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simpson.hh
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1/* -*- mia-c++ -*-
2 *
3 * This file is part of MIA - a toolbox for medical image analysis
4 * Copyright (c) Leipzig, Madrid 1999-2017 Gert Wollny
5 *
6 * MIA is free software; you can redistribute it and/or modify
7 * it under the terms of the GNU General Public License as published by
8 * the Free Software Foundation; either version 3 of the License, or
9 * (at your option) any later version.
10 *
11 * This program is distributed in the hope that it will be useful,
12 * but WITHOUT ANY WARRANTY; without even the implied warranty of
13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 * GNU General Public License for more details.
15 *
16 * You should have received a copy of the GNU General Public License
17 * along with MIA; if not, see <http://www.gnu.org/licenses/>.
18 *
19 */
20
21#include <mia/core/msgstream.hh>
22
24
35template <class F>
36double simpson(double from, double to, size_t intervals, const F& function)
37{
38 double sum = 0.0;
39 double dx = (to - from) / intervals;
40 sum = 0.5 * (function(from) + function(to));
41 double x = from + dx;
42
43 for (size_t ix = 1; ix < intervals; ++ix, x += dx)
44 sum += function(x);
45
46 x = from + .5 * dx;
47
48 for (size_t ix = 0; ix < intervals; ++ix, x += dx)
49 sum += 2 * function(x);
50
51 return sum * dx / 3.0;
52}
53
#define NS_MIA_BEGIN
conveniance define to start the mia namespace
Definition: defines.hh:33
#define NS_MIA_END
conveniance define to end the mia namespace
Definition: defines.hh:36
double simpson(double from, double to, size_t intervals, const F &function)
Definition: simpson.hh:36