## From \$ROOTSYS/tutorials/roofit/rf313_paramranges.C

```//////////////////////////////////////////////////////////////////////////
//
// 'MULTIDIMENSIONAL MODELS' RooFit tutorial macro #313
//
// Working with parameterized ranges to define non-rectangular regions
// for fitting and integration
//
//
//
// 07/2008 - Wouter Verkerke
//
/////////////////////////////////////////////////////////////////////////

#ifndef __CINT__
#include "RooGlobalFunc.h"
#endif
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "RooPolynomial.h"
#include "RooProdPdf.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit ;

void rf313_paramranges()
{

// C r e a t e   3 D   p d f
// -------------------------

// Define observable (x,y,z)
RooRealVar x("x","x",0,10) ;
RooRealVar y("y","y",0,10) ;
RooRealVar z("z","z",0,10) ;

// Define 3 dimensional pdf
RooRealVar z0("z0","z0",-0.1,1) ;
RooPolynomial px("px","px",x,RooConst(0)) ;
RooPolynomial py("py","py",y,RooConst(0)) ;
RooPolynomial pz("pz","pz",z,z0) ;
RooProdPdf pxyz("pxyz","pxyz",RooArgSet(px,py,pz)) ;

// D e f i n e d   n o n - r e c t a n g u l a r   r e g i o n   R   i n   ( x , y , z )
// -------------------------------------------------------------------------------------

//
// R = Z[0 - 0.1*Y^2] * Y[0.1*X - 0.9*X] * X[0 - 10]
//

// Construct range parameterized in "R" in y [ 0.1*x, 0.9*x ]
RooFormulaVar ylo("ylo","0.1*x",x) ;
RooFormulaVar yhi("yhi","0.9*x",x) ;
y.setRange("R",ylo,yhi) ;

// Construct parameterized ranged "R" in z [ 0, 0.1*y^2 ]
RooFormulaVar zlo("zlo","0.0*y",y) ;
RooFormulaVar zhi("zhi","0.1*y*y",y) ;
z.setRange("R",zlo,zhi) ;

// C a l c u l a t e   i n t e g r a l   o f   n o r m a l i z e d   p d f   i n   R
// ----------------------------------------------------------------------------------

// Create integral over normalized pdf model over x,y,z in "R" region
RooAbsReal* intPdf = pxyz.createIntegral(RooArgSet(x,y,z),RooArgSet(x,y,z),"R") ;

// Plot value of integral as function of pdf parameter z0
RooPlot* frame = z0.frame(Title("Integral of pxyz over x,y,z in region R")) ;
intPdf->plotOn(frame) ;

new TCanvas("rf313_paramranges","rf313_paramranges",600,600) ;
gPad->SetLeftMargin(0.15) ; frame->GetYaxis()->SetTitleOffset(1.6) ; frame->Draw() ;

return ;
}
```
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