acos.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/symbolic_operator/symbolic_operator.hpp>

double dAcos(double x){
  return -1/sqrt(1-x*x);
}


double ddAcos(double x){
  double v1 = sqrt(1-x*x);
  return 2*x*(-0.5/v1/v1/v1);
}

BEGIN_NAMESPACE_ACADO


Acos::Acos():UnaryOperator(){
  cName = "acos";

  fcn = &acos;
  dfcn = &dAcos;
  ddfcn = &ddAcos;

  operatorName = ON_ACOS;

}

Acos::Acos( Operator *_argument ):UnaryOperator(_argument){
  cName = "acos";

  fcn = &acos;
  dfcn = &dAcos;
  ddfcn = &ddAcos;

  operatorName = ON_ACOS;
}


Acos::Acos( const Acos &arg ):UnaryOperator(arg){
  cName = "acos";

  fcn = &acos;
  dfcn = &dAcos;
  ddfcn = &ddAcos;

  operatorName = ON_ACOS;
}


Acos::~Acos(){

}


Acos& Acos::operator=( const Acos &arg ){

  UnaryOperator::operator=(arg);

  return *this;
}


returnValue Acos::evaluate( EvaluationBase *x ){
 
    x->Acos(*argument);
    return SUCCESSFUL_RETURN;
}


Operator* Acos::substitute( int index, const Operator *sub ){

    return new Acos( argument->substitute( index , sub ) );

}

Operator* Acos::clone() const{

    return new Acos(*this);
}

returnValue Acos::initDerivative() {

        if( initialized ) return SUCCESSFUL_RETURN;
        initialized = BT_TRUE;

        derivative = convert2TreeProjection(
                        new Product( new DoubleConstant( -1.0 , NE_NEITHER_ONE_NOR_ZERO ),
                                        new Power(
                                                        new Addition(
                                                                        new DoubleConstant(1.0 , NE_ONE),
                                                                        new Product(
                                                                                        new DoubleConstant( -1.0, NE_NEITHER_ONE_NOR_ZERO),
                                                                                        new Power_Int(
                                                                                                        argument->clone(),
                                                                                                        2
                                                                                        )
                                                                        )
                                                        ),
                                                        new DoubleConstant( -0.5 , NE_NEITHER_ONE_NOR_ZERO )
                                        )
                        ));
        derivative2 = convert2TreeProjection(
                        new Product( new DoubleConstant( -1.0 , NE_NEITHER_ONE_NOR_ZERO ),
                                        new Product(
                                                        new Power(
                                                                        new Addition(
                                                                                        new DoubleConstant(1.0 , NE_ONE),
                                                                                        new Product(
                                                                                                        new DoubleConstant( -1.0, NE_NEITHER_ONE_NOR_ZERO),
                                                                                                        new Power_Int(
                                                                                                                        argument->clone(),
                                                                                                                        2
                                                                                                        )
                                                                                        )
                                                                        ),
                                                                        new DoubleConstant( -1.5 , NE_NEITHER_ONE_NOR_ZERO )
                                                        ),
                                                        argument->clone()
                                        )
                        ));

        return argument->initDerivative();
}


CLOSE_NAMESPACE_ACADO

// end of file.