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1/// \file
2/// \ingroup tutorial_fit
3/// \notebook
4/// Illustrates TVirtualFitter::GetConfidenceIntervals
5/// This method computes confidence intervals for the fitted function
7/// \macro_image
8/// \macro_output
9/// \macro_code
11/// \author Rene Brun
13#include "TGraphErrors.h"
14#include "TGraph2DErrors.h"
15#include "TCanvas.h"
16#include "TF2.h"
17#include "TH1.h"
18#include "TVirtualFitter.h"
19#include "TRandom.h"
21void ConfidenceIntervals()
23 TCanvas *myc = new TCanvas("myc",
24 "Confidence intervals on the fitted function",1200, 500);
25 myc->Divide(3,1);
27//### 1. A graph
28 //Create and fill a graph
29 Int_t ngr = 100;
30 TGraph *gr = new TGraph(ngr);
31 gr->SetName("GraphNoError");
32 Double_t x, y;
33 Int_t i;
34 for (i=0; i<ngr; i++){
35 x = gRandom->Uniform(-1, 1);
36 y = -1 + 2*x + gRandom->Gaus(0, 1);
37 gr->SetPoint(i, x, y);
38 }
39 //Create the fitting function
40 TF1 *fpol = new TF1("fpol", "pol1", -1, 1);
41 fpol->SetLineWidth(2);
42 gr->Fit(fpol, "Q");
44 /*Create a TGraphErrors to hold the confidence intervals*/
45 TGraphErrors *grint = new TGraphErrors(ngr);
46 grint->SetTitle("Fitted line with .95 conf. band");
47 for (i=0; i<ngr; i++)
48 grint->SetPoint(i, gr->GetX()[i], 0);
49 /*Compute the confidence intervals at the x points of the created graph*/
51 //Now the "grint" graph contains function values as its y-coordinates
52 //and confidence intervals as the errors on these coordinates
53 //Draw the graph, the function and the confidence intervals
54 myc->cd(1);
55 grint->SetLineColor(kRed);
56 grint->Draw("ap");
58 gr->SetMarkerSize(0.7);
59 gr->Draw("psame");
61//### 2. A histogram
62 myc->cd(2);
63 //Create, fill and fit a histogram
64 Int_t nh=5000;
65 TH1D *h = new TH1D("h",
66 "Fitted gaussian with .95 conf.band", 100, -3, 3);
67 h->FillRandom("gaus", nh);
68 TF1 *f = new TF1("fgaus", "gaus", -3, 3);
69 f->SetLineWidth(2);
70 h->Fit(f, "Q");
71 h->Draw();
73 /*Create a histogram to hold the confidence intervals*/
74 TH1D *hint = new TH1D("hint",
75 "Fitted gaussian with .95 conf.band", 100, -3, 3);
77 //Now the "hint" histogram has the fitted function values as the
78 //bin contents and the confidence intervals as bin errors
79 hint->SetStats(kFALSE);
80 hint->SetFillColor(2);
81 hint->Draw("e3 same");
83//### 3. A 2d graph
84 //Create and fill the graph
85 Int_t ngr2 = 100;
86 Double_t z, rnd, e=0.3;
87 TGraph2D *gr2 = new TGraph2D(ngr2);
88 gr2->SetName("Graph2DNoError");
89 TF2 *f2 = new TF2("f2",
90 "1000*(([0]*sin(x)/x)*([1]*sin(y)/y))+250",-6,6,-6,6);
91 f2->SetParameters(1,1);
92 for (i=0; i<ngr2; i++){
93 f2->GetRandom2(x,y);
94 // Generate a random number in [-e,e]
95 rnd = 2*gRandom->Rndm()*e-e;
96 z = f2->Eval(x,y)*(1+rnd);
97 gr2->SetPoint(i,x,y,z);
98 }
99 //Create a graph with errors to store the intervals
100 TGraph2DErrors *grint2 = new TGraph2DErrors(ngr2);
101 for (i=0; i<ngr2; i++)
102 grint2->SetPoint(i, gr2->GetX()[i], gr2->GetY()[i], 0);
104 //Fit the graph
105 f2->SetParameters(0.5,1.5);
106 gr2->Fit(f2, "Q");
107 /*Compute the confidence intervals*/
109 //Now the "grint2" graph contains function values as z-coordinates
110 //and confidence intervals as their errors
111 //draw
112 myc->cd(3);
113 f2->SetNpx(30);
114 f2->SetNpy(30);
115 f2->SetFillColor(kBlue);
116 f2->Draw("surf4");
117 grint2->SetNpx(20);
118 grint2->SetNpy(20);
119 grint2->SetMarkerStyle(24);
120 grint2->SetMarkerSize(0.7);
121 grint2->SetMarkerColor(kRed);
122 grint2->SetLineColor(kRed);
123 grint2->Draw("E0 same");
124 grint2->SetTitle("Fitted 2d function with .95 error bars");
126 myc->cd();
#define f(i)
Definition RSha256.hxx:104
#define h(i)
Definition RSha256.hxx:106
#define e(i)
Definition RSha256.hxx:103
int Int_t
Definition RtypesCore.h:45
const Bool_t kFALSE
Definition RtypesCore.h:92
double Double_t
Definition RtypesCore.h:59
@ kRed
Definition Rtypes.h:66
@ kBlue
Definition Rtypes.h:66
R__EXTERN TRandom * gRandom
Definition TRandom.h:62
virtual void SetFillColor(Color_t fcolor)
Set the fill area color.
Definition TAttFill.h:37
virtual void SetLineWidth(Width_t lwidth)
Set the line width.
Definition TAttLine.h:43
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition TAttLine.h:40
virtual void SetMarkerColor(Color_t mcolor=1)
Set the marker color.
Definition TAttMarker.h:38
virtual void SetMarkerStyle(Style_t mstyle=1)
Set the marker style.
Definition TAttMarker.h:40
virtual void SetMarkerSize(Size_t msize=1)
Set the marker size.
Definition TAttMarker.h:41
The Canvas class.
Definition TCanvas.h:23
TVirtualPad * cd(Int_t subpadnumber=0) override
Set current canvas & pad.
Definition TCanvas.cxx:708
1-Dim function class
Definition TF1.h:213
virtual void SetNpx(Int_t npx=100)
Set the number of points used to draw the function.
Definition TF1.cxx:3446
virtual void SetParameters(const Double_t *params)
Definition TF1.h:644
virtual Double_t Eval(Double_t x, Double_t y=0, Double_t z=0, Double_t t=0) const
Evaluate this function.
Definition TF1.cxx:1434
A 2-Dim function with parameters.
Definition TF2.h:29
virtual void GetRandom2(Double_t &xrandom, Double_t &yrandom, TRandom *rng=nullptr)
Return 2 random numbers following this function shape.
Definition TF2.cxx:529
virtual void SetNpy(Int_t npy=100)
Set the number of points used to draw the function.
Definition TF2.cxx:936
virtual void Draw(Option_t *option="")
Draw this function with its current attributes.
Definition TF2.cxx:241
Graph 2D class with errors.
virtual void SetPoint(Int_t i, Double_t x, Double_t y, Double_t z)
Set x, y and z values for point number i.
Graphics object made of three arrays X, Y and Z with the same number of points each.
Definition TGraph2D.h:41
Double_t * GetY() const
Definition TGraph2D.h:122
Double_t * GetX() const
Definition TGraph2D.h:121
virtual TFitResultPtr Fit(const char *formula, Option_t *option="", Option_t *goption="")
Fits this graph with function with name fname Predefined functions such as gaus, expo and poln are au...
Definition TGraph2D.cxx:765
void SetNpy(Int_t npx=40)
Sets the number of bins along Y used to draw the function.
virtual void SetTitle(const char *title="")
Sets the 2D graph title.
virtual void SetName(const char *name)
Changes the name of this 2D graph.
virtual void SetPoint(Int_t point, Double_t x, Double_t y, Double_t z)
Sets point number n.
virtual void Draw(Option_t *option="P0")
Specific drawing options can be used to paint a TGraph2D:
Definition TGraph2D.cxx:712
void SetNpx(Int_t npx=40)
Sets the number of bins along X used to draw the function.
A TGraphErrors is a TGraph with error bars.
A TGraph is an object made of two arrays X and Y with npoints each.
Definition TGraph.h:41
virtual void SetPoint(Int_t i, Double_t x, Double_t y)
Set x and y values for point number i.
Definition TGraph.cxx:2284
virtual void SetName(const char *name="")
Set graph name.
Definition TGraph.cxx:2323
virtual void SetTitle(const char *title="")
Change (i.e.
Definition TGraph.cxx:2339
virtual TFitResultPtr Fit(const char *formula, Option_t *option="", Option_t *goption="", Axis_t xmin=0, Axis_t xmax=0)
Fit this graph with function with name fname.
Definition TGraph.cxx:1073
virtual void Draw(Option_t *chopt="")
Draw this graph with its current attributes.
Definition TGraph.cxx:769
Double_t * GetX() const
Definition TGraph.h:131
1-D histogram with a double per channel (see TH1 documentation)}
Definition TH1.h:618
virtual void Draw(Option_t *option="")
Draw this histogram with options.
Definition TH1.cxx:3073
virtual void SetStats(Bool_t stats=kTRUE)
Set statistics option on/off.
Definition TH1.cxx:8830
void Divide(Int_t nx=1, Int_t ny=1, Float_t xmargin=0.01, Float_t ymargin=0.01, Int_t color=0) override
Automatic pad generation by division.
Definition TPad.cxx:1177
virtual Double_t Gaus(Double_t mean=0, Double_t sigma=1)
Samples a random number from the standard Normal (Gaussian) Distribution with the given mean and sigm...
Definition TRandom.cxx:274
virtual Double_t Uniform(Double_t x1=1)
Returns a uniform deviate on the interval (0, x1).
Definition TRandom.cxx:672
virtual Double_t Rndm()
Machine independent random number generator.
Definition TRandom.cxx:552
static TVirtualFitter * GetFitter()
static: return the current Fitter
Double_t y[n]
Definition legend1.C:17
Double_t x[n]
Definition legend1.C:17
TGraphErrors * gr
Definition legend1.C:25
bool GetConfidenceIntervals(const TH1 *h1, const ROOT::Fit::FitResult &r, TGraphErrors *gr, double cl=0.95)
compute confidence intervals at level cl for a fitted histogram h1 in a TGraphErrors gr