Ellipsoid.h

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/*!
 * 
 *
 * \brief       Convex quadratic benchmark function.
 * 
 *
 * \author      T.Voss
 * \date        2010-2011
 *
 *
 * \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_BENCHMARKS_ELLIPSOID_H
#define SHARK_OBJECTIVEFUNCTIONS_BENCHMARKS_ELLIPSOID_H

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

namespace shark {
/**
*  \brief Convex quadratic benchmark function
*
*  The eigenvalues of the Hessian of this convex quadratic benchmark
*  function are equally distributed on logarithmic scale.
*/
struct Ellipsoid : public SingleObjectiveFunction {
    Ellipsoid(size_t numberOfVariables = 5, double alpha=1E-3) : m_alpha(alpha) {
        m_features |= CAN_PROPOSE_STARTING_POINT;
        m_features |= HAS_FIRST_DERIVATIVE;
        m_features |= HAS_SECOND_DERIVATIVE;
        m_numberOfVariables = numberOfVariables;
    }

    /// \brief From INameable: return the class name.
    std::string name() const
    { return "Ellipsoid"; }
    
    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, 0,1);
        }
        return x;
    }

    double eval( const SearchPointType & p ) const {
        m_evaluationCounter++;
        double sum = 0;
        double sizeMinusOne = p.size() - 1.;
        for( std::size_t i = 0; i < p.size(); i++ ){
            sum += ::pow( m_alpha, i / sizeMinusOne ) * sqr(p( i ) );
        }

        return sum;
    }

    double evalDerivative( const SearchPointType & p, FirstOrderDerivative & derivative ) const {
        double sizeMinusOne=p.size() - 1.;
        derivative.resize(p.size());
        for (std::size_t i = 0; i < p.size(); i++) {
            derivative(i) = 2 * ::pow(m_alpha, i / sizeMinusOne) * p(i);
        }
        return eval(p);
    }
    double evalDerivative(const SearchPointType &p, SecondOrderDerivative &derivative)const {
        std::size_t size=p.size();
        double sizeMinusOne=p.size() - 1.;
        derivative.gradient.resize(size);
        derivative.hessian.resize(size,size);
        derivative.hessian.clear();
        for (std::size_t i = 0; i < size; i++) {
            derivative.gradient(i) = 2 * std::pow(m_alpha, i / sizeMinusOne ) * p(i);
            derivative.hessian(i,i) = 2 * std::pow(m_alpha, i /sizeMinusOne );
        }
        return eval(p);
    }
private:
    std::size_t m_numberOfVariables;
    double m_alpha;
};

}

#endif