Regularizer.h

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//===========================================================================
/*!
 * 
 *
 * \brief       Regularizer
 * 
 * 
 *
 * \author      T. Glasmachers
 * \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_REGULARIZER_H
#define SHARK_OBJECTIVEFUNCTIONS_REGULARIZER_H


#include <shark/ObjectiveFunctions/AbstractObjectiveFunction.h>

namespace shark {


///
/// \brief One-norm of the input as an objective function
///
/// \par
/// The OneNormRegularizer is intended to be used together with other
/// objective functions within a CombinedObjectiveFunction, in order to
/// obtain a more smooth and more sparse solution.
///
class OneNormRegularizer : public SingleObjectiveFunction
{
public:

    /// Constructor
    OneNormRegularizer(std::size_t numVariables = 0):m_numberOfVariables(numVariables)
    {
        m_features|=HAS_FIRST_DERIVATIVE;
        m_features|=HAS_SECOND_DERIVATIVE;
    }

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

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

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

    void setMask(const RealVector& mask){
        m_mask = mask;
    }
    const RealVector& mask()const{
        return m_mask;
    }
    /// Evaluates the objective function.
    double eval( RealVector const& input ) const{
        if(m_mask.empty()){
            return norm_1(input);
        }
        else
        {
            return norm_1(input * m_mask);
        }
    }

    /// Evaluates the objective function
    /// and calculates its gradient.
    double evalDerivative( RealVector const& input, FirstOrderDerivative & derivative ) const {
        std::size_t ic = input.size();
        derivative.resize(ic);
        if(m_mask.empty()){
            for (std::size_t i = 0; i != ic; i++){
                derivative(i) = boost::math::sign(input(i));
            }
        }
        else
        {
            SIZE_CHECK(m_mask.size() == input.size());
            for (std::size_t i=0; i != ic; i++){
                derivative(i) = m_mask(i)*boost::math::sign(input(i));
            }
        }
        return eval(input);
    }
    double evalDerivative( RealVector const& input, SecondOrderDerivative & derivative ) const {
        std::size_t ic = input.size();
        derivative.gradient.resize(ic);
        derivative.hessian.resize(ic,ic);
        derivative.hessian.clear();
        if(m_mask.empty()){
            for (std::size_t i=0; i != ic; i++){
                derivative.gradient(i) = boost::math::sign(input(i));
            }
        }
        else
        {
            SIZE_CHECK(m_mask.size() == input.size());
            for (std::size_t i=0; i != ic; i++){
                derivative.gradient(i) = m_mask(i)*boost::math::sign(input(i));
            }
        }
        return eval(input);
    }
private:
    RealVector m_mask;
    std::size_t m_numberOfVariables;
};


///
/// \brief Two-norm of the input as an objective function
///
/// \par
/// The TwoNormRegularizer is intended to be used together with other
/// objective functions within a CombinedObjectiveFunction, in order to
/// obtain a more smooth solution.
///
class TwoNormRegularizer : public AbstractObjectiveFunction<RealVector, double>
{
public:
    typedef RealVector SearchPointType;
    typedef double ResultType;

    typedef AbstractObjectiveFunction<RealVector, double> super;

    /// Constructor
    TwoNormRegularizer(std::size_t numVariables = 0):m_numberOfVariables(numVariables)
    {
        m_features|=HAS_FIRST_DERIVATIVE;
        m_features|=HAS_SECOND_DERIVATIVE;
    }

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

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

    void setNumberOfVariables( std::size_t numberOfVariables ){
        m_numberOfVariables = numberOfVariables;
    }
    
    void setMask(const RealVector& mask){
        m_mask = mask;
    }
    const RealVector& mask()const{
        return m_mask;
    }

    /// Evaluates the objective function.
    virtual double eval( RealVector const& input ) const
    { 
        if(m_mask.empty()){
            return 0.5*norm_sqr(input);
        }
        else{
            return 0.5 * sum(m_mask*sqr(input));
        }
    }

    /// Evaluates the objective function
    /// and calculates its gradient.
    virtual double evalDerivative( RealVector const& input, FirstOrderDerivative & derivative ) const {
        if(m_mask.empty()){
            derivative = input;
        }
        else{
            derivative = m_mask*input;
        }
        return eval(input);
    }

    /// Evaluates the objective function
    /// and calculates its gradient and
    /// its Hessian.
    virtual ResultType evalDerivative( const SearchPointType & input, SecondOrderDerivative & derivative )const {
        derivative.gradient = input;
        derivative.hessian = blas::identity_matrix<double>(input.size());
        return 0.5 * norm_sqr(input);
    }
private:
    std::size_t m_numberOfVariables;
    RealVector m_mask;
};


}
#endif // SHARK_CORE_REGULARIZER_H