[29] | 1 | /* integrate.hpp header file |
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| 2 | * |
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| 3 | * Copyright Jens Maurer 2000 |
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| 4 | * Distributed under the Boost Software License, Version 1.0. (See |
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| 5 | * accompanying file LICENSE_1_0.txt or copy at |
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| 6 | * http://www.boost.org/LICENSE_1_0.txt) |
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| 7 | * |
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| 8 | * $Id: integrate.hpp,v 1.5 2004/07/27 03:43:34 dgregor Exp $ |
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| 9 | * |
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| 10 | * Revision history |
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| 11 | * 01 April 2001: Modified to use new <boost/limits.hpp> header. (JMaddock) |
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| 12 | */ |
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| 13 | |
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| 14 | #ifndef INTEGRATE_HPP |
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| 15 | #define INTEGRATE_HPP |
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| 16 | |
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| 17 | #include <boost/limits.hpp> |
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| 18 | |
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| 19 | template<class UnaryFunction> |
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| 20 | inline typename UnaryFunction::result_type |
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| 21 | trapezoid(UnaryFunction f, typename UnaryFunction::argument_type a, |
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| 22 | typename UnaryFunction::argument_type b, int n) |
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| 23 | { |
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| 24 | typename UnaryFunction::result_type tmp = 0; |
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| 25 | for(int i = 1; i <= n-1; ++i) |
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| 26 | tmp += f(a+(b-a)/n*i); |
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| 27 | return (b-a)/2/n * (f(a) + f(b) + 2*tmp); |
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| 28 | } |
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| 29 | |
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| 30 | template<class UnaryFunction> |
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| 31 | inline typename UnaryFunction::result_type |
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| 32 | simpson(UnaryFunction f, typename UnaryFunction::argument_type a, |
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| 33 | typename UnaryFunction::argument_type b, int n) |
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| 34 | { |
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| 35 | typename UnaryFunction::result_type tmp1 = 0; |
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| 36 | for(int i = 1; i <= n-1; ++i) |
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| 37 | tmp1 += f(a+(b-a)/n*i); |
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| 38 | typename UnaryFunction::result_type tmp2 = 0; |
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| 39 | for(int i = 1; i <= n ; ++i) |
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| 40 | tmp2 += f(a+(b-a)/2/n*(2*i-1)); |
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| 41 | |
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| 42 | return (b-a)/6/n * (f(a) + f(b) + 2*tmp1 + 4*tmp2); |
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| 43 | } |
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| 44 | |
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| 45 | // compute b so that f(b) = y; assume f is monotone increasing |
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| 46 | template<class UnaryFunction> |
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| 47 | inline typename UnaryFunction::argument_type |
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| 48 | invert_monotone_inc(UnaryFunction f, typename UnaryFunction::result_type y, |
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| 49 | typename UnaryFunction::argument_type lower = -1, |
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| 50 | typename UnaryFunction::argument_type upper = 1) |
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| 51 | { |
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| 52 | while(upper-lower > 1e-6) { |
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| 53 | double middle = (upper+lower)/2; |
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| 54 | if(f(middle) > y) |
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| 55 | upper = middle; |
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| 56 | else |
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| 57 | lower = middle; |
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| 58 | } |
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| 59 | return (upper+lower)/2; |
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| 60 | } |
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| 61 | |
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| 62 | // compute b so that I(f(x), a, b) == y |
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| 63 | template<class UnaryFunction> |
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| 64 | inline typename UnaryFunction::argument_type |
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| 65 | quantil(UnaryFunction f, typename UnaryFunction::argument_type a, |
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| 66 | typename UnaryFunction::result_type y, |
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| 67 | typename UnaryFunction::argument_type step) |
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| 68 | { |
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| 69 | typedef typename UnaryFunction::result_type result_type; |
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| 70 | if(y >= 1.0) |
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| 71 | return std::numeric_limits<result_type>::infinity(); |
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| 72 | typename UnaryFunction::argument_type b = a; |
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| 73 | for(result_type result = 0; result < y; b += step) |
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| 74 | result += step*f(b); |
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| 75 | return b; |
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| 76 | } |
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| 77 | |
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| 78 | |
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| 79 | #endif /* INTEGRATE_HPP */ |
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