2009-03-23 22:38:59 +08:00
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// This file is part of Eigen, a lightweight C++ template library
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2009-05-23 02:25:33 +08:00
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// for linear algebra.
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2009-03-23 22:38:59 +08:00
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//
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2010-06-25 05:21:58 +08:00
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// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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2012-07-24 22:17:59 +08:00
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// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
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2009-03-23 22:38:59 +08:00
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//
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2012-07-14 02:42:47 +08:00
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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2009-03-23 22:38:59 +08:00
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#include "main.h"
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2010-06-04 05:59:57 +08:00
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#include <limits>
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2009-09-04 15:23:38 +08:00
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#include <Eigen/Eigenvalues>
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2009-03-23 22:38:59 +08:00
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2018-12-13 00:30:08 +08:00
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template<typename EigType,typename MatType>
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void check_eigensolver_for_given_mat(const EigType &eig, const MatType& a)
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{
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typedef typename NumTraits<typename MatType::Scalar>::Real RealScalar;
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typedef Matrix<RealScalar, MatType::RowsAtCompileTime, 1> RealVectorType;
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typedef typename std::complex<RealScalar> Complex;
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Index n = a.rows();
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VERIFY_IS_EQUAL(eig.info(), Success);
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VERIFY_IS_APPROX(a * eig.pseudoEigenvectors(), eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix());
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VERIFY_IS_APPROX(a.template cast<Complex>() * eig.eigenvectors(),
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eig.eigenvectors() * eig.eigenvalues().asDiagonal());
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VERIFY_IS_APPROX(eig.eigenvectors().colwise().norm(), RealVectorType::Ones(n).transpose());
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VERIFY_IS_APPROX(a.eigenvalues(), eig.eigenvalues());
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}
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2009-03-23 22:38:59 +08:00
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template<typename MatrixType> void eigensolver(const MatrixType& m)
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{
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/* this test covers the following files:
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EigenSolver.h
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*/
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2010-06-20 23:37:56 +08:00
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Index rows = m.rows();
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Index cols = m.cols();
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2009-03-23 22:38:59 +08:00
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typedef typename MatrixType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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typedef typename std::complex<RealScalar> Complex;
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2009-03-23 22:38:59 +08:00
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MatrixType a = MatrixType::Random(rows,cols);
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MatrixType a1 = MatrixType::Random(rows,cols);
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MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
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EigenSolver<MatrixType> ei0(symmA);
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2010-06-04 05:59:57 +08:00
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VERIFY_IS_EQUAL(ei0.info(), Success);
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2009-03-23 22:38:59 +08:00
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VERIFY_IS_APPROX(symmA * ei0.pseudoEigenvectors(), ei0.pseudoEigenvectors() * ei0.pseudoEigenvalueMatrix());
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VERIFY_IS_APPROX((symmA.template cast<Complex>()) * (ei0.pseudoEigenvectors().template cast<Complex>()),
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(ei0.pseudoEigenvectors().template cast<Complex>()) * (ei0.eigenvalues().asDiagonal()));
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EigenSolver<MatrixType> ei1(a);
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2018-12-13 00:30:08 +08:00
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CALL_SUBTEST( check_eigensolver_for_given_mat(ei1,a) );
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2009-03-23 22:38:59 +08:00
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2012-07-24 22:17:59 +08:00
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EigenSolver<MatrixType> ei2;
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2012-07-29 04:30:09 +08:00
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ei2.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);
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2012-07-24 22:17:59 +08:00
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VERIFY_IS_EQUAL(ei2.info(), Success);
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VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());
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VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());
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if (rows > 2) {
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2012-07-29 04:30:09 +08:00
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ei2.setMaxIterations(1).compute(a);
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2012-07-24 22:17:59 +08:00
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VERIFY_IS_EQUAL(ei2.info(), NoConvergence);
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2012-07-29 04:30:09 +08:00
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VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);
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2012-07-24 22:17:59 +08:00
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}
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2010-06-01 01:17:47 +08:00
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EigenSolver<MatrixType> eiNoEivecs(a, false);
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2010-06-04 05:59:57 +08:00
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VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
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2010-06-01 01:17:47 +08:00
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VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
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VERIFY_IS_APPROX(ei1.pseudoEigenvalueMatrix(), eiNoEivecs.pseudoEigenvalueMatrix());
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2010-05-25 00:43:50 +08:00
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MatrixType id = MatrixType::Identity(rows, cols);
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VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
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2010-06-04 05:59:57 +08:00
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2015-10-31 01:06:03 +08:00
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if (rows > 2 && rows < 20)
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2010-06-04 05:59:57 +08:00
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{
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// Test matrix with NaN
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a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
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EigenSolver<MatrixType> eiNaN(a);
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VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
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}
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2015-10-26 23:00:25 +08:00
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// regression test for bug 1098
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{
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EigenSolver<MatrixType> eig(a.adjoint() * a);
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eig.compute(a.adjoint() * a);
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}
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2017-01-31 21:22:42 +08:00
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// regression test for bug 478
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{
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a.setZero();
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EigenSolver<MatrixType> ei3(a);
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VERIFY_IS_EQUAL(ei3.info(), Success);
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VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1));
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VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity());
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}
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2009-03-23 22:38:59 +08:00
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}
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2010-06-01 01:17:47 +08:00
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template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
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2009-05-22 20:27:58 +08:00
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{
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EigenSolver<MatrixType> eig;
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2010-06-01 01:17:47 +08:00
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VERIFY_RAISES_ASSERT(eig.eigenvectors());
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VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
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VERIFY_RAISES_ASSERT(eig.pseudoEigenvalueMatrix());
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VERIFY_RAISES_ASSERT(eig.eigenvalues());
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MatrixType a = MatrixType::Random(m.rows(),m.cols());
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eig.compute(a, false);
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VERIFY_RAISES_ASSERT(eig.eigenvectors());
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VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
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2009-05-22 20:27:58 +08:00
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}
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2018-12-13 00:30:08 +08:00
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template<typename CoeffType>
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Matrix<typename CoeffType::Scalar,Dynamic,Dynamic>
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make_companion(const CoeffType& coeffs)
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{
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Index n = coeffs.size()-1;
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Matrix<typename CoeffType::Scalar,Dynamic,Dynamic> res(n,n);
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res.setZero();
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res.row(0) = -coeffs.tail(n) / coeffs(0);
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res.diagonal(-1).setOnes();
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return res;
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}
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2018-07-17 21:52:58 +08:00
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template<int>
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void eigensolver_generic_extra()
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{
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{
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// regression test for bug 793
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MatrixXd a(3,3);
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a << 0, 0, 1,
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1, 1, 1,
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1, 1e+200, 1;
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Eigen::EigenSolver<MatrixXd> eig(a);
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double scale = 1e-200; // scale to avoid overflow during the comparisons
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VERIFY_IS_APPROX(a * eig.pseudoEigenvectors()*scale, eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()*scale);
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VERIFY_IS_APPROX(a * eig.eigenvectors()*scale, eig.eigenvectors() * eig.eigenvalues().asDiagonal()*scale);
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}
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{
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// check a case where all eigenvalues are null.
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MatrixXd a(2,2);
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a << 1, 1,
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-1, -1;
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Eigen::EigenSolver<MatrixXd> eig(a);
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VERIFY_IS_APPROX(eig.pseudoEigenvectors().squaredNorm(), 2.);
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VERIFY_IS_APPROX((a * eig.pseudoEigenvectors()).norm()+1., 1.);
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VERIFY_IS_APPROX((eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()).norm()+1., 1.);
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VERIFY_IS_APPROX((a * eig.eigenvectors()).norm()+1., 1.);
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VERIFY_IS_APPROX((eig.eigenvectors() * eig.eigenvalues().asDiagonal()).norm()+1., 1.);
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}
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2018-12-13 00:30:08 +08:00
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// regression test for bug 933
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{
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{
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VectorXd coeffs(5); coeffs << 1, -3, -175, -225, 2250;
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MatrixXd C = make_companion(coeffs);
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EigenSolver<MatrixXd> eig(C);
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CALL_SUBTEST( check_eigensolver_for_given_mat(eig,C) );
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}
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{
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// this test is tricky because it requires high accuracy in smallest eigenvalues
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VectorXd coeffs(5); coeffs << 6.154671e-15, -1.003870e-10, -9.819570e-01, 3.995715e+03, 2.211511e+08;
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MatrixXd C = make_companion(coeffs);
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EigenSolver<MatrixXd> eig(C);
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CALL_SUBTEST( check_eigensolver_for_given_mat(eig,C) );
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Index n = C.rows();
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for(Index i=0;i<n;++i)
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{
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typedef std::complex<double> Complex;
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MatrixXcd ac = C.cast<Complex>();
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ac.diagonal().array() -= eig.eigenvalues()(i);
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VectorXd sv = ac.jacobiSvd().singularValues();
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// comparing to sv(0) is not enough here to catch the "bug",
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// the hard-coded 1.0 is important!
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VERIFY_IS_MUCH_SMALLER_THAN(sv(n-1), 1.0);
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}
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}
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}
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// regression test for bug 1557
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{
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// this test is interesting because it contains zeros on the diagonal.
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MatrixXd A_bug1557(3,3);
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A_bug1557 << 0, 0, 0, 1, 0, 0.5887907064808635127, 0, 1, 0;
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EigenSolver<MatrixXd> eig(A_bug1557);
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CALL_SUBTEST( check_eigensolver_for_given_mat(eig,A_bug1557) );
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}
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2018-07-17 21:52:58 +08:00
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}
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2018-07-17 20:46:15 +08:00
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EIGEN_DECLARE_TEST(eigensolver_generic)
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2009-03-23 22:38:59 +08:00
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{
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2013-06-24 01:11:32 +08:00
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int s = 0;
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2009-03-23 22:38:59 +08:00
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for(int i = 0; i < g_repeat; i++) {
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2009-10-29 06:19:29 +08:00
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CALL_SUBTEST_1( eigensolver(Matrix4f()) );
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2011-07-12 20:41:00 +08:00
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s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
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CALL_SUBTEST_2( eigensolver(MatrixXd(s,s)) );
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2015-02-18 18:30:44 +08:00
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TEST_SET_BUT_UNUSED_VARIABLE(s)
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2009-03-23 22:38:59 +08:00
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// some trivial but implementation-wise tricky cases
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2009-10-29 06:19:29 +08:00
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CALL_SUBTEST_2( eigensolver(MatrixXd(1,1)) );
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CALL_SUBTEST_2( eigensolver(MatrixXd(2,2)) );
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CALL_SUBTEST_3( eigensolver(Matrix<double,1,1>()) );
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CALL_SUBTEST_4( eigensolver(Matrix2d()) );
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2009-03-23 22:38:59 +08:00
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}
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2010-06-01 01:17:47 +08:00
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CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4f()) );
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2011-07-12 20:41:00 +08:00
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s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
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CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXd(s,s)) );
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2010-06-01 01:17:47 +08:00
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CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<double,1,1>()) );
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CALL_SUBTEST_4( eigensolver_verify_assert(Matrix2d()) );
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2010-04-21 23:15:57 +08:00
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// Test problem size constructors
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2013-06-24 01:11:32 +08:00
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CALL_SUBTEST_5(EigenSolver<MatrixXf> tmp(s));
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2012-01-26 02:02:31 +08:00
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// regression test for bug 410
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CALL_SUBTEST_2(
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{
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MatrixXd A(1,1);
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2014-06-02 18:42:42 +08:00
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A(0,0) = std::sqrt(-1.); // is Not-a-Number
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2012-01-26 02:02:31 +08:00
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Eigen::EigenSolver<MatrixXd> solver(A);
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2014-06-02 18:42:42 +08:00
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VERIFY_IS_EQUAL(solver.info(), NumericalIssue);
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2012-01-26 02:02:31 +08:00
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}
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);
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2011-10-31 11:55:20 +08:00
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2018-07-17 21:52:58 +08:00
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CALL_SUBTEST_2( eigensolver_generic_extra<0>() );
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2014-04-14 17:43:08 +08:00
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2013-06-25 17:42:04 +08:00
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TEST_SET_BUT_UNUSED_VARIABLE(s)
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2009-05-22 20:27:58 +08:00
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}
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