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/* integrate.hpp header file
*
* Copyright Jens Maurer 2000
* Permission to use, copy, modify, sell, and distribute this software
* is hereby granted without fee provided that the above copyright notice
* appears in all copies and that both that copyright notice and this
* permission notice appear in supporting documentation,
*
* Jens Maurer makes no representations about the suitability of this
* software for any purpose. It is provided "as is" without express or
* implied warranty.
*
* $Id: integrate.hpp,v 1.4 2001/11/19 22:13:04 jmaurer Exp $
*
* Revision history
* 01 April 2001: Modified to use new <boost/limits.hpp> header. (JMaddock)
*/
#ifndef INTEGRATE_HPP
#define INTEGRATE_HPP
#include <boost/limits.hpp>
template<class UnaryFunction>
inline typename UnaryFunction::result_type
trapezoid(UnaryFunction f, typename UnaryFunction::argument_type a,
typename UnaryFunction::argument_type b, int n)
{
typename UnaryFunction::result_type tmp = 0;
for(int i = 1; i <= n-1; ++i)
tmp += f(a+(b-a)/n*i);
return (b-a)/2/n * (f(a) + f(b) + 2*tmp);
}
template<class UnaryFunction>
inline typename UnaryFunction::result_type
simpson(UnaryFunction f, typename UnaryFunction::argument_type a,
typename UnaryFunction::argument_type b, int n)
{
typename UnaryFunction::result_type tmp1 = 0;
for(int i = 1; i <= n-1; ++i)
tmp1 += f(a+(b-a)/n*i);
typename UnaryFunction::result_type tmp2 = 0;
for(int i = 1; i <= n ; ++i)
tmp2 += f(a+(b-a)/2/n*(2*i-1));
return (b-a)/6/n * (f(a) + f(b) + 2*tmp1 + 4*tmp2);
}
// compute b so that f(b) = y; assume f is monotone increasing
template<class UnaryFunction>
inline typename UnaryFunction::argument_type
invert_monotone_inc(UnaryFunction f, typename UnaryFunction::result_type y,
typename UnaryFunction::argument_type lower = -1,
typename UnaryFunction::argument_type upper = 1)
{
while(upper-lower > 1e-6) {
double middle = (upper+lower)/2;
if(f(middle) > y)
upper = middle;
else
lower = middle;
}
return (upper+lower)/2;
}
// compute b so that I(f(x), a, b) == y
template<class UnaryFunction>
inline typename UnaryFunction::argument_type
quantil(UnaryFunction f, typename UnaryFunction::argument_type a,
typename UnaryFunction::result_type y,
typename UnaryFunction::argument_type step)
{
typedef typename UnaryFunction::result_type result_type;
if(y >= 1.0)
return std::numeric_limits<result_type>::infinity();
typename UnaryFunction::argument_type b = a;
for(result_type result = 0; result < y; b += step)
result += step*f(b);
return b;
}
#endif /* INTEGRATE_HPP */
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