ground/gcs/src/libs/eigen/test/eigensolver_complex.cpp

   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@inria.fr>
   5 // Copyright (C) 2010 Jitse Niesen <jitse@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
  45   MatrixType a = MatrixType::Random(rows,cols);
  46   MatrixType symmA =  a.adjoint() * a;
  47
  48   ComplexEigenSolver<MatrixType> ei0(symmA);
  49   VERIFY_IS_EQUAL(ei0.info(), Success);
  50   VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal());
  51
  52   ComplexEigenSolver<MatrixType> ei1(a);
  53   VERIFY_IS_EQUAL(ei1.info(), Success);
  54   VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
  55   // Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus
  56   // another algorithm so results may differ slightly
  57   verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues());
  58
  59   ComplexEigenSolver<MatrixType> ei2;
  60   ei2.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);
  61   VERIFY_IS_EQUAL(ei2.info(), Success);
  62   VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());
  63   VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());
  64   if (rows > 2) {
  65     ei2.setMaxIterations(1).compute(a);
  66     VERIFY_IS_EQUAL(ei2.info(), NoConvergence);
  67     VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);
  68   }
  69
  70   ComplexEigenSolver<MatrixType> eiNoEivecs(a, false);
  71   VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
  72   VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
  73
  74   // Regression test for issue #66
  75   MatrixType z = MatrixType::Zero(rows,cols);
  76   ComplexEigenSolver<MatrixType> eiz(z);
  77   VERIFY((eiz.eigenvalues().cwiseEqual(0)).all());
  78
  79   MatrixType id = MatrixType::Identity(rows, cols);
  80   VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
  81
  82   if (rows > 1)
  83   {
  84     // Test matrix with NaN
  85     a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
  86     ComplexEigenSolver<MatrixType> eiNaN(a);
  87     VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
  88   }
  89 }
  90
  91 template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
  92 {
  93   ComplexEigenSolver<MatrixType> eig;
  94   VERIFY_RAISES_ASSERT(eig.eigenvectors());
  95   VERIFY_RAISES_ASSERT(eig.eigenvalues());
  96
  97   MatrixType a = MatrixType::Random(m.rows(),m.cols());
  98   eig.compute(a, false);
  99   VERIFY_RAISES_ASSERT(eig.eigenvectors());
 100 }
 101
 102 void test_eigensolver_complex()
 103 {
 104   int s = 0;
 105   for(int i = 0; i < g_repeat; i++) {
 106     CALL_SUBTEST_1( eigensolver(Matrix4cf()) );
 107     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
 108     CALL_SUBTEST_2( eigensolver(MatrixXcd(s,s)) );
 109     CALL_SUBTEST_3( eigensolver(Matrix<std::complex<float>, 1, 1>()) );
 110     CALL_SUBTEST_4( eigensolver(Matrix3f()) );
 111   }
 112   CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4cf()) );
 113   s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
 114   CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXcd(s,s)) );
 115   CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<std::complex<float>, 1, 1>()) );
 116   CALL_SUBTEST_4( eigensolver_verify_assert(Matrix3f()) );
 117
 118   // Test problem size constructors
 119   CALL_SUBTEST_5(ComplexEigenSolver<MatrixXf> tmp(s));
 120
 121   TEST_SET_BUT_UNUSED_VARIABLE(s)
 122 }