1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2008-2009 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 #include <Eigen/LU> 15 16 /* Check that two column vectors are approximately equal upto permutations, 17 by checking that the k-th power sums are equal for k = 1, ..., vec1.rows() */ 18 template<typename VectorType> 19 void verify_is_approx_upto_permutation(const VectorType& vec1, const VectorType& vec2) 20 { 21 typedef typename NumTraits<typename VectorType::Scalar>::Real RealScalar; 22 23 VERIFY(vec1.cols() == 1); 24 VERIFY(vec2.cols() == 1); 25 VERIFY(vec1.rows() == vec2.rows()); 26 for (int k = 1; k <= vec1.rows(); ++k) 27 { 28 VERIFY_IS_APPROX(vec1.array().pow(RealScalar(k)).sum(), vec2.array().pow(RealScalar(k)).sum()); 29 } 30 } 31 32 33 template<typename MatrixType> void eigensolver(const MatrixType& m) 34 { 35 typedef typename MatrixType::Index Index; 36 /* this test covers the following files: 37 ComplexEigenSolver.h, and indirectly ComplexSchur.h 38 */ 39 Index rows = m.rows(); 40 Index cols = m.cols(); 41 42 typedef typename MatrixType::Scalar Scalar; 43 typedef typename NumTraits<Scalar>::Real RealScalar; 44 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; 45 typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType; 46 typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex; 47 48 MatrixType a = MatrixType::Random(rows,cols); 49 MatrixType symmA = a.adjoint() * a; 50 51 ComplexEigenSolver<MatrixType> ei0(symmA); 52 VERIFY_IS_EQUAL(ei0.info(), Success); 53 VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal()); 54 55 ComplexEigenSolver<MatrixType> ei1(a); 56 VERIFY_IS_EQUAL(ei1.info(), Success); 57 VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal()); 58 // Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus 59 // another algorithm so results may differ slightly 60 verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues()); 61 62 ComplexEigenSolver<MatrixType> eiNoEivecs(a, false); 63 VERIFY_IS_EQUAL(eiNoEivecs.info(), Success); 64 VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues()); 65 66 // Regression test for issue #66 67 MatrixType z = MatrixType::Zero(rows,cols); 68 ComplexEigenSolver<MatrixType> eiz(z); 69 VERIFY((eiz.eigenvalues().cwiseEqual(0)).all()); 70 71 MatrixType id = MatrixType::Identity(rows, cols); 72 VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1)); 73 74 if (rows > 1) 75 { 76 // Test matrix with NaN 77 a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN(); 78 ComplexEigenSolver<MatrixType> eiNaN(a); 79 VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence); 80 } 81 } 82 83 template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m) 84 { 85 ComplexEigenSolver<MatrixType> eig; 86 VERIFY_RAISES_ASSERT(eig.eigenvectors()); 87 VERIFY_RAISES_ASSERT(eig.eigenvalues()); 88 89 MatrixType a = MatrixType::Random(m.rows(),m.cols()); 90 eig.compute(a, false); 91 VERIFY_RAISES_ASSERT(eig.eigenvectors()); 92 } 93 94 void test_eigensolver_complex() 95 { 96 int s; 97 for(int i = 0; i < g_repeat; i++) { 98 CALL_SUBTEST_1( eigensolver(Matrix4cf()) ); 99 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 100 CALL_SUBTEST_2( eigensolver(MatrixXcd(s,s)) ); 101 CALL_SUBTEST_3( eigensolver(Matrix<std::complex<float>, 1, 1>()) ); 102 CALL_SUBTEST_4( eigensolver(Matrix3f()) ); 103 } 104 105 CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4cf()) ); 106 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 107 CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXcd(s,s)) ); 108 CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<std::complex<float>, 1, 1>()) ); 109 CALL_SUBTEST_4( eigensolver_verify_assert(Matrix3f()) ); 110 111 // Test problem size constructors 112 CALL_SUBTEST_5(ComplexEigenSolver<MatrixXf>(s)); 113 114 EIGEN_UNUSED_VARIABLE(s) 115 } 116
