Observables vs parameters
// dependents vs parameters
intro9()
{
// This example demonstrates RFCs dynamic concept of dependents vs parameters
//
// Definition:
// 'dependent' = a variable of a function that is loaded from a dataset
// 'parameter' = any variable that is not a dependent
//
// For probability density functions this distinction is non-trivial because,
// by construction, they must be normalized over all dependent variables:
//
// Int(dDep) Pdf(Dep,Par) == 1 (Dep = set of dependent variables ,
// Par = set parameter variables)
//
// In RooFit, the dep/par status of each variable of a RooAbsPdf object is
// explicitly dynamic: each variable can be a parameter or a dependent
// at any time. This only depends on the context in which the PDF is used, i.e.
// the status of each variables is only explicit when a PDF is associated
// with a dataset, which determines the set of dependents.
//
// A consequence of this dynamic concept is that a complete set
// of values for all PDF variables does not yield a unique return value:
// the dep/par status of each variables must be specified in addition.
//
// To achieve this dynamic property, the normalization of a PDF is decoupled
// from the calculation of its raw unnormalized value.
//
// A simple gaussian PDF has 3 variables: x,mean,sigma
RooRealVar x("x","x",-10,10) ;
RooRealVar mean("mean","mean of gaussian",-1,-10,10) ;
RooRealVar sigma("sigma","width of gaussian",3,1,20) ;
RooGaussian gauss("gauss","gaussian PDF",x,mean,sigma) ;
// For getVal() without any arguments all variables are interpreted as parameters,
// and no normalization is enforced
x = 0 ;
Double_t rawVal = gauss.getVal() ; // = exp(-[(x-mean)/sigma]^2)
cout << "gauss(x=0,mean=-1,width=3)_raw = " << rawVal << endl ;
// If we supply getVal() with the subset of its variables that should be interpreted as dependents,
// it will apply the correct normalization for that set of dependents
Double_t xnormVal = gauss.getVal(x) ; // NB: RooAbsArg& implicitly converts to RooArgSet(RooAbsArg&)
cout << "gauss(x=0,mean=-1,width=3)_normalized_x[-10,10] = " << xnormVal << endl ;
//*** gauss.getVal(x) = gauss.getVal() / Int(-10,10) gauss() dx
// If we adjust the limits on x, the normalization will change accordingly
x.setFitRange(-1,1) ;
Double_t xnorm2Val = gauss.getVal(x) ;
cout << "gauss(x=0,mean=-1,width=3)_normalized_x[-1,1] = " << xnorm2Val << endl ;
//*** gauss.getVal(x) = gauss.getVal() / Int(-1,1) gauss() dx
// We can also add sigma as dependent
Double_t xsnormVal = gauss.getVal(RooArgSet(x,sigma)) ;
cout << "gauss(x=0,mean=-1,width=3)_normalized_x[-1,1]_width[1,20] = " << xsnormVal << endl ;
//*** gauss.getVal(RooArgSet(x,sigma)) = gauss.getVal() / Int(-1,1)(1,20) gauss() dx dsigma
// (!) The set of arguments passed in RooAbsPdf::getVal() determines _only_ which
// the variables are interpreted as dependents/parameters. No values are passed,
// these are _always_ taken from the arguments supplied in the constructor
//
// Objects passed in RooAbsPdf::getVal() that are not variables of the PDF are
// silently ignored
}
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