+++ /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 TestEigen(t *testing.T) {
- for i, test := range []struct {
- a *Dense
-
- values []complex128
- left *Dense
- right *Dense
- }{
- {
- a: NewDense(3, 3, []float64{
- 1, 0, 0,
- 0, 1, 0,
- 0, 0, 1,
- }),
- values: []complex128{1, 1, 1},
- left: NewDense(3, 3, []float64{
- 1, 0, 0,
- 0, 1, 0,
- 0, 0, 1,
- }),
- right: NewDense(3, 3, []float64{
- 1, 0, 0,
- 0, 1, 0,
- 0, 0, 1,
- }),
- },
- } {
- var e1, e2, e3, e4 Eigen
- ok := e1.Factorize(test.a, true, true)
- if !ok {
- panic("bad factorization")
- }
- e2.Factorize(test.a, false, true)
- e3.Factorize(test.a, true, false)
- e4.Factorize(test.a, false, false)
-
- v1 := e1.Values(nil)
- if !cmplxEqual(v1, test.values) {
- t.Errorf("eigenvector mismatch. Case %v", i)
- }
- if !Equal(e1.LeftVectors(), test.left) {
- t.Errorf("left eigenvector mismatch. Case %v", i)
- }
- if !Equal(e1.Vectors(), test.right) {
- t.Errorf("right eigenvector mismatch. Case %v", i)
- }
-
- // Check that the eigenvectors and values are the same in all combinations.
- if !cmplxEqual(v1, e2.Values(nil)) {
- t.Errorf("eigenvector mismatch. Case %v", i)
- }
- if !cmplxEqual(v1, e3.Values(nil)) {
- t.Errorf("eigenvector mismatch. Case %v", i)
- }
- if !cmplxEqual(v1, e4.Values(nil)) {
- t.Errorf("eigenvector mismatch. Case %v", i)
- }
- if !Equal(e1.Vectors(), e2.Vectors()) {
- t.Errorf("right eigenvector mismatch. Case %v", i)
- }
- if !Equal(e1.LeftVectors(), e3.LeftVectors()) {
- t.Errorf("right eigenvector mismatch. Case %v", i)
- }
-
- // TODO(btracey): Also add in a test for correctness when #308 is
- // resolved and we have a CMat.Mul().
- }
-}
-
-func cmplxEqual(v1, v2 []complex128) bool {
- for i, v := range v1 {
- if v != v2[i] {
- return false
- }
- }
- return true
-}
-
-func TestSymEigen(t *testing.T) {
- // Hand coded tests with results from lapack.
- for _, test := range []struct {
- mat *SymDense
-
- values []float64
- vectors *Dense
- }{
- {
- mat: NewSymDense(3, []float64{8, 2, 4, 2, 6, 10, 4, 10, 5}),
- values: []float64{-4.707679201365891, 6.294580208480216, 17.413098992885672},
- vectors: NewDense(3, 3, []float64{
- -0.127343483135656, -0.902414161226903, -0.411621572466779,
- -0.664177720955769, 0.385801900032553, -0.640331827193739,
- 0.736648893495999, 0.191847792659746, -0.648492738712395,
- }),
- },
- } {
- var es EigenSym
- ok := es.Factorize(test.mat, true)
- if !ok {
- t.Errorf("bad factorization")
- }
- if !floats.EqualApprox(test.values, es.values, 1e-14) {
- t.Errorf("Eigenvalue mismatch")
- }
- if !EqualApprox(test.vectors, es.vectors, 1e-14) {
- t.Errorf("Eigenvector mismatch")
- }
-
- var es2 EigenSym
- es2.Factorize(test.mat, false)
- if !floats.EqualApprox(es2.values, es.values, 1e-14) {
- t.Errorf("Eigenvalue mismatch when no vectors computed")
- }
- }
-
- // Randomized tests
- rnd := rand.New(rand.NewSource(1))
- for _, n := range []int{3, 5, 10, 70} {
- for cas := 0; cas < 10; cas++ {
- a := make([]float64, n*n)
- for i := range a {
- a[i] = rnd.NormFloat64()
- }
- s := NewSymDense(n, a)
- var es EigenSym
- ok := es.Factorize(s, true)
- if !ok {
- t.Errorf("Bad test")
- }
-
- // Check that the eigenvectors are orthonormal.
- if !isOrthonormal(es.vectors, 1e-8) {
- t.Errorf("Eigenvectors not orthonormal")
- }
-
- // Check that the eigenvalues are actually eigenvalues.
- for i := 0; i < n; i++ {
- v := NewVecDense(n, Col(nil, i, es.vectors))
- var m VecDense
- m.MulVec(s, v)
-
- var scal VecDense
- scal.ScaleVec(es.values[i], v)
-
- if !EqualApprox(&m, &scal, 1e-8) {
- t.Errorf("Eigenvalue does not match")
- }
- }
- }
- }
-}
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