# Author: Ika, 2013-08-24

import math as m
import numpy as np
import matplotlib.pyplot as plt
import scipy.special as sp
# import matplotlib.animation as animation
def draw_frame(n,filename,line_color):
	fig = plt.figure()
	plt.axes([0.02,0.13,0.9,0.8])
	plt.hold(True)
	plt.xlim(-3,3)
	plt.ylim(-2,4)
	# Set up the spines
	ax = plt.gca()
	ax.spines['right'].set_color('none')
	ax.spines['top'].set_color('none')
	ax.xaxis.set_ticks_position('bottom')
	ax.spines['bottom'].set_position(('data',0))
	ax.yaxis.set_ticks_position('left')
	ax.spines['left'].set_position(('data',0))
	# Set up the label
	ax.text(2,3,'N='+str(n),fontsize=24,color=line_color)

	Q = []
	X = np.arange(-3, 3, 0.001)
	# Draw the original function (ORG) curve
	ORG = np.exp(-1/(X*X))
	a = plt.plot(X, ORG, '-', color='black', lw=4)
	Q.append(a)
	# Draw the approximation function (APPR) curve
	i=1
	APPR = 1+(-1)**i*(X**(-2*i))/m.factorial(i)
	while (i<n):
		i = i+1
		APPR = APPR+(-1)**i*(X**(-2*i))/m.factorial(i)
	a = plt.plot(X, APPR, '-', color=line_color, lw=4)
	Q.append(a)
	
	plt.savefig(filename)

draw_frame(1,'frame01.eps','#b30000')
draw_frame(2,'frame02.eps','#00b300')
draw_frame(3,'frame03.eps','#0000b3')
draw_frame(4,'frame04.eps','#b3b300')
draw_frame(5,'frame05.eps','#00b3b3')
draw_frame(6,'frame06.eps','#b300b3')
draw_frame(7,'frame07.eps','#b3b3b3')
draw_frame(10,'frame08.eps','#3300b3')
draw_frame(50,'frame09.eps','#33b300')
draw_frame(65,'frame10.eps','#0033b3')
draw_frame(80,'frame11.eps','#b3b333')

# To generate the final GIF file, use the shell command:
# convert -antialias -loop 0 -delay 100 -compress LZW frame* Expinvsqlau_GIF.gif