new tutorial for numerical minimization using Minimizer class

git-svn-id: http://root.cern.ch/svn/root/trunk@37449 27541ba8-7e3a-0410-8455-c3a389f83636

tutorials/fit/NumericalMinimization.C

+// tutorial showing how to use the Minimizer class in ROOT
+//  and all the possible minimizer 
+// Minimize the Rosenbrock function (a 2D -function)
+// This example is described also in 
+// http://root.cern.ch/drupal/content/numerical-minimization#multidim_minim
+// input : minimizer name + algorithm name
+// randomSeed: = <0 : fixed value: 0 random with seed 0; >0 random with given seed 
+
+#include "Math/Minimizer.h"
+#include "Math/Factory.h"
+#include "Math/Functor.h"
+#include "TRandom2.h"
+#include "TError.h"
+#include <iostream>
+ 
+double RosenBrock(const double *xx )
+{
+  const Double_t x = xx[0];
+  const Double_t y = xx[1];
+  const Double_t tmp1 = y-x*x;
+  const Double_t tmp2 = 1-x;
+  return 100*tmp1*tmp1+tmp2*tmp2;
+}
+ 
+int NumericalMinimization(const char * minName = "Minuit2",const char *algoName = "" , int randomSeed = -1)
+{
+   // create minimizer giving a name and a name (optionally) for the specific algorithm
+   // possible choices are: 
+   //     minName                  algoName
+   // Minuit /Minuit2             Migrad, Simplex,Combined,Scan  (default is Migrad)
+   //  Minuit2                     Fumili2
+   //  Fumili
+   //  GSLMultiMin                ConjugateFR, ConjugatePR, BFGS, BFGS2, SteepestDescent
+   //  GSLMultiFit
+   //   GSLSimAn
+   //   Genetic
+   ROOT::Math::Minimizer* min = ROOT::Math::Factory::CreateMinimizer(minName, algoName);
+
+   // set tolerance , etc...
+   min->SetMaxFunctionCalls(1000000); // for Minuit/Minuit2 
+   min->SetMaxIterations(10000);  // for GSL 
+   min->SetTolerance(0.001);
+   min->SetPrintLevel(1);
+
+   // create funciton wrapper for minmizer
+   // a IMultiGenFunction type 
+   ROOT::Math::Functor f(&RosenBrock,2); 
+   double step[2] = {0.01,0.01};
+   // starting point
+    
+   double variable[2] = { -1.,1.2};
+   if (randomSeed >= 0) { 
+      TRandom2 r(randomSeed);
+      variable[0] = r.Uniform(-20,20);
+      variable[1] = r.Uniform(-20,20);
+   }
+ 
+   min->SetFunction(f);
+ 
+   // Set the free variables to be minimized!
+   min->SetVariable(0,"x",variable[0], step[0]);
+   min->SetVariable(1,"y",variable[1], step[1]);
+ 
+   // do the minimization
+   min->Minimize(); 
+ 
+   const double *xs = min->X();
+   std::cout << "Minimum: f(" << xs[0] << "," << xs[1] << "): " 
+             << min->MinValue()  << std::endl;
+
+   // expected minimum is 0
+   if ( min->MinValue()  < 1.E-4  && f(xs) < 1.E-4) 
+      std::cout << "Minimizer " << minName << " - " << algoName << "   converged to the right minimum" << std::endl;
+   else {
+      std::cout << "Minimizer " << minName << " - " << algoName << "   failed to converge !!!" << std::endl;
+      Error("NumericalMinimization","fail to converge");
+   }
+ 
+   return 0;
+}