cart-elc

Source code for CART-ELC
git clone git://git.laack.co/cart-elc.git
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eigensolver_generalized_real.cpp (4046B)

      1 // This file is part of Eigen, a lightweight C++ template library
      2 // for linear algebra.
      3 //
      4 // Copyright (C) 2012-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
      5 //
      6 // This Source Code Form is subject to the terms of the Mozilla
      7 // Public License v. 2.0. If a copy of the MPL was not distributed
      8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
      9 
     10 #define EIGEN_RUNTIME_NO_MALLOC
     11 #include "main.h"
     12 #include <limits>
     13 #include <Eigen/Eigenvalues>
     14 #include <Eigen/LU>
     15 
     16 template<typename MatrixType> void generalized_eigensolver_real(const MatrixType& m)
     17 {
     18   /* this test covers the following files:
     19      GeneralizedEigenSolver.h
     20   */
     21   Index rows = m.rows();
     22   Index cols = m.cols();
     23 
     24   typedef typename MatrixType::Scalar Scalar;
     25   typedef std::complex<Scalar> ComplexScalar;
     26   typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
     27 
     28   MatrixType a = MatrixType::Random(rows,cols);
     29   MatrixType b = MatrixType::Random(rows,cols);
     30   MatrixType a1 = MatrixType::Random(rows,cols);
     31   MatrixType b1 = MatrixType::Random(rows,cols);
     32   MatrixType spdA =  a.adjoint() * a + a1.adjoint() * a1;
     33   MatrixType spdB =  b.adjoint() * b + b1.adjoint() * b1;
     34 
     35   // lets compare to GeneralizedSelfAdjointEigenSolver
     36   {
     37     GeneralizedSelfAdjointEigenSolver<MatrixType> symmEig(spdA, spdB);
     38     GeneralizedEigenSolver<MatrixType> eig(spdA, spdB);
     39 
     40     VERIFY_IS_EQUAL(eig.eigenvalues().imag().cwiseAbs().maxCoeff(), 0);
     41 
     42     VectorType realEigenvalues = eig.eigenvalues().real();
     43     std::sort(realEigenvalues.data(), realEigenvalues.data()+realEigenvalues.size());
     44     VERIFY_IS_APPROX(realEigenvalues, symmEig.eigenvalues());
     45 
     46     // check eigenvectors
     47     typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType D = eig.eigenvalues().asDiagonal();
     48     typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType V = eig.eigenvectors();
     49     VERIFY_IS_APPROX(spdA*V, spdB*V*D);
     50   }
     51 
     52   // non symmetric case:
     53   {
     54     GeneralizedEigenSolver<MatrixType> eig(rows);
     55     // TODO enable full-prealocation of required memory, this probably requires an in-place mode for HessenbergDecomposition
     56     //Eigen::internal::set_is_malloc_allowed(false);
     57     eig.compute(a,b);
     58     //Eigen::internal::set_is_malloc_allowed(true);
     59     for(Index k=0; k<cols; ++k)
     60     {
     61       Matrix<ComplexScalar,Dynamic,Dynamic> tmp = (eig.betas()(k)*a).template cast<ComplexScalar>() - eig.alphas()(k)*b;
     62       if(tmp.size()>1 && tmp.norm()>(std::numeric_limits<Scalar>::min)())
     63         tmp /= tmp.norm();
     64       VERIFY_IS_MUCH_SMALLER_THAN( std::abs(tmp.determinant()), Scalar(1) );
     65     }
     66     // check eigenvectors
     67     typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType D = eig.eigenvalues().asDiagonal();
     68     typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType V = eig.eigenvectors();
     69     VERIFY_IS_APPROX(a*V, b*V*D);
     70   }
     71 
     72   // regression test for bug 1098
     73   {
     74     GeneralizedSelfAdjointEigenSolver<MatrixType> eig1(a.adjoint() * a,b.adjoint() * b);
     75     eig1.compute(a.adjoint() * a,b.adjoint() * b);
     76     GeneralizedEigenSolver<MatrixType> eig2(a.adjoint() * a,b.adjoint() * b);
     77     eig2.compute(a.adjoint() * a,b.adjoint() * b);
     78   }
     79 
     80   // check without eigenvectors
     81   {
     82     GeneralizedEigenSolver<MatrixType> eig1(spdA, spdB, true);
     83     GeneralizedEigenSolver<MatrixType> eig2(spdA, spdB, false);
     84     VERIFY_IS_APPROX(eig1.eigenvalues(), eig2.eigenvalues());
     85   }
     86 }
     87 
     88 EIGEN_DECLARE_TEST(eigensolver_generalized_real)
     89 {
     90   for(int i = 0; i < g_repeat; i++) {
     91     int s = 0;
     92     CALL_SUBTEST_1( generalized_eigensolver_real(Matrix4f()) );
     93     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
     94     CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(s,s)) );
     95 
     96     // some trivial but implementation-wise special cases
     97     CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(1,1)) );
     98     CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(2,2)) );
     99     CALL_SUBTEST_3( generalized_eigensolver_real(Matrix<double,1,1>()) );
    100     CALL_SUBTEST_4( generalized_eigensolver_real(Matrix2d()) );
    101     TEST_SET_BUT_UNUSED_VARIABLE(s)
    102   }
    103 }