##P460 Machine Learning.

#Akshay Priyadarshi's Code to show an example of Confidence Interval

#Some of the values can be changed to check how the confidence interval holds in different number ranges.

#importing necessary libraries
import numpy as np
import random
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches

#Total population.
population=100000
#Approximate Probability of 1 in the generated sample.
probability=0.54 

#To generate a list of 0's and 1's with probability of 1 being nearly 'p'
Total=np.zeros(population)
count=0
for i in range(population):
    r=random.randint(1, 100)/100
    if r>probability:
        Total[i]=0
    else:
        Total[i]=1
        count=count+1
        
#Printing the actual Probability of 1 in population.    
p=count/population
print('The actual probability of 1 in the genrated population of',population,'numbers, is:',p)
sd=(p*(1-p)*population)**0.5
low=p-(2*sd)
high=p+(2*sd)


#Choosing a sample

#number 'n' of samples to be randomly selected from the list
n=1000
c=0
d=0

#Number of times the code is going to run.
times=1000
y1=times/5
sum1=0
p1=np.zeros(times)
fig, ax = plt.subplots(figsize =(10, 5)) 
for i in range(times):
    sample = random.choices(Total, k=n)
    p1[i] = sample.count(1)/n
    sd1=(p1[i]*(1-p1[i])/n)**0.5
    low1=p1[i]-(2*sd1)
    high1=p1[i]+(2*sd1)
    if p1[i] >low:
        if p1[i]<high:
            c=c+1
    if p>low1:
        if p<high1:
            d=d+1
    sum1=sum1+p1[i]        
    ax.axvline(x=low1,ymin=0, ymax=y1,  alpha=0.01,color='green')
    ax.axvline(x=high1, ymin=0, ymax=y1, alpha=0.01,color='black')            
    
#print(c*100/times,'% of the times,','p1 lies within 2 standard deviations of p.')      
print(d*100/times,'% of the times,','p lies within 2 standard deviations of p1.')
print('Here p1 is the probablity of occurance of 1 in a random sample of',n,'numbers out of the original list of numbers.')
print('The sampling was performed',times,'times.')

# Creating histogram 
ax.hist(p1, bins = 'auto',density=None,label='Occurances') 
ax.grid(alpha=0.1)
plt.xlabel('Probability of 1 in the sample -->',fontsize=12)
plt.ylabel('Number of Occurances -->',fontsize=12)
plt.title('Histogram of probabilities in generated samples with replacement',fontsize=14)
ax.axvline(x=p,ymin=0, ymax=y1, color='red',label='Probability in original population')
ax.legend(loc='best')
blue=mpatches.Patch(color='blue', label='Occurances')
red=mpatches.Patch(color='red', label='Probability in original population')
lower = mpatches.Patch(color='green', label=r'$-2\sigma$')
higher= mpatches.Patch(color='black', label=r'$+2\sigma$')
ax.legend(handles=[red, blue,lower,higher])
ax.text(0.5, -times/23, r'Black lines are for "p1$+2\sigma$" upper limits, Green lines are for "p1$-2\sigma$" lower limits.',wrap=True, ha='center',fontsize=13)  
plt.savefig('ml.png', bbox_inches='tight')
plt.show() 
print( 'The darkness of the green and black lines is proportional to frequency of their occurances.')