__author__ = 'elianasullivan'

#THIS CODE GRAPHS HOW THE ESTIMATE OF PI CHANGES WITH ERROR BARS THAT ARE EQUAL TO THE ABS(MATH.PI-PI_ESTIMATE)

import random
import math
import matplotlib.pyplot as plt

def error_bar_estimator(min_size,max_size, step):

    circle_count = 0
    square_count = 0

    sampsize_list = []
    error_list = []
    estimates_list = []

    for samp_size in range(min_size,max_size,step):
        for dart in range(samp_size):
            x_coord = random.random()
            y_coord = random.random()
            if ((x_coord)**2)+((y_coord)**2) <= 1:
                circle_count += 1
                square_count += 1
            else:
                square_count += 1

        #calculate the error of each estimate
        pi_estimate = 4*(float(circle_count)/square_count)
        error = abs((math.pi)-(pi_estimate))

        #create lists to prepare for graphing
        estimates_list.append(pi_estimate)
        sampsize_list.append(samp_size)
        error_list.append(error)

    #creates graph
    plt.errorbar(sampsize_list,estimates_list, yerr=error_list, linewidth = 1.5)
    plt.xlabel("Number of Darts")
    plt.ylabel("Pi Estimate")
    plt.title("Pi Estimate with Varying Number of Darts")
    plt.plot((0, max_size), (math.pi, math.pi), linewidth=2.0)
    plt.show()

print error_bar_estimator(1000,10000,50)