def rooFit202(): print ">>> setup model component: gaussian signals and Chebychev polynomial background..." x = RooRealVar("x", "x", 0, 10) mean = RooRealVar("mean", "mean of gaussian", 5) sigma1 = RooRealVar("sigma1", "width of gaussian", 0.5) sigma2 = RooRealVar("sigma2", "width of gaussian", 1.0) sig1 = RooGaussian("sig1", "Signal component 1", x, mean, sigma1) sig2 = RooGaussian("sig2", "Signal component 2", x, mean, sigma2) a0 = RooRealVar("a0", "a0", 0.5, 0., 1.) a1 = RooRealVar("a1", "a1", -0.2, 0., 1.) bkg = RooChebychev("bkg", "Background", x, RooArgList(a0, a1)) # Sum the signal components into a composite signal p.d.f. sig1frac = RooRealVar("sig1frac", "fraction of component 1 in signal", 0.8, 0., 1.) sig = RooAddPdf("sig", "Signal", RooArgList(sig1, sig2), RooArgList(sig1frac)) print ">>>\n>>> METHOD 1" print ">>> construct extended composite model..." # Sum the composite signal and background into an extended pdf nsig*sig+nbkg*bkg nsig = RooRealVar("nsig", "number of signal events", 500, 0., 10000) nbkg = RooRealVar("nbkg", "number of background events", 500, 0, 10000) model = RooAddPdf("model", "(g1+g2)+a", RooArgList(bkg, sig), RooArgList(nbkg, nsig)) print ">>> sample, fit and plot extended model...\n" # Generate a data sample of expected number events in x from model # nsig + nbkg = model.expectedEvents() # NOTE: since the model predicts a specific number events, one can # omit the requested number of events to be generated # Introduce Poisson fluctuation with Extended(kTRUE) data = model.generate(RooArgSet(x), Extended(kTRUE)) # RooDataSet # Fit model to data, extended ML term automatically included # NOTE: Composite extended pdfs can only be successfully fit if the extended likelihood # term -log(Poisson(Nobs,Nexp)) is included in the minimization because they have # one extra degree of freedom in their parameterization that is constrained by # this extended term. If a pdf is capable of calculating an extended term (i.e. # any extended RooAddPdf), the extended term is AUTOMATICALLY included in the # likelihood calculation. Override this behaviour with Extended(): # Extended(kTRUE) ADD extended likelihood term # Extended(kFALSE) DO NOT ADD extended likelihood #model.fitTo(data,Extended(kTRUE)) model.fitTo(data) print "\n>>> plot data, model and model components..." # Plot data and PDF overlaid, use expected number of events for pdf projection # normalization, rather than observed number of events, data.numEntries() frame1 = x.frame(Title("extended ML fit example")) # RooPlot data.plotOn(frame1, Binning(30), Name("data")) model.plotOn(frame1, Normalization(1.0, RooAbsReal.RelativeExpected), Name("model")) # Overlay the background components of model # NOTE: By default, the pdf is normalized to event count of the last dataset added # to the plot frame. Use "RelativeExpected" to normalize to the expected # event count of the pdf instead argset1 = RooArgSet(bkg) argset2 = RooArgSet(sig1) argset3 = RooArgSet(sig2) argset4 = RooArgSet(bkg, sig2) model.plotOn(frame1, Components(argset1), LineStyle(kDashed), LineColor(kBlue), Normalization(1.0, RooAbsReal.RelativeExpected), Name("bkg")) #model.plotOn(frame1,Components(argset1),LineStyle(kDashed),LineColor(kBlue), Name("bkg2")) model.plotOn(frame1, Components(argset2), LineStyle(kDotted), LineColor(kMagenta), Normalization(1.0, RooAbsReal.RelativeExpected), Name("sig1")) model.plotOn(frame1, Components(argset3), LineStyle(kDotted), LineColor(kPink), Normalization(1.0, RooAbsReal.RelativeExpected), Name("sig2")) model.plotOn(frame1, Components(argset4), LineStyle(kDashed), LineColor(kAzure - 4), Normalization(1.0, RooAbsReal.RelativeExpected), Name("bkgsig2")) print "\n>>> structure of composite pdf:" model.Print("t") # "tree" mode print "\n>>> parameters:" params = model.getVariables() # RooArgSet params.Print("v") params.Print() print "\n>>> params.find(\"...\").getVal():" print ">>> sigma1 = %.2f" % params.find("sigma1").getVal() print ">>> sigma2 = %.2f" % params.find("sigma2").getVal() print ">>> nsig = %6.2f, sig1frac = %5.2f" % ( params.find("nsig").getVal(), params.find("sig1frac").getVal()) print ">>> nbkg = %6.2f" % params.find("nbkg").getVal() print ">>>\n>>> components:" comps = model.getComponents() # RooArgSet sig = comps.find("sig") # RooAbsArg sigVars = sig.getVariables() # RooArgSet sigVars.Print() print ">>>\n>>> METHOD 2" print ">>> construct extended components first..." # Associated nsig/nbkg as expected number of events with sig/bkg nsig = RooRealVar("nsig", "number of signal events", 500, 0., 10000) nbkg = RooRealVar("nbkg", "number of background events", 500, 0, 10000) esig = RooExtendPdf("esig", "extended signal pdf", sig, nsig) ebkg = RooExtendPdf("ebkg", "extended background pdf", bkg, nbkg) print ">>> sum extended components without coefficients..." # Construct sum of two extended p.d.f. (no coefficients required) model2 = RooAddPdf("model2", "(g1+g2)+a", RooArgList(ebkg, esig)) # METHOD 2 is functionally completely equivalent to METHOD 1. # Its advantage is that the yield parameter is associated to the shape pdf # directly, while in METHOD 1 the association is made after constructing # a RooAddPdf. Also, class RooExtendPdf offers extra functionality to # interpret event counts in a different range. print ">>> plot model..." model2.plotOn(frame1, LineStyle(kDashed), LineColor(kRed), Normalization(1.0, RooAbsReal.RelativeExpected), Name("model2")) print ">>> draw on canvas..." canvas = TCanvas("canvas", "canvas", 100, 100, 800, 600) legend = TLegend(0.2, 0.85, 0.4, 0.65) legend.SetTextSize(0.032) legend.SetBorderSize(0) legend.SetFillStyle(0) gPad.SetLeftMargin(0.14) gPad.SetRightMargin(0.02) frame1.GetYaxis().SetLabelOffset(0.008) frame1.GetYaxis().SetTitleOffset(1.4) frame1.GetYaxis().SetTitleSize(0.045) frame1.GetXaxis().SetTitleSize(0.045) frame1.Draw() legend.AddEntry("data", "data", 'LEP') legend.AddEntry("model", "composite model", 'L') legend.AddEntry("model2", "composite model (method 2)", 'L') legend.AddEntry("bkg", "background only", 'L') #legend.AddEntry("bkg2", "background only (no extended norm)", 'L') legend.AddEntry("sig1", "signal 1", 'L') legend.AddEntry("sig2", "signal 2", 'L') legend.AddEntry("bkgsig2", "background + signal 2", 'L') legend.Draw() canvas.SaveAs("rooFit202.png")
def rooFit207(): print ">>> setup model signal components: gaussians..." x = RooRealVar("x","x",0,10) mean = RooRealVar("mean","mean of gaussians",5) sigma = RooRealVar("sigma","width of gaussians",0.5) sig = RooGaussian("sig","Signal",x,mean,sigma) print ">>> setup model background components: Chebychev polynomial plus exponential..." a0 = RooRealVar("a0","a0",0.5,0.,1.) a1 = RooRealVar("a1","a1",-0.2,0.,1.) bkg1 = RooChebychev("bkg1","Background 1",x,RooArgList(a0,a1)) alpha = RooRealVar("alpha","alpha",-1) bkg2 = RooExponential("bkg2","Background 2",x,alpha) bkg1frac = RooRealVar("bkg1frac","fraction of component 1 in background",0.2,0.,1.) bkg = RooAddPdf("bkg","Signal",RooArgList(bkg1,bkg2),RooArgList(bkg1frac)) print ">>> sum signal and background component..." bkgfrac = RooRealVar("bkgfrac","fraction of background",0.5,0.,1.) model = RooAddPdf("model","g1+g2+a",RooArgList(bkg,sig),RooArgList(bkgfrac)) # Create dummy dataset that has more observables than the above pdf y = RooRealVar("y","y",-10,10) data = RooDataSet("data","data",RooArgSet(x,y)) # Basic information requests:" print ">>> get list of observables of pdf in context of a dataset..." # Observables are define each context as the variables # shared between a model and a dataset. In this case # that is the variable 'x' model_obs = model.getObservables(data) # RooArgSet model_obs.Print('v') print "\n>>> get list of parameters..." # Get list of parameters, given list of observables model_params = model.getParameters(RooArgSet(x)) # RooArgSet print ">>> model_params.getStringValue(\"a0\") = %s" % (model_params.getStringValue("a0")) print ">>> model_params.getRealValue(\"a0\") = %s" % (model_params.getRealValue("a0")) print ">>> model_params.find(\"a0\").GetName() = %s" % (model_params.find("a0").GetName()) print ">>> model_params.find(\"a0\").getVal() = %s" % (model_params.find("a0").getVal()) # print ">>> for param in model_params:" # for param in model_params.(): # print ">>> %s"%(model_params.first()) # print ">>> %s"%(model_params.first()) # model_params.selectByName("a*").Print('v') model_params.Print('v') print "\n>>> get list of parameters of a dataset..." # Gives identical results to operation above model_params2 = model.getParameters(data) # RooArgSet model_params2.Print() print "\n>>> get list of components..." # Get list of component objects, including top-level node model_comps = model.getComponents() # RooArgSet model_comps.Print('v') print "\n>>> modifications to structure of composites..." sigma2 = RooRealVar("sigma2","width of gaussians",1) sig2 = RooGaussian("sig2","Signal component 1",x,mean,sigma2) sig1frac = RooRealVar("sig1frac","fraction of component 1 in signal",0.8,0.,1.) sigsum = RooAddPdf("sigsum","sig+sig2",RooArgList(sig,sig2),RooArgList(sig1frac)) print ">>> construct a customizer utility to customize model..." cust = RooCustomizer(model,"cust") print ">>> instruct the customizer to replace node 'sig' with node 'sigsum'..." cust.replaceArg(sig,sigsum) # Build a clone of the input pdf according to the above customization # instructions. Each node that requires modified is clone so that the # original pdf remained untouched. The name of each cloned node is that # of the original node suffixed by the name of the customizer object # # The returned head node own all nodes that were cloned as part of # the build process so when cust_clone is deleted so will all other # nodes that were created in the process. cust_clone = cust.build(kTRUE) # RooAbsPdf # Print structure of clone of model with sig->sigsum replacement. cust_clone.Print("t") # delete clone del cust_clone
def rooFit201(): print ">>> setup model component: gaussian signals and Chebychev polynomial background..." x = RooRealVar("x","x",0,11) mean = RooRealVar("mean","mean of gaussians",5) sigma1 = RooRealVar("sigma1","width of gaussians",0.5) sigma2 = RooRealVar("sigma2","width of gaussians",1) sig1 = RooGaussian("sig1","Signal component 1",x,mean,sigma1) sig2 = RooGaussian("sig2","Signal component 2",x,mean,sigma2) a0 = RooRealVar("a0","a0",0.5,0.,1.) a1 = RooRealVar("a1","a1",-0.2,0.,1.) bkg = RooChebychev("bkg","Background",x,RooArgList(a0,a1)) print ">>>\n>>> METHOD 1 - Two RooAddPdfs" print ">>> add signal components..." # Sum the signal components into a composite signal p.d.f. sig1frac = RooRealVar("sig1frac","fraction of component 1 in signal",0.8,0.,1.) sig = RooAddPdf("sig","Signal",RooArgList(sig1,sig2),RooArgList(sig1frac)) print ">>> add signal and background..." # Sum the composite signal and background bkgfrac = RooRealVar("bkgfrac","fraction of background",0.5,0.,1.) model = RooAddPdf("model","g1+g2+a",RooArgList(bkg,sig),RooArgList(bkgfrac)) print ">>> sample, fit and plot model..." data = model.generate(RooArgSet(x),1000) # RooDataSet model.fitTo(data) frame1 = x.frame(Title("Example of composite pdf=(sig1+sig2)+bkg")) # RooPlot data.plotOn(frame1,Binning(50),Name("data")) model.plotOn(frame1,Name("model")) # Overlay the background component of model with a dashed line argset1 = RooArgSet(bkg) model.plotOn(frame1,Components(argset1),LineWidth(2),Name("bkg")) #,LineStyle(kDashed) # Overlay the background+sig2 components of model with a dotted line argset2 = RooArgSet(bkg,sig2) model.plotOn(frame1,Components(argset2),LineWidth(2),LineStyle(kDashed),LineColor(kAzure-4),Name("bkgsig2")) #,LineStyle(kDotted) print "\n>>> structure of composite pdf:" model.Print("t") # "tree" mode print "\n>>> parameters:" params = model.getVariables() # RooArgSet params.Print("v") params.Print() print "\n>>> params.find(\"...\").getVal():" print ">>> sigma1 = %.2f" % params.find("sigma1").getVal() print ">>> sigma2 = %.2f" % params.find("sigma2").getVal() print ">>> bkgfrac = %5.2f" % params.find("bkgfrac").getVal() print ">>> sig1frac = %5.2f" % params.find("sig1frac").getVal() print ">>>\n>>> components:" comps = model.getComponents() # RooArgSet sig = comps.find("sig") # RooAbsArg sigVars = sig.getVariables() # RooArgSet sigVars.Print() print ">>>\n>>> METHOD 2 - One RooAddPdf with recursive fractions" # Construct sum of models on one go using recursive fraction interpretations # model2 = bkg + (sig1 + sig2) model2 = RooAddPdf("model","g1+g2+a",RooArgList(bkg,sig1,sig2),RooArgList(bkgfrac,sig1frac),kTRUE) # NB: Each coefficient is interpreted as the fraction of the # left-hand component of the i-th recursive sum, i.e. # sum4 = A + ( B + ( C + D ) ) # with fraction fA, fB and fC expands to # sum4 = fA*A + (1-fA)*(fB*B + (1-fB)*(fC*C + (1-fC)*D)) print ">>> plot recursive addition model..." argset3 = RooArgSet(bkg,sig2) model2.plotOn(frame1,LineColor(kRed),LineStyle(kDashDotted),LineWidth(3),Name("model2")) model2.plotOn(frame1,Components(argset3),LineColor(kMagenta),LineStyle(kDashDotted),LineWidth(3),Name("bkgsig22")) model2.Print("t") print ">>> draw pdfs and fits on canvas..." canvas = TCanvas("canvas","canvas",100,100,800,600) legend = TLegend(0.57,0.87,0.95,0.65) legend.SetTextSize(0.030) legend.SetBorderSize(0) legend.SetFillStyle(0) gPad.SetLeftMargin(0.14); gPad.SetRightMargin(0.02) frame1.GetYaxis().SetLabelOffset(0.008) frame1.GetYaxis().SetTitleOffset(1.4) frame1.GetYaxis().SetTitleSize(0.045) frame1.GetXaxis().SetTitleSize(0.045) frame1.Draw() legend.AddEntry("data", "data", 'LEP') legend.AddEntry("model", "composite model", 'L') legend.AddEntry("model2", "composite model (method 2)", 'L') legend.AddEntry("bkg", "background only", 'L') legend.AddEntry("bkgsig2", "background + signal 2", 'L') legend.AddEntry("bkgsig22","background + signal 2 (method 2)",'L') legend.Draw() canvas.SaveAs("rooFit201.png")