1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
5 // Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
6 //
7 // This Source Code Form is subject to the terms of the Mozilla
8 // Public License v. 2.0. If a copy of the MPL was not distributed
9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10
11 #include "main.h"
12 #include <limits>
13 #include <Eigen/Eigenvalues>
14
eigensolver(const MatrixType & m)15 template<typename MatrixType> void eigensolver(const MatrixType& m)
16 {
17 typedef typename MatrixType::Index Index;
18 /* this test covers the following files:
19 EigenSolver.h
20 */
21 Index rows = m.rows();
22 Index cols = m.cols();
23
24 typedef typename MatrixType::Scalar Scalar;
25 typedef typename NumTraits<Scalar>::Real RealScalar;
26 typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;
27 typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex;
28
29 MatrixType a = MatrixType::Random(rows,cols);
30 MatrixType a1 = MatrixType::Random(rows,cols);
31 MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
32
33 EigenSolver<MatrixType> ei0(symmA);
34 VERIFY_IS_EQUAL(ei0.info(), Success);
35 VERIFY_IS_APPROX(symmA * ei0.pseudoEigenvectors(), ei0.pseudoEigenvectors() * ei0.pseudoEigenvalueMatrix());
36 VERIFY_IS_APPROX((symmA.template cast<Complex>()) * (ei0.pseudoEigenvectors().template cast<Complex>()),
37 (ei0.pseudoEigenvectors().template cast<Complex>()) * (ei0.eigenvalues().asDiagonal()));
38
39 EigenSolver<MatrixType> ei1(a);
40 VERIFY_IS_EQUAL(ei1.info(), Success);
41 VERIFY_IS_APPROX(a * ei1.pseudoEigenvectors(), ei1.pseudoEigenvectors() * ei1.pseudoEigenvalueMatrix());
42 VERIFY_IS_APPROX(a.template cast<Complex>() * ei1.eigenvectors(),
43 ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
44 VERIFY_IS_APPROX(ei1.eigenvectors().colwise().norm(), RealVectorType::Ones(rows).transpose());
45 VERIFY_IS_APPROX(a.eigenvalues(), ei1.eigenvalues());
46
47 EigenSolver<MatrixType> ei2;
48 ei2.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);
49 VERIFY_IS_EQUAL(ei2.info(), Success);
50 VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());
51 VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());
52 if (rows > 2) {
53 ei2.setMaxIterations(1).compute(a);
54 VERIFY_IS_EQUAL(ei2.info(), NoConvergence);
55 VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);
56 }
57
58 EigenSolver<MatrixType> eiNoEivecs(a, false);
59 VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
60 VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
61 VERIFY_IS_APPROX(ei1.pseudoEigenvalueMatrix(), eiNoEivecs.pseudoEigenvalueMatrix());
62
63 MatrixType id = MatrixType::Identity(rows, cols);
64 VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
65
66 if (rows > 2)
67 {
68 // Test matrix with NaN
69 a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
70 EigenSolver<MatrixType> eiNaN(a);
71 VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
72 }
73 }
74
eigensolver_verify_assert(const MatrixType & m)75 template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
76 {
77 EigenSolver<MatrixType> eig;
78 VERIFY_RAISES_ASSERT(eig.eigenvectors());
79 VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
80 VERIFY_RAISES_ASSERT(eig.pseudoEigenvalueMatrix());
81 VERIFY_RAISES_ASSERT(eig.eigenvalues());
82
83 MatrixType a = MatrixType::Random(m.rows(),m.cols());
84 eig.compute(a, false);
85 VERIFY_RAISES_ASSERT(eig.eigenvectors());
86 VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
87 }
88
test_eigensolver_generic()89 void test_eigensolver_generic()
90 {
91 int s = 0;
92 for(int i = 0; i < g_repeat; i++) {
93 CALL_SUBTEST_1( eigensolver(Matrix4f()) );
94 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
95 CALL_SUBTEST_2( eigensolver(MatrixXd(s,s)) );
96
97 // some trivial but implementation-wise tricky cases
98 CALL_SUBTEST_2( eigensolver(MatrixXd(1,1)) );
99 CALL_SUBTEST_2( eigensolver(MatrixXd(2,2)) );
100 CALL_SUBTEST_3( eigensolver(Matrix<double,1,1>()) );
101 CALL_SUBTEST_4( eigensolver(Matrix2d()) );
102 }
103
104 CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4f()) );
105 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
106 CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXd(s,s)) );
107 CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<double,1,1>()) );
108 CALL_SUBTEST_4( eigensolver_verify_assert(Matrix2d()) );
109
110 // Test problem size constructors
111 CALL_SUBTEST_5(EigenSolver<MatrixXf> tmp(s));
112
113 // regression test for bug 410
114 CALL_SUBTEST_2(
115 {
116 MatrixXd A(1,1);
117 A(0,0) = std::sqrt(-1.);
118 Eigen::EigenSolver<MatrixXd> solver(A);
119 MatrixXd V(1, 1);
120 V(0,0) = solver.eigenvectors()(0,0).real();
121 }
122 );
123
124 TEST_SET_BUT_UNUSED_VARIABLE(s)
125 }
126