matrix: imported matrix as a subtree

matrix/mat64/gsvd_test.go

@@ -0,0 +1,119 @@
+// Copyright ©2017 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 mat64
+
+import (
+	"math/rand"
+	"testing"
+
+	"github.com/gonum/floats"
+	"github.com/gonum/matrix"
+)
+
+func TestGSVD(t *testing.T) {
+	const tol = 1e-10
+	rnd := rand.New(rand.NewSource(1))
+	for _, test := range []struct {
+		m, p, n int
+	}{
+		{5, 3, 5},
+		{5, 3, 3},
+		{3, 3, 5},
+		{5, 5, 5},
+		{5, 5, 3},
+		{3, 5, 5},
+		{150, 150, 150},
+		{200, 150, 150},
+		{150, 150, 200},
+		{150, 200, 150},
+		{200, 200, 150},
+		{150, 200, 200},
+	} {
+		m := test.m
+		p := test.p
+		n := test.n
+		for trial := 0; trial < 10; trial++ {
+			a := NewDense(m, n, nil)
+			for i := range a.mat.Data {
+				a.mat.Data[i] = rnd.NormFloat64()
+			}
+			aCopy := DenseCopyOf(a)
+
+			b := NewDense(p, n, nil)
+			for i := range b.mat.Data {
+				b.mat.Data[i] = rnd.NormFloat64()
+			}
+			bCopy := DenseCopyOf(b)
+
+			// Test Full decomposition.
+			var gsvd GSVD
+			ok := gsvd.Factorize(a, b, matrix.GSVDU|matrix.GSVDV|matrix.GSVDQ)
+			if !ok {
+				t.Errorf("GSVD factorization failed")
+			}
+			if !Equal(a, aCopy) {
+				t.Errorf("A changed during call to GSVD.Factorize with GSVDU|GSVDV|GSVDQ")
+			}
+			if !Equal(b, bCopy) {
+				t.Errorf("B changed during call to GSVD.Factorize with GSVDU|GSVDV|GSVDQ")
+			}
+			c, s, sigma1, sigma2, zeroR, u, v, q := extractGSVD(&gsvd)
+			var ansU, ansV, d1R, d2R Dense
+			ansU.Product(u.T(), a, q)
+			ansV.Product(v.T(), b, q)
+			d1R.Mul(sigma1, zeroR)
+			d2R.Mul(sigma2, zeroR)
+			if !EqualApprox(&ansU, &d1R, tol) {
+				t.Errorf("Answer mismatch with GSVDU|GSVDV|GSVDQ\nU^T * A * Q:\n% 0.2f\nΣ₁ * [ 0 R ]:\n% 0.2f",
+					Formatted(&ansU), Formatted(&d1R))
+			}
+			if !EqualApprox(&ansV, &d2R, tol) {
+				t.Errorf("Answer mismatch with GSVDU|GSVDV|GSVDQ\nV^T * B  *Q:\n% 0.2f\nΣ₂ * [ 0 R ]:\n% 0.2f",
+					Formatted(&d2R), Formatted(&ansV))
+			}
+
+			// Check C^2 + S^2 = I.
+			for i := range c {
+				d := c[i]*c[i] + s[i]*s[i]
+				if !floats.EqualWithinAbsOrRel(d, 1, 1e-14, 1e-14) {
+					t.Errorf("c_%d^2 + s_%d^2 != 1: got: %v", i, i, d)
+				}
+			}
+
+			// Test None decomposition.
+			ok = gsvd.Factorize(a, b, matrix.GSVDNone)
+			if !ok {
+				t.Errorf("GSVD factorization failed")
+			}
+			if !Equal(a, aCopy) {
+				t.Errorf("A changed during call to GSVD with GSVDNone")
+			}
+			if !Equal(b, bCopy) {
+				t.Errorf("B changed during call to GSVD with GSVDNone")
+			}
+			cNone := gsvd.ValuesA(nil)
+			if !floats.EqualApprox(c, cNone, tol) {
+				t.Errorf("Singular value mismatch between GSVDU|GSVDV|GSVDQ and GSVDNone decomposition")
+			}
+			sNone := gsvd.ValuesB(nil)
+			if !floats.EqualApprox(s, sNone, tol) {
+				t.Errorf("Singular value mismatch between GSVDU|GSVDV|GSVDQ and GSVDNone decomposition")
+			}
+		}
+	}
+}
+
+func extractGSVD(gsvd *GSVD) (c, s []float64, s1, s2, zR, u, v, q *Dense) {
+	var s1m, s2m, zeroR, um, vm, qm Dense
+	s1m.SigmaAFromGSVD(gsvd)
+	s2m.SigmaBFromGSVD(gsvd)
+	zeroR.ZeroRFromGSVD(gsvd)
+	um.UFromGSVD(gsvd)
+	vm.VFromGSVD(gsvd)
+	qm.QFromGSVD(gsvd)
+	c = gsvd.ValuesA(nil)
+	s = gsvd.ValuesB(nil)
+	return c, s, &s1m, &s2m, &zeroR, &um, &vm, &qm
+}