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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Claire Maurice
// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_COMPLEX_EIGEN_SOLVER_H
#define EIGEN_COMPLEX_EIGEN_SOLVER_H
/** \eigenvalues_module \ingroup Eigenvalues_Module
* \nonstableyet
*
* \class ComplexEigenSolver
*
* \brief Eigen values/vectors solver for general complex matrices
*
* \param MatrixType the type of the matrix of which we are computing the eigen decomposition
*
* \sa class EigenSolver, class SelfAdjointEigenSolver
*/
template<typename _MatrixType> class ComplexEigenSolver
{
public:
typedef _MatrixType MatrixType;
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef std::complex<RealScalar> Complex;
typedef Matrix<Complex, MatrixType::ColsAtCompileTime,1> EigenvalueType;
typedef Matrix<Complex, MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime> EigenvectorType;
/**
* \brief Default Constructor.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via ComplexEigenSolver::compute(const MatrixType&).
*/
ComplexEigenSolver() : m_eivec(), m_eivalues(), m_isInitialized(false)
{}
ComplexEigenSolver(const MatrixType& matrix)
: m_eivec(matrix.rows(),matrix.cols()),
m_eivalues(matrix.cols()),
m_isInitialized(false)
{
compute(matrix);
}
EigenvectorType eigenvectors(void) const
{
ei_assert(m_isInitialized && "ComplexEigenSolver is not initialized.");
return m_eivec;
}
EigenvalueType eigenvalues() const
{
ei_assert(m_isInitialized && "ComplexEigenSolver is not initialized.");
return m_eivalues;
}
void compute(const MatrixType& matrix);
protected:
MatrixType m_eivec;
EigenvalueType m_eivalues;
bool m_isInitialized;
};
template<typename MatrixType>
void ComplexEigenSolver<MatrixType>::compute(const MatrixType& matrix)
{
// this code is inspired from Jampack
assert(matrix.cols() == matrix.rows());
int n = matrix.cols();
m_eivalues.resize(n,1);
m_eivec.resize(n,n);
RealScalar eps = epsilon<RealScalar>();
// Reduce to complex Schur form
ComplexSchur<MatrixType> schur(matrix);
m_eivalues = schur.matrixT().diagonal();
m_eivec.setZero();
Scalar d2, z;
RealScalar norm = matrix.norm();
// compute the (normalized) eigenvectors
for(int k=n-1 ; k>=0 ; k--)
{
d2 = schur.matrixT().coeff(k,k);
m_eivec.coeffRef(k,k) = Scalar(1.0,0.0);
for(int i=k-1 ; i>=0 ; i--)
{
m_eivec.coeffRef(i,k) = -schur.matrixT().coeff(i,k);
if(k-i-1>0)
m_eivec.coeffRef(i,k) -= (schur.matrixT().row(i).segment(i+1,k-i-1) * m_eivec.col(k).segment(i+1,k-i-1)).value();
z = schur.matrixT().coeff(i,i) - d2;
if(z==Scalar(0))
ei_real_ref(z) = eps * norm;
m_eivec.coeffRef(i,k) = m_eivec.coeff(i,k) / z;
}
m_eivec.col(k).normalize();
}
m_eivec = schur.matrixU() * m_eivec;
m_isInitialized = true;
// sort the eigenvalues
{
for (int i=0; i<n; i++)
{
int k;
m_eivalues.cwise().abs().tail(n-i).minCoeff(&k);
if (k != 0)
{
k += i;
std::swap(m_eivalues[k],m_eivalues[i]);
m_eivec.col(i).swap(m_eivec.col(k));
}
}
}
}
#endif // EIGEN_COMPLEX_EIGEN_SOLVER_H
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