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 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<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
27 typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;
28 typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex;
29
30 MatrixType a = MatrixType::Random(rows,cols);
31 MatrixType a1 = MatrixType::Random(rows,cols);
32 MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
33
34 EigenSolver<MatrixType> ei0(symmA);
35 VERIFY_IS_EQUAL(ei0.info(), Success);
36 VERIFY_IS_APPROX(symmA * ei0.pseudoEigenvectors(), ei0.pseudoEigenvectors() * ei0.pseudoEigenvalueMatrix());
37 VERIFY_IS_APPROX((symmA.template cast<Complex>()) * (ei0.pseudoEigenvectors().template cast<Complex>()),
38 (ei0.pseudoEigenvectors().template cast<Complex>()) * (ei0.eigenvalues().asDiagonal()));
39
40 EigenSolver<MatrixType> ei1(a);
41 VERIFY_IS_EQUAL(ei1.info(), Success);
42 VERIFY_IS_APPROX(a * ei1.pseudoEigenvectors(), ei1.pseudoEigenvectors() * ei1.pseudoEigenvalueMatrix());
43 VERIFY_IS_APPROX(a.template cast<Complex>() * ei1.eigenvectors(),
44 ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
45 VERIFY_IS_APPROX(ei1.eigenvectors().colwise().norm(), RealVectorType::Ones(rows).transpose());
46 VERIFY_IS_APPROX(a.eigenvalues(), ei1.eigenvalues());
47
48 EigenSolver<MatrixType> eiNoEivecs(a, false);
49 VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
50 VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
51 VERIFY_IS_APPROX(ei1.pseudoEigenvalueMatrix(), eiNoEivecs.pseudoEigenvalueMatrix());
52
53 MatrixType id = MatrixType::Identity(rows, cols);
54 VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
55
56 if (rows > 2)
57 {
58 // Test matrix with NaN
59 a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
60 EigenSolver<MatrixType> eiNaN(a);
61 VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
62 }
63 }
64
eigensolver_verify_assert(const MatrixType & m)65 template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
66 {
67 EigenSolver<MatrixType> eig;
68 VERIFY_RAISES_ASSERT(eig.eigenvectors());
69 VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
70 VERIFY_RAISES_ASSERT(eig.pseudoEigenvalueMatrix());
71 VERIFY_RAISES_ASSERT(eig.eigenvalues());
72
73 MatrixType a = MatrixType::Random(m.rows(),m.cols());
74 eig.compute(a, false);
75 VERIFY_RAISES_ASSERT(eig.eigenvectors());
76 VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
77 }
78
test_eigensolver_generic()79 void test_eigensolver_generic()
80 {
81 int s;
82 for(int i = 0; i < g_repeat; i++) {
83 CALL_SUBTEST_1( eigensolver(Matrix4f()) );
84 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
85 CALL_SUBTEST_2( eigensolver(MatrixXd(s,s)) );
86
87 // some trivial but implementation-wise tricky cases
88 CALL_SUBTEST_2( eigensolver(MatrixXd(1,1)) );
89 CALL_SUBTEST_2( eigensolver(MatrixXd(2,2)) );
90 CALL_SUBTEST_3( eigensolver(Matrix<double,1,1>()) );
91 CALL_SUBTEST_4( eigensolver(Matrix2d()) );
92 }
93
94 CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4f()) );
95 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
96 CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXd(s,s)) );
97 CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<double,1,1>()) );
98 CALL_SUBTEST_4( eigensolver_verify_assert(Matrix2d()) );
99
100 // Test problem size constructors
101 CALL_SUBTEST_5(EigenSolver<MatrixXf>(s));
102
103 // regression test for bug 410
104 CALL_SUBTEST_2(
105 {
106 MatrixXd A(1,1);
107 A(0,0) = std::sqrt(-1.);
108 Eigen::EigenSolver<MatrixXd> solver(A);
109 MatrixXd V(1, 1);
110 V(0,0) = solver.eigenvectors()(0,0).real();
111 }
112 );
113
114 EIGEN_UNUSED_VARIABLE(s)
115 }
116