# Exercise 5.39
# S(x;M,N) = sum f_k(x) for k=M,....,N

import numpy as np
import matplotlib.pyplot as plt
import glob
import os

def animate_series(fk, M, N, xmin, xmax, ymin, ymax, n, exact):
	# A) Remove existing image files
	for file in glob.glob("*.png"):
		os.remove(file)
	# B) Set up plot
	plt.axis([xmin, xmax, ymin, ymax])
	plt.xlabel("x")
	plt.ylabel("S(x;M,N)")
	# C) Define grid of x- and s-values
	x = np.linspace(xmin, xmax, n)
	s = np.zeros(n)
	# D) Plot points for k=M,...,N
	lines = plt.plot(x, fk(x,M))
	for k in range(M,N+1):
	    # Add one more term to Taylor series
		s = s + fk(x,k)
		# Update vertical plot values:        
		lines[0].set_ydata(s)  
		# Exact solution:
		plt.plot(x, exact(x), 'g')
		# Update drawing:  
		plt.draw()
		# Save to file:             
		plt.savefig("tmp_%04d.png" % (k-M)) 

# First example: Sin(x)

exact = np.sin
fk = lambda x,k: 1.0 * (-1)**k * x**(2*k+1) / np.math.factorial(2*k+1)
M = 0
N = 40
xmin = 0
xmax = 13*np.pi
ymin = -2
ymax = 2
n = 200
animate_series(fk, M, N, xmin, xmax, ymin, ymax, n, exact)

"""
Terminal> convert -delay 40 tmp_*.png movie.gif
"""


"""
# Second example: exp(-x)

exact = lambda x: np.exp(-x)
fk = lambda x,k: 1.0 * (-x)**k / np.math.factorial(k)
M = 0
N = 30
xmin = 0
xmax = 15
ymin = -0.5
ymax = 1.4
n = 200
animate_series(fk, M, N, xmin, xmax, ymin, ymax, n, exact)
"""

"""
Terminal> convert -delay 40 tmp_*.png movie.gif
"""