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

   1 // This file is part of Eigen, a lightweight C++ template library
   2 // for linear algebra.
   3 //
   4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
   5 // Copyright (C) 2010,2012 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
  15 template<typename MatrixType> void eigensolver(const MatrixType& m)
  16 {
  17   typedef typename MatrixType::Index Index;
  18   /* this test covers the following files:
  19      EigenSolver.h
  20   */
  21   Index rows = m.rows();
  22   Index cols = m.cols();
  23
  24   typedef typename MatrixType::Scalar Scalar;
  25   typedef typename NumTraits<Scalar>::Real RealScalar;
  26   typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;
  27   typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex;
  28
  29   MatrixType a = MatrixType::Random(rows,cols);
  30   MatrixType a1 = MatrixType::Random(rows,cols);
  31   MatrixType symmA =  a.adjoint() * a + a1.adjoint() * a1;
  32
  33   EigenSolver<MatrixType> ei0(symmA);
  34   VERIFY_IS_EQUAL(ei0.info(), Success);
  35   VERIFY_IS_APPROX(symmA * ei0.pseudoEigenvectors(), ei0.pseudoEigenvectors() * ei0.pseudoEigenvalueMatrix());
  36   VERIFY_IS_APPROX((symmA.template cast<Complex>()) * (ei0.pseudoEigenvectors().template cast<Complex>()),
  37     (ei0.pseudoEigenvectors().template cast<Complex>()) * (ei0.eigenvalues().asDiagonal()));
  38
  39   EigenSolver<MatrixType> ei1(a);
  40   VERIFY_IS_EQUAL(ei1.info(), Success);
  41   VERIFY_IS_APPROX(a * ei1.pseudoEigenvectors(), ei1.pseudoEigenvectors() * ei1.pseudoEigenvalueMatrix());
  42   VERIFY_IS_APPROX(a.template cast<Complex>() * ei1.eigenvectors(),
  43                    ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
  44   VERIFY_IS_APPROX(ei1.eigenvectors().colwise().norm(), RealVectorType::Ones(rows).transpose());
  45   VERIFY_IS_APPROX(a.eigenvalues(), ei1.eigenvalues());
  46
  47   EigenSolver<MatrixType> ei2;
  48   ei2.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);
  49   VERIFY_IS_EQUAL(ei2.info(), Success);
  50   VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());
  51   VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());
  52   if (rows > 2) {
  53     ei2.setMaxIterations(1).compute(a);
  54     VERIFY_IS_EQUAL(ei2.info(), NoConvergence);
  55     VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);
  56   }
  57
  58   EigenSolver<MatrixType> eiNoEivecs(a, false);
  59   VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
  60   VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
  61   VERIFY_IS_APPROX(ei1.pseudoEigenvalueMatrix(), eiNoEivecs.pseudoEigenvalueMatrix());
  62
  63   MatrixType id = MatrixType::Identity(rows, cols);
  64   VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
  65
  66   if (rows > 2)
  67   {
  68     // Test matrix with NaN
  69     a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
  70     EigenSolver<MatrixType> eiNaN(a);
  71     VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
  72   }
  73 }
  74
  75 template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
  76 {
  77   EigenSolver<MatrixType> eig;
  78   VERIFY_RAISES_ASSERT(eig.eigenvectors());
  79   VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
  80   VERIFY_RAISES_ASSERT(eig.pseudoEigenvalueMatrix());
  81   VERIFY_RAISES_ASSERT(eig.eigenvalues());
  82
  83   MatrixType a = MatrixType::Random(m.rows(),m.cols());
  84   eig.compute(a, false);
  85   VERIFY_RAISES_ASSERT(eig.eigenvectors());
  86   VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
  87 }
  88
  89 void test_eigensolver_generic()
  90 {
  91   int s = 0;
  92   for(int i = 0; i < g_repeat; i++) {
  93     CALL_SUBTEST_1( eigensolver(Matrix4f()) );
  94     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
  95     CALL_SUBTEST_2( eigensolver(MatrixXd(s,s)) );
  96
  97     // some trivial but implementation-wise tricky cases
  98     CALL_SUBTEST_2( eigensolver(MatrixXd(1,1)) );
  99     CALL_SUBTEST_2( eigensolver(MatrixXd(2,2)) );
 100     CALL_SUBTEST_3( eigensolver(Matrix<double,1,1>()) );
 101     CALL_SUBTEST_4( eigensolver(Matrix2d()) );
 102   }
 103
 104   CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4f()) );
 105   s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
 106   CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXd(s,s)) );
 107   CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<double,1,1>()) );
 108   CALL_SUBTEST_4( eigensolver_verify_assert(Matrix2d()) );
 109
 110   // Test problem size constructors
 111   CALL_SUBTEST_5(EigenSolver<MatrixXf> tmp(s));
 112
 113   // regression test for bug 410
 114   CALL_SUBTEST_2(
 115   {
 116      MatrixXd A(1,1);
 117      A(0,0) = std::sqrt(-1.);
 118      Eigen::EigenSolver<MatrixXd> solver(A);
 119      MatrixXd V(1, 1);
 120      V(0,0) = solver.eigenvectors()(0,0).real();
 121   }
 122   );
 123
 124   TEST_SET_BUT_UNUSED_VARIABLE(s)
 125 }