simpson.hh

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/* -*- mia-c++  -*-
 *
 * This file is part of MIA - a toolbox for medical image analysis 
 * Copyright (c) Leipzig, Madrid 1999-2017 Gert Wollny
 *
 * MIA is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program 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 General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with MIA; if not, see <http://www.gnu.org/licenses/>.
 *
 */

#include <mia/core/msgstream.hh>

NS_MIA_BEGIN

template <class F>
double simpson(double from, double to, size_t intervals, const F& function)
{
        double sum = 0.0; 
        double dx = (to - from) / intervals; 
        
        sum = 0.5 * (function(from) + function(to)); 
        double x = from + dx; 
        for (size_t ix = 1; ix < intervals; ++ix, x+=dx) 
                sum += function(x); 

        x = from + .5 * dx; 
        for (size_t ix = 0; ix < intervals; ++ix, x+=dx) 
                sum += 2 * function(x); 
        
        return sum * dx / 3.0; 
}

NS_MIA_END