# -*- coding: utf-8 -*-
"""
Created on Wed Mar  4 18:10:08 2020

@author: Johan Rene van Dorp
"""
import numpy as np
import matplotlib.pyplot as plt

def Example_6_3_pdf(x,a,b):
    n = len(x)
    values = np.zeros(n)
    for i in np.arange(0,n): 
        if not((x[i]<a) or (x[i]>b)):
            values[i] = 2*(x[i]-a)/(b-a)**2
    return values  

def Example_6_3_cdf(x,a,b):
    n = len(x)
    values = np.zeros(n)
    for i in np.arange(0,n): 
        if (x[i]<=a):
            values[i] = 0
        elif (x[i]<=b):
            values[i] = ((x[i]-a)/(b-a))**2
        else:
            values[i] = 1
    return values 

def Example_6_3_cdf_inv(u,a,b):
    n = len(u)
    values = np.zeros(n)
    for i in np.arange(0,n): 
        values[i] = (b-a)*u[i]**0.5+a
    return values

# Evaluationg the cdf of example 6_3         
a = 1
b = 3
six_3_x = np.linspace(-1,4,1000,endpoint=True)
six_3_cdf = Example_6_3_cdf(six_3_x,a,b)

# Sampling from the distribution of example 6_3
m = 100
sample = np.random.uniform(0,1,m)
sample = Example_6_3_cdf_inv(sample,a,b)

# Transforming the Uniform Sample to a discrete distribution Sample
x_points = [1.75,2.25,2.75]
y_points = Example_6_3_cdf(x_points,a,b)
y_points_emp = np.zeros(3)
y_points_emp[0] = len(sample[sample <= x_points[0]])/m
y_points_emp[1] = len(sample[sample <= x_points[1]])/m
y_points_emp[2] = len(sample[sample <= x_points[2]])/m

#Plotting the Exponential PDF and CDF

plt.rc('font', family='serif', size='12')
Figure = plt.figure()
Figure.set_figwidth(9)
Figure.set_figheight(5)
Figure.subplots_adjust(left=0.1, bottom=0.1, right=0.95, top=0.85, hspace=0.1, wspace=0.25)

#***************************************************************************************

# Adding the right panel with the empirical pmf
LB_x = 0
UB_x = 3.25
off_set_x = 0.05*(UB_x-LB_x)
x_lims = (LB_x-off_set_x,UB_x+off_set_x)
LB_y = 0
UB_y = 1
off_set_y = 0.1*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

Panel = Figure.add_subplot(1,1,1)
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('Cumulative Distribution Function $F(x)$')
text_str = r'CDF - Example 6.3'
plt.title(text_str)
plt.axvline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.plot(six_3_x,six_3_cdf,color='red')
plt.axhline(1, lw=1, ls = '--',color = 'darkgray',alpha=0.5)
plt.scatter(x_points,y_points,color = 'green',alpha=0.5,s=100)
plt.scatter(x_points,y_points_emp,color = 'blue')

text_str = r'sample size = '+ f'{m:0.0f}'
plt.text(0.025,0.9,text_str,horizontalalignment = 'left',verticalalignment = 'center', color = 'red')

for i in np.arange(0,3):
    text_str = f'{y_points[i]:0.2f}'
    plt.text(x_points[i]+0.1,y_points[i],text_str,horizontalalignment = 'left',verticalalignment = 'center', color = 'green')
    
    x_values = [x_points[i], x_points[i]]
    y_values = [0, y_points[i]]
    plt.plot(x_values, y_values,color='green',lw=5,alpha=0.5)
    
    x_values = [x_points[i], x_points[i]]
    y_values = [0, y_points_emp[i]]
    plt.plot(x_values, y_values,color='blue',lw=2,alpha=0.5)
    
    text_str = r'$\widehat{p} = $'+ f'{y_points_emp[i]:0.3f}'
    plt.text(x_points[i]-0.1,y_points_emp[i],text_str,horizontalalignment = 'right',verticalalignment = 'center', color = 'blue')
      
plt.savefig('Example_6_3_Sampler.png', dpi=300)