gauss_legendre8_export.cpp

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/*
 *    This file is part of ACADO Toolkit.
 *
 *    ACADO Toolkit -- A Toolkit for Automatic Control and Dynamic Optimization.
 *    Copyright (C) 2008-2014 by Boris Houska, Hans Joachim Ferreau,
 *    Milan Vukov, Rien Quirynen, KU Leuven.
 *    Developed within the Optimization in Engineering Center (OPTEC)
 *    under supervision of Moritz Diehl. All rights reserved.
 *
 *    ACADO Toolkit 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.
 *
 *    ACADO Toolkit 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 for more details.
 *
 *    You should have received a copy of the GNU Lesser General Public
 *    License along with ACADO Toolkit; if not, write to the Free Software
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 */



#include <acado/code_generation/integrators/gauss_legendre8_export.hpp>

#include <acado/code_generation/export_algorithm_factory.hpp>

BEGIN_NAMESPACE_ACADO


//
// PUBLIC MEMBER FUNCTIONS:
//

GaussLegendre8Export::GaussLegendre8Export(     UserInteraction* _userInteraction,
                                                                        const std::string& _commonHeaderName
                                                                        ) : ImplicitRungeKuttaExport( _userInteraction,_commonHeaderName )
{
        numStages = 4;
}


GaussLegendre8Export::GaussLegendre8Export(     const GaussLegendre8Export& arg
                                                                        ) : ImplicitRungeKuttaExport( arg )
{
        numStages = 4;
        copy( arg );
}


GaussLegendre8Export::~GaussLegendre8Export( )
{
        clear( );
}


// PROTECTED:

//
// Register the integrator
//

IntegratorExport* createGaussLegendre8Export(   UserInteraction* _userInteraction,
                                                                                                const std::string &_commonHeaderName)
{
        DMatrix AA(4,4);
        DVector bb(4);
        DVector cc(4);

        AA(0,0) = (1/(double)144)*(double)sqrt((double)(double)30)+(double)1/(double)8;
        AA(0,1) = -(double)(1/(double)840)*(double)sqrt((double)(double)525-(double)70*(double)sqrt((double)(double)30))*(double)sqrt((double)(double)30)+(double)(1/(double)144)*(double)sqrt((double)(double)30)-(double)(1/(double)105)*(double)sqrt((double)(double)525-(double)70*(double)sqrt((double)(double)30))+(double)1/(double)8;           
        AA(0,2) = (1/(double)2352)*(double)sqrt((double)(double)525+(double)70*(double)sqrt((double)(double)30))*(double)sqrt((double)(double)30)-(double)(1/(double)144)*(double)sqrt((double)(double)30)+(double)(1/(double)1680)*(double)sqrt((double)(double)525-(double)70*(double)sqrt((double)(double)30))*(double)sqrt((double)(double)30)+(double)1/(double)8+(double)(1/(double)1470)*(double)sqrt((double)(double)525+(double)70*(double)sqrt((double)(double)30))-(double)(1/(double)420)*(double)sqrt((double)(double)525-(double)70*(double)sqrt((double)(double)30));    
        AA(0,3) = -(double)(1/(double)2352)*(double)sqrt((double)(double)525+(double)70*(double)sqrt((double)(double)30))*(double)sqrt((double)(double)30)-(double)(1/(double)144)*(double)sqrt((double)(double)30)+(double)(1/(double)1680)*(double)sqrt((double)(double)525-(double)70*(double)sqrt((double)(double)30))*(double)sqrt((double)(double)30)+(double)1/(double)8-(double)(1/(double)1470)*(double)sqrt((double)(double)525+(double)70*(double)sqrt((double)(double)30))-(double)(1/(double)420)*(double)sqrt((double)(double)525-(double)70*(double)sqrt((double)(double)30));
        AA(1,0) = (1/(double)840)*(double)sqrt((double)(double)525-(double)70*(double)sqrt((double)(double)30))*(double)sqrt((double)(double)30)+(double)(1/(double)144)*(double)sqrt((double)(double)30)+(double)(1/(double)105)*(double)sqrt((double)(double)525-(double)70*(double)sqrt((double)(double)30))+(double)1/(double)8;                    
        AA(1,1) = (1/(double)144)*(double)sqrt((double)(double)30)+(double)1/(double)8;         
        AA(1,2) = (1/(double)2352)*(double)sqrt((double)(double)525+(double)70*(double)sqrt((double)(double)30))*(double)sqrt((double)(double)30)-(double)(1/(double)144)*(double)sqrt((double)(double)30)-(double)(1/(double)1680)*(double)sqrt((double)(double)525-(double)70*(double)sqrt((double)(double)30))*(double)sqrt((double)(double)30)+(double)1/(double)8+(double)(1/(double)1470)*(double)sqrt((double)(double)525+(double)70*(double)sqrt((double)(double)30))+(double)(1/(double)420)*(double)sqrt((double)(double)525-(double)70*(double)sqrt((double)(double)30));
        AA(1,3) = -(double)(1/(double)2352)*(double)sqrt((double)(double)525+(double)70*(double)sqrt((double)(double)30))*(double)sqrt((double)(double)30)-(double)(1/(double)144)*(double)sqrt((double)(double)30)-(double)(1/(double)1680)*(double)sqrt((double)(double)525-(double)70*(double)sqrt((double)(double)30))*(double)sqrt((double)(double)30)+(double)1/(double)8-(double)(1/(double)1470)*(double)sqrt((double)(double)525+(double)70*(double)sqrt((double)(double)30))+(double)(1/(double)420)*(double)sqrt((double)(double)525-(double)70*(double)sqrt((double)(double)30));
        AA(2,0) = -(double)(1/(double)2352)*(double)sqrt((double)(double)525-(double)70*(double)sqrt((double)(double)30))*(double)sqrt((double)(double)30)+(double)(1/(double)144)*(double)sqrt((double)(double)30)-(double)(1/(double)1680)*(double)sqrt((double)(double)525+(double)70*(double)sqrt((double)(double)30))*(double)sqrt((double)(double)30)+(double)(1/(double)1470)*(double)sqrt((double)(double)525-(double)70*(double)sqrt((double)(double)30))+(double)1/(double)8-(double)(1/(double)420)*(double)sqrt((double)(double)525+(double)70*(double)sqrt((double)(double)30));   
        AA(2,1) = (1/(double)2352)*(double)sqrt((double)(double)525-(double)70*(double)sqrt((double)(double)30))*(double)sqrt((double)(double)30)+(double)(1/(double)144)*(double)sqrt((double)(double)30)-(double)(1/(double)1680)*(double)sqrt((double)(double)525+(double)70*(double)sqrt((double)(double)30))*(double)sqrt((double)(double)30)-(double)(1/(double)1470)*(double)sqrt((double)(double)525-(double)70*(double)sqrt((double)(double)30))+(double)1/(double)8-(double)(1/(double)420)*(double)sqrt((double)(double)525+(double)70*(double)sqrt((double)(double)30));                            
        AA(2,2) = -(double)(1/(double)144)*(double)sqrt((double)(double)30)+(double)1/(double)8;        
        AA(2,3) = (1/(double)840)*(double)sqrt((double)(double)525+(double)70*(double)sqrt((double)30))*(double)sqrt((double)30)-(double)(1/(double)144)*(double)sqrt((double)30)-(double)(1/(double)105)*(double)sqrt((double)525+(double)70*(double)sqrt((double)30))+(double)1/(double)8;
        AA(3,0) = -(double)(1/(double)2352)*(double)sqrt((double)525-(double)70*(double)sqrt((double)30))*(double)sqrt((double)30)+(double)(1/(double)144)*(double)sqrt((double)30)+(double)(1/(double)1680)*(double)sqrt((double)525+(double)70*(double)sqrt((double)30))*(double)sqrt((double)30)+(double)(1/(double)1470)*(double)sqrt((double)525-(double)70*(double)sqrt((double)30))+(double)1/(double)8+(double)(1/(double)420)*(double)sqrt((double)525+(double)70*(double)sqrt((double)30));
        AA(3,1) = (1/(double)2352)*(double)sqrt((double)525-(double)70*(double)sqrt((double)30))*(double)sqrt((double)30)+(double)(1/(double)144)*(double)sqrt((double)30)+(double)(1/(double)1680)*(double)sqrt((double)525+(double)70*(double)sqrt((double)30))*(double)sqrt((double)30)-(double)(1/(double)1470)*(double)sqrt((double)525-(double)70*(double)sqrt((double)30))+(double)1/(double)8+(double)(1/(double)420)*(double)sqrt((double)525+(double)70*(double)sqrt((double)30));
        AA(3,2) = -(double)(1/(double)840)*(double)sqrt((double)525+(double)70*(double)sqrt((double)30))*(double)sqrt((double)30)-(double)(1/(double)144)*(double)sqrt((double)30)+(double)(1/(double)105)*(double)sqrt((double)525+(double)70*(double)sqrt((double)30))+(double)1/(double)8;
        AA(3,3) = -(double)(1/(double)144)*(double)sqrt((double)30)+(double)1/(double)8;                

        bb(0) = (1/(double)72)*(double)sqrt((double)30)+(double)1/(double)4;            
        bb(1) = (1/(double)72)*(double)sqrt((double)30)+(double)1/(double)4;                                    
        bb(2) = -(double)(1/(double)72)*(double)sqrt((double)30)+(double)1/(double)4;
        bb(3) = -(double)(1/(double)72)*(double)sqrt((double)30)+(double)1/(double)4;

        cc(0) = 1/(double)2-(double)(1/(double)70)*(double)sqrt((double)525-(double)70*(double)sqrt((double)30));               
        cc(1) = 1/(double)2+(double)(1/(double)70)*(double)sqrt((double)525-(double)70*(double)sqrt((double)30));       
        cc(2) = 1/(double)2-(double)(1/(double)70)*(double)sqrt((double)525+(double)70*(double)sqrt((double)30));
        cc(3) = 1/(double)2+(double)(1/(double)70)*(double)sqrt((double)525+(double)70*(double)sqrt((double)30));


        // SIMPLIFIED NEWTON:
        DMatrix _eig(2,2);
        _eig(0,0) = 4.207578794359248;  _eig(0,1) = 5.314836083713501;  // the second column is the imaginary part
        _eig(1,0) = 5.792421205640746;  _eig(1,1) = 1.734468257869010;

        DMatrix _simplified_transf1(4,4);
        _simplified_transf1(0,0) = -4.511944766014135e+00;      _simplified_transf1(0,1) = 1.410200318172509e+01;               _simplified_transf1(0,2) = -6.490069796781762e+01;              _simplified_transf1(0,3) = -3.260131534153535e+00;
        _simplified_transf1(1,0) = 4.646043280390278e+01;       _simplified_transf1(1,1) = -7.224788843443845e+00;              _simplified_transf1(1,2) = 1.062619320722611e+01;               _simplified_transf1(1,3) = 1.316684254020140e-01;
        _simplified_transf1(2,0) = 7.890091964536154e+00;       _simplified_transf1(2,1) = -4.304210837983620e-01;              _simplified_transf1(2,2) = -7.755516515388237e+01;              _simplified_transf1(2,3) = 4.826224952821270e+00;
        _simplified_transf1(3,0) = 7.293296595763626e+01;       _simplified_transf1(3,1) = 1.055652513964904e+01;               _simplified_transf1(3,2) = 1.646623485807168e+02;               _simplified_transf1(3,3) = -2.099157718135189e-01;

        DMatrix _simplified_transf2(4,4);
        _simplified_transf2(0,0) = 1.134792325317037e-01;               _simplified_transf2(0,1) = 3.649668660358009e-02;               _simplified_transf2(0,2) = 2.786586696875059e-02;               _simplified_transf2(0,3) = 1.176262506147764e-02;
        _simplified_transf2(1,0) = -8.997398076613361e-02;              _simplified_transf2(1,1) = -3.394498084881714e-01;              _simplified_transf2(1,2) = 1.792676149982848e-01;               _simplified_transf2(1,3) = 1.094022826731096e-01;
        _simplified_transf2(2,0) = -4.567693894474303e-02;              _simplified_transf2(2,1) = 5.596900829318879e-03;               _simplified_transf2(2,2) = -1.205649800968665e-02;              _simplified_transf2(2,3) = 2.295382130562243e-02;
        _simplified_transf2(3,0) = -9.275512157844222e-01;              _simplified_transf2(3,1) = 0.0;                                                 _simplified_transf2(3,2) = 9.768864620884530e-01;               _simplified_transf2(3,3) = 0.0;

        DMatrix _simplified_transf1_T(4,4);
        _simplified_transf1_T(0,0) = 6.714467192972491e-01;             _simplified_transf1_T(0,1) = -2.182692704278241e+00;            _simplified_transf1_T(0,2) = -1.624427092105129e-01;                    _simplified_transf1_T(0,3) = -3.902744826216674e+00;
        _simplified_transf1_T(1,0) = -4.495608351940147e-01;            _simplified_transf1_T(1,1) = -9.500648563729466e-01;            _simplified_transf1_T(1,2) = 2.663148445406726e-01;                     _simplified_transf1_T(1,3) = 4.929782671143375e+00;
        _simplified_transf1_T(2,0) = 1.818127385417024e-01;             _simplified_transf1_T(2,1) = 1.228148321235627e+00;             _simplified_transf1_T(2,2) = -3.002364028567489e-02;                    _simplified_transf1_T(2,3) = 5.658537858504520e+00;
        _simplified_transf1_T(3,0) = 1.980161710480598e-02;     _simplified_transf1_T(3,1) = 3.227701142228159e-01;                     _simplified_transf1_T(3,2) = 1.538698143800381e-01;                     _simplified_transf1_T(3,3) = -1.694378560034379e+00;

        DMatrix _simplified_transf2_T(4,4);
        _simplified_transf2_T(0,0) = 4.960593241309737e+00;             _simplified_transf2_T(0,1) = 4.776070474379495e+00;             _simplified_transf2_T(0,2) = 4.710070689435160e+00;             _simplified_transf2_T(0,3) = 1.118073005316397e+01;
        _simplified_transf2_T(1,0) = 4.556294554649469e-01;             _simplified_transf2_T(1,1) = -2.292621287825622e+00;            _simplified_transf2_T(1,2) = 4.326190112822336e-01;             _simplified_transf2_T(1,3) = 1.692929579651415e+00;
        _simplified_transf2_T(2,0) = -4.713659630803845e+00;            _simplified_transf2_T(2,1) = 8.479584873656380e+00;             _simplified_transf2_T(2,2) = -4.475607853136751e+00;            _simplified_transf2_T(2,3) = 2.976737053733966e+01;
        _simplified_transf2_T(3,0) = -2.832888732208244e-01;            _simplified_transf2_T(3,1) = 3.891317146824644e-01;             _simplified_transf2_T(3,2) = 7.546783478294038e-01;             _simplified_transf2_T(3,3) = -2.622187436137307e-01;


        // SINGLE NEWTON:
        double _single_tau = 1.561969968460128e-01;
        DVector _lower_triang(6);
        _lower_triang(0) = 9.627423789846739e-01;       _lower_triang(1) = -1.194428300588649e+00;      _lower_triang(2) = 1.918753137082504e+00;
        _lower_triang(3) = 1.649572580382698e+00;       _lower_triang(4) = -2.628995768624925e+00;      _lower_triang(5) = 2.357166809194904e+00;

        DMatrix _single_transf1(4,4);
        _single_transf1(0,0) = 1.000000000000000e+00;   _single_transf1(0,1) = 6.677448107835342e-01;   _single_transf1(0,2) = 1.416759981647328e-02;   _single_transf1(0,3) = -6.505535658246753e-02;
        _single_transf1(1,0) = -9.627423789846739e-01;  _single_transf1(1,1) = 3.571337723115894e-01;   _single_transf1(1,2) = 2.017094296173482e-01;   _single_transf1(1,3) = -2.664322715789577e-02;
        _single_transf1(2,0) = 1.194428300588649e+00;   _single_transf1(2,1) = -1.121179837511438e+00;  _single_transf1(2,2) = 6.037202706082401e-01;   _single_transf1(2,3) = 1.783722705962468e-02;
        _single_transf1(3,0) = -1.649572580382698e+00;  _single_transf1(3,1) = 1.527502238063574e+00;   _single_transf1(3,2) = -1.814385214672611e+00;  _single_transf1(3,3) = 1.051177861607520e+00;

        DMatrix _single_transf2(4,4);
        _single_transf2(0,0) = 1.0;             _single_transf2(0,1) = -6.677448107835342e-01;  _single_transf2(0,2) = 1.296306965460327e-01;   _single_transf2(0,3) = 1.526277075698497e-02;
        _single_transf2(1,0) = 0.0;             _single_transf2(1,1) = 1.0;                                     _single_transf2(1,2) = -2.153491783691625e-01;  _single_transf2(1,3) = 7.296098377515141e-02;
        _single_transf2(2,0) = 0.0;             _single_transf2(2,1) = 0.0;                                     _single_transf2(2,2) = 1.0;                                     _single_transf2(2,3) = 7.575507029183778e-02;
        _single_transf2(3,0) = 0.0;             _single_transf2(3,1) = 0.0;                                     _single_transf2(3,2) = 0.0;                                     _single_transf2(3,3) = 1.0;

        DMatrix _single_transf1_T(4,4);
        _single_transf1_T(0,0) = 1.772523752126622e+00;         _single_transf1_T(0,1) = -1.340315970410551e+00;        _single_transf1_T(0,2) = 1.069464813810269e+00;         _single_transf1_T(0,3) = -1.649572580382698e+00;
        _single_transf1_T(1,0) = -8.763483567058189e-01;        _single_transf1_T(1,1) = 1.605016029183555e+00;         _single_transf1_T(1,2) = -1.719593377833379e+00;        _single_transf1_T(1,3) = 2.628995768624925e+00;
        _single_transf1_T(2,0) = 9.365379990131717e-02;         _single_transf1_T(2,1) = -3.873303876901573e-01;        _single_transf1_T(2,2) = 8.214326626798530e-01;         _single_transf1_T(2,3) = -2.357166809194904e+00;
        _single_transf1_T(3,0) = 1.526277075698497e-02;         _single_transf1_T(3,1) = 7.296098377515141e-02;         _single_transf1_T(3,2) = 7.575507029183778e-02;         _single_transf1_T(3,3) = 1.000000000000000e+00;

        DMatrix _single_transf2_T(4,4);
        _single_transf2_T(0,0) = 1.0;                                                   _single_transf2_T(0,1) = 0.0;                                           _single_transf2_T(0,2) = 0.0;                                           _single_transf2_T(0,3) = 0.0;
        _single_transf2_T(1,0) = 6.677448107835342e-01;                 _single_transf2_T(1,1) = 1.0;                                           _single_transf2_T(1,2) = 0.0;                                           _single_transf2_T(1,3) = 0.0;
        _single_transf2_T(2,0) = 1.416759981647328e-02;                 _single_transf2_T(2,1) = 2.153491783691625e-01;         _single_transf2_T(2,2) = 1.0;                                           _single_transf2_T(2,3) = 0.0;
        _single_transf2_T(3,0) = -6.505535658246753e-02;                _single_transf2_T(3,1) = -8.927477591979682e-02;        _single_transf2_T(3,2) = -7.575507029183778e-02;        _single_transf2_T(3,3) = 1.0;


        ImplicitRungeKuttaExport* integrator = createImplicitRungeKuttaExport(_userInteraction, _commonHeaderName);
        integrator->initializeButcherTableau(AA, bb, cc);

        integrator->setEigenvalues(_eig);
        integrator->setSimplifiedTransformations(_simplified_transf1, _simplified_transf2,_simplified_transf1_T, _simplified_transf2_T);

        integrator->setSingleTransformations(_single_tau, _lower_triang, _single_transf1, _single_transf2, _single_transf1_T, _single_transf2_T);

        return integrator;
}

CLOSE_NAMESPACE_ACADO

// end of file.