# -*- coding: utf-8 -*-
"""
Created on Mon Feb 28 08:46:50 2022

@author: Rene
"""

import GeneralizedTrapezoidal as GT
import numpy as np
from scipy.stats import uniform
import matplotlib.pyplot as plt

LB_x = -0.5
UB_x = 2.5
x = np.linspace(LB_x,UB_x,1000)

a = 0
b = 1
pdf_1 = uniform.pdf(x,loc = a,scale = b)
cdf_1 = uniform.cdf(x,loc = a,scale = b)

pdf_1

a = 0
b = 1
c = 1
d = 2
m = 2
n = 2
alpha = 1

pdf_2 = GT.GT_pdf(x,a,b,c,d,m,n,alpha)
cdf_2 = GT.GT_cdf(x,a,b,c,d,m,n,alpha)

# Plotting a four panel figure

plt.rc('font', family='serif', size='10')
plt.figure(figsize=(10, 5))
Figure = plt.figure(0)
Figure.set_figwidth(9)
Figure.set_figheight(4.75)
Figure.subplots_adjust(hspace=0.5, wspace=0.25)

# Adding a panel to the figure
Panel = Figure.add_subplot(2,2,1)  
LB_x = -0.25
UB_x = 2.25
off_set_x = 0.025*(UB_x-LB_x)
x_lims = (LB_x-off_set_x,UB_x+off_set_x)
LB_y = 0
UB_y = max(pdf_1)
off_set_y = 0.1*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

the_x = x
the_y = pdf_1
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('PDF $f(x)$')
title_str = r'PDF : $X \sim Unif(0,1)$'
plt.title(title_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(the_x,the_y, color='blue', lw=1)

# Adding a panel to the figure
Panel = Figure.add_subplot(2,2,2)  
LB_x = -0.25
UB_x = 2.25
off_set_x = 0.025*(UB_x-LB_x)
x_lims = (LB_x-off_set_x,UB_x+off_set_x)
LB_y = 0
UB_y = max(pdf_2)
off_set_y = 0.1*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

the_x = x
the_y = pdf_2
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('PDF $f(x)$')
title_str = r'PDF : $X \sim$ Sum of two $Unif(0,1)$'
plt.title(title_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(the_x,the_y, color='red', lw=1)
x_values = [1,1]
y_values = [0,GT.GT_pdf(1,a,b,c,d,m,n,alpha)[0]]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')

# Adding a panel to the figure
Panel = Figure.add_subplot(2,2,3)  
LB_x = -0.25
UB_x = 2.25
off_set_x = 0.025*(UB_x-LB_x)
x_lims = (LB_x-off_set_x,UB_x+off_set_x)
LB_y = 0
UB_y = max(cdf_1)
off_set_y = 0.1*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

the_x = x
the_y = cdf_1
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('CDF $F(x) = Pr(X \leq x)$')
title_str = r'CDF : $X \sim Unif(0,1)$'
plt.title(title_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(the_x,the_y, color='blue', lw=1)
x_values = [1,1]
y_values = [0,uniform.pdf(1,loc = a,scale = b)]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')

# Adding a panel to the figure
Panel = Figure.add_subplot(2,2,4)  
LB_x = -0.25
UB_x = 2.25
off_set_x = 0.025*(UB_x-LB_x)
x_lims = (LB_x-off_set_x,UB_x+off_set_x)
LB_y = 0
UB_y = max(cdf_2)
off_set_y = 0.1*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

the_x = x
the_y = cdf_2
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('CDF $F(x) = Pr(X \leq x)$')
title_str = r'PDF : $X \sim$ Sum of two $Unif(0,1)$'
plt.title(title_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(the_x,the_y, color='red', lw=1)
x_values = [1,1]
y_values = [0,GT.GT_cdf(1,a,b,c,d,m,n,alpha)[0]]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')

x_values = [0,1]
y_values = [GT.GT_cdf(1,a,b,c,d,m,n,alpha)[0],GT.GT_cdf(1,a,b,c,d,m,n,alpha)[0]]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')

plt.savefig('SUM_OF_UNFORMS.png', dpi=300)