"""
Exercise 7.12 from "A primer on..."
Make a class for summing a series. Main points:
1. Defining a function as an attribute to a class
2. Test functions for classes
"""



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


#a) Write the class Sum:
class Sum:
    def __init__(self, term, M, N):
        self.term = term
        self.M = M
        self.N = N
  
    def __call__(self, x):
        s = 0
        for k in range(self.M, self.N+1):
            s += self.term(k, x)
        return s


#b) A test function for the Sum class
def test_Sum():
    def term(k, x):
        return (-x)**k
    
    tol = 1e-10
    S = Sum(term, M=0, N=3)
    x = 0.5
    expected = 0.625
    computed = S(x)
    assert abs(expected-computed) < tol



if __name__ == "__main__":
    test_Sum()

    #c) use class Sum to compute the Taylor series of sin(x)

    #The term in the taylor series:
    def sin_term(k,x):
        return (-1)**k * x**(2*k + 1)/factorial(2*k +1) 

    x = np.linspace(0, 4* np.pi)

    #Two instances of Sum, same term function but different number of terms:
    sin_approx1 = Sum(sin_term,0,2)
    sin_approx2 = Sum(sin_term,0,6)
    
    #plot both, as well as the exact solution:
    plt.axis([0, 4*np.pi, -1.1, 1.1])
    plt.plot(x, sin_approx1(x))
    plt.plot(x, sin_approx2(x))
    plt.plot(x, np.sin(x))
    plt.show()

"""
Terminal> python Sum.py 
(output is a plot)
"""