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) 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 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 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
