"""
The purpose of this exercise is to animate how the accuracy
of a Taylor series approximation improves as we include more
terms in the series. The recipe used is the same as in
'animate_gauss1.py'
"""

import numpy as np
from math import factorial
import matplotlib.pyplot as plt


""" Define a function to create the animation. The function takes
a function fk as argument, which is the function that defines each term
in the taylor series. See the book for an explanation of the other arguments.
"""

def animate_series(fk, M, N, xmin, xmax, ymin, ymax, n, exact):

    x = np.linspace(xmin,xmax,n)
    s = np.zeros(n)

    #set the axis and create the object 'lines'
    plt.axis([xmin,xmax,ymin,ymax])
    plt.plot(x,exact(x))
    lines = plt.plot(x,s)

    for k in range(M,N+1):
        s = s + fk(x,k)
        lines[0].set_ydata(s)
        plt.draw()
        plt.pause(0.2)

#a single term in the Taylor series for sin(x), as a function of k and x:
def fk_sin(x,k):
    return (-1)**k*x**(2*k+1)/factorial(2*k+1)

#Taylor series term for exp(-x):
def fk_expinv(x,k):
    return (-x)**k/factorial(k)

def expinv(x):
    return np.exp(-x)

#call the function to animate the two series:
animate_series(fk_sin,0,40,0,13*np.pi,-2,2,200,np.sin)

#animate_series(fk_expinv,0,30,0,15,-0.5,1.4,200,expinv)