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Derivator.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 Derivator
26//
27// class for calculating Derivative of functions
28//
29// Created by: moneta at Sat Nov 13 14:46:00 2004
30//
31// Last update: Sat Nov 13 14:46:00 2004
32//
33#ifndef ROOT_Math_Derivator
34#define ROOT_Math_Derivator
35
36
37#include "Math/IFunctionfwd.h"
38
40
41
42namespace ROOT {
43namespace Math {
44
45
46
47class GSLDerivator;
48
49//_______________________________________________________________________
50/**
51 Class for computing numerical derivative of a function.
52 Presently this class is implemented only using the numerical derivatives
53 algorithms provided by GSL
54 using the implementation class ROOT::Math::GSLDerivator
55
56 This class does not support copying
57
58 @ingroup Deriv
59*/
60
61class Derivator {
62
63public:
64
65 /**
66 signature for function pointers used by GSL
67 */
68 typedef double ( * GSLFuncPointer ) ( double, void * );
69
70 /**
71 Empty Construct for a Derivator class
72 Need to set the function afterwards with Derivator::SetFunction
73 */
74 Derivator();
75 /**
76 Construct using a ROOT::Math::IGenFunction interface
77 */
78 explicit Derivator(const IGenFunction &f);
79 /**
80 Construct using a GSL function pointer type
81 @param f : free function pointer of the GSL required type
82 @param p : pointer to the object carrying the function state
83 (for example the function object itself)
84 */
85 explicit Derivator(const GSLFuncPointer &f, void * p = 0);
86
87 /// destructor
88 virtual ~Derivator();
89
90 // disable copying
91private:
92
93 Derivator(const Derivator &);
95
96public:
97
98
99#ifdef LATER
100 /**
101 Template methods for generic functions
102 Set the function f for evaluating the derivative.
103 The function type must implement the assigment operator,
104 <em> double operator() ( double x ) </em>
105 */
106 template <class UserFunc>
107 inline void SetFunction(const UserFunc &f) {
108 const void * p = &f;
109 SetFunction( &GSLFunctionAdapter<UserFunc>::F, const_cast<void *>(p) );
110 }
111#endif
112
113 /**
114 Set the function for calculating the derivatives.
115 The function must implement the ROOT::Math::IGenFunction signature
116 */
117 void SetFunction(const IGenFunction &f);
118
119
120 /**
121 Set the function f for evaluating the derivative using a GSL function pointer type
122 @param f : free function pointer of the GSL required type
123 @param p : pointer to the object carrying the function state
124 (for example the function object itself)
125 */
126 void SetFunction( const GSLFuncPointer &f, void * p = 0);
127
128
129
130 /**
131 Computes the numerical derivative of a function f at a point x.
132 It uses Derivator::EvalCentral to compute the derivative using an
133 adaptive central difference algorithm with a step size h
134 */
135
136 double Eval(double x, double h = 1E-8) const;
137
138
139
140 /**
141 Computes the numerical derivative at a point x using an adaptive central
142 difference algorithm with a step size h.
143 */
144 double EvalCentral( double x, double h = 1E-8) const;
145
146 /**
147 Computes the numerical derivative at a point x using an adaptive forward
148 difference algorithm with a step size h.
149 The function is evaluated only at points greater than x and at x itself.
150 */
151 double EvalForward( double x, double h = 1E-8) const;
152
153 /**
154 Computes the numerical derivative at a point x using an adaptive backward
155 difference algorithm with a step size h.
156 The function is evaluated only at points less than x and at x itself.
157 */
158 double EvalBackward( double x, double h = 1E-8) const;
159
160 /** @name --- Static methods ---
161 This methods don't require to use a Derivator object, and are designed to be used in
162 fast calculation. Error and status code cannot be retrieved in this case
163 */
164
165 /**
166 Computes the numerical derivative of a function f at a point x.
167 It uses Derivator::EvalCentral to compute the derivative using an
168 adaptive central difference algorithm with a step size h
169 */
170 static double Eval(const IGenFunction & f, double x, double h = 1E-8);
171
172 /**
173 Computes the numerical derivative of a function f at a point x using an adaptive central
174 difference algorithm with a step size h
175 */
176 static double EvalCentral(const IGenFunction & f, double x, double h = 1E-8);
177
178
179 /**
180 Computes the numerical derivative of a function f at a point x using an adaptive forward
181 difference algorithm with a step size h.
182 The function is evaluated only at points greater than x and at x itself
183 */
184 static double EvalForward(const IGenFunction & f, double x, double h = 1E-8);
185
186 /**
187 Computes the numerical derivative of a function f at a point x using an adaptive backward
188 difference algorithm with a step size h.
189 The function is evaluated only at points less than x and at x itself
190 */
191 static double EvalBackward(const IGenFunction & f, double x, double h = 1E-8);
192
193 // Derivatives for multi-dimension functions
194 /**
195 Evaluate the partial derivative of a multi-dim function
196 with respect coordinate x_icoord at the point x[]
197 */
198 static double Eval(const IMultiGenFunction & f, const double * x, unsigned int icoord = 0, double h = 1E-8);
199
200 /**
201 Evaluate the derivative with respect a parameter for one-dim parameteric function
202 at the point ( x,p[]) with respect the parameter p_ipar
203 */
204 static double Eval(IParamFunction & f, double x, const double * p, unsigned int ipar = 0, double h = 1E-8);
205
206 /**
207 Evaluate the derivative with respect a parameter for a multi-dim parameteric function
208 at the point ( x[],p[]) with respect the parameter p_ipar
209 */
210 static double Eval(IParamMultiFunction & f, const double * x, const double * p, unsigned int ipar = 0, double h = 1E-8);
211
212
213 /**
214 return the error status of the last derivative calculation
215 */
216 int Status() const;
217
218 /**
219 return the result of the last derivative calculation
220 */
221 double Result() const;
222
223 /**
224 return the estimate of the absolute error of the last derivative calculation
225 */
226 double Error() const;
227
228
229private:
230
231
233
234};
235
236
237
238
239} // namespace Math
240} // namespace ROOT
241
242
243#endif /* ROOT_Math_Derivator */
double
Definition: Converters.cxx:939
#define f(i)
Definition: RSha256.hxx:104
#define h(i)
Definition: RSha256.hxx:106
Class for computing numerical derivative of a function.
Definition: Derivator.h:61
void SetFunction(const IGenFunction &f)
Set the function for calculating the derivatives.
Definition: Derivator.cxx:84
GSLDerivator * fDerivator
Definition: Derivator.h:232
double Result() const
return the result of the last derivative calculation
Definition: Derivator.cxx:152
virtual ~Derivator()
destructor
Definition: Derivator.cxx:66
double EvalBackward(double x, double h=1E-8) const
Computes the numerical derivative at a point x using an adaptive backward difference algorithm with a...
Definition: Derivator.cxx:105
int Status() const
return the error status of the last derivative calculation
Definition: Derivator.cxx:156
Derivator & operator=(const Derivator &)
Definition: Derivator.cxx:76
double(* GSLFuncPointer)(double, void *)
signature for function pointers used by GSL
Definition: Derivator.h:68
Derivator()
Empty Construct for a Derivator class Need to set the function afterwards with Derivator::SetFunction...
Definition: Derivator.cxx:47
double Error() const
return the estimate of the absolute error of the last derivative calculation
Definition: Derivator.cxx:154
double Eval(double x, double h=1E-8) const
Computes the numerical derivative of a function f at a point x.
Definition: Derivator.cxx:93
double EvalCentral(double x, double h=1E-8) const
Computes the numerical derivative at a point x using an adaptive central difference algorithm with a ...
Definition: Derivator.cxx:97
double EvalForward(double x, double h=1E-8) const
Computes the numerical derivative at a point x using an adaptive forward difference algorithm with a ...
Definition: Derivator.cxx:101
Class for computing numerical derivative of a function based on the GSL numerical algorithm This clas...
Definition: GSLDerivator.h:62
Class for adapting any C++ functor class to C function pointers used by GSL.
Documentation for the abstract class IBaseFunctionMultiDim.
Definition: IFunction.h:62
Interface (abstract class) for generic functions objects of one-dimension Provides a method to evalua...
Definition: IFunction.h:135
Specialized IParamFunction interface (abstract class) for one-dimensional parametric functions It is ...
Double_t x[n]
Definition: legend1.C:17
Namespace for new Math classes and functions.
tbb::task_arena is an alias of tbb::interface7::task_arena, which doesn't allow to forward declare tb...
constexpr Double_t E()
Base of natural log:
Definition: TMath.h:96