# -*- coding: utf-8 -*-

from math import *
from numpy import *
import matplotlib.pyplot as plt

def trapezoidal(f, a, b, n):
    h = float(b - a)/n
    result = 0.5*(f(a) + f(b))
    for i in range(1, n):
        result += f(a + i*h)
    result *= h
    return result

def integrate_coeffs(f, N, M):
    result = zeros(N)
    for n in range(1, N+1):
        result[n-1] = trapezoidal(lambda x: 1.0/pi*f(x)*sin(n*x), -pi, pi, M)
    return result

def plot_approx(f, N, M):
    x = linspace(-pi, pi, num=1000)
    y = array([f(i) for i in x])
    bn = integrate_coeffs(f, N, M)
    y_approx = array([sum(array([bn[j-1]*sin(j*i) for j in range(1, N+1)])) for i in x])
    plt.plot(x, y, color='r', label="initial function")
    plt.plot(x, y_approx, color='g', label="approximation")
    plt.legend(loc="best")
    plt.show()



f1 = lambda x: 1/pi*x
integrate_coeffs(f, 3, 100)
plot_approx(f, 24, 1000)
f2 = lambda x: exp(-(x-pi))
plot_approx(f2, 100, 1000)