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 (at) inria.fr> 5 // Copyright (C) 2010,2012 Jitse Niesen <jitse (at) 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 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 && 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 90 template<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 } 103 104 void 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
