LogNormal.h

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/*!
 * 
 *
 * \brief       Provides a log-normal distribution.
 * 
 * 
 *
 * \author      O. Krause
 * \date        2010-01-01
 *
 *
 * \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_RNG_LOGNORMAL_H
#define SHARK_RNG_LOGNORMAL_H

#include <shark/Core/Math.h>

#include <boost/random/lognormal_distribution.hpp>

#include <cmath>

namespace shark {
    /**
    * \brief Implements a log-normal distribution with parameters location m and Scale s.
    *
    *  The propability distribution is
    * \f[ p(x)= \frac {1} {x s \sqrt{2 \pi}}e^{-\frac{(\ln x -m)^2}{2 s^2}}\f]
    */
    //unfortunately, boost::math::lognormal_distribution uses scale/location as parameters as well as the next c++ standard, while
    //boost::lognormal_distribution uses mean and sigma. in boost 1.47 there exists boost::random::lognormal_distribution which uses
    //scale/location as well, but we use boost 1.44. For forward compliance, we use the new parameter set but transform them back to boost
    //parameters.
    template<typename RngType = shark::DefaultRngType>
    class LogNormal : public boost::variate_generator<RngType*,boost::lognormal_distribution<> >
    {
    private:
        typedef boost::variate_generator<RngType*,boost::lognormal_distribution<> > Base;
        double m_location;
        double m_scale;
    
        
        boost::lognormal_distribution<> createDistribution(double location,double scale){
            double mean = std::exp(location+scale*scale/2.0);
            double variance = (std::exp(scale*scale)-1.0)* std::exp(2*location+scale*scale);
            return boost::lognormal_distribution<>(mean,std::sqrt(variance));
        }
    public:
        /**
        * \brief C'tor, associates the distribution with a custom RNG.
        * \param [in,out] rng The custom rng.
        * \param [in] location The location of the distribution, default value is 0.
        * \param [in] scale The scale of the distribution, default value is 1.
        */
        LogNormal( RngType & rng, 
               double location = 0,
               double scale= 1 )
            : Base(&rng,boost::lognormal_distribution<>(1,1)),m_location(location),m_scale(scale)
        {
            Base::distribution() = createDistribution(location,scale); 
        }

        /** \brief Injects the default sampling operator. */
        using Base::operator();

        /**
        * \brief Samples a random number.
        * \param [in] location The location of the distribution.
        * \param [in] scale The scale of the distribution.
        */
        double operator()(double location, double scale) {
            return dist(createDistribution(location,scale) );
        }

        /**
        * \brief Accesses the location of the distribution.
        */
        double location() const { 
            return m_location; 
        }

        /**
        * \brief Accesses the scale of the distribution.
        */
        double scale() const { 
            return m_scale; 
        }

        /**
        * \brief Adjusts the location of the distribution.
        */
        void location(double newLocation)
        { 
            m_location = newLocation;
            
            Base::distribution() = createDistribution(location(),scale()); 
        }

        /**
        * \brief Adjusts the scale of the distribution.
        */
        void scale(double newScale)
        { 
            m_scale = newScale;
            Base::distribution() = createDistribution(location(),scale()); 
        }

        /**
        * \brief Calculates the probability of x > 0.
        */
        double p(double x) const {

            double y = (std::log(x) - location()) / scale();
            return x > 0 ? std::exp(-y*y / 2.0) / (boost::math::constants::root_two_pi<double>() * scale() * x) : 0;
        }
    };


}
#endif