"""
This code does the same as animate_Taylor_series.py, but uses
a FuncAnimation object to create the animation."""


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

def animate_series(fk, M, N, xmin, xmax, ymin, ymax, n, exact):
    x = np.linspace(xmin,xmax,n)

    """
    When using this method, it is easiest to precompute all the
    s values and store them in a two-dimensional array.
    The function to update the frames will then simply get
    values out of this array and update the plot."""

    s = np.zeros((n,N+1-M))
    s[:,0] = fk(x,M)
    for k in range(M+1,N+1):
        s[:,k-M] = s[:,k-1-M] + fk(x,k)


    plt.plot(x,exact(x))
    plt.axis([xmin,xmax,ymin,ymax])
    lines = plt.plot(x,s[:,0])

    def next_frame(frame):
        lines[0].set_ydata(s[:,frame])
        return lines

    ani = FuncAnimation(plt.gcf(), next_frame, frames=range(M,N+1), interval=250)
    #ani.save('movie.mp4',fps=20)
    plt.show()


def fk_sin(x,k):
    return ((-1)**k) * x**(2*k+1)/factorial(2*k+1)

animate_series(fk_sin,0,40,0,13*np.pi,-2,2,200,np.sin)