void solve(TString outFileName){
ROOT::Math::Minimizer* min = ROOT::Math::Factory::CreateMinimizer("Minuit2", "MIGRAD");
min->SetMaxFunctionCalls(1000000);
min->SetTolerance(0.001);
min->SetPrintLevel(10);
ROOT::Math::Functor f(&totalDist,4);
double step[4] = {0.01,0.01,.01,.01};
double variable[4] = { 0,0,50,0};
min->SetFunction(f);
min->SetVariable(0,"x" ,variable[0], step[0]);
min->SetVariable(1,"y" ,variable[1], step[1]);
min->SetVariable(2,"z" ,variable[2], step[2]);
min->SetVariable(3,"phi",variable[3], step[3]);
// do the minimization
min->Minimize();
const double *xs = min->X();
std::cout << "Minimum: f(" << xs[0] << "," << xs[1]<< "," << xs[2]<< "," << xs[3] << "): "
<< min->MinValue() << std::endl;
setZ=xs[2];
ROOT::Math::Minimizer* min2 = ROOT::Math::Factory::CreateMinimizer("Minuit2", "MIGRAD");
min2->SetMaxFunctionCalls(1000000);
min2->SetTolerance(0.001);
min2->SetPrintLevel(10);
ROOT::Math::Functor f2(&totalDistWithoutZ,3);
double step2[3] = {0.01,0.01,.01};
double variable2[3] = { xs[0],xs[1],xs[3]};
min2->SetFunction(f2);
min2->SetVariable(0,"x" ,variable2[0], step2[0]);
min2->SetVariable(1,"y" ,variable2[1], step2[1]);
min2->SetVariable(2,"phi",variable2[2], step2[2]);
// do the minimization
min2->Minimize();
const double *xs2 = min2->X();
std::cout << "Minimum: f(" << xs2[0] << "," << xs2[1]<< "," << xs2[2] << "): "
<< min2->MinValue() << std::endl;
// // expected minimum is 0
// if ( min->MinValue() < 1.E-4 && f(xs) < 1.E-4)
// std::cout << " converged to the right minimum" << std::endl;
// else {
// std::cout << " failed to converge !!!" << std::endl;
// Error("NumericalMinimization","fail to converge");
// }
}
void find_chisqMin()
{
chisq=0.;
for(int i=0; i<numSpectra; i++)
{
// for more information see minimizer class documentation
// https://root.cern.ch/root/html/ROOT__Math__Minimizer.html
char minName[132] = "Minuit";
char algoName[132] = ""; // default conjugate gradient type method
ROOT::Math::Minimizer* min = ROOT::Math::Factory::CreateMinimizer(minName, algoName);
// set tolerance , etc...
min->SetMaxFunctionCalls(1000000); // for Minuit
min->SetMaxIterations(10000); // for GSL
min->SetTolerance(0.001);
min->SetPrintLevel(0); // set to 1 for more info
// communication to the likelihood ratio function
// (via global parameters)
for(int j=0; j<S32K; j++)
{
expCurrent[j] = (double)expHist[spectrum[i]][j];
simCurrent[j] = (double)dOutHist[spectrum[i]][j];
}
spCurrent = i;
// create funciton wrapper for minmizer
// a IMultiGenFunction type
ROOT::Math::Functor lr(&lrchisq,3);
// behaves best when these are small
// starting point
double variable[3] = {0.001,0.001,0.001};
// step size
double step[3] = {0.0001,0.0001,0.0001};
min->SetFunction(lr);
// Set pars for minimization
min->SetVariable(0,"a0",variable[0],step[0]);
min->SetVariable(1,"a1",variable[1],step[1]);
min->SetVariable(2,"a2",variable[2],step[2]);
// do the minimization
min->Minimize();
// grab parameters from minimum
const double *xs = min->X();
// print results
/* std::cout << "Minimum: f(" << xs[0] << "," << xs[1] << "," << xs[2] << "): " */
/* << min->MinValue() << std::endl; */
// assuming 3 parameters
// save pars
for(int j=0;j<3;j++)
aFinal[j][i] = xs[j];
// add to total chisq
chisq += min->MinValue();
}
}
/* Main part of macro */
void fitData( TGraphErrors *gdata , TF1* ffit , double *startval )
{
cout << "\n***** fitData.C: Starting fitting procedure... *****" << endl;
g_data_global = gdata;
f_fit_global = ffit;
if ( g_data_global == NULL )
{
cout << "fitData.C: Did no find any data to fit." << endl;
return NULL;
}
const char * minName = "Minuit2";
const char *algoName = "Migrad";
// 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);
/* Alternatice constructor for Minuit */
//ROOT::Minuit2::Minuit2Minimizer *min = new ROOT::Minuit2::Minuit2Minimizer();
//TMinuit *min = new TMinuit();
// 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(&Chi2_log,3);
double step[3] = {0.1,0.1,10};
// starting point
double variable[3] = { startval[0],startval[1],startval[2]};
// set function to minimize (this is the Chi2 function)
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]);
min->SetVariable(2,"z",variable[2], step[2]);
// do the minimization
min->Minimize();
/* set function parameters to best fit results */
const double *xs = min->X();
f_fit_global->SetParameter(0, xs[0]);
f_fit_global->SetParameter(1, xs[1]);
f_fit_global->SetParameter(2, xs[2]);
/* Print summaries of minimization process */
std::cout << "Minimum: f(" << xs[0] << ", " << xs[1] << ", " << xs[2] << "): "
<< 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");
}
/* Get degrees of freedom NDF */
unsigned ndf = 0;
/* get range of function used for fit */
double fit_min, fit_max;
f_fit_global->GetRange(fit_min,fit_max);
/* count data points in range of function */
for ( int p = 0; p < g_data_global->GetN(); p++ )
{
if ( g_data_global->GetX()[p] >= fit_min && g_data_global->GetX()[p] <= fit_max )
{
ndf++;
}
}
ndf -= 3; // 3 parameters in fit
cout << "Degrees of freedom: " << ndf << " --> chi2 / NDF = " << min->MinValue() / ndf << endl;
/* Get error covariance matrix from minimizer */
TMatrixD matrix0(3,3);
for ( unsigned i = 0; i < 3; i++ )
{
for ( unsigned j = 0; j < 3; j++ )
{
matrix0[i][j] = min->CovMatrix(i,j);
}
}
matrix0.Print();
/* Get minos error */
double par0_minos_error_up = 0;
double par0_minos_error_low = 0;
double par1_minos_error_up = 0;
double par1_minos_error_low = 0;
double par2_minos_error_up = 0;
double par2_minos_error_low = 0;
min->GetMinosError( 0, par0_minos_error_low, par0_minos_error_up );
min->GetMinosError( 1, par1_minos_error_low, par1_minos_error_up );
min->GetMinosError( 2, par2_minos_error_low, par2_minos_error_up );
cout << "Minos uncertainty parameter 0: up = " << par0_minos_error_up << ", low = " << par0_minos_error_low << endl;
cout << "Minos uncertainty parameter 1: up = " << par1_minos_error_up << ", low = " << par1_minos_error_low << endl;
cout << "Minos uncertainty parameter 2: up = " << par2_minos_error_up << ", low = " << par2_minos_error_low << endl;
/* Plot chi2 */
/* sigmas symmetric from covariance matrix */
//double sigmas[6] = {sqrt(matrix0[0][0]), sqrt(matrix0[0][0]), sqrt(matrix0[1][1]), sqrt(matrix0[1][1]), sqrt(matrix0[2][2]), sqrt(matrix0[2][2])};
/* sigmas asymmetric from minos */
double sigmas[6] = {par0_minos_error_low, par0_minos_error_up, par1_minos_error_low, par1_minos_error_up, par2_minos_error_low, par2_minos_error_up};
plotChi2( g_data_global, f_fit_global, 3, sigmas );
/* Draw contour plots */
TGraph2D* gcontour3D = plotContour( min , 3 , ndf );
/* Find error boundaries */
TF1* flow = (TF1*)f_fit_global->Clone("flow");
TF1* fup = (TF1*)f_fit_global->Clone("fup");
flow->SetRange(0,100000);
flow->SetLineColor(kBlue);
flow->SetLineStyle(2);
fup->SetRange(0,100000);
fup->SetLineColor(kBlue);
fup->SetLineStyle(2);
findErrorBounds( f_fit_global, flow, fup, gcontour3D );
/* plot residuals data w.r.t. fit */
plotResiduals( g_data_global, f_fit_global, flow, fup );
/* Draw data, best fit, and 1-sigma band */
TCanvas *cfit = new TCanvas();
g_data_global->Draw("AP");
//f_fit_global->SetRange(0,4000);
f_fit_global->Draw("same");
flow->Draw("same");
fup->Draw("same");
cfit->Print("new_FitResult.png");
/* Fit Extrapolation */
double t_extrapolate_months = 6;
double t_extrapolate_s = t_extrapolate_months * 30 * 24 * 60 * 60;
cout << "Extrapolation to " << t_extrapolate_months
<< " months: " << ffit->Eval( t_extrapolate_s )
<< " , up: " << fup->Eval( t_extrapolate_s ) - ffit->Eval( t_extrapolate_s )
<< " , low: " << flow->Eval( t_extrapolate_s ) - ffit->Eval( t_extrapolate_s )
<< endl;
return f_fit_global;
}
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* minimum =
ROOT::Math::Factory::CreateMinimizer(minName, algoName);
// set tolerance , etc...
minimum->SetMaxFunctionCalls(1000000); // for Minuit/Minuit2
minimum->SetMaxIterations(10000); // for GSL
minimum->SetTolerance(0.001);
minimum->SetPrintLevel(1);
// create function wrapper for minimizer
// 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);
}
minimum->SetFunction(f);
// Set the free variables to be minimized !
minimum->SetVariable(0,"x",variable[0], step[0]);
minimum->SetVariable(1,"y",variable[1], step[1]);
// do the minimization
minimum->Minimize();
const double *xs = minimum->X();
std::cout << "Minimum: f(" << xs[0] << "," << xs[1] << "): "
<< minimum->MinValue() << std::endl;
// expected minimum is 0
if ( minimum->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;
}