part of eigenvalue for %v: got %v, want %v or %v", mat, rt2r, aa, dd)
+		}
+		if math.Abs(math.Hypot(cs, sn)-1) > 1e-14 {
+			t.Errorf("Unexpected unitary matrix for %v: got cs %v, sn %v", mat, cs, sn)
+		}
+
+		gota := cs*(aa*cs-bb*sn) - sn*(cc*cs-dd*sn)
+		gotb := cs*(aa*sn+bb*cs) - sn*(cc*sn+dd*cs)
+		gotc := sn*(aa*cs-bb*sn) + cs*(cc*cs-dd*sn)
+		gotd := sn*(aa*sn+bb*cs) + cs*(cc*sn+dd*cs)
+		if math.Abs(gota-a) > 1e-14 ||
+			math.Abs(gotb-b) > 1e-14 ||
+			math.Abs(gotc-c) > 1e-14 ||
+			math.Abs(gotd-d) > 1e-14 {
+			t.Errorf("Unexpected factorization: got [%v %v; %v %v], want [%v %v; %v %v]", gota, gotb, gotc, gotd, a, b, c, d)
+		}
+	}
+}