# -*- coding: utf-8 -*-
"""
Created on Thu Feb  3 18:47:48 2022

@author: Rene
"""
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import gamma
import pandas as pd
import matplotlib.patches as patches
import Dist_Library

m = 500

alpha=4
beta=2

x = np.arange(0,1001)/1000
LB_x = 0
UB_x = 11
x = (UB_x-LB_x)*x+LB_x
pdf_gamma = gamma.pdf(x,a = alpha,scale = 1/beta)

mean_gamma = alpha/beta
random_gamma = np.random.gamma(alpha, 1/beta, m)

h = 0.25
bounds = np.arange(0,20)
bounds = bounds*(2*h)
pmf_hat = Dist_Library.Estimate_empirical_histogram(bounds, random_gamma)

#pdf_hat = pmf_hat/(2*h)

df = pd.DataFrame({'The_Sample':random_gamma})

x1 = 2
lb_1 = x1-h
ub_1 = x1+h
cdf_lb = df[df<=lb_1].count()/m
cdf_ub = df[df<=ub_1].count()/m
density_x1 = (cdf_ub-cdf_lb)/(2*h)

h = 0.25
x2 = 4
lb_2 = x2-h
ub_2 = x2+h
cdf_lb = df[df<=lb_2].count()/m
cdf_ub = df[df<=ub_2].count()/m
density_x2 = (cdf_ub-cdf_lb)/(2*h)



# 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(1,2,1)  
LB_x = 0
UB_x = 10
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 = 0.5
off_set_y = 0.05*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

the_x = x
the_y = pdf_gamma
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('Probability Density Function')
title_str = r'$Gamma[2,4]-PDF$'
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')

Panel.add_patch(patches.Rectangle(
                          (lb_1, 0), 
                           2*h, 
                           density_x1,
                           facecolor = 'none',
                           edgecolor = 'red',
                           linewidth = 1,
                           alpha = 1))
x_values = [x1,x1]
y_values = [0,density_x1]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')

Panel.add_patch(patches.Rectangle(
                          (lb_2, 0), 
                           2*h, 
                           density_x2,
                           facecolor = 'none',
                           edgecolor = 'red',
                           linewidth = 1,
                           alpha = 1))
x_values = [x2,x2]
y_values = [0,density_x2]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')


# Adding a panel to the figure
Panel2 = Figure.add_subplot(1,2,2)  
LB_x = 0
UB_x = 10
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 = 0.5
off_set_y = 0.05*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

the_x = x
the_y = pdf_gamma
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('Probability Density Function')
title_str = r'$Gamma[2,4]-PDF$'
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')

for i in np.arange(0,len(bounds)-1):
    Panel2.add_patch(patches.Rectangle(
                          (bounds[i],0), 
                           2*h, 
                           pmf_hat[i+1],
                           facecolor = 'none',
                           edgecolor = 'red',
                           linewidth = 1,
                           alpha = 1))
    mid_point = (bounds[i]+bounds[i+1])/2
    x_values = [mid_point,mid_point]
    y_values = [0,pmf_hat[i+1]]
    plt.plot(x_values,y_values, color='black', lw=1, ls=':')

plt.savefig('Recover_Gamma_Density_2.png', dpi=300)