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

# # rf103_interprfuncs
# Basic functionality: interpreted functions and pdfs
# 
# 
# 
# 
# **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 11:16 AM.</small></i>

# In[1]:


import ROOT


# Generic interpreted pdf
# ------------------------------

# Declare observable x

# In[2]:


x = ROOT.RooRealVar("x", "x", -20, 20)


# Construct generic pdf from interpreted expression
# ------------------------------------------------------

# ROOT.To construct a proper pdf, the formula expression is explicitly normalized internally by dividing
# it by a numeric integral of the expression over x in the range [-20,20]

# In[3]:


alpha = ROOT.RooRealVar("alpha", "alpha", 5, 0.1, 10)
genpdf = ROOT.RooGenericPdf("genpdf", "genpdf", "(1+0.1*abs(x)+sin(sqrt(abs(x*alpha+0.1))))", [x, alpha])


# Sample, fit and plot generic pdf
# ---------------------------------------------------------------

# Generate a toy dataset from the interpreted pdf

# In[4]:


data = genpdf.generate({x}, 10000)


# Fit the interpreted pdf to the generated data

# In[5]:


genpdf.fitTo(data, PrintLevel=-1)


# Make a plot of the data and the pdf overlaid

# In[6]:


xframe = x.frame(Title="Interpreted expression pdf")
data.plotOn(xframe)
genpdf.plotOn(xframe)


# Standard pdf adjust with interpreted helper function
# ------------------------------------------------------------------------------------------------------------
# Make a gauss(x,sqrt(mean2),sigma) from a standard ROOT.RooGaussian                                               #
# 
# Construct standard pdf with formula replacing parameter
# ------------------------------------------------------------------------------------------------------------

# Construct parameter mean2 and sigma

# In[7]:


mean2 = ROOT.RooRealVar("mean2", "mean^2", 10, 0, 200)
sigma = ROOT.RooRealVar("sigma", "sigma", 3, 0.1, 10)


# Construct interpreted function mean = sqrt(mean^2)

# In[8]:


mean = ROOT.RooFormulaVar("mean", "mean", "sqrt(mean2)", [mean2])


# Construct a gaussian g2(x,sqrt(mean2),sigma)

# In[9]:


g2 = ROOT.RooGaussian("g2", "h2", x, mean, sigma)


# Generate toy data
# ---------------------------------

# Construct a separate gaussian g1(x,10,3) to generate a toy Gaussian
# dataset with mean 10 and width 3

# In[10]:


g1 = ROOT.RooGaussian("g1", "g1", x, 10, 3)
data2 = g1.generate({x}, 1000)


# Fit and plot tailored standard pdf
# -------------------------------------------------------------------

# Fit g2 to data from g1

# In[11]:


r = g2.fitTo(data2, Save=True, PrintLevel=-1)  # ROOT.RooFitResult
r.Print()


# Plot data on frame and overlay projection of g2

# In[12]:


xframe2 = x.frame(Title="Tailored Gaussian pdf")
data2.plotOn(xframe2)
g2.plotOn(xframe2)


# Draw all frames on a canvas

# In[13]:


c = ROOT.TCanvas("rf103_interprfuncs", "rf103_interprfuncs", 800, 400)
c.Divide(2)
c.cd(1)
ROOT.gPad.SetLeftMargin(0.15)
xframe.GetYaxis().SetTitleOffset(1.4)
xframe.Draw()
c.cd(2)
ROOT.gPad.SetLeftMargin(0.15)
xframe2.GetYaxis().SetTitleOffset(1.4)
xframe2.Draw()

c.SaveAs("rf103_interprfuncs.png")


# Draw all canvases 

# In[14]:


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