eigensolver_complex.cpp File Reference

#include "main.h"
#include <limits>
#include <Eigen/Eigenvalues>
#include <Eigen/LU>

Functions
template<typename MatrixType >
bool	find_pivot (typename MatrixType::Scalar tol, MatrixType &diffs, Index col=0)
template<typename VectorType >
void	verify_is_approx_upto_permutation (const VectorType &vec1, const VectorType &vec2)
template<typename MatrixType >
void	eigensolver (const MatrixType &m)
template<typename MatrixType >
void	eigensolver_verify_assert (const MatrixType &m)
	EIGEN_DECLARE_TEST (eigensolver_complex)

Function Documentation

EIGEN_DECLARE_TEST()

EIGEN_DECLARE_TEST

(

eigensolver_complex

)

                                        {
  int s = 0;
  for (int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1(eigensolver(Matrix4cf()));
    s = internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 4);
    CALL_SUBTEST_2(eigensolver(MatrixXcd(s, s)));
    CALL_SUBTEST_3(eigensolver(Matrix<std::complex<float>, 1, 1>()));
    CALL_SUBTEST_4(eigensolver(Matrix3f()));
    TEST_SET_BUT_UNUSED_VARIABLE(s)
  }
  CALL_SUBTEST_1(eigensolver_verify_assert(Matrix4cf()));
  s = internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 4);
  CALL_SUBTEST_2(eigensolver_verify_assert(MatrixXcd(s, s)));
  CALL_SUBTEST_3(eigensolver_verify_assert(Matrix<std::complex<float>, 1, 1>()));
  CALL_SUBTEST_4(eigensolver_verify_assert(Matrix3f()));
 
  // Test problem size constructors
  CALL_SUBTEST_5(ComplexEigenSolver<MatrixXf> tmp(s));
 
  TEST_SET_BUT_UNUSED_VARIABLE(s)
}

References CALL_SUBTEST_1, CALL_SUBTEST_2, CALL_SUBTEST_3, CALL_SUBTEST_4, CALL_SUBTEST_5, EIGEN_TEST_MAX_SIZE, eigensolver(), eigensolver_verify_assert(), Eigen::g_repeat, i, s, TEST_SET_BUT_UNUSED_VARIABLE, and tmp.

eigensolver()

template<typename MatrixType >

void eigensolver

(

const MatrixType &

m

)

                                      {
  /* this test covers the following files:
     ComplexEigenSolver.h, and indirectly ComplexSchur.h
  */
  Index rows = m.rows();
  Index cols = m.cols();
 
  typedef typename MatrixType::Scalar Scalar;
  typedef typename NumTraits<Scalar>::Real RealScalar;
 
  MatrixType a = MatrixType::Random(rows, cols);
  MatrixType symmA = a.adjoint() * a;
 
  ComplexEigenSolver<MatrixType> ei0(symmA);
  VERIFY_IS_EQUAL(ei0.info(), Success);
  VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal());
 
  ComplexEigenSolver<MatrixType> ei1(a);
  VERIFY_IS_EQUAL(ei1.info(), Success);
  VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
  // Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus
  // another algorithm so results may differ slightly
  verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues());
 
  ComplexEigenSolver<MatrixType> ei2;
  ei2.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);
  VERIFY_IS_EQUAL(ei2.info(), Success);
  VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());
  VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());
  if (rows > 2) {
    ei2.setMaxIterations(1).compute(a);
    VERIFY_IS_EQUAL(ei2.info(), NoConvergence);
    VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);
  }
 
  ComplexEigenSolver<MatrixType> eiNoEivecs(a, false);
  VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
  VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
 
  // Regression test for issue #66
  MatrixType z = MatrixType::Zero(rows, cols);
  ComplexEigenSolver<MatrixType> eiz(z);
  VERIFY((eiz.eigenvalues().cwiseEqual(0)).all());
 
  MatrixType id = MatrixType::Identity(rows, cols);
  VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
 
  if (rows > 1 && rows < 20) {
    // Test matrix with NaN
    a(0, 0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
    ComplexEigenSolver<MatrixType> eiNaN(a);
    VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
  }
 
  // regression test for bug 1098
  {
    ComplexEigenSolver<MatrixType> eig(a.adjoint() * a);
    eig.compute(a.adjoint() * a);
  }
 
  // regression test for bug 478
  {
    a.setZero();
    ComplexEigenSolver<MatrixType> ei3(a);
    VERIFY_IS_EQUAL(ei3.info(), Success);
    VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(), RealScalar(1));
    VERIFY((ei3.eigenvectors().transpose() * ei3.eigenvectors().transpose()).eval().isIdentity());
  }
}

References a, cols, Eigen::ComplexEigenSolver< MatrixType_ >::compute(), Eigen::ComplexEigenSolver< MatrixType_ >::eigenvalues(), Eigen::ComplexEigenSolver< MatrixType_ >::eigenvectors(), Eigen::ComplexEigenSolver< MatrixType_ >::getMaxIterations(), Eigen::ComplexEigenSolver< MatrixType_ >::info(), m, Eigen::NoConvergence, rows, Eigen::ComplexEigenSolver< MatrixType_ >::setMaxIterations(), Eigen::Success, VERIFY, VERIFY_IS_APPROX, verify_is_approx_upto_permutation(), VERIFY_IS_EQUAL, VERIFY_IS_MUCH_SMALLER_THAN, and oomph::PseudoSolidHelper::Zero.

Referenced by EIGEN_DECLARE_TEST(), and main().

eigensolver_verify_assert()

template<typename MatrixType >

void eigensolver_verify_assert

(

const MatrixType &

m

)

                                                    {
  ComplexEigenSolver<MatrixType> eig;
  VERIFY_RAISES_ASSERT(eig.eigenvectors());
  VERIFY_RAISES_ASSERT(eig.eigenvalues());
 
  MatrixType a = MatrixType::Random(m.rows(), m.cols());
  eig.compute(a, false);
  VERIFY_RAISES_ASSERT(eig.eigenvectors());
}

References a, Eigen::ComplexEigenSolver< MatrixType_ >::compute(), Eigen::ComplexEigenSolver< MatrixType_ >::eigenvalues(), Eigen::ComplexEigenSolver< MatrixType_ >::eigenvectors(), m, and VERIFY_RAISES_ASSERT.

Referenced by EIGEN_DECLARE_TEST().

find_pivot()

template<typename MatrixType >

bool find_pivot	(	typename MatrixType::Scalar	tol,
		MatrixType &	diffs,
		Index	col = 0
	)

                                                                                 {
  bool match = diffs.diagonal().sum() <= tol;
  if (match || col == diffs.cols()) {
    return match;
  } else {
    Index n = diffs.cols();
    std::vector<std::pair<Index, Index> > transpositions;
    for (Index i = col; i < n; ++i) {
      Index best_index(0);
      if (diffs.col(col).segment(col, n - i).minCoeff(&best_index) > tol) break;
 
      best_index += col;
 
      diffs.row(col).swap(diffs.row(best_index));
      if (find_pivot(tol, diffs, col + 1)) return true;
      diffs.row(col).swap(diffs.row(best_index));
 
      // move current pivot to the end
      diffs.row(n - (i - col) - 1).swap(diffs.row(best_index));
      transpositions.push_back(std::pair<Index, Index>(n - (i - col) - 1, best_index));
    }
    // restore
    for (Index k = transpositions.size() - 1; k >= 0; --k)
      diffs.row(transpositions[k].first).swap(diffs.row(transpositions[k].second));
  }
  return false;
}

References col(), i, k, match(), and n.

Referenced by verify_is_approx_upto_permutation().

verify_is_approx_upto_permutation()

template<typename VectorType >

void verify_is_approx_upto_permutation	(	const VectorType &	vec1,
		const VectorType &	vec2
	)

                                                                                       {
  typedef typename VectorType::Scalar Scalar;
  typedef typename NumTraits<Scalar>::Real RealScalar;
 
  VERIFY(vec1.cols() == 1);
  VERIFY(vec2.cols() == 1);
  VERIFY(vec1.rows() == vec2.rows());
 
  Index n = vec1.rows();
  RealScalar tol = test_precision<RealScalar>() * test_precision<RealScalar>() *
                   numext::maxi(vec1.squaredNorm(), vec2.squaredNorm());
  Matrix<RealScalar, Dynamic, Dynamic> diffs =
      (vec1.rowwise().replicate(n) - vec2.rowwise().replicate(n).transpose()).cwiseAbs2();
 
  VERIFY(find_pivot(tol, diffs));
}

References find_pivot(), Eigen::numext::maxi(), n, vec1(), and VERIFY.

Referenced by eigensolver().