+++ /dev/null
-// Copyright ©2013 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 mat
-
-import (
- "testing"
-
- "golang.org/x/exp/rand"
-
- "gonum.org/v1/gonum/floats"
-)
-
-func TestSVD(t *testing.T) {
- // Hand coded tests
- for _, test := range []struct {
- a *Dense
- u *Dense
- v *Dense
- s []float64
- }{
- {
- a: NewDense(4, 2, []float64{2, 4, 1, 3, 0, 0, 0, 0}),
- u: NewDense(4, 2, []float64{
- -0.8174155604703632, -0.5760484367663209,
- -0.5760484367663209, 0.8174155604703633,
- 0, 0,
- 0, 0,
- }),
- v: NewDense(2, 2, []float64{
- -0.4045535848337571, -0.9145142956773044,
- -0.9145142956773044, 0.4045535848337571,
- }),
- s: []float64{5.464985704219041, 0.365966190626258},
- },
- {
- // Issue #5.
- a: NewDense(3, 11, []float64{
- 1, 1, 0, 1, 0, 0, 0, 0, 0, 11, 1,
- 1, 0, 0, 0, 0, 0, 1, 0, 0, 12, 2,
- 1, 1, 0, 0, 0, 0, 0, 0, 1, 13, 3,
- }),
- u: NewDense(3, 3, []float64{
- -0.5224167862273765, 0.7864430360363114, 0.3295270133658976,
- -0.5739526766688285, -0.03852203026050301, -0.8179818935216693,
- -0.6306021141833781, -0.6164603833618163, 0.4715056408282468,
- }),
- v: NewDense(11, 3, []float64{
- -0.08123293141915189, 0.08528085505260324, -0.013165501690885152,
- -0.05423546426886932, 0.1102707844980355, 0.622210623111631,
- 0, 0, 0,
- -0.0245733326078166, 0.510179651760153, 0.25596360803140994,
- 0, 0, 0,
- 0, 0, 0,
- -0.026997467150282436, -0.024989929445430496, -0.6353761248025164,
- 0, 0, 0,
- -0.029662131661052707, -0.3999088672621176, 0.3662470150802212,
- -0.9798839760830571, 0.11328174160898856, -0.047702613241813366,
- -0.16755466189153964, -0.7395268089170608, 0.08395240366704032,
- }),
- s: []float64{21.259500881097434, 1.5415021616856566, 1.2873979074613628},
- },
- } {
- var svd SVD
- ok := svd.Factorize(test.a, SVDThin)
- if !ok {
- t.Errorf("SVD failed")
- }
- s, u, v := extractSVD(&svd)
- if !floats.EqualApprox(s, test.s, 1e-10) {
- t.Errorf("Singular value mismatch. Got %v, want %v.", s, test.s)
- }
- if !EqualApprox(u, test.u, 1e-10) {
- t.Errorf("U mismatch.\nGot:\n%v\nWant:\n%v", Formatted(u), Formatted(test.u))
- }
- if !EqualApprox(v, test.v, 1e-10) {
- t.Errorf("V mismatch.\nGot:\n%v\nWant:\n%v", Formatted(v), Formatted(test.v))
- }
- m, n := test.a.Dims()
- sigma := NewDense(min(m, n), min(m, n), nil)
- for i := 0; i < min(m, n); i++ {
- sigma.Set(i, i, s[i])
- }
-
- var ans Dense
- ans.Product(u, sigma, v.T())
- if !EqualApprox(test.a, &ans, 1e-10) {
- t.Errorf("A reconstruction mismatch.\nGot:\n%v\nWant:\n%v\n", Formatted(&ans), Formatted(test.a))
- }
- }
-
- for _, test := range []struct {
- m, n int
- }{
- {5, 5},
- {5, 3},
- {3, 5},
- {150, 150},
- {200, 150},
- {150, 200},
- } {
- m := test.m
- n := test.n
- for trial := 0; trial < 10; trial++ {
- a := NewDense(m, n, nil)
- for i := range a.mat.Data {
- a.mat.Data[i] = rand.NormFloat64()
- }
- aCopy := DenseCopyOf(a)
-
- // Test Full decomposition.
- var svd SVD
- ok := svd.Factorize(a, SVDFull)
- if !ok {
- t.Errorf("SVD factorization failed")
- }
- if !Equal(a, aCopy) {
- t.Errorf("A changed during call to SVD with full")
- }
- s, u, v := extractSVD(&svd)
- sigma := NewDense(m, n, nil)
- for i := 0; i < min(m, n); i++ {
- sigma.Set(i, i, s[i])
- }
- var ansFull Dense
- ansFull.Product(u, sigma, v.T())
- if !EqualApprox(&ansFull, a, 1e-8) {
- t.Errorf("Answer mismatch when SVDFull")
- }
-
- // Test Thin decomposition.
- ok = svd.Factorize(a, SVDThin)
- if !ok {
- t.Errorf("SVD factorization failed")
- }
- if !Equal(a, aCopy) {
- t.Errorf("A changed during call to SVD with Thin")
- }
- sThin, u, v := extractSVD(&svd)
- if !floats.EqualApprox(s, sThin, 1e-8) {
- t.Errorf("Singular value mismatch between Full and Thin decomposition")
- }
- sigma = NewDense(min(m, n), min(m, n), nil)
- for i := 0; i < min(m, n); i++ {
- sigma.Set(i, i, sThin[i])
- }
- ansFull.Reset()
- ansFull.Product(u, sigma, v.T())
- if !EqualApprox(&ansFull, a, 1e-8) {
- t.Errorf("Answer mismatch when SVDFull")
- }
-
- // Test None decomposition.
- ok = svd.Factorize(a, SVDNone)
- if !ok {
- t.Errorf("SVD factorization failed")
- }
- if !Equal(a, aCopy) {
- t.Errorf("A changed during call to SVD with none")
- }
- sNone := make([]float64, min(m, n))
- svd.Values(sNone)
- if !floats.EqualApprox(s, sNone, 1e-8) {
- t.Errorf("Singular value mismatch between Full and None decomposition")
- }
- }
- }
-}
-
-func extractSVD(svd *SVD) (s []float64, u, v *Dense) {
- return svd.Values(nil), svd.UTo(nil), svd.VTo(nil)
-}
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