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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
23double 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
32int 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
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}
ROOT::R::TRInterface & r
Definition Object.C:4
#define f(i)
Definition RSha256.hxx:104
double Double_t
Definition RtypesCore.h:59
void Error(const char *location, const char *msgfmt,...)
Use this function in case an error occurred.
Definition TError.cxx:187
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
Documentation for class Functor class.
Definition Functor.h:400
Abstract Minimizer class, defining the interface for the various minimizer (like Minuit2,...
Definition Minimizer.h:75
virtual const double * X() const =0
return pointer to X values at the minimum
void SetMaxIterations(unsigned int maxiter)
set maximum iterations (one iteration can have many function calls)
Definition Minimizer.h:450
virtual void SetFunction(const ROOT::Math::IMultiGenFunction &func)=0
set the function to minimize
void SetTolerance(double tol)
set the tolerance
Definition Minimizer.h:453
virtual bool Minimize()=0
method to perform the minimization
void SetPrintLevel(int level)
set print level
Definition Minimizer.h:444
virtual bool SetVariable(unsigned int ivar, const std::string &name, double val, double step)=0
set a new free variable
void SetMaxFunctionCalls(unsigned int maxfcn)
set maximum of function calls
Definition Minimizer.h:447
virtual double MinValue() const =0
return minimum function value
Random number generator class based on the maximally quidistributed combined Tausworthe generator by ...
Definition TRandom2.h:27
Double_t y[n]
Definition legend1.C:17
Double_t x[n]
Definition legend1.C:17