Rosenbrock.h

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//===========================================================================
/*!
 * 
 *
 * \brief       Generalized Rosenbrock benchmark function 
 * 
 * This non-convex benchmark function for real-valued optimization is
 * a generalization from two to multiple dimensions of a classic
 * function first proposed in:
 * 
 * H. H. Rosenbrock. An automatic method for finding the greatest or
 * least value of a function. The Computer Journal 3: 175-184, 1960
 * 
 * 
 *
 * \author      -
 * \date        -
 *
 *
 * \par Copyright 1995-2017 Shark Development Team
 * 
 * <BR><HR>
 * This file is part of Shark.
 * <http://shark-ml.org/>
 * 
 * Shark 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.
 * 
 * Shark 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 Shark.  If not, see <http://www.gnu.org/licenses/>.
 *
 */
//===========================================================================

#ifndef SHARK_OBJECTIVEFUNCTIONS_BENCHMARK_ROSENBROCK_H
#define SHARK_OBJECTIVEFUNCTIONS_BENCHMARK_ROSENBROCK_H

#include <shark/ObjectiveFunctions/AbstractObjectiveFunction.h>
#include <shark/Core/Random.h>

namespace shark {
/*! \brief Generalized Rosenbrock benchmark function 
*
*  This non-convex benchmark function for real-valued optimization is a
*  generalization from two to multiple dimensions of a classic
*  function first proposed in:
*
*  H. H. Rosenbrock. An automatic method for finding the greatest or
*  least value of a function. The Computer Journal 3: 175-184,
*  1960  
*/
struct Rosenbrock : public SingleObjectiveFunction {

    /// \brief Constructs the problem
    ///
    /// \param dimensions number of dimensions to optimize
    /// \param initialSpread spread of the initial starting point
    Rosenbrock(std::size_t dimensions=23, double initialSpread = 1.0)
    :m_numberOfVariables(dimensions), m_initialSpread(initialSpread) {
        m_features|=CAN_PROPOSE_STARTING_POINT;
        m_features|=HAS_FIRST_DERIVATIVE;
        m_features|=HAS_SECOND_DERIVATIVE;
    }

    /// \brief From INameable: return the class name.
    std::string name() const
    { return "Rosenbrock"; }

    std::size_t numberOfVariables()const{
        return m_numberOfVariables;
    }
    
    bool hasScalableDimensionality()const{
        return true;
    }

    void setNumberOfVariables( std::size_t numberOfVariables ){
        m_numberOfVariables = numberOfVariables;
    }

    SearchPointType proposeStartingPoint() const {
        RealVector x(numberOfVariables());

        for (std::size_t i = 0; i < x.size(); i++) {
            x(i) = random::uni(*mep_rng, 0, m_initialSpread );
        }
        return x;
    }

    double eval( const SearchPointType & p ) const {
        m_evaluationCounter++;

        double sum = 0;

        for( std::size_t i = 0; i < p.size()-1; i++ ) {
            sum += 100*sqr( p(i+1) - sqr( p( i ) ) ) +sqr( 1. - p( i ) );
        }

        return( sum );
    }

    virtual ResultType evalDerivative( const SearchPointType & p, FirstOrderDerivative & derivative )const {
        double result = eval(p);
        size_t size = p.size();
        derivative.resize(size);
        derivative(0) = 2*( p(0) - 1 ) - 400 * ( p(1) - sqr( p(0) ) ) * p(0);
        derivative(size-1) = 200 * ( p(size - 1) - sqr( p( size - 2 ) ) ) ;
        for(size_t i=1; i != size-1; ++i){
            derivative( i ) = 2 * ( p(i) - 1 ) - 400 * (p(i+1) - sqr( p(i) ) ) * p( i )+200 * ( p( i )- sqr( p(i-1) ) );
        }
        return result;

    }

    virtual ResultType evalDerivative( const SearchPointType & p, SecondOrderDerivative & derivative )const {
        double result = eval(p);
        size_t size = p.size();
        derivative.gradient.resize(size);
        derivative.hessian.resize(size,size);
        derivative.hessian.clear();

        derivative.gradient(0) = 2*( p(0) - 1 ) - 400 * ( p(1) - sqr( p(0) ) ) * p(0);
        derivative.gradient(size-1) = 200 * ( p(size - 1) - sqr( p( size - 2 ) ) ) ;

        derivative.hessian(0,0) = 2 - 400* (p(1) - 3*sqr(p(0))) ;
        derivative.hessian(0,1) = -400 * p(0) ;

        derivative.hessian(size-1,size-1) = 200;
        derivative.hessian(size-1,size-2) = -400 * p( size - 2 );

        for(size_t i=1; i != size-1; ++i){
            derivative.gradient( i ) = 2 * ( p(i) - 1 ) - 400 * (p(i+1) - sqr( p(i) ) ) * p( i )+200 * ( p( i )- sqr( p(i-1) ) );

            derivative.hessian(i,i) = 202 - 400 * ( p(i+1) - 3 * sqr(p(i)));
            derivative.hessian(i,i+1) = - 400 * ( p(i) );
            derivative.hessian(i,i-1) = - 400 * ( p(i-1) );

        }
        return result;
    }

private:
    std::size_t m_numberOfVariables;
    double m_initialSpread;
};

}

#endif