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

# # rf301_composition
# Multidimensional models: multi-dimensional pdfs through composition, e.g. substituting
# a pdf parameter with a function that depends on other observables
# 
# `pdf = gauss(x,f(y),s)` with `f(y) = a0 + a1*y`
# 
# 
# 
# 
# **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 11:18 AM.</small></i>

# In[1]:


import ROOT


# Setup composed model gauss(x, m(y), s)
# -----------------------------------------------------------------------

# Create observables

# In[2]:


x = ROOT.RooRealVar("x", "x", -5, 5)
y = ROOT.RooRealVar("y", "y", -5, 5)


# Create function f(y) = a0 + a1*y

# In[3]:


a0 = ROOT.RooRealVar("a0", "a0", -0.5, -5, 5)
a1 = ROOT.RooRealVar("a1", "a1", -0.5, -1, 1)
fy = ROOT.RooPolyVar("fy", "fy", y, [a0, a1])


# Creat gauss(x,f(y),s)

# In[4]:


sigma = ROOT.RooRealVar("sigma", "width of gaussian", 0.5)
model = ROOT.RooGaussian("model", "Gaussian with shifting mean", x, fy, sigma)


# Sample data, plot data and pdf on x and y
# ---------------------------------------------------------------------------------

# Generate 10000 events in x and y from model

# In[5]:


data = model.generate({x, y}, 10000)


# Plot x distribution of data and projection of model x = Int(dy)
# model(x,y)

# In[6]:


xframe = x.frame()
data.plotOn(xframe)
model.plotOn(xframe)


# Plot x distribution of data and projection of model y = Int(dx)
# model(x,y)

# In[7]:


yframe = y.frame()
data.plotOn(yframe)
model.plotOn(yframe)


# Make two-dimensional plot in x vs y

# In[8]:


hh_model = model.createHistogram("hh_model", x, Binning=50, YVar=dict(var=y, Binning=50))
hh_model.SetLineColor(ROOT.kBlue)


# Make canvas and draw ROOT.RooPlots

# In[9]:


c = ROOT.TCanvas("rf301_composition", "rf301_composition", 1200, 400)
c.Divide(3)
c.cd(1)
ROOT.gPad.SetLeftMargin(0.15)
xframe.GetYaxis().SetTitleOffset(1.4)
xframe.Draw()
c.cd(2)
ROOT.gPad.SetLeftMargin(0.15)
yframe.GetYaxis().SetTitleOffset(1.4)
yframe.Draw()
c.cd(3)
ROOT.gPad.SetLeftMargin(0.20)
hh_model.GetZaxis().SetTitleOffset(2.5)
hh_model.Draw("surf")

c.SaveAs("rf301_composition.png")


# Draw all canvases 

# In[10]:


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