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
NS_MIA_BEGIN
#define NS_MIA_BEGIN
conveniance define to start the mia namespace
Definition defines.hh:33
NS_MIA_END
#define NS_MIA_END
conveniance define to end the mia namespace
Definition defines.hh:36
simpson
double simpson(double from, double to, size_t intervals, const F &function)
Definition simpson.hh:36
msgstream.hh