/// \file
/// \ingroup tutorial_roofit
/// \notebook -js
///
/// Addition and convolution: decay function p.d.fs with optional B physics effects (mixing and CP violation)
///
/// that can be analytically convolved with e.g. Gaussian resolution functions
///
/// ```
///  pdf1 = decay(t,tau) (x) delta(t)
///  pdf2 = decay(t,tau) (x) gauss(t,m,s)
///  pdf3 = decay(t,tau) (x) (f*gauss1(t,m1,s1) + (1-f)*gauss2(t,m1,s1))
/// ```
///
/// \macro_image
/// \macro_output
/// \macro_code
///
/// \date 07/2008
/// \author Wouter Verkerke

#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussModel.h"
#include "RooAddModel.h"
#include "RooTruthModel.h"
#include "RooDecay.h"
#include "RooPlot.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "TH1.h"
using namespace RooFit;

void rf209_anaconv()
{
   // B - p h y s i c s   p d f   w i t h   t r u t h   r e s o l u t i o n
   // ---------------------------------------------------------------------

   // Variables of decay p.d.f.
   RooRealVar dt("dt", "dt", -10, 10);
   RooRealVar tau("tau", "tau", 1.548);

   // Build a truth resolution model (delta function)
   RooTruthModel tm1("tm", "truth model", dt);

   // Construct decay(t) (x) delta(t)
   RooDecay decay_tm("decay_tm", "decay", dt, tau, tm1, RooDecay::DoubleSided);

   // Plot p.d.f. (dashed)
   RooPlot *frame = dt.frame(Title("Bdecay (x) resolution"));
   decay_tm.plotOn(frame, LineStyle(kDashed));

   // B - p h y s i c s   p d f   w i t h   G a u s s i a n   r e s o l u t i o n
   // ----------------------------------------------------------------------------

   // Build a gaussian resolution model
   RooRealVar bias1("bias1", "bias1", 0);
   RooRealVar sigma1("sigma1", "sigma1", 1);
   RooGaussModel gm1("gm1", "gauss model 1", dt, bias1, sigma1);

   // Construct decay(t) (x) gauss1(t)
   RooDecay decay_gm1("decay_gm1", "decay", dt, tau, gm1, RooDecay::DoubleSided);

   // Plot p.d.f.
   decay_gm1.plotOn(frame);

   // B - p h y s i c s   p d f   w i t h   d o u b l e   G a u s s i a n   r e s o l u t i o n
   // ------------------------------------------------------------------------------------------

   // Build another gaussian resolution model
   RooRealVar bias2("bias2", "bias2", 0);
   RooRealVar sigma2("sigma2", "sigma2", 5);
   RooGaussModel gm2("gm2", "gauss model 2", dt, bias2, sigma2);

   // Build a composite resolution model f*gm1+(1-f)*gm2
   RooRealVar gm1frac("gm1frac", "fraction of gm1", 0.5);
   RooAddModel gmsum("gmsum", "sum of gm1 and gm2", RooArgList(gm1, gm2), gm1frac);

   // Construct decay(t) (x) (f*gm1 + (1-f)*gm2)
   RooDecay decay_gmsum("decay_gmsum", "decay", dt, tau, gmsum, RooDecay::DoubleSided);

   // Plot p.d.f. (red)
   decay_gmsum.plotOn(frame, LineColor(kRed));

   // Draw all frames on canvas
   new TCanvas("rf209_anaconv", "rf209_anaconv", 600, 600);
   gPad->SetLeftMargin(0.15);
   frame->GetYaxis()->SetTitleOffset(1.6);
   frame->Draw();
}