1c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This file is part of Eigen, a lightweight C++ template library 2c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// for linear algebra. Eigen itself is part of the KDE project. 3c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 4c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> 5c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 6c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This Source Code Form is subject to the terms of the Mozilla 7c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Public License v. 2.0. If a copy of the MPL was not distributed 8c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 10c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include "main.h" 11c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include <Eigen/QR> 12c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 13c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#ifdef HAS_GSL 14c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include "gsl_helper.h" 15c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#endif 16c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 17c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType> void selfadjointeigensolver(const MatrixType& m) 18c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 19c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /* this test covers the following files: 20c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.h) 21c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 22c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int rows = m.rows(); 23c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int cols = m.cols(); 24c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 25c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename MatrixType::Scalar Scalar; 26c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename NumTraits<Scalar>::Real RealScalar; 27c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; 28c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType; 29c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex; 30c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 31c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath RealScalar largerEps = 10*test_precision<RealScalar>(); 32c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 33c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType a = MatrixType::Random(rows,cols); 34c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType a1 = MatrixType::Random(rows,cols); 35c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1; 36c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 37c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType b = MatrixType::Random(rows,cols); 38c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType b1 = MatrixType::Random(rows,cols); 39c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1; 40c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 41c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath SelfAdjointEigenSolver<MatrixType> eiSymm(symmA); 42c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // generalized eigen pb 43c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath SelfAdjointEigenSolver<MatrixType> eiSymmGen(symmA, symmB); 44c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 45c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath #ifdef HAS_GSL 46c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (ei_is_same_type<RealScalar,double>::ret) 47c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 48c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef GslTraits<Scalar> Gsl; 49c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typename Gsl::Matrix gEvec=0, gSymmA=0, gSymmB=0; 50c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typename GslTraits<RealScalar>::Vector gEval=0; 51c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath RealVectorType _eval; 52c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType _evec; 53c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath convert<MatrixType>(symmA, gSymmA); 54c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath convert<MatrixType>(symmB, gSymmB); 55c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath convert<MatrixType>(symmA, gEvec); 56c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath gEval = GslTraits<RealScalar>::createVector(rows); 57c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 58c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Gsl::eigen_symm(gSymmA, gEval, gEvec); 59c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath convert(gEval, _eval); 60c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath convert(gEvec, _evec); 61c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 62c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test gsl itself ! 63c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY((symmA * _evec).isApprox(_evec * _eval.asDiagonal(), largerEps)); 64c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 65c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // compare with eigen 66c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(_eval, eiSymm.eigenvalues()); 67c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(_evec.cwise().abs(), eiSymm.eigenvectors().cwise().abs()); 68c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 69c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // generalized pb 70c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Gsl::eigen_symm_gen(gSymmA, gSymmB, gEval, gEvec); 71c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath convert(gEval, _eval); 72c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath convert(gEvec, _evec); 73c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test GSL itself: 74c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY((symmA * _evec).isApprox(symmB * (_evec * _eval.asDiagonal()), largerEps)); 75c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 76c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // compare with eigen 77c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType normalized_eivec = eiSymmGen.eigenvectors()*eiSymmGen.eigenvectors().colwise().norm().asDiagonal().inverse(); 78c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(_eval, eiSymmGen.eigenvalues()); 79c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(_evec.cwiseAbs(), normalized_eivec.cwiseAbs()); 80c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 81c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Gsl::free(gSymmA); 82c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Gsl::free(gSymmB); 83c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath GslTraits<RealScalar>::free(gEval); 84c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Gsl::free(gEvec); 85c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 86c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath #endif 87c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 88c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY((symmA * eiSymm.eigenvectors()).isApprox( 89c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal(), largerEps)); 90c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 91c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // generalized eigen problem Ax = lBx 92c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY((symmA * eiSymmGen.eigenvectors()).isApprox( 93c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath symmB * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); 94c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 95c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType sqrtSymmA = eiSymm.operatorSqrt(); 96c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(symmA, sqrtSymmA*sqrtSymmA); 97c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(sqrtSymmA, symmA*eiSymm.operatorInverseSqrt()); 98c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 99c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 100c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType> void eigensolver(const MatrixType& m) 101c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 102c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /* this test covers the following files: 103c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath EigenSolver.h 104c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 105c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int rows = m.rows(); 106c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int cols = m.cols(); 107c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 108c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename MatrixType::Scalar Scalar; 109c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename NumTraits<Scalar>::Real RealScalar; 110c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; 111c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType; 112c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex; 113c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 114c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // RealScalar largerEps = 10*test_precision<RealScalar>(); 115c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 116c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType a = MatrixType::Random(rows,cols); 117c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType a1 = MatrixType::Random(rows,cols); 118c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1; 119c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 120c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath EigenSolver<MatrixType> ei0(symmA); 121c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(symmA * ei0.pseudoEigenvectors(), ei0.pseudoEigenvectors() * ei0.pseudoEigenvalueMatrix()); 122c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX((symmA.template cast<Complex>()) * (ei0.pseudoEigenvectors().template cast<Complex>()), 123c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath (ei0.pseudoEigenvectors().template cast<Complex>()) * (ei0.eigenvalues().asDiagonal())); 124c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 125c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath EigenSolver<MatrixType> ei1(a); 126c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(a * ei1.pseudoEigenvectors(), ei1.pseudoEigenvectors() * ei1.pseudoEigenvalueMatrix()); 127c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(a.template cast<Complex>() * ei1.eigenvectors(), 128c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath ei1.eigenvectors() * ei1.eigenvalues().asDiagonal()); 129c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 130c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 131c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 132c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathvoid test_eigen2_eigensolver() 133c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 134c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for(int i = 0; i < g_repeat; i++) { 135c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // very important to test a 3x3 matrix since we provide a special path for it 136c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_1( selfadjointeigensolver(Matrix3f()) ); 137c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) ); 138c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(7,7)) ); 139c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_4( selfadjointeigensolver(MatrixXcd(5,5)) ); 140c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_5( selfadjointeigensolver(MatrixXd(19,19)) ); 141c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 142c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_6( eigensolver(Matrix4f()) ); 143c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_5( eigensolver(MatrixXd(17,17)) ); 144c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 145c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 146c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 147