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

# # rf604_constraints
# Likelihood and minimization: fitting with constraints
# 
# 
# 
# 
# **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 11:19 AM.</small></i>

# In[1]:


from __future__ import print_function
import ROOT


# Create model and dataset
# ----------------------------------------------

# Construct a Gaussian pdf

# In[2]:


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

m = ROOT.RooRealVar("m", "m", 0, -10, 10)
s = ROOT.RooRealVar("s", "s", 2, 0.1, 10)
gauss = ROOT.RooGaussian("gauss", "gauss(x,m,s)", x, m, s)


# Construct a flat pdf (polynomial of 0th order)

# In[3]:


poly = ROOT.RooPolynomial("poly", "poly(x)", x)


# model = f*gauss + (1-f)*poly

# In[4]:


f = ROOT.RooRealVar("f", "f", 0.5, 0.0, 1.0)
model = ROOT.RooAddPdf("model", "model", [gauss, poly], [f])


# Generate small dataset for use in fitting below

# In[5]:


d = model.generate({x}, 50)


# Create constraint pdf
# -----------------------------------------

# Construct Gaussian constraint pdf on parameter f at 0.8 with
# resolution of 0.1

# In[6]:


fconstraint = ROOT.RooGaussian("fconstraint", "fconstraint", f, 0.8, 0.1)


# Method 1 - add internal constraint to model
# -------------------------------------------------------------------------------------

# Multiply constraint term with regular pdf using ROOT.RooProdPdf Specify in
# fitTo() that internal constraints on parameter f should be used

# Multiply constraint with pdf

# In[7]:


modelc = ROOT.RooProdPdf("modelc", "model with constraint", [model, fconstraint])


# Fit model (without use of constraint term)

# In[8]:


r1 = model.fitTo(d, Save=True, PrintLevel=-1)


# Fit modelc with constraint term on parameter f

# In[9]:


r2 = modelc.fitTo(d, Constrain={f}, Save=True, PrintLevel=-1)


# Method 2 - specify external constraint when fitting
# ------------------------------------------------------------------------------------------

# Construct another Gaussian constraint pdf on parameter f at 0.8 with
# resolution of 0.1

# In[10]:


fconstext = ROOT.RooGaussian("fconstext", "fconstext", f, 0.2, 0.1)


# Fit with external constraint

# In[11]:


r3 = model.fitTo(d, ExternalConstraints={fconstext}, Save=True, PrintLevel=-1)


# Print the fit results

# In[12]:


print("fit result without constraint (data generated at f=0.5)")
r1.Print("v")
print("fit result with internal constraint (data generated at f=0.5, is f=0.8+/-0.2)")
r2.Print("v")
print("fit result with (another) external constraint (data generated at f=0.5, is f=0.2+/-0.1)")
r3.Print("v")