RealDiracMatrix.h

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//
// Class: RealDiracMatrix
//   Real Dirac matrix class.
//   They're ordered after the paper of Dr. C. Baumgarten: "Use of real Dirac matrices in two-dimensional coupled linear optics".
//   The diagonalizing method is based on the paper "Geometrical method of decoupling" (2012) of Dr. C. Baumgarten.
//
// Copyright (c) 2014, 2020 Christian Baumgarten, Paul Scherrer Institut, Villigen PSI, Switzerland
//                          Matthias Frey, ETH Zürich
// All rights reserved
//
// Implemented as part of the Semester thesis by Matthias Frey
// "Matched Distributions in Cyclotrons"
//
// This file is part of OPAL.
//
// OPAL is free software: 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 3 of the License, or
// (at your option) any later version.
//
// You should have received a copy of the GNU General Public License
// along with OPAL. If not, see <https://www.gnu.org/licenses/>.
//
#ifndef RDM_H
#define RDM_H
 
#include <boost/numeric/ublas/matrix_sparse.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/vector.hpp>
 
class RealDiracMatrix
{
public:
    typedef boost::numeric::ublas::compressed_matrix<
        double,
        boost::numeric::ublas::row_major
    > sparse_matrix_t;
 
    typedef boost::numeric::ublas::matrix<double> matrix_t;
    typedef boost::numeric::ublas::vector<
        double,
        std::vector<double>
    > vector_t;
 
    RealDiracMatrix();
 
    sparse_matrix_t getRDM(short);
 
    void diagonalize(matrix_t&, sparse_matrix_t&, sparse_matrix_t&);
 
    sparse_matrix_t diagonalize(matrix_t&);
 
    matrix_t symplex(const matrix_t&);
 
private:
    void transform(matrix_t&, short, double, sparse_matrix_t&, sparse_matrix_t&);
 
    void transform(short, double, sparse_matrix_t&, sparse_matrix_t&);
 
    void update(matrix_t& sigma, short i, sparse_matrix_t& R, sparse_matrix_t& invR);
};
 
#endif