__author__ = 'elianasullivan'
import random
import math
import numpy as np
import pylab
from scipy.optimize import curve_fit


def error_graph(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

        pi_estimate = 4*(float(circle_count)/square_count)
        error = abs((math.pi)-(pi_estimate))

        estimates_list.append(pi_estimate)
        sampsize_list.append(samp_size)
        error_list.append(error)

    #makes a function to define what kind of best fit line I am looking for. I want something exponential.
    def line(sampsize_list,x):
        return sampsize_list**x

    #finds the best fit value to fit the function n^x when n = sample size
    popt, pcov = curve_fit(line,sampsize_list,error_list)
    popt
    print "The exponent of your best fit line is:",popt

    #graps the fluctuations in error bars (in blue) and the best fit line generated above (in purple)
    x = np.linspace(min_size,max_size,step)
    y = x**popt

    # compose plot
    pylab.plot(sampsize_list,error_list, color="blue")
    pylab.plot(x,y, color= "purple")
    pylab.xlabel("Number of Darts"), pylab.ylabel("Error"), pylab.title("Error Values with Varying Number of Darts")
    #pylab.ylim(0,0.1) #uncomment this to see a zoomed in view

    pylab.show() # show the plot

print error_graph(1000,100000,50)