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GSLMultiRootFinder.h
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1// @(#)root/mathmore:$Id$
2// Author: L. Moneta 03/2011
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 *
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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. *
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23 **********************************************************************/
24
25// Header file for class GSLMultiRootFinder
26//
27
28#ifndef ROOT_Math_GSLMultiRootFinder
29#define ROOT_Math_GSLMultiRootFinder
30
31
32
33#include "Math/IFunction.h"
34
36
37#include <vector>
38
39#include <iostream>
40
41namespace ROOT {
42namespace Math {
43
44
45 class GSLMultiRootBaseSolver;
46
47 /** @defgroup MultiRoot Multidimensional ROOT finding
48 Classes for finding the roots of a multi-dimensional system.
49 @ingroup NumAlgo
50 */
51
52 /**
53 Class for Multidimensional root finding algorithms bassed on GSL. This class is used to solve a
54 non-linear system of equations:
55
56 f1(x1,....xn) = 0
57 f2(x1,....xn) = 0
58 ..................
59 fn(x1,....xn) = 0
60
61 See the GSL <A HREF="http://www.gnu.org/software/gsl/manual/html_node/Multidimensional-Root_002dFinding.html"> online manual</A> for
62 information on the GSL MultiRoot finding algorithms
63
64 The available GSL algorithms require the derivatives of the supplied functions or not (they are
65 computed internally by GSL). In the first case the user needs to provide a list of multidimensional functions implementing the
66 gradient interface (ROOT::Math::IMultiGradFunction) while in the second case it is enough to supply a list of
67 functions impelmenting the ROOT::Math::IMultiGenFunction interface.
68 The available algorithms requiring derivatives (see also the GSL
69 <A HREF="http://www.gnu.org/software/gsl/manual/html_node/Algorithms-using-Derivatives.html">documentation</A> )
70 are the followings:
71 <ul>
72 <li><tt>ROOT::Math::GSLMultiRootFinder::kHybridSJ</tt> with name <it>"HybridSJ"</it>: modified Powell's hybrid
73 method as implemented in HYBRJ in MINPACK
74 <li><tt>ROOT::Math::GSLMultiRootFinder::kHybridJ</tt> with name <it>"HybridJ"</it>: unscaled version of the
75 previous algorithm</li>
76 <li><tt>ROOT::Math::GSLMultiRootFinder::kNewton</tt> with name <it>"Newton"</it>: Newton method </li>
77 <li><tt>ROOT::Math::GSLMultiRootFinder::kGNewton</tt> with name <it>"GNewton"</it>: modified Newton method </li>
78 </ul>
79 The algorithms without derivatives (see also the GSL
80 <A HREF="http://www.gnu.org/software/gsl/manual/html_node/Algorithms-without-Derivatives.html">documentation</A> )
81 are the followings:
82 <ul>
83 <li><tt>ROOT::Math::GSLMultiRootFinder::kHybridS</tt> with name <it>"HybridS"</it>: same as HybridSJ but using
84 finate difference approximation for the derivatives</li>
85 <li><tt>ROOT::Math::GSLMultiRootFinder::kHybrid</tt> with name <it>"Hybrid"</it>: unscaled version of the
86 previous algorithm</li>
87 <li><tt>ROOT::Math::GSLMultiRootFinder::kDNewton</tt> with name <it>"DNewton"</it>: discrete Newton algorithm </li>
88 <li><tt>ROOT::Math::GSLMultiRootFinder::kBroyden</tt> with name <it>"Broyden"</it>: Broyden algorithm </li>
89 </ul>
90
91 @ingroup MultiRoot
92 */
93
94
96
97 public:
98
99 /**
100 enumeration specifying the types of GSL multi root finders
101 requiring the derivatives
102
103 */
109 };
110 /**
111 enumeration specifying the types of GSL multi root finders
112 which do not require the derivatives
113
114 */
115 enum EType {
120 };
121
122
123
124 /// create a multi-root finder based on an algorithm not requiring function derivative
126
127 /// create a multi-root finder based on an algorithm requiring function derivative
129
130 /*
131 create a multi-root finder using a string.
132 The names are those defined in the GSL manuals
133 after having remived the GSL prefix (gsl_multiroot_fsolver).
134 Default algorithm is "hybrids" (without derivative).
135 */
136 GSLMultiRootFinder(const char * name = 0);
137
138 /// destructor
139 virtual ~GSLMultiRootFinder();
140
141 private:
142 // usually copying is non trivial, so we make this unaccessible
145
146 public:
147
148 /// set the type for an algorithm without derivatives
150 fType = type; fUseDerivAlgo = false;
151 }
152
153 /// set the type of algorithm using derivatives
155 fType = type; fUseDerivAlgo = true;
156 }
157
158 /// set the type using a string
159 void SetType(const char * name);
160
161 /*
162 add the list of functions f1(x1,..xn),...fn(x1,...xn). The list must contain pointers of
163 ROOT::Math::IMultiGenFunctions. The method requires the
164 the begin and end of the list iterator.
165 The list can be any stl container or a simple array of ROOT::Math::IMultiGenFunctions* or
166 whatever implementing an iterator.
167 If using a derivative type algorithm the function pointers must implement the
168 ROOT::Math::IMultiGradFunction interface
169 */
170 template<class FuncIterator>
171 bool SetFunctionList( FuncIterator begin, FuncIterator end) {
172 bool ret = true;
173 for (FuncIterator itr = begin; itr != end; ++itr) {
174 const ROOT::Math::IMultiGenFunction * f = *itr;
175 ret &= AddFunction( *f);
176 }
177 return ret;
178 }
179
180 /*
181 add (set) a single function fi(x1,...xn) which is part of the system of
182 specifying the begin and end of the iterator.
183 If using a derivative type algorithm the function must implement the
184 ROOT::Math::IMultiGradFunction interface
185 Return the current number of function in the list and 0 if failed to add the function
186 */
188
189 /// same method as before but using any function implementing
190 /// the operator(), so can be wrapped in a IMultiGenFunction interface
191 template <class Function>
192 int AddFunction( Function & f, int ndim) {
193 // no need to care about lifetime of wfunc. It will be cloned inside AddFunction
195 return AddFunction(wfunc);
196 }
197
198 /**
199 return the number of sunctions set in the class.
200 The number must be equal to the dimension of the functions
201 */
202 unsigned int Dim() const { return fFunctions.size(); }
203
204 /// clear list of functions
205 void Clear();
206
207 /// return the root X values solving the system
208 const double * X() const;
209
210 /// return the function values f(X) solving the system
211 /// i.e. they must be close to zero at the solution
212 const double * FVal() const;
213
214 /// return the last step size
215 const double * Dx() const;
216
217
218 /**
219 Find the root starting from the point X;
220 Use the number of iteration and tolerance if given otherwise use
221 default parameter values which can be defined by
222 the static method SetDefault...
223 */
224 bool Solve(const double * x, int maxIter = 0, double absTol = 0, double relTol = 0);
225
226 /// Return number of iterations
227 int Iterations() const {
228 return fIter;
229 }
230
231 /// Return the status of last root finding
232 int Status() const { return fStatus; }
233
234 /// Return the algorithm name used for solving
235 /// Note the name is available only after having called solved
236 /// Otherwise an empyty string is returned
237 const char * Name() const;
238
239 /*
240 set print level
241 level = 0 quiet (no messages print)
242 = 1 print only the result
243 = 3 max debug. Print result at each iteration
244 */
245 void SetPrintLevel(int level) { fPrintLevel = level; }
246
247 /// return the print level
248 int PrintLevel() const { return fPrintLevel; }
249
250
251 //-- static methods to set configurations
252
253 /// set tolerance (absolute and relative)
254 /// relative tolerance is only use to verify the convergence
255 /// do it is a minor parameter
256 static void SetDefaultTolerance(double abstol, double reltol = 0 );
257
258 /// set maximum number of iterations
259 static void SetDefaultMaxIterations(int maxiter);
260
261 /// print iteration state
262 void PrintState(std::ostream & os = std::cout);
263
264
265 protected:
266
267 // return type given a name
268 std::pair<bool,int> GetType(const char * name);
269 // clear list of functions
270 void ClearFunctions();
271
272
273 private:
274
275 int fIter; // current numer of iterations
276 int fStatus; // current status
277 int fPrintLevel; // print level
278
279 // int fMaxIter; // max number of iterations
280 // double fAbsTolerance; // absolute tolerance
281 // double fRelTolerance; // relative tolerance
282 int fType; // type of algorithm
283 bool fUseDerivAlgo; // algorithm using derivative
284
286 std::vector<ROOT::Math::IMultiGenFunction *> fFunctions; //! transient Vector of the functions
287
288
289 };
290
291 // use typedef for most sensible name
293
294} // namespace Math
295} // namespace ROOT
296
297
298#endif /* ROOT_Math_GSLMultiRootFinder */
#define f(i)
Definition: RSha256.hxx:104
char name[80]
Definition: TGX11.cxx:109
int type
Definition: TGX11.cxx:120
Double_t(* Function)(Double_t)
Definition: Functor.C:4
GSLMultiRootBaseSolver, internal class for implementing GSL multi-root finders This is the base class...
Class for Multidimensional root finding algorithms bassed on GSL.
GSLMultiRootFinder & operator=(const GSLMultiRootFinder &)
unsigned int Dim() const
return the number of sunctions set in the class.
const double * Dx() const
return the last step size
virtual ~GSLMultiRootFinder()
destructor
const double * FVal() const
return the function values f(X) solving the system i.e.
void SetType(EDerivType type)
set the type of algorithm using derivatives
void SetType(EType type)
set the type for an algorithm without derivatives
std::vector< ROOT::Math::IMultiGenFunction * > fFunctions
bool Solve(const double *x, int maxIter=0, double absTol=0, double relTol=0)
Find the root starting from the point X; Use the number of iteration and tolerance if given otherwise...
EType
enumeration specifying the types of GSL multi root finders which do not require the derivatives
std::pair< bool, int > GetType(const char *name)
bool SetFunctionList(FuncIterator begin, FuncIterator end)
const char * Name() const
Return the algorithm name used for solving Note the name is available only after having called solved...
void PrintState(std::ostream &os=std::cout)
print iteration state
int PrintLevel() const
return the print level
GSLMultiRootBaseSolver * fSolver
int Status() const
Return the status of last root finding.
EDerivType
enumeration specifying the types of GSL multi root finders requiring the derivatives
GSLMultiRootFinder(EType type)
create a multi-root finder based on an algorithm not requiring function derivative
int AddFunction(Function &f, int ndim)
same method as before but using any function implementing the operator(), so can be wrapped in a IMul...
void Clear()
clear list of functions
static void SetDefaultTolerance(double abstol, double reltol=0)
set tolerance (absolute and relative) relative tolerance is only use to verify the convergence do it ...
int AddFunction(const ROOT::Math::IMultiGenFunction &func)
const double * X() const
return the root X values solving the system
static void SetDefaultMaxIterations(int maxiter)
set maximum number of iterations
int Iterations() const
Return number of iterations.
Documentation for the abstract class IBaseFunctionMultiDim.
Definition: IFunction.h:62
Template class to wrap any C++ callable object implementing operator() (const double * x) in a multi-...
Double_t x[n]
Definition: legend1.C:17
Namespace for new Math classes and functions.
GSLMultiRootFinder MultiRootFinder
Namespace for new ROOT classes and functions.
Definition: StringConv.hxx:21