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ChebyshevApprox.h
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1// @(#)root/mathmore:$Id$
2// Authors: L. Moneta, A. Zsenei 08/2005
3
4 /**********************************************************************
5 * *
6 * Copyright (c) 2004 ROOT Foundation, CERN/PH-SFT *
7 * *
8 * This library is free software; you can redistribute it and/or *
9 * modify it under the terms of the GNU General Public License *
10 * as published by the Free Software Foundation; either version 2 *
11 * of the License, or (at your option) any later version. *
12 * *
13 * This library 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. *
17 * *
18 * You should have received a copy of the GNU General Public License *
19 * along with this library (see file COPYING); if not, write *
20 * to the Free Software Foundation, Inc., 59 Temple Place, Suite *
21 * 330, Boston, MA 02111-1307 USA, or contact the author. *
22 * *
23 **********************************************************************/
24
25// Header file for class ChebyshevApprox
26//
27// Created by: moneta at Thu Dec 2 14:51:15 2004
28//
29// Last update: Thu Dec 2 14:51:15 2004
30//
31#ifndef ROOT_Math_ChebyshevApprox
32#define ROOT_Math_ChebyshevApprox
33
34
35
36/**
37 @defgroup FuncApprox Function Approximation (ChebyshevApprox)
38 Numerical algorithm from the \ref MathMore library and implemented using the
39 <A HREF="http://www.gnu.org/software/gsl/manual/html_node/">GSL</A> library
40
41 @ingroup NumAlgo
42 */
43
44
45#include "Math/IFunctionfwd.h"
46
48
49#include <utility>
50#include <cstddef>
51
52
53namespace ROOT {
54namespace Math {
55
56class GSLChebSeries;
57class GSLFunctionWrapper;
58
59//____________________________________________________________________________
60/**
61 Class describing a Chebyshev series which can be used to approximate a
62 function in a defined range [a,b] using Chebyshev polynomials.
63 It uses the algorithm from
64 <A HREF="http://www.gnu.org/software/gsl/manual/html_node/Chebyshev-Approximations.html">GSL</A>
65
66 This class does not support copying
67 @ingroup FuncApprox
68 */
69
70
72
73public:
74
75
76 /**
77 Construct a Chebyshev series approximation to a Function f in range [a,b];
78 constructor based on functions of type IGenFunction
79 */
80
81 ChebyshevApprox(const ROOT::Math::IGenFunction & f, double a, double b, size_t n);
82
83 /**
84 Construct a Chebyshev series approximation to a Function f in range [a,b];
85 constructor based on free functions with gsl_function type signature
86 */
87 ChebyshevApprox(GSLFuncPointer f, void *p, double a, double b, size_t n);
88
89 // destructor
90 virtual ~ChebyshevApprox();
91
92
93private:
94
95 /**
96 construct a Chebyshev series or order n
97 The series must be initialized from a function
98 */
99 ChebyshevApprox(size_t n);
100
101// usually copying is non trivial, so we make this unaccessible
104
105public:
106
107 /**
108 Evaluate the series at a given point x
109 */
110 double operator() ( double x) const;
111
112 /**
113 Evaluate the series at a given point x estimating both the series result and its absolute error.
114 The error estimate is made from the first neglected term in the series.
115 A pair containing result and error is returned
116 */
117 std::pair<double, double> EvalErr( double x) const;
118
119 /**
120 Evaluate the series at a given point, to (at most) the given order n
121 */
122 double operator() ( double x, size_t n) const;
123
124 /**
125 evaluate the series at a given point x to the given order n,
126 estimating both the series result and its absolute error.
127 The error estimate is made from the first neglected term in the series.
128 A pair containing result and error is returned
129 */
130 std::pair<double, double> EvalErr( double x, size_t n) const;
131
132 /**
133 Compute the derivative of the series and return a pointer to a new Chebyshev series with the
134 derivatives coefficients. The returned pointer must be managed by the user.
135 */
136 //TO DO: implement copying to return by value
138
139 /**
140 Compute the integral of the series and return a pointer to a new Chebyshev series with the
141 integral coefficients. The lower limit of the integration is the left range value a.
142 The returned pointer must be managed by the user
143 */
144 //TO DO: implement copying to return by value
146
147protected:
148
149 /**
150 Initialize series passing function and range
151 */
152 void Initialize( GSLFuncPointer f, void * params, double a, double b);
153
154private:
155
156 size_t fOrder;
157
159 GSLFunctionWrapper * fFunction; // pointer to function
160
161};
162
163} // namespace Math
164} // namespace ROOT
165
166#endif /* ROOT_Math_ChebyshevApprox */
#define b(i)
Definition: RSha256.hxx:100
#define f(i)
Definition: RSha256.hxx:104
Class describing a Chebyshev series which can be used to approximate a function in a defined range [a...
ChebyshevApprox & operator=(const ChebyshevApprox &)
ChebyshevApprox * Integral()
Compute the integral of the series and return a pointer to a new Chebyshev series with the integral c...
std::pair< double, double > EvalErr(double x) const
Evaluate the series at a given point x estimating both the series result and its absolute error.
double operator()(double x) const
Evaluate the series at a given point x.
ChebyshevApprox(const ROOT::Math::IGenFunction &f, double a, double b, size_t n)
Construct a Chebyshev series approximation to a Function f in range [a,b]; constructor based on funct...
void Initialize(GSLFuncPointer f, void *params, double a, double b)
Initialize series passing function and range.
ChebyshevApprox * Deriv()
Compute the derivative of the series and return a pointer to a new Chebyshev series with the derivati...
GSLFunctionWrapper * fFunction
wrapper class for C struct gsl_cheb_series
Definition: GSLChebSeries.h:44
Wrapper class to the gsl_function C structure.
Interface (abstract class) for generic functions objects of one-dimension Provides a method to evalua...
Definition: IFunction.h:135
Double_t x[n]
Definition: legend1.C:17
const Int_t n
Definition: legend1.C:16
Namespace for new Math classes and functions.
double(* GSLFuncPointer)(double, void *)
Function pointer corresponding to gsl_function signature.
tbb::task_arena is an alias of tbb::interface7::task_arena, which doesn't allow to forward declare tb...
auto * a
Definition: textangle.C:12