RooSimultaneous fit on categories with different x variables - bad combined data

[yu_shitov]

I am trying to fit two lines in the spectrum at the same time, while two simultaneously fitted categories have different axes (in all examples with RooSimultaneous, the categories have the same axis). Below is the code of the program. Almost everything works, the only problem is that after creating the combined data, when accessing them, I see a strange “doubling” of the first line, in general, the amount of data is different. It seems that the combined data is not generated quite correctly due to the different axes in the added categories. How can I fix this error?

#include <TH1.h>
#include <TF1.h>
#include <RooRealVar.h>
#include <RooGaussian.h>

// try to fit two lines simultaneously
void rf_example() {

  double emin=100,emax=600;

  // generate 3 gaus lines
  TH1F *h= new TH1F("hMain","Main histo",1024,emin,emax);
  TF1 *f = new TF1("f","gaus",emin,emax);
  f->SetParameters(10,200,10);
  h->FillRandom("f",2000);
  f->SetParameters(10,300,20);
  h->FillRandom("f",5000);
  f->SetParameters(10,450,10);
  h->FillRandom("f",1000);

  h->Draw();

  // simultenous fit of 2 lines (1 & 2)
  RooRealVar E1("E1","energy range of 1 line",170,230);
  RooRealVar E2("E2","energy range of 2 line",400,500);
  RooRealVar P1("P1","Position of 1 line",180,220);
  RooRealVar P2("P2","Positions of 2 line",420,470);
  RooRealVar S("S","sigma of lines",0,20) ;
  RooGaussian L1("Line1","Line 1",E1,P1,S) ;
  RooGaussian L2("Line2","Line 2",E2,P2,S) ;

  RooCategory category("category","Category");
  category.defineType("Line1");
  category.defineType("Line2");
  
  RooSimultaneous model("model","Simultaneous fit of 2 lines",category) ;   
  model.addPdf(L1,"Line1");
  model.addPdf(L2,"Line2");

  // build data set 
  //  RooRealVar E("E","Full energy range",emin,emax);
  RooDataHist dE1("dE1","Line 1 data",E1,h);
  RooDataHist dE2("dE2","Line 2 data",E2,h);

  // Construct combined dataset in (x,sample)
  RooDataHist combData("combData", "combined data", RooArgSet(E1,E2), RooFit::Index(category), RooFit::Import("Line1", dE1),
                       RooFit::Import("Line2",dE2));

  // Plot results
  RooPlot *frame1 = E1.frame(RooFit::Title("RooDataHist: Line 1"))
	 ,*frame2 = E2.frame(RooFit::Title("RooDataHist: Line 2"));
  
  dE1.plotOn(frame1);
  dE2.plotOn(frame2);

  // fit 
  model.fitTo(combData);

  RooPlot *frame3 = E1.frame(RooFit::Title("Combined data: Line 1"))
	 ,*frame4 = E2.frame(RooFit::Title("Combined data: Line 2"));

  combData.plotOn(frame3, RooFit::Cut("category==category::Line1"));
  combData.plotOn(frame4, RooFit::Cut("category==category::Line2"));
  model.plotOn(frame3,RooFit::Slice(category, "Line1"), RooFit::ProjWData(category,combData));
  model.plotOn(frame4,RooFit::Slice(category, "Line2"), RooFit::ProjWData(category,combData));

  // Plot results

  TCanvas *c = new TCanvas("rf_sample", "rf_sample", 800, 400);
  c->Divide(2,2);
  c->cd(1);
  frame1->Draw();
  c->cd(2);
  frame2->Draw();
  c->cd(3);
  frame3->Draw();
  c->cd(4);
  frame4->Draw();

} // rf_example

[yu_shitov]

Scripts build 3 line spectrum (left picture) and tries to fit 1 and 3 lines simulteniosly with the same sigma. Separate datahist look ok (right up), but combined data are incorrect (right left).

[moneta]

Hi,
I can reproduce your problem and I will investigate it. It is probably in the way the RooDataHIst is built for combined data, where in this case a 2D data set is done for E1 and E2.
I would simply to a multi-range fit in your case, importing the original histogram in a single data set. Any reason for not doing it ?

Lorenzo

[moneta]

It looks to be a bug when building the combined data set. When importing it seems to use the default number of bins of the RooRealVar instead of the dataset.
Adding these 2 first lines before creating the combined data set, seems to fix the issue:

E1.setBins(dE1.numEntries());
E2.setBins(dE2.numEntries());

  // Construct combined dataset in (x,sample)
 RooDataHist combData("combData", "combined data", RooArgSet(E1,E2),RooFit::Index(category), RooFit::Import("Line1", dE1),
                       RooFit::Import("Line2",dE2));

Cheers

Lorenzo

[yu_shitov]

Dear Lorenzo,
It works, thank you very much!

@moneta

I would simply to a multi-range fit in your case, importing the original histogram in a single data set. Any reason for not doing it ?

In fact, I forgot about this second option, which also works in this case.

But my version with different scales is interesting because it is more general, when you really need to fit at the same time fundamentally different distributions, for example, energy and time signals described by a model with common fit parameters. In this case, the multi-range option will not work.
It may be useful to add RooSimultaneous fit of distributions with different scales to the collection of roofit examples - there is no such option, afaik

Thanks again for your help and good luck!

[moneta]

Thank you for the feedback. We will add an example for this.
One another thing is that is not efficient to build RooDataHist objects with multi-variables. For example for 2 variables with n1 and n2 bins, RooFit will allocate n1 x n2 bins. It is more convenient to use a weighted RooDataSet with a weight equal to the number of bins.

Best regards

Lorenzo