normal_kernel.hpp

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/*
 * PoPS model - normal dispersal kernel
 *
 * Copyright (C) 2015-2020 by the authors.
 *
 * Authors: Margaret Lawrimore malawrim ncsu edu
 *
 * The code contained herein is licensed under the GNU General Public
 * License. You may obtain a copy of the GNU General Public License
 * Version 2 or later at the following locations:
 *
 * http://www.opensource.org/licenses/gpl-license.html
 * http://www.gnu.org/copyleft/gpl.html
 */
 
#ifndef POPS_NORMAL_KERNEL_HPP
#define POPS_NORMAL_KERNEL_HPP
 
#include "kernel_types.hpp"
#include "raster.hpp"
 
#include <random>
 
namespace pops {
 
using std::pow;
using std::exp;
using std::log;
using std::sqrt;
 
class NormalKernel
{
protected:
    double sigma;
    std::normal_distribution<double> normal_distribution;
 
public:
    NormalKernel(double s) : sigma(s), normal_distribution(0.0, sigma)
    {
        if (sigma == 0) {
            throw std::invalid_argument("sigma cannot be zero");
        }
    }
 
    template<class Generator>
    double random(Generator& generator)
    {
        return std::abs(normal_distribution(generator));
    }
 
    double pdf(double x)
    {
        if (sigma == 1) {
            return 1.0 / (sqrt(2 * M_PI)) * exp(-0.5 * pow(x, 2));
        }
        return 1.0 / (sigma * sqrt(2 * M_PI)) * exp(-0.5 * pow(x / sigma, 2));
    }
 
    double icdf(double x)
    {
        if (x <= 0 || x >= 1) {
            throw std::invalid_argument("icdf: x must be between 0.0 and 1.0");
        }
        //  approximation for inverse error function
        double y = (2 * x) - 1;
        float sign = (y < 0) ? -1.0f : 1.0f;
        double a = 0.140012;
        double t = 2.0 / (M_PI * a);
        double l = log(1 - pow(y, 2));
        double inverf =
            sign * sqrt(sqrt(pow(t + (l / 2.0), 2) - (l / a)) - (t + (l / 2.0)));
        return sigma * std::sqrt(2) * inverf;
    }
};
 
}  // namespace pops
 
#endif  // POPS_NORMAL_KERNEL_HPP