numeric_differentiation.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
 *    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 *
 */



#include <acado/utils/acado_utils.hpp>
#include <acado/user_interaction/user_interaction.hpp>
#include <acado/symbolic_expression/symbolic_expression.hpp>
#include <acado/function/function.hpp>

using namespace std;

USING_NAMESPACE_ACADO

/* >>> start tutorial code >>> */
void my_function( double *x_, double *f, void *user_data ){

//  double          t =  x_[ 0];    // the time
    double          x =  x_[ 1];    // the first  differential state
    double          y =  x_[ 2];    // the second differential state

    f[0] = x*x + pow(y,3);
}

int main( )
{
        DifferentialState a, b;
        TIME t;

        CFunction myFunction(1, my_function);

        IntermediateState x(3);

        return 0;

        x(0) = t;
        x(1) = a;
        x(2) = b;

        Function f;
        f << myFunction(x);

        // TEST THE FUNCTION f:
        // --------------------
        int x_index, y_index;

        x_index = f.index(VT_DIFFERENTIAL_STATE, 0);
        y_index = f.index(VT_DIFFERENTIAL_STATE, 1);

        double *xx = new double[f.getNumberOfVariables() + 1];
        double *seed = new double[f.getNumberOfVariables() + 1];
        double *ff = new double[f.getDim()];
        double *df = new double[f.getDim()];

        xx[x_index] = 1.0;
        xx[y_index] = 1.0;

        seed[x_index] = 0.5;
        seed[y_index] = 0.5;

        // FORWARD DIFFERENTIATION:
        // ------------------------
        f.evaluate(0, xx, ff);
        f.AD_forward(0, seed, df);

        // PRINT THE RESULTS:
        // ------------------
        cout << scientific
                 << "     x = " << xx[x_index] << endl
                 << "     y = " << xx[y_index] << endl
                 << "seed_x = " << seed[x_index] << endl
                 << "seed_y = " << seed[y_index] << endl
                 << "     f = " << ff[0] << endl
                 << "    df = " << df[0] << endl;

        delete[] xx;
        delete[] seed;
        delete[] ff;
        delete[] df;

        return 0;
}
/* <<< end tutorial code <<< */