#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu Oct 17 12:34:11 2019

@author: gullholm
"""

import random
import numpy as np
import matplotlib.pyplot as plt

theta = 0
M = 10000

#question 2

for i in range((M-1)):
	U = random.uniform(0,1)
	theta += U**2
print(2*theta/M, "question 2")
# Question 3

theta = 0
count = 0

for i in range((M-1)):
	U_1 = random.uniform(0,1)
	U_2 = random.uniform(0,1)
	if U_2 < (U_1**2):
		count += 1

print(float(2*count)/float(M),"Question 3")

# Question 5

theta = 0
N = 1000
theta_2 = 0
crude = [0]*N
HM = [0]*N

for j in range((N-1)):
	theta_2=0
	count = 0
	for i in range((M-1)):
		U_1 = np.random.uniform(0,1)
		U_2 = np.random.uniform(0,1)
		theta_2 += U_1**2
		if U_2 <= (U_1**2):
			count += 1
	crude[j+1] = 2*(theta_2/M)
	HM[j+1] = 2*(float(count)/M)

#crude
print(float(16)/float(45))
print(np.var(crude), "var Crude")
#HM
print(np.sqrt(np.var(HM)), "RMSE HM")

# question 6

N = 20
sample_size = np.zeros(N)
err_HM = np.zeros(N)
err_crude = np.zeros(N)

for n in range(N):
    sample_size[n] = 2**(n+1)


for i in range((N)):
    M = 2**(i+1)
    theta_2 = 0
    count = 0
    for m in range((M-1)):
        U_1 = np.random.uniform(0,1)
        U_2 = np.random.uniform(0,1)
        theta_2 += U_1**2
        if U_2 <= (U_1**2):
            count += 1
    err_crude[i] = np.abs((2*(theta_2)/M)-(2/3))
    err_HM[i] = np.abs((2*(float(count)/M))-(2/3))

plt.loglog(sample_size, (sample_size)**(-0.5))
plt.loglog(sample_size,err_crude)
plt.loglog(sample_size, err_HM)




#err_HM = np.zeros(N)
#err_crude = np.zeros(N)

#average_1 = 0

#for m in range(int(sample_size[N-1])):
#	U_1 = np.random.uniform(0,1)
#	U_2 = np.random.uniform(0,1)
#	theta_2 += U_1**2
#	if U_2 <= (U_1**2):
#			count += 1
#	for n in range(N):
 #       	if m==(int(sample_size[n])-1):
##			err_crude[n] = np.abs(2*(theta_2/sample_size[n])-(2/3))
#			err_HM[n] = np.abs(2*(float(count)/sample_size[n])-(2/3))
 #       		theta_2=0
#			count=0

#print(err_HM)