Notebook

Ifit¶

Example of a program to fit non-equidistant data points

The fitting function fcn is a simple chisquare function The data consists of 5 data points (arrays x,y,z) + the errors in errorsz More details on the various functions or parameters for these functions can be obtained in an interactive ROOT session with:

Root > TMinuit *minuit = new TMinuit(10);

Root > minuit->mnhelp("*")  to see the list of possible keywords
   Root > minuit->mnhelp("SET") explains most parameters

Author: Rene Brun
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Monday, March 27, 2023 at 09:47 AM.

In [1]:

%%cpp -d
#include "TMinuit.h"

float z[5],x[5],y[5],errorz[5];

In [2]:

%%cpp -d
double func(float x,float y,double *par)
{
 double value=( (par[0]*par[0])/(x*x)-1)/ ( par[1]+par[2]*y-par[3]*y*y);
 return value;
}

In [3]:

%%cpp -d
void fcn(int &npar, double *gin, double &f, double *par, int iflag)
{
   const int nbins = 5;
   int i;

//calculate chisquare
   double chisq = 0;
   double delta;
   for (i=0;i<nbins; i++) {
     delta  = (z[i]-func(x[i],y[i],par))/errorz[i];
     chisq += delta*delta;
   }
   f = chisq;
}

The z values

In [4]:

z[0]=1;
z[1]=0.96;
z[2]=0.89;
z[3]=0.85;
z[4]=0.78;

The errors on z values

In [5]:

float error = 0.01;
errorz[0]=error;
errorz[1]=error;
errorz[2]=error;
errorz[3]=error;
errorz[4]=error;

the x values

In [6]:

x[0]=1.5751;
x[1]=1.5825;
x[2]=1.6069;
x[3]=1.6339;
x[4]=1.6706;

the y values

In [7]:

y[0]=1.0642;
y[1]=0.97685;
y[2]=1.13168;
y[3]=1.128654;
y[4]=1.44016;

TMinuit *gMinuit = new TMinuit(5);  //initialize TMinuit with a maximum of 5 params
gMinuit->SetFCN(fcn);

double arglist[10];
int ierflg = 0;

arglist[0] = 1;
gMinuit->mnexcm("SET ERR", arglist ,1,ierflg);

 **********
 **    1 **SET ERR           1
 **********

Set starting values and step sizes for parameters

In [8]:

static double vstart[4] = {3, 1 , 0.1 , 0.01};
static double step[4] = {0.1 , 0.1 , 0.01 , 0.001};
gMinuit->mnparm(0, "a1", vstart[0], step[0], 0,0,ierflg);
gMinuit->mnparm(1, "a2", vstart[1], step[1], 0,0,ierflg);
gMinuit->mnparm(2, "a3", vstart[2], step[2], 0,0,ierflg);
gMinuit->mnparm(3, "a4", vstart[3], step[3], 0,0,ierflg);

input_line_58:4:1: error: reference to 'gMinuit' is ambiguous
gMinuit->mnparm(0, "a1", vstart[0], step[0], 0,0,ierflg);
^
input_line_57:8:10: note: candidate found by name lookup is '__cling_N523::gMinuit'
TMinuit *gMinuit = new TMinuit(5);  //initialize TMinuit with a maximum of 5 params
         ^
/home/sftnight/build/workspace/root-makedoc-master/rootspi/rdoc/src/master.build/include/TMinuit.h:271:21: note: candidate found by name lookup is 'gMinuit'
R__EXTERN TMinuit  *gMinuit;
                    ^
input_line_58:5:1: error: reference to 'gMinuit' is ambiguous
gMinuit->mnparm(1, "a2", vstart[1], step[1], 0,0,ierflg);
^
input_line_57:8:10: note: candidate found by name lookup is '__cling_N523::gMinuit'
TMinuit *gMinuit = new TMinuit(5);  //initialize TMinuit with a maximum of 5 params
         ^
/home/sftnight/build/workspace/root-makedoc-master/rootspi/rdoc/src/master.build/include/TMinuit.h:271:21: note: candidate found by name lookup is 'gMinuit'
R__EXTERN TMinuit  *gMinuit;
                    ^
input_line_58:6:1: error: reference to 'gMinuit' is ambiguous
gMinuit->mnparm(2, "a3", vstart[2], step[2], 0,0,ierflg);
^
input_line_57:8:10: note: candidate found by name lookup is '__cling_N523::gMinuit'
TMinuit *gMinuit = new TMinuit(5);  //initialize TMinuit with a maximum of 5 params
         ^
/home/sftnight/build/workspace/root-makedoc-master/rootspi/rdoc/src/master.build/include/TMinuit.h:271:21: note: candidate found by name lookup is 'gMinuit'
R__EXTERN TMinuit  *gMinuit;
                    ^
input_line_58:7:1: error: reference to 'gMinuit' is ambiguous
gMinuit->mnparm(3, "a4", vstart[3], step[3], 0,0,ierflg);
^
input_line_57:8:10: note: candidate found by name lookup is '__cling_N523::gMinuit'
TMinuit *gMinuit = new TMinuit(5);  //initialize TMinuit with a maximum of 5 params
         ^
/home/sftnight/build/workspace/root-makedoc-master/rootspi/rdoc/src/master.build/include/TMinuit.h:271:21: note: candidate found by name lookup is 'gMinuit'
R__EXTERN TMinuit  *gMinuit;
                    ^

Now ready for minimization step

In [9]:

arglist[0] = 500;
arglist[1] = 1.;
gMinuit->mnexcm("MIGRAD", arglist ,2,ierflg);

input_line_59:4:1: error: reference to 'gMinuit' is ambiguous
gMinuit->mnexcm("MIGRAD", arglist ,2,ierflg);
^
input_line_57:8:10: note: candidate found by name lookup is '__cling_N523::gMinuit'
TMinuit *gMinuit = new TMinuit(5);  //initialize TMinuit with a maximum of 5 params
         ^
/home/sftnight/build/workspace/root-makedoc-master/rootspi/rdoc/src/master.build/include/TMinuit.h:271:21: note: candidate found by name lookup is 'gMinuit'
R__EXTERN TMinuit  *gMinuit;
                    ^

Print results

In [10]:

double amin,edm,errdef;
int nvpar,nparx,icstat;
gMinuit->mnstat(amin,edm,errdef,nvpar,nparx,icstat);

input_line_60:4:1: error: reference to 'gMinuit' is ambiguous
gMinuit->mnstat(amin,edm,errdef,nvpar,nparx,icstat);
^
input_line_57:8:10: note: candidate found by name lookup is '__cling_N523::gMinuit'
TMinuit *gMinuit = new TMinuit(5);  //initialize TMinuit with a maximum of 5 params
         ^
/home/sftnight/build/workspace/root-makedoc-master/rootspi/rdoc/src/master.build/include/TMinuit.h:271:21: note: candidate found by name lookup is 'gMinuit'
R__EXTERN TMinuit  *gMinuit;
                    ^

gMinuit->mnprin(3,amin);