# -*- 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 norm


def running_sum(sample):
  n = len(sample)  
  r_sum=np.zeros(n)
  sum = 0
  for i in np.arange(0,n):
      sum = sum+sample[i]
      r_sum[i] = sum
  return(r_sum)

m = 1000

a = -0.5
b = 0.5
mu = 0
sigma = (1/12)**0.5
x_points = np.arange(0,1001)/1000
LB_x = -15
UB_x = 15
x_points = (UB_x-LB_x)*x_points+LB_x
norm_100_pdf = norm.pdf(x_points,100*mu,sigma*(100)**0.5)
norm_500_pdf = norm.pdf(x_points,500*mu,sigma*(500)**0.5)
norm_900_pdf = norm.pdf(x_points,900*mu,sigma*(900)**0.5)

p_100 = 2*norm.cdf(-10,100*mu,sigma*(100)**0.5)
p_500 = 2*norm.cdf(-10,500*mu,sigma*(500)**0.5)
p_900 = 2*norm.cdf(-10,900*mu,sigma*(900)**0.5)

random_unif = np.random.uniform(a,b,m)
r_sum_unif = running_sum(random_unif)

# 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)
Figure.tight_layout() 

# Adding a panel to the figure
Panel = Figure.add_subplot(1,2,1)  
LB_x = 0
UB_x = m
off_set_x = 0.025*(UB_x-LB_x)
x_lims = (LB_x-off_set_x,UB_x+off_set_x)
LB_y = -0.6
UB_y = 0.6
off_set_y = 0.05*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

the_x = np.arange(0,m)
the_y = random_unif
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('k')
plt.ylabel('Random Sample')
title_str = r'$Unif[-0.5,0.5]-Sample$'
plt.title(title_str,size = '10')
plt.axvline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.scatter(the_x,the_y, color='blue',s=1)
plt.axhline(mu, lw=2, ls = '--',color = 'black',alpha=0.5)
plt.axhline(-0.5, lw=2, ls = ':',color = 'black',alpha=0.5)
plt.axhline(+0.5, lw=2, ls = ':',color = 'black',alpha=0.5)


# Adding a panel to the figure
Panel = Figure.add_subplot(1,2,2)  
LB_x = 0
UB_x = m
off_set_x = 0.025*(UB_x-LB_x)
x_lims = (LB_x-off_set_x,UB_x+off_set_x)
LB_y = -15
UB_y = 15
off_set_y = 0.05*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

the_x = np.arange(0,m)
the_y = r_sum_unif
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('k')
plt.ylabel('Running Average')
title_str = r'Sum of $Uniform[-0.5,0.5]$ Sample'
plt.title(title_str,size = '10')
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,alpha=0.75)

plt.plot(100+2000*norm_100_pdf,x_points, color='green', lw=1,ls = '--')
plt.plot(500+2000*norm_500_pdf,x_points, color='green', lw=1,ls = '--')
plt.plot(900+2000*norm_900_pdf,x_points, color='green', lw=1,ls = '--')

plt.axhline(-10, lw=2, ls = '--',color = 'black',alpha=0.5)
plt.axhline(10, lw=2, ls = '--',color = 'black',alpha=0.5)

plt.axvline(100, lw=1, ls = ':',color = 'black',alpha=0.5)
plt.axvline(500, lw=1, ls = ':',color = 'black',alpha=0.5)
plt.axvline(900, lw=1, ls = ':',color = 'black',alpha=0.5)

plt.scatter([100,500,900],[r_sum_unif[100],r_sum_unif[500],r_sum_unif[900]],color="blue")


text_str = r'$p = $'+ f'{p_100:2.5f}'
plt.text(110,15,text_str,color = 'red', size = 10,horizontalalignment  = 'left', verticalalignment  = 'center')

text_str = r'$p = $'+ f'{p_500:2.2f}'
plt.text(510,-15,text_str,color = 'red', size = 10,horizontalalignment  = 'left', verticalalignment  = 'center')

text_str = r'$p = $'+ f'{p_900:2.2f}'
plt.text(890,15,text_str,color = 'red', size = 10,horizontalalignment  = 'right', verticalalignment  = 'center')


# adding a title to the plot
text_str = 'Graphical Depiction of LOLN & CLT - Sum of Uniform[-0.5,0.5] RV\'s'
plt.suptitle(text_str,size='12',y=0.99)

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