1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "main.h"
#include <limits>
#include <Eigen/Eigenvalues>
#include <Eigen/LU>
template<typename MatrixType> bool find_pivot(typename MatrixType::Scalar tol, MatrixType &diffs, Index col=0)
{
bool match = diffs.diagonal().sum() <= tol;
if(match || col==diffs.cols())
{
return match;
}
else
{
Index n = diffs.cols();
std::vector<std::pair<Index,Index> > transpositions;
for(Index i=col; i<n; ++i)
{
Index best_index(0);
if(diffs.col(col).segment(col,n-i).minCoeff(&best_index) > tol)
break;
best_index += col;
diffs.row(col).swap(diffs.row(best_index));
if(find_pivot(tol,diffs,col+1)) return true;
diffs.row(col).swap(diffs.row(best_index));
// move current pivot to the end
diffs.row(n-(i-col)-1).swap(diffs.row(best_index));
transpositions.push_back(std::pair<Index,Index>(n-(i-col)-1,best_index));
}
// restore
for(Index k=transpositions.size()-1; k>=0; --k)
diffs.row(transpositions[k].first).swap(diffs.row(transpositions[k].second));
}
return false;
}
/* Check that two column vectors are approximately equal upto permutations.
* Initially, this method checked that the k-th power sums are equal for all k = 1, ..., vec1.rows(),
* however this strategy is numerically inacurate because of numerical cancellation issues.
*/
template<typename VectorType>
void verify_is_approx_upto_permutation(const VectorType& vec1, const VectorType& vec2)
{
typedef typename VectorType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
VERIFY(vec1.cols() == 1);
VERIFY(vec2.cols() == 1);
VERIFY(vec1.rows() == vec2.rows());
Index n = vec1.rows();
RealScalar tol = test_precision<RealScalar>()*test_precision<RealScalar>()*numext::maxi(vec1.squaredNorm(),vec2.squaredNorm());
Matrix<RealScalar,Dynamic,Dynamic> diffs = (vec1.rowwise().replicate(n) - vec2.rowwise().replicate(n).transpose()).cwiseAbs2();
VERIFY( find_pivot(tol, diffs) );
}
template<typename MatrixType> void eigensolver(const MatrixType& m)
{
/* this test covers the following files:
ComplexEigenSolver.h, and indirectly ComplexSchur.h
*/
Index rows = m.rows();
Index cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
MatrixType a = MatrixType::Random(rows,cols);
MatrixType symmA = a.adjoint() * a;
ComplexEigenSolver<MatrixType> ei0(symmA);
VERIFY_IS_EQUAL(ei0.info(), Success);
VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal());
ComplexEigenSolver<MatrixType> ei1(a);
VERIFY_IS_EQUAL(ei1.info(), Success);
VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
// Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus
// another algorithm so results may differ slightly
verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues());
ComplexEigenSolver<MatrixType> ei2;
ei2.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);
VERIFY_IS_EQUAL(ei2.info(), Success);
VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());
VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());
if (rows > 2) {
ei2.setMaxIterations(1).compute(a);
VERIFY_IS_EQUAL(ei2.info(), NoConvergence);
VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);
}
ComplexEigenSolver<MatrixType> eiNoEivecs(a, false);
VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
// Regression test for issue #66
MatrixType z = MatrixType::Zero(rows,cols);
ComplexEigenSolver<MatrixType> eiz(z);
VERIFY((eiz.eigenvalues().cwiseEqual(0)).all());
MatrixType id = MatrixType::Identity(rows, cols);
VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
if (rows > 1 && rows < 20)
{
// Test matrix with NaN
a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
ComplexEigenSolver<MatrixType> eiNaN(a);
VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
}
// regression test for bug 1098
{
ComplexEigenSolver<MatrixType> eig(a.adjoint() * a);
eig.compute(a.adjoint() * a);
}
// regression test for bug 478
{
a.setZero();
ComplexEigenSolver<MatrixType> ei3(a);
VERIFY_IS_EQUAL(ei3.info(), Success);
VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1));
VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity());
}
}
template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
{
ComplexEigenSolver<MatrixType> eig;
VERIFY_RAISES_ASSERT(eig.eigenvectors());
VERIFY_RAISES_ASSERT(eig.eigenvalues());
MatrixType a = MatrixType::Random(m.rows(),m.cols());
eig.compute(a, false);
VERIFY_RAISES_ASSERT(eig.eigenvectors());
}
void test_eigensolver_complex()
{
int s = 0;
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( eigensolver(Matrix4cf()) );
s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
CALL_SUBTEST_2( eigensolver(MatrixXcd(s,s)) );
CALL_SUBTEST_3( eigensolver(Matrix<std::complex<float>, 1, 1>()) );
CALL_SUBTEST_4( eigensolver(Matrix3f()) );
TEST_SET_BUT_UNUSED_VARIABLE(s)
}
CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4cf()) );
s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXcd(s,s)) );
CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<std::complex<float>, 1, 1>()) );
CALL_SUBTEST_4( eigensolver_verify_assert(Matrix3f()) );
// Test problem size constructors
CALL_SUBTEST_5(ComplexEigenSolver<MatrixXf> tmp(s));
TEST_SET_BUT_UNUSED_VARIABLE(s)
}
|
