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 template<typename MatrixType> bool find_pivot(typename MatrixType::Scalar tol, MatrixType &diffs, Index col=0) 17 { 18 bool match = diffs.diagonal().sum() <= tol; 19 if(match || col==diffs.cols()) 20 { 21 return match; 22 } 23 else 24 { 25 Index n = diffs.cols(); 26 std::vector<std::pair<Index,Index> > transpositions; 27 for(Index i=col; i<n; ++i) 28 { 29 Index best_index(0); 30 if(diffs.col(col).segment(col,n-i).minCoeff(&best_index) > tol) 31 break; 32 33 best_index += col; 34 35 diffs.row(col).swap(diffs.row(best_index)); 36 if(find_pivot(tol,diffs,col+1)) return true; 37 diffs.row(col).swap(diffs.row(best_index)); 38 39 // move current pivot to the end 40 diffs.row(n-(i-col)-1).swap(diffs.row(best_index)); 41 transpositions.push_back(std::pair<Index,Index>(n-(i-col)-1,best_index)); 42 } 43 // restore 44 for(Index k=transpositions.size()-1; k>=0; --k) 45 diffs.row(transpositions[k].first).swap(diffs.row(transpositions[k].second)); 46 } 47 return false; 48 } 49 50 /* Check that two column vectors are approximately equal upto permutations. 51 * Initially, this method checked that the k-th power sums are equal for all k = 1, ..., vec1.rows(), 52 * however this strategy is numerically inacurate because of numerical cancellation issues. 53 */ 54 template<typename VectorType> 55 void verify_is_approx_upto_permutation(const VectorType& vec1, const VectorType& vec2) 56 { 57 typedef typename VectorType::Scalar Scalar; 58 typedef typename NumTraits<Scalar>::Real RealScalar; 59 60 VERIFY(vec1.cols() == 1); 61 VERIFY(vec2.cols() == 1); 62 VERIFY(vec1.rows() == vec2.rows()); 63 64 Index n = vec1.rows(); 65 RealScalar tol = test_precision<RealScalar>()*test_precision<RealScalar>()*numext::maxi(vec1.squaredNorm(),vec2.squaredNorm()); 66 Matrix<RealScalar,Dynamic,Dynamic> diffs = (vec1.rowwise().replicate(n) - vec2.rowwise().replicate(n).transpose()).cwiseAbs2(); 67 68 VERIFY( find_pivot(tol, diffs) ); 69 } 70 71 72 template<typename MatrixType> void eigensolver(const MatrixType& m) 73 { 74 typedef typename MatrixType::Index Index; 75 /* this test covers the following files: 76 ComplexEigenSolver.h, and indirectly ComplexSchur.h 77 */ 78 Index rows = m.rows(); 79 Index cols = m.cols(); 80 81 typedef typename MatrixType::Scalar Scalar; 82 typedef typename NumTraits<Scalar>::Real RealScalar; 83 84 MatrixType a = MatrixType::Random(rows,cols); 85 MatrixType symmA = a.adjoint() * a; 86 87 ComplexEigenSolver<MatrixType> ei0(symmA); 88 VERIFY_IS_EQUAL(ei0.info(), Success); 89 VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal()); 90 91 ComplexEigenSolver<MatrixType> ei1(a); 92 VERIFY_IS_EQUAL(ei1.info(), Success); 93 VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal()); 94 // Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus 95 // another algorithm so results may differ slightly 96 verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues()); 97 98 ComplexEigenSolver<MatrixType> ei2; 99 ei2.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a); 100 VERIFY_IS_EQUAL(ei2.info(), Success); 101 VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors()); 102 VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues()); 103 if (rows > 2) { 104 ei2.setMaxIterations(1).compute(a); 105 VERIFY_IS_EQUAL(ei2.info(), NoConvergence); 106 VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1); 107 } 108 109 ComplexEigenSolver<MatrixType> eiNoEivecs(a, false); 110 VERIFY_IS_EQUAL(eiNoEivecs.info(), Success); 111 VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues()); 112 113 // Regression test for issue #66 114 MatrixType z = MatrixType::Zero(rows,cols); 115 ComplexEigenSolver<MatrixType> eiz(z); 116 VERIFY((eiz.eigenvalues().cwiseEqual(0)).all()); 117 118 MatrixType id = MatrixType::Identity(rows, cols); 119 VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1)); 120 121 if (rows > 1 && rows < 20) 122 { 123 // Test matrix with NaN 124 a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN(); 125 ComplexEigenSolver<MatrixType> eiNaN(a); 126 VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence); 127 } 128 129 // regression test for bug 1098 130 { 131 ComplexEigenSolver<MatrixType> eig(a.adjoint() * a); 132 eig.compute(a.adjoint() * a); 133 } 134 135 // regression test for bug 478 136 { 137 a.setZero(); 138 ComplexEigenSolver<MatrixType> ei3(a); 139 VERIFY_IS_EQUAL(ei3.info(), Success); 140 VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1)); 141 VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity()); 142 } 143 } 144 145 template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m) 146 { 147 ComplexEigenSolver<MatrixType> eig; 148 VERIFY_RAISES_ASSERT(eig.eigenvectors()); 149 VERIFY_RAISES_ASSERT(eig.eigenvalues()); 150 151 MatrixType a = MatrixType::Random(m.rows(),m.cols()); 152 eig.compute(a, false); 153 VERIFY_RAISES_ASSERT(eig.eigenvectors()); 154 } 155 156 void test_eigensolver_complex() 157 { 158 int s = 0; 159 for(int i = 0; i < g_repeat; i++) { 160 CALL_SUBTEST_1( eigensolver(Matrix4cf()) ); 161 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 162 CALL_SUBTEST_2( eigensolver(MatrixXcd(s,s)) ); 163 CALL_SUBTEST_3( eigensolver(Matrix<std::complex<float>, 1, 1>()) ); 164 CALL_SUBTEST_4( eigensolver(Matrix3f()) ); 165 TEST_SET_BUT_UNUSED_VARIABLE(s) 166 } 167 CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4cf()) ); 168 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 169 CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXcd(s,s)) ); 170 CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<std::complex<float>, 1, 1>()) ); 171 CALL_SUBTEST_4( eigensolver_verify_assert(Matrix3f()) ); 172 173 // Test problem size constructors 174 CALL_SUBTEST_5(ComplexEigenSolver<MatrixXf> tmp(s)); 175 176 TEST_SET_BUT_UNUSED_VARIABLE(s) 177 } 178
