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
15template<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 && rows < 20)
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  // regression test for bug 1098
75  {
76    EigenSolver<MatrixType> eig(a.adjoint() * a);
77    eig.compute(a.adjoint() * a);
78  }
79
80  // regression test for bug 478
81  {
82    a.setZero();
83    EigenSolver<MatrixType> ei3(a);
84    VERIFY_IS_EQUAL(ei3.info(), Success);
85    VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1));
86    VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity());
87  }
88}
89
90template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
91{
92  EigenSolver<MatrixType> eig;
93  VERIFY_RAISES_ASSERT(eig.eigenvectors());
94  VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
95  VERIFY_RAISES_ASSERT(eig.pseudoEigenvalueMatrix());
96  VERIFY_RAISES_ASSERT(eig.eigenvalues());
97
98  MatrixType a = MatrixType::Random(m.rows(),m.cols());
99  eig.compute(a, false);
100  VERIFY_RAISES_ASSERT(eig.eigenvectors());
101  VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
102}
103
104void test_eigensolver_generic()
105{
106  int s = 0;
107  for(int i = 0; i < g_repeat; i++) {
108    CALL_SUBTEST_1( eigensolver(Matrix4f()) );
109    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
110    CALL_SUBTEST_2( eigensolver(MatrixXd(s,s)) );
111    TEST_SET_BUT_UNUSED_VARIABLE(s)
112
113    // some trivial but implementation-wise tricky cases
114    CALL_SUBTEST_2( eigensolver(MatrixXd(1,1)) );
115    CALL_SUBTEST_2( eigensolver(MatrixXd(2,2)) );
116    CALL_SUBTEST_3( eigensolver(Matrix<double,1,1>()) );
117    CALL_SUBTEST_4( eigensolver(Matrix2d()) );
118  }
119
120  CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4f()) );
121  s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
122  CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXd(s,s)) );
123  CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<double,1,1>()) );
124  CALL_SUBTEST_4( eigensolver_verify_assert(Matrix2d()) );
125
126  // Test problem size constructors
127  CALL_SUBTEST_5(EigenSolver<MatrixXf> tmp(s));
128
129  // regression test for bug 410
130  CALL_SUBTEST_2(
131  {
132     MatrixXd A(1,1);
133     A(0,0) = std::sqrt(-1.); // is Not-a-Number
134     Eigen::EigenSolver<MatrixXd> solver(A);
135     VERIFY_IS_EQUAL(solver.info(), NumericalIssue);
136  }
137  );
138
139#ifdef EIGEN_TEST_PART_2
140  {
141    // regression test for bug 793
142    MatrixXd a(3,3);
143    a << 0,  0,  1,
144        1,  1, 1,
145        1, 1e+200,  1;
146    Eigen::EigenSolver<MatrixXd> eig(a);
147    double scale = 1e-200; // scale to avoid overflow during the comparisons
148    VERIFY_IS_APPROX(a * eig.pseudoEigenvectors()*scale, eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()*scale);
149    VERIFY_IS_APPROX(a * eig.eigenvectors()*scale, eig.eigenvectors() * eig.eigenvalues().asDiagonal()*scale);
150  }
151  {
152    // check a case where all eigenvalues are null.
153    MatrixXd a(2,2);
154    a << 1,  1,
155        -1, -1;
156    Eigen::EigenSolver<MatrixXd> eig(a);
157    VERIFY_IS_APPROX(eig.pseudoEigenvectors().squaredNorm(), 2.);
158    VERIFY_IS_APPROX((a * eig.pseudoEigenvectors()).norm()+1., 1.);
159    VERIFY_IS_APPROX((eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()).norm()+1., 1.);
160    VERIFY_IS_APPROX((a * eig.eigenvectors()).norm()+1., 1.);
161    VERIFY_IS_APPROX((eig.eigenvectors() * eig.eigenvalues().asDiagonal()).norm()+1., 1.);
162  }
163#endif
164
165  TEST_SET_BUT_UNUSED_VARIABLE(s)
166}
167