80 lines
2.2 KiB
C++
80 lines
2.2 KiB
C++
/* integrate.hpp header file
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*
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* Copyright Jens Maurer 2000
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* Distributed under the Boost Software License, Version 1.0. (See
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* accompanying file LICENSE_1_0.txt or copy at
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* http://www.boost.org/LICENSE_1_0.txt)
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*
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* $Id$
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*
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* Revision history
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* 01 April 2001: Modified to use new <boost/limits.hpp> header. (JMaddock)
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*/
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#ifndef INTEGRATE_HPP
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#define INTEGRATE_HPP
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#include <boost/limits.hpp>
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template<class UnaryFunction>
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inline typename UnaryFunction::result_type
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trapezoid(UnaryFunction f, typename UnaryFunction::argument_type a,
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typename UnaryFunction::argument_type b, int n)
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{
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typename UnaryFunction::result_type tmp = 0;
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for(int i = 1; i <= n-1; ++i)
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tmp += f(a+(b-a)/n*i);
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return (b-a)/2/n * (f(a) + f(b) + 2*tmp);
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}
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template<class UnaryFunction>
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inline typename UnaryFunction::result_type
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simpson(UnaryFunction f, typename UnaryFunction::argument_type a,
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typename UnaryFunction::argument_type b, int n)
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{
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typename UnaryFunction::result_type tmp1 = 0;
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for(int i = 1; i <= n-1; ++i)
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tmp1 += f(a+(b-a)/n*i);
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typename UnaryFunction::result_type tmp2 = 0;
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for(int i = 1; i <= n ; ++i)
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tmp2 += f(a+(b-a)/2/n*(2*i-1));
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return (b-a)/6/n * (f(a) + f(b) + 2*tmp1 + 4*tmp2);
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}
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// compute b so that f(b) = y; assume f is monotone increasing
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template<class UnaryFunction, class T>
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inline T
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invert_monotone_inc(UnaryFunction f, typename UnaryFunction::result_type y,
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T lower = -1,
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T upper = 1)
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{
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while(upper-lower > 1e-6) {
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double middle = (upper+lower)/2;
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if(f(middle) > y)
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upper = middle;
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else
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lower = middle;
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}
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return (upper+lower)/2;
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}
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// compute b so that I(f(x), a, b) == y
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template<class UnaryFunction>
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inline typename UnaryFunction::argument_type
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quantil(UnaryFunction f, typename UnaryFunction::argument_type a,
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typename UnaryFunction::result_type y,
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typename UnaryFunction::argument_type step)
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{
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typedef typename UnaryFunction::result_type result_type;
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if(y >= 1.0)
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return std::numeric_limits<result_type>::infinity();
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typename UnaryFunction::argument_type b = a;
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for(result_type result = 0; result < y; b += step)
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result += step*f(b);
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return b;
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}
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#endif /* INTEGRATE_HPP */
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