# -*- coding: utf-8 -*-
"""
Created on Thu Aug 11 16:22:27 2022

@author: Rene
"""

import numpy as np
import matplotlib.pyplot as plt
import Dist_Library as dl

n = 10
m = 100000
sample_matrix = np.zeros((m, n))
for i in np.arange(0,m):
    x = np.random.choice(a=n, size=n, replace=False)
    x = x + 1
    sample_matrix[i,:] = x

outcomes = np.arange(1,n+1)


plt.rc('font', family='serif', size='10')
Figure = plt.figure()
Figure.set_figwidth(10)
Figure.set_figheight(4)
Figure.subplots_adjust(hspace=0.4, wspace=0.4)

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



LB_x = 1
UB_x = 10
off_set_x = 1

LB_y = 0
UB_y = 0.2
off_set_y = 0.01

x_lims = (LB_x-off_set_x,UB_x+off_set_x)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

Panel = Figure.add_subplot(1,2,1)

j = 0
pmf = dl.Estimate_empirical_pmf(outcomes,sample_matrix[:,j]) 

plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('i')
plt.ylabel('$Pr(X_1 = i)$')
ticks = np.arange(1,11)
plt.xticks(ticks)
plt.grid(b=None, which='major', axis='both',ls='--',lw=0.5)
plt.axvline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)

plt.scatter(ticks,pmf,color='red')
for i in np.arange(0,10):
    x_values = [ticks[i],ticks[i]]
    y_values = [0,pmf[i]]
    plt.plot(x_values,y_values,color='blue',alpha=0.5)
    
text_str = "repetitions =" + f'{m:,}'    
plt.text(0.5,0.2,text_str, size=15, color = 'red', horizontalalignment = 'left', verticalalignment = 'center')    

Panel.title.set_text('PMF First draw without Replacement')

Panel = Figure.add_subplot(1,2,2)

j = 1
pmf = dl.Estimate_empirical_pmf(outcomes,sample_matrix[:,j]) 

plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('i')
plt.ylabel('$Pr(X_2 = i)$')
ticks = np.arange(1,11)
plt.xticks(ticks)
plt.grid(b=None, which='major', axis='both',ls='--',lw=0.5)
plt.axvline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)

plt.scatter(ticks,pmf,color='red')
for i in np.arange(0,10):
    x_values = [ticks[i],ticks[i]]
    y_values = [0,pmf[i]]
    plt.plot(x_values,y_values,color='blue',alpha=0.5)
    
text_str = "repetitions =" + f'{m:,}'    
plt.text(0.5,0.2,text_str, size=15, color = 'red', horizontalalignment = 'left', verticalalignment = 'center')
    

Panel.title.set_text('PMF Second draw without Replacement')

plt.savefig("PMFS_sampling_without_replacement_1.png", dpi=300)