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 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 }