#!/usr/bin/env python
# coding: utf-8

# # rf201_composite
# Addition and convolution: composite pdf with signal and background component
# 
# ```
# pdf = f_bkg * bkg(x,a0,a1) + (1-fbkg) * (f_sig1 * sig1(x,m,s1 + (1-f_sig1) * sig2(x,m,s2)))
# ```
# 
# 
# 
# 
# **Author:**  Clemens Lange, Wouter Verkerke (C++ version)  
# <i><small>This notebook tutorial was automatically generated with <a href= "https://github.com/root-project/root/blob/master/documentation/doxygen/converttonotebook.py">ROOTBOOK-izer</a> from the macro found in the ROOT repository  on Wednesday, April 17, 2024 at 11:17 AM.</small></i>

# In[1]:


import ROOT


# Setup component pdfs
# ---------------------------------------

# Declare observable x

# In[2]:


x = ROOT.RooRealVar("x", "x", 0, 10)


# Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and
# their parameters

# In[3]:


mean = ROOT.RooRealVar("mean", "mean of gaussians", 5)
sigma1 = ROOT.RooRealVar("sigma1", "width of gaussians", 0.5)
sigma2 = ROOT.RooRealVar("sigma2", "width of gaussians", 1)

sig1 = ROOT.RooGaussian("sig1", "Signal component 1", x, mean, sigma1)
sig2 = ROOT.RooGaussian("sig2", "Signal component 2", x, mean, sigma2)


# Build Chebychev polynomial pdf

# In[4]:


a0 = ROOT.RooRealVar("a0", "a0", 0.5, 0.0, 1.0)
a1 = ROOT.RooRealVar("a1", "a1", -0.2, 0.0, 1.0)
bkg = ROOT.RooChebychev("bkg", "Background", x, [a0, a1])


# Method 1 - Two RooAddPdfs
# ------------------------------------------
# Add signal components

# Sum the signal components into a composite signal pdf

# In[5]:


sig1frac = ROOT.RooRealVar("sig1frac", "fraction of component 1 in signal", 0.8, 0.0, 1.0)
sig = ROOT.RooAddPdf("sig", "Signal", [sig1, sig2], [sig1frac])


# Add signal and background
# ------------------------------------------------

# Sum the composite signal and background

# In[6]:


bkgfrac = ROOT.RooRealVar("bkgfrac", "fraction of background", 0.5, 0.0, 1.0)
model = ROOT.RooAddPdf("model", "g1+g2+a", [bkg, sig], [bkgfrac])


# Sample, fit and plot model
# ---------------------------------------------------

# Generate a data sample of 1000 events in x from model

# In[7]:


data = model.generate({x}, 1000)


# Fit model to data

# In[8]:


model.fitTo(data, PrintLevel=-1)


# Plot data and PDF overlaid

# In[9]:


xframe = x.frame(Title="Example of composite pdf=(sig1+sig2)+bkg")
data.plotOn(xframe)
model.plotOn(xframe)


# Overlay the background component of model with a dashed line

# In[10]:


model.plotOn(xframe, Components={bkg}, LineStyle="--")


# Overlay the background+sig2 components of model with a dotted line

# In[11]:


model.plotOn(xframe, Components={bkg, sig2}, LineStyle=":")


# Print structure of composite pdf

# In[12]:


model.Print("t")


# Method 2 - One RooAddPdf with recursive fractions
# ---------------------------------------------------

# Construct sum of models on one go using recursive fraction interpretations
# 
#   model2 = bkg + (sig1 + sig2)

# In[13]:


model2 = ROOT.RooAddPdf("model", "g1+g2+a", [bkg, sig1, sig2], [bkgfrac, sig1frac], True)


# 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, and fC expands to
# 
#   sum4 = fA*A + (1-fA)*(fB*B + (1-fB)*(fC*C + (1-fC)*D))

# Plot recursive addition model
# ---------------------------------------------------------

# In[14]:


model2.plotOn(xframe, LineColor="r", LineStyle="--")
model2.plotOn(xframe, Components={bkg, sig2}, LineColor="r", LineStyle="--")
model2.Print("t")


# Draw the frame on the canvas

# In[15]:


c = ROOT.TCanvas("rf201_composite", "rf201_composite", 600, 600)
ROOT.gPad.SetLeftMargin(0.15)
xframe.GetYaxis().SetTitleOffset(1.4)
xframe.Draw()

c.SaveAs("rf201_composite.png")


# Draw all canvases 

# In[16]:


from ROOT import gROOT 
gROOT.GetListOfCanvases().Draw()