Hello!
I am a student trying to understand the wonderful tutorial macro NumericalMinimization.C: I have a few questions, which I put in bold below (I have tried to research these online but haven’t found explanation beyond the macro itself…)
// Example on how to use the new Minimizer class in ROOT
// Show usage with all the possible minimizers.
// Minimize the Rosenbrock function (a 2D -function)
// This example is described also in
// root.cern.ch/drupal/content/nume … idim_minim
// input : minimizer name + algorithm name
// randomSeed: = <0 : fixed value: 0 random with seed 0; >0 random with given seed What does this parameter do?
//
//Author: L. Moneta Dec 2010
#include “Math/Minimizer.h”
#include “Math/Factory.h”
#include “Math/Functor.h”
#include “TRandom2.h”
#include “TError.h”
#include
double RosenBrock(const double xx )
{
const Double_t x = xx[0];
const Double_t y = xx[1];
const Double_t tmp1 = y-xx;
const Double_t tmp2 = 1-x;
return 100tmp1tmp1+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::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}; How was this double determined, and what does it do?
// starting point
double variable[2] = { -1.,1.2}; How was this double determined, and what does it do?
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;
}