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BrentRootFinder.h
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1// @(#)root/mathcore:$Id$
2// Authors: David Gonzalez Maline 01/2008
3
4/**********************************************************************
5 * *
6 * Copyright (c) 2006 , LCG ROOT MathLib Team *
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. *
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23 **********************************************************************/
24
25// Header for the RootFinder
26//
27// Created by: David Gonzalez Maline : Wed Jan 21 2008
28//
29
30#ifndef ROOT_Math_BrentRootFinder
31#define ROOT_Math_BrentRootFinder
32
33#include "Math/IFunctionfwd.h"
34
36
37namespace ROOT {
38namespace Math {
39
40//___________________________________________________________________________________________
41/**
42 Class for finding the root of a one dimensional function using the Brent algorithm.
43 It will use the Brent Method for finding function roots in a given interval.
44 First, a grid search is used to bracket the root value
45 with the a step size = (xmax-xmin)/npx. The step size
46 can be controlled via the SetNpx() function. A default value of npx = 100 is used.
47 The default value con be changed using the static method SetDefaultNpx.
48 If the function is unimodal or if its extrema are far apart, setting the fNpx to
49 a small value speeds the algorithm up many times.
50 Then, Brent's method is applied on the bracketed interval.
51 It will use the Brent Method for finding function roots in a given interval.
52 If the Brent method fails to converge the bracketing is repeted on the latest best estimate of the
53 interval. The procedure is repeted with a maximum value (default =10) which can be set for all
54 BrentRootFinder classes with the method SetDefaultNSearch
55
56 This class is implemented from TF1::GetX() method.
57
58 @ingroup RootFinders
59
60 */
61
63 public:
64
65
66 /** Default Constructor. */
68
69
70 /** Default Destructor. */
71 virtual ~BrentRootFinder() {}
72
73
74 /** Set function to solve and the interval in where to look for the root.
75
76 \@param f Function to be minimized.
77 \@param xlow Lower bound of the search interval.
78 \@param xup Upper bound of the search interval.
79 */
81 bool SetFunction(const ROOT::Math::IGenFunction& f, double xlow, double xup);
82
83
84 /** Returns the X value corresponding to the function value fy for (xmin<x<xmax).
85 Method:
86 First, the grid search is used to bracket the maximum
87 with the step size = (xmax-xmin)/fNpx. This way, the step size
88 can be controlled via the SetNpx() function. If the function is
89 unimodal or if its extrema are far apart, setting the fNpx to
90 a small value speeds the algorithm up many times.
91 Then, Brent's method is applied on the bracketed interval.
92
93 \@param maxIter maximum number of iterations.
94 \@param absTol desired absolute error in the minimum position.
95 \@param absTol desired relative error in the minimum position.
96 */
97 bool Solve(int maxIter = 100, double absTol = 1E-8, double relTol = 1E-10);
98
99 /** Set the number of point used to bracket root using a grid */
100 void SetNpx(int npx) { fNpx = npx; }
101
102 /**
103 Set a log grid scan (default is equidistant bins)
104 will work only if xlow > 0
105 */
106 void SetLogScan(bool on) { fLogScan = on; }
107
108 /** Returns root value. Need to call first Solve(). */
109 double Root() const { return fRoot; }
110
111 /** Returns status of last estimate. If = 0 is OK */
112 int Status() const { return fStatus; }
113
114 /** Return number of iteration used to find minimum */
115 int Iterations() const { return fNIter; }
116
117 /** Return name of root finder algorithm ("BrentRootFinder"). */
118 const char* Name() const;
119
120 // static function used to modify the default parameters
121
122 /** set number of default Npx used at construction time (when SetNpx is not called)
123 Default value is 100
124 */
125 static void SetDefaultNpx(int npx);
126
127 /** set number of times the bracketing search in combination with is done to find a good interval
128 Default value is 10
129 */
130 static void SetDefaultNSearch(int n);
131
132
133 private:
134
135 const IGenFunction* fFunction; // Pointer to the function.
136 bool fLogScan; // flag to control usage of a log scan
137 int fNIter; // Number of iterations needed for the last estimation.
138 int fNpx; // Number of points to bracket root with initial grid (def is 100)
139 int fStatus; // Status of code of the last estimate
140 double fXMin; // Lower bound of the search interval.
141 double fXMax; // Upper bound of the search interval
142 double fRoot; // Current stimation of the function root.
143 };
144
145} // namespace Math
146} // namespace ROOT
147
148#endif /* ROOT_Math_BrentRootFinder */
#define f(i)
Definition: RSha256.hxx:104
Class for finding the root of a one dimensional function using the Brent algorithm.
const char * Name() const
Return name of root finder algorithm ("BrentRootFinder").
double Root() const
Returns root value.
BrentRootFinder()
Default Constructor.
int Status() const
Returns status of last estimate.
const IGenFunction * fFunction
bool Solve(int maxIter=100, double absTol=1E-8, double relTol=1E-10)
Returns the X value corresponding to the function value fy for (xmin<x<xmax).
static void SetDefaultNpx(int npx)
set number of default Npx used at construction time (when SetNpx is not called) Default value is 100
static void SetDefaultNSearch(int n)
set number of times the bracketing search in combination with is done to find a good interval Default...
void SetNpx(int npx)
Set the number of point used to bracket root using a grid.
bool SetFunction(const ROOT::Math::IGenFunction &f, double xlow, double xup)
Sets the function for the rest of the algorithms.
void SetLogScan(bool on)
Set a log grid scan (default is equidistant bins) will work only if xlow > 0.
int Iterations() const
Return number of iteration used to find minimum.
virtual ~BrentRootFinder()
Default Destructor.
Interface (abstract class) for generic functions objects of one-dimension Provides a method to evalua...
Definition: IFunction.h:135
Interface for finding function roots of one-dimensional functions.
virtual bool SetFunction(const ROOT::Math::IGradFunction &, double)
Sets the function for algorithms using derivatives.
const Int_t n
Definition: legend1.C:16
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