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FittingDemo.C File Reference
Tutorials » Math tutorials » Fit Tutorials

Detailed Description

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Example for fitting signal/background.

This example can be executed with:

root > .x FittingDemo.C (using the cling interpreter)
root > .x FittingDemo.C+ (using the native complier via ACLIC)
****************************************
Minimizer is Minuit2 / Migrad
Chi2 = 58.9284
NDf = 54
Edm = 9.73335e-07
NCalls = 606
p0 = -0.864746 +/- 0.887832
p1 = 45.8428 +/- 2.65453
p2 = -13.3213 +/- 0.980305
p3 = 13.8087 +/- 2.24457
p4 = 0.172313 +/- 0.0374057
p5 = 0.987278 +/- 0.0112928
Minuit2Minimizer: Minimize with max-calls 1780 convergence for edm < 0.01 strategy 1
Number of iterations 10
----------> Iteration 0
FVAL = 60.856975016 Edm = 2.04157626492 Nfcn = 23
Error matrix change = 1
Parameters : p0 = -0.864746 p1 = 45.8428 p2 = -13.3213 p3 = 13.8087 p4 = 0.2 p5 = 1
----------> Iteration 1
FVAL = 59.0984738211 Edm = 0.192336813475 Nfcn = 40
Error matrix change = 0.589159
Parameters : p0 = -0.913462 p1 = 45.8154 p2 = -13.3295 p3 = 14.3068 p4 = 0.176677 p5 = 0.990619
----------> Iteration 2
FVAL = 58.9599783699 Edm = 0.018918033963 Nfcn = 54
Error matrix change = 0.342284
Parameters : p0 = -0.906747 p1 = 45.8363 p2 = -13.3167 p3 = 14.116 p4 = 0.177064 p5 = 0.986977
----------> Iteration 3
FVAL = 58.9376425149 Edm = 0.00958566000238 Nfcn = 68
Error matrix change = 0.364189
Parameters : p0 = -0.924256 p1 = 45.83 p2 = -13.3146 p3 = 13.9161 p4 = 0.174171 p5 = 0.987051
----------> Iteration 4
FVAL = 58.9318510093 Edm = 0.00157028886174 Nfcn = 82
Error matrix change = 0.246637
Parameters : p0 = -0.905334 p1 = 45.839 p2 = -13.3101 p3 = 13.8652 p4 = 0.172941 p5 = 0.987268
----------> Iteration 5
FVAL = 58.9287717045 Edm = 0.000439744580493 Nfcn = 96
Error matrix change = 0.274881
Parameters : p0 = -0.867943 p1 = 45.8302 p2 = -13.3151 p3 = 13.8162 p4 = 0.172792 p5 = 0.987388
----------> Iteration 6
FVAL = 58.9284179879 Edm = 9.10495513083e-07 Nfcn = 110
Error matrix change = 0.141986
Parameters : p0 = -0.862363 p1 = 45.8286 p2 = -13.316 p3 = 13.8144 p4 = 0.172388 p5 = 0.987291
----------> Iteration 7
FVAL = 58.9284179879 Edm = 3.19179962054e-05 Nfcn = 150
Error matrix change = 0
Parameters : p0 = -0.862363 p1 = 45.8286 p2 = -13.316 p3 = 13.8144 p4 = 0.172388 p5 = 0.987291
----------> Iteration 8
FVAL = 58.9283860619 Edm = 4.4843686043e-13 Nfcn = 163
Error matrix change = 3.09334e-05
Parameters : p0 = -0.864713 p1 = 45.8434 p2 = -13.3214 p3 = 13.8074 p4 = 0.172309 p5 = 0.987281
----------> Iteration 9
FVAL = 58.9283860619 Edm = 4.4843686043e-13 Nfcn = 163
Error matrix change = 3.09334e-05
Parameters : p0 = -0.864713 p1 = 45.8434 p2 = -13.3214 p3 = 13.8074 p4 = 0.172309 p5 = 0.987281
Minuit2Minimizer : Valid minimum - status = 0
FVAL = 58.9283860619491762
Edm = 4.48436860430199946e-13
Nfcn = 163
p0 = -0.864713 +/- 0.891795
p1 = 45.8434 +/- 2.64223
p2 = -13.3214 +/- 0.976969
p3 = 13.8074 +/- 2.1776
p4 = 0.172309 +/- 0.0358282
p5 = 0.987281 +/- 0.0112683
Covariance Matrix:
p0 p1 p2 p3 p4 p5
p0 0.7953 -1.2054 0.34842 -0.15946 -0.0037284 0.00042265
p1 -1.2054 6.9814 -2.5255 -3.0272 -0.037043 -0.0018129
p2 0.34842 -2.5255 0.95447 1.1587 0.014337 0.00058758
p3 -0.15946 -3.0272 1.1587 4.7419 0.05537 0.0017371
p4 -0.0037284 -0.037043 0.014337 0.05537 0.0012837 2.8395e-05
p5 0.00042265 -0.0018129 0.00058758 0.0017371 2.8395e-05 0.00012697
Correlation Matrix:
p0 p1 p2 p3 p4 p5
p0 1 -0.51155 0.39991 -0.08211 -0.11669 0.042058
p1 -0.51155 1 -0.97834 -0.52614 -0.3913 -0.060891
p2 0.39991 -0.97834 1 0.54464 0.40958 0.053373
p3 -0.08211 -0.52614 0.54464 1 0.7097 0.070794
p4 -0.11669 -0.3913 0.40958 0.7097 1 0.070334
p5 0.042058 -0.060891 0.053373 0.070794 0.070334 1
****************************************
Minimizer is Minuit2 / Migrad
Chi2 = 58.9284
NDf = 54
Edm = 4.48437e-13
NCalls = 163
p0 = -0.864713 +/- 0.891795
p1 = 45.8434 +/- 2.64223
p2 = -13.3214 +/- 0.976969
p3 = 13.8074 +/- 2.1776
p4 = 0.172309 +/- 0.0358282
p5 = 0.987281 +/- 0.0112683
#include "TH1.h"
#include "TMath.h"
#include "TF1.h"
#include "TLegend.h"
#include "TCanvas.h"
// Quadratic background function
double background(double *x, double *par) {
return par[0] + par[1]*x[0] + par[2]*x[0]*x[0];
}
// Lorenzian Peak function
double lorentzianPeak(double *x, double *par) {
return (0.5*par[0]*par[1]/TMath::Pi()) /
TMath::Max( 1.e-10,(x[0]-par[2])*(x[0]-par[2])
+ .25*par[1]*par[1]);
}
// Sum of background and peak function
double fitFunction(double *x, double *par) {
return background(x,par) + lorentzianPeak(x,&par[3]);
}
void FittingDemo() {
//Bevington Exercise by Peter Malzacher, modified by Rene Brun
const int nBins = 60;
double data[nBins] = { 6, 1,10,12, 6,13,23,22,15,21,
23,26,36,25,27,35,40,44,66,81,
75,57,48,45,46,41,35,36,53,32,
40,37,38,31,36,44,42,37,32,32,
43,44,35,33,33,39,29,41,32,44,
26,39,29,35,32,21,21,15,25,15};
TCanvas *c1 = new TCanvas("c1","Fitting Demo",10,10,700,500);
c1->SetFillColor(33);
c1->SetFrameFillColor(41);
c1->SetGrid();
TH1F *histo = new TH1F("histo",
"Lorentzian Peak on Quadratic Background",60,0,3);
histo->SetMarkerStyle(21);
histo->SetMarkerSize(0.8);
histo->SetStats(false);
for(int i=0; i < nBins; i++) histo->SetBinContent(i+1,data[i]);
// create a TF1 with the range from 0 to 3 and 6 parameters
TF1 *fitFcn = new TF1("fitFcn",fitFunction,0,3,6);
fitFcn->SetNpx(500);
fitFcn->SetLineWidth(4);
fitFcn->SetLineColor(kMagenta);
// first try without starting values for the parameters
// This defaults to 1 for each param.
// this results in an ok fit for the polynomial function
// however the non-linear part (lorenzian) does not
// respond well.
fitFcn->SetParameters(1,1,1,1,1,1);
histo->Fit("fitFcn","0");
// second try: set start values for some parameters
fitFcn->SetParameter(4,0.2); // width
fitFcn->SetParameter(5,1); // peak
histo->Fit("fitFcn","V+","ep");
// improve the picture:
TF1 *backFcn = new TF1("backFcn",background,0,3,3);
backFcn->SetLineColor(kRed);
TF1 *signalFcn = new TF1("signalFcn",lorentzianPeak,0,3,3);
signalFcn->SetLineColor(kBlue);
signalFcn->SetNpx(500);
double par[6];
// writes the fit results into the par array
fitFcn->GetParameters(par);
backFcn->SetParameters(par);
backFcn->Draw("same");
signalFcn->SetParameters(&par[3]);
signalFcn->Draw("same");
// draw the legend
TLegend *legend=new TLegend(0.6,0.65,0.88,0.85);
legend->SetTextFont(72);
legend->SetTextSize(0.04);
legend->AddEntry(histo,"Data","lpe");
legend->AddEntry(backFcn,"Background fit","l");
legend->AddEntry(signalFcn,"Signal fit","l");
legend->AddEntry(fitFcn,"Global Fit","l");
legend->Draw();
}
kRed
@ kRed
Definition Rtypes.h:66
kMagenta
@ kMagenta
Definition Rtypes.h:66
kBlue
@ kBlue
Definition Rtypes.h:66
data
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void data
Definition TGWin32VirtualXProxy.cxx:104
TAttLine::SetLineWidth
virtual void SetLineWidth(Width_t lwidth)
Set the line width.
Definition TAttLine.h:43
TAttLine::SetLineColor
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition TAttLine.h:40
TAttMarker::SetMarkerStyle
virtual void SetMarkerStyle(Style_t mstyle=1)
Set the marker style.
Definition TAttMarker.h:40
TAttMarker::SetMarkerSize
virtual void SetMarkerSize(Size_t msize=1)
Set the marker size.
Definition TAttMarker.h:45
TAttText::SetTextFont
virtual void SetTextFont(Font_t tfont=62)
Set the text font.
Definition TAttText.h:46
TAttText::SetTextSize
virtual void SetTextSize(Float_t tsize=1)
Set the text size.
Definition TAttText.h:47
TCanvas
The Canvas class.
Definition TCanvas.h:23
TF1
1-Dim function class
Definition TF1.h:233
TF1::SetNpx
virtual void SetNpx(Int_t npx=100)
Set the number of points used to draw the function.
Definition TF1.cxx:3433
TF1::GetParameters
virtual Double_t * GetParameters() const
Definition TF1.h:548
TF1::Draw
void Draw(Option_t *option="") override
Draw this function with its current attributes.
Definition TF1.cxx:1333
TF1::SetParameters
virtual void SetParameters(const Double_t *params)
Definition TF1.h:677
TF1::SetParameter
virtual void SetParameter(Int_t param, Double_t value)
Definition TF1.h:667
TH1F
1-D histogram with a float per channel (see TH1 documentation)
Definition TH1.h:623
TH1::Fit
virtual TFitResultPtr Fit(const char *formula, Option_t *option="", Option_t *goption="", Double_t xmin=0, Double_t xmax=0)
Fit histogram with function fname.
Definition TH1.cxx:3906
TH1::SetBinContent
virtual void SetBinContent(Int_t bin, Double_t content)
Set bin content see convention for numbering bins in TH1::GetBin In case the bin number is greater th...
Definition TH1.cxx:9255
TH1::SetStats
virtual void SetStats(Bool_t stats=kTRUE)
Set statistics option on/off.
Definition TH1.cxx:9023
TLegend
This class displays a legend box (TPaveText) containing several legend entries.
Definition TLegend.h:23
TLegend::AddEntry
TLegendEntry * AddEntry(const TObject *obj, const char *label="", Option_t *option="lpf")
Add a new entry to this legend.
Definition TLegend.cxx:320
TLegend::Draw
void Draw(Option_t *option="") override
Draw this legend with its current attributes.
Definition TLegend.cxx:425
c1
return c1
Definition legend1.C:41
x
Double_t x[n]
Definition legend1.C:17
TMath::Max
Short_t Max(Short_t a, Short_t b)
Returns the largest of a and b.
Definition TMathBase.h:250
TMath::Pi
constexpr Double_t Pi()
Definition TMath.h:37
Author
Rene Brun

Definition in file FittingDemo.C.