1 /*! ========================================================================
2 ** Extended Template and Library
3 ** Calculus Functional Classes Implementation
6 ** Copyright (c) 2002 Robert B. Quattlebaum Jr.
8 ** This package is free software; you can redistribute it and/or
9 ** modify it under the terms of the GNU General Public License as
10 ** published by the Free Software Foundation; either version 2 of
11 ** the License, or (at your option) any later version.
13 ** This package is distributed in the hope that it will be useful,
14 ** but WITHOUT ANY WARRANTY; without even the implied warranty of
15 ** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
16 ** General Public License for more details.
18 ** === N O T E S ===========================================================
20 ** ========================================================================= */
22 /* === S T A R T =========================================================== */
24 #ifndef __ETL__CALCULUS_H
25 #define __ETL__CALCULUS_H
27 /* === H E A D E R S ======================================================= */
33 /* === M A C R O S ========================================================= */
36 //#define _EPSILON 0.0000001
39 /* === T Y P E D E F S ===================================================== */
41 /* === C L A S S E S & S T R U C T S ======================================= */
46 class derivative : public std::unary_function<typename T::argument_type,typename T::result_type>
49 typename T::argument_type epsilon;
51 explicit derivative(const T &x, const typename T::argument_type &epsilon=0.000001):func(x),epsilon(epsilon) { }
53 typename T::result_type
54 operator()(const typename T::argument_type &x)const
56 return (func(x+epsilon)-func(x))/epsilon;
61 class derivative<hermite<T> > : public std::unary_function<typename hermite<T>::argument_type,typename hermite<T>::result_type>
65 explicit derivative(const hermite<T> &x):func(x) { }
67 typename hermite<T>::result_type
68 operator()(const typename hermite<T>::argument_type &x)const
70 T a = func[0], b = func[1], c = func[2], d = func[3];
71 typename hermite<T>::argument_type y(1-x);
72 return ((b-a)*y*y + (c-b)*x*y*2 + (d-c)*x*x) * 3;
77 class integral : public std::binary_function<typename T::argument_type,typename T::argument_type,typename T::result_type>
82 explicit integral(const T &x, const int &samples=500):func(x),samples(samples) { }
84 typename T::result_type
85 operator()(typename T::argument_type x,typename T::argument_type y)const
87 typename T::result_type ret=0;
89 const typename T::argument_type increment=(y-x)/i;
91 for(;i;i--,x+=increment)
92 ret+=(func(x)+func(x+increment))*increment/2;
99 /* === E N D =============================================================== */