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 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<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 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 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
