ConfidenceIntervals.C

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/// \file
/// \ingroup tutorial_fit
/// \notebook
/// Illustrates TVirtualFitter::GetConfidenceIntervals
/// This method computes confidence intervals for the fitted function
///
/// \macro_image
/// \macro_output
/// \macro_code
///
/// \author Rene Brun

#include "TGraphErrors.h"
#include "TGraph2DErrors.h"
#include "TCanvas.h"
#include "TF2.h"
#include "TH1.h"
#include "TVirtualFitter.h"
#include "TRandom.h"

void ConfidenceIntervals()
{
   TCanvas *myc = new TCanvas("myc",
      "Confidence intervals on the fitted function",1200, 500);
   myc->Divide(3,1);

//### 1. A graph
   //Create and fill a graph
   Int_t ngr = 100;
   TGraph *gr = new TGraph(ngr);
   gr->SetName("GraphNoError");
   Double_t x, y;
   Int_t i;
   for (i=0; i<ngr; i++){
      x = gRandom->Uniform(-1, 1);
      y = -1 + 2*x + gRandom->Gaus(0, 1);
      gr->SetPoint(i, x, y);
   }
   //Create the fitting function
   TF1 *fpol = new TF1("fpol", "pol1", -1, 1);
   fpol->SetLineWidth(2);
   gr->Fit(fpol, "Q");

   /*Create a TGraphErrors to hold the confidence intervals*/
   TGraphErrors *grint = new TGraphErrors(ngr);
   grint->SetTitle("Fitted line with .95 conf. band");
   for (i=0; i<ngr; i++)
      grint->SetPoint(i, gr->GetX()[i], 0);
   /*Compute the confidence intervals at the x points of the created graph*/
   (TVirtualFitter::GetFitter())->GetConfidenceIntervals(grint);
   //Now the "grint" graph contains function values as its y-coordinates
   //and confidence intervals as the errors on these coordinates
   //Draw the graph, the function and the confidence intervals
   myc->cd(1);
   grint->SetLineColor(kRed);
   grint->Draw("ap");
   gr->SetMarkerStyle(5);
   gr->SetMarkerSize(0.7);
   gr->Draw("psame");

//### 2. A histogram
   myc->cd(2);
   //Create, fill and fit a histogram
   Int_t nh=5000;
   TH1D *h = new TH1D("h",
      "Fitted gaussian with .95 conf.band", 100, -3, 3);
   h->FillRandom("gaus", nh);
   TF1 *f = new TF1("fgaus", "gaus", -3, 3);
   f->SetLineWidth(2);
   h->Fit(f, "Q");
   h->Draw();

   /*Create a histogram to hold the confidence intervals*/
   TH1D *hint = new TH1D("hint",
      "Fitted gaussian with .95 conf.band", 100, -3, 3);
   (TVirtualFitter::GetFitter())->GetConfidenceIntervals(hint);
   //Now the "hint" histogram has the fitted function values as the
   //bin contents and the confidence intervals as bin errors
   hint->SetStats(kFALSE);
   hint->SetFillColor(2);
   hint->Draw("e3 same");

//### 3. A 2d graph
   //Create and fill the graph
   Int_t ngr2 = 100;
   Double_t z, rnd, e=0.3;
   TGraph2D *gr2 = new TGraph2D(ngr2);
   gr2->SetName("Graph2DNoError");
   TF2  *f2 = new TF2("f2",
      "1000*(([0]*sin(x)/x)*([1]*sin(y)/y))+250",-6,6,-6,6);
   f2->SetParameters(1,1);
   for (i=0; i<ngr2; i++){
      f2->GetRandom2(x,y);
      // Generate a random number in [-e,e]
      rnd = 2*gRandom->Rndm()*e-e;
      z = f2->Eval(x,y)*(1+rnd);
      gr2->SetPoint(i,x,y,z);
   }
   //Create a graph with errors to store the intervals
   TGraph2DErrors *grint2 = new TGraph2DErrors(ngr2);
   for (i=0; i<ngr2; i++)
      grint2->SetPoint(i, gr2->GetX()[i], gr2->GetY()[i], 0);

   //Fit the graph
   f2->SetParameters(0.5,1.5);
   gr2->Fit(f2, "Q");
   /*Compute the confidence intervals*/
   (TVirtualFitter::GetFitter())->GetConfidenceIntervals(grint2);
   //Now the "grint2" graph contains function values as z-coordinates
   //and confidence intervals as their errors
   //draw
   myc->cd(3);
   f2->SetNpx(30);
   f2->SetNpy(30);
   f2->SetFillColor(kBlue);
   f2->Draw("surf4");
   grint2->SetNpx(20);
   grint2->SetNpy(20);
   grint2->SetMarkerStyle(24);
   grint2->SetMarkerSize(0.7);
   grint2->SetMarkerColor(kRed);
   grint2->SetLineColor(kRed);
   grint2->Draw("E0 same");
   grint2->SetTitle("Fitted 2d function with .95 error bars");

   myc->cd();

}