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Reference Guide
NumericalMinimization.C
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1 /// \file
2 /// \ingroup tutorial_fit
3 /// \notebook -nodraw
4 /// Example on how to use the new Minimizer class in ROOT
5 /// Show usage with all the possible minimizers.
6 /// Minimize the Rosenbrock function (a 2D -function)
7 /// This example is described also in
8 /// http://root.cern.ch/drupal/content/numerical-minimization#multidim_minim
9 /// input : minimizer name + algorithm name
10 /// randomSeed: = <0 : fixed value: 0 random with seed 0; >0 random with given seed
11 ///
12 /// \macro_code
13 ///
14 /// \author Lorenzo Moneta
15 
16 #include "Math/Minimizer.h"
17 #include "Math/Factory.h"
18 #include "Math/Functor.h"
19 #include "TRandom2.h"
20 #include "TError.h"
21 #include <iostream>
22 
23 double RosenBrock(const double *xx )
24 {
25  const Double_t x = xx[0];
26  const Double_t y = xx[1];
27  const Double_t tmp1 = y-x*x;
28  const Double_t tmp2 = 1-x;
29  return 100*tmp1*tmp1+tmp2*tmp2;
30 }
31 
32 int NumericalMinimization(const char * minName = "Minuit2",
33  const char *algoName = "" ,
34  int randomSeed = -1)
35 {
36  // create minimizer giving a name and a name (optionally) for the specific
37  // algorithm
38  // possible choices are:
39  // minName algoName
40  // Minuit /Minuit2 Migrad, Simplex,Combined,Scan (default is Migrad)
41  // Minuit2 Fumili2
42  // Fumili
43  // GSLMultiMin ConjugateFR, ConjugatePR, BFGS,
44  // BFGS2, SteepestDescent
45  // GSLMultiFit
46  // GSLSimAn
47  // Genetic
48  ROOT::Math::Minimizer* minimum =
49  ROOT::Math::Factory::CreateMinimizer(minName, algoName);
50 
51  // set tolerance , etc...
52  minimum->SetMaxFunctionCalls(1000000); // for Minuit/Minuit2
53  minimum->SetMaxIterations(10000); // for GSL
54  minimum->SetTolerance(0.001);
55  minimum->SetPrintLevel(1);
56 
57  // create function wrapper for minimizer
58  // a IMultiGenFunction type
59  ROOT::Math::Functor f(&RosenBrock,2);
60  double step[2] = {0.01,0.01};
61  // starting point
62 
63  double variable[2] = { -1.,1.2};
64  if (randomSeed >= 0) {
65  TRandom2 r(randomSeed);
66  variable[0] = r.Uniform(-20,20);
67  variable[1] = r.Uniform(-20,20);
68  }
69 
70  minimum->SetFunction(f);
71 
72  // Set the free variables to be minimized !
73  minimum->SetVariable(0,"x",variable[0], step[0]);
74  minimum->SetVariable(1,"y",variable[1], step[1]);
75 
76  // do the minimization
77  minimum->Minimize();
78 
79  const double *xs = minimum->X();
80  std::cout << "Minimum: f(" << xs[0] << "," << xs[1] << "): "
81  << minimum->MinValue() << std::endl;
82 
83  // expected minimum is 0
84  if ( minimum->MinValue() < 1.E-4 && f(xs) < 1.E-4)
85  std::cout << "Minimizer " << minName << " - " << algoName
86  << " converged to the right minimum" << std::endl;
87  else {
88  std::cout << "Minimizer " << minName << " - " << algoName
89  << " failed to converge !!!" << std::endl;
90  Error("NumericalMinimization","fail to converge");
91  }
92 
93  return 0;
94 }
void SetMaxIterations(unsigned int maxiter)
set maximum iterations (one iteration can have many function calls)
Definition: Minimizer.h:451
Documentation for class Functor class.
Definition: Functor.h:392
Random number generator class based on the maximally quidistributed combined Tausworthe generator by ...
Definition: TRandom2.h:27
static ROOT::Math::Minimizer * CreateMinimizer(const std::string &minimizerType="", const std::string &algoType="")
static method to create the corrisponding Minimizer given the string Supported Minimizers types are: ...
Definition: Factory.cxx:63
Double_t x[n]
Definition: legend1.C:17
Abstract Minimizer class, defining the interface for the various minimizer (like Minuit2, Minuit, GSL, etc..) Plug-in&#39;s exist in ROOT to be able to instantiate the derived classes like ROOT::Math::GSLMinimizer or ROOT::Math::Minuit2Minimizer via the plug-in manager.
Definition: Minimizer.h:78
virtual double MinValue() const =0
return minimum function value
virtual bool Minimize()=0
method to perform the minimization
virtual const double * X() const =0
return pointer to X values at the minimum
void Error(const char *location, const char *msgfmt,...)
virtual void SetFunction(const ROOT::Math::IMultiGenFunction &func)=0
set the function to minimize
ROOT::R::TRInterface & r
Definition: Object.C:4
void SetMaxFunctionCalls(unsigned int maxfcn)
set maximum of function calls
Definition: Minimizer.h:448
double Double_t
Definition: RtypesCore.h:55
void SetTolerance(double tol)
set the tolerance
Definition: Minimizer.h:454
Double_t y[n]
Definition: legend1.C:17
virtual bool SetVariable(unsigned int ivar, const std::string &name, double val, double step)=0
set a new free variable
void SetPrintLevel(int level)
set print level
Definition: Minimizer.h:445