# -*- coding: utf-8 -*-

from tkinter import *
from random import choice     # http://docs.python.org/library/random.html
import numpy as np
import matplotlib.pyplot as plt     # http://matplotlib.sourceforge.net/api/pyplot_api.html#module-matplotlib.pyplot
import matplotlib.mlab as mlab    # http://matplotlib.sourceforge.net/api/mlab_api.html#module-matplotlib.mlab

window = Tk()
sizex = 400
sizey = 400
canvas = Canvas(window, width = sizex, height = sizey)
canvas.pack()
x = 200		# initial left-most edge of first ball
y = 1		# initial top-most edge of first ball
r = 4                  # ball diameter 
depx = 1            # displacement at each move in x direction
depy = 0

# create balls:
no_particles = 1000
dy = (sizey-2.)/(no_particles+1)         # y initial separation between balls
#print dy
ball_list=[]
for i in range(no_particles):
    ball = canvas.create_oval(x,y,x+r,y+r,fill="blue")
    y = y+dy
    ball_list.append(ball)

#moves
no_moves = 400
for j in range(no_moves):
    for ball in ball_list:
        canvas.move(ball, choice([-1,-1,-1,-1,1,1,1,1,1,1])*depx, depy) #drift
    canvas.after(1)
    canvas.update()

#analysis - histogram
# see http://matplotlib.sourceforge.net/examples/api/histogram_demo.html
xpos = []
for ball in ball_list:
    posi = canvas.coords(ball)
    xpos.append(posi[0]-x)
xh = np.array(xpos)  # see http://www.scipy.org/Cookbook/BuildingArrays
#  compute the mean mu and sigma  from xh (and/or theoretical value from random walk result)
mu = np.mean(xh)
sigma = np.std(xh)
fig = plt.figure()
ax = fig.add_subplot(111)
# print xh 
n, bins, patches = ax.hist(xh, 20, facecolor='green', alpha=0.75)
print(mu, sigma)
print(n,bins, patches)
# hist uses np.histogram to create 'n' and 'bins'.
# np.histogram returns the bin edges, so there will be ii probability
# density values in n, ii+1 bin edges in bins and ii patches.  To get
# everything lined up, we'll compute the bin centers
bincenters = 0.5*(bins[1:]+bins[:-1])
# add a 'best fit' line for the normal PDF
yh = (bins[1]-bins[0])*no_particles*mlab.normpdf( bincenters, mu, sigma)  # http://matplotlib.sourceforge.net/api/mlab_api.html#matplotlib.mlab.normpdf
l = ax.plot(bincenters, yh, 'r--', linewidth=1)
#print n
ax.set_xlabel('X positions')
ax.set_ylabel('Occurences')

ax.grid(True)

plt.show()

#window.mainloop()