import numpy as np
import matplotlib.pyplot as plt

def coefs(z):
  n = len(z)

  h = 1/(n+1)
  inds = np.arange(1,n+1)
  mul_table = np.outer(inds,inds)
  T = np.sin(np.pi*h * mul_table)

  return 2*h*T@z


f = lambda x : np.where(x >= 1/2, 1-x, x)

x = np.linspace(0,1,1000)
plt.plot(x, f(x), label='f(x)')

n_list = [1,5,10,100]

for n in n_list:
  h = 1/(n+1)
  sample_x = np.linspace(h,1-h,n)
  c = coefs(f(sample_x))
  g = c @ np.sin(np.pi * np.outer(sample_x/h, x))
  plt.plot(x, g, label = f'g(x) for n = {n}')

plt.xlabel('x')
plt.legend()
plt.show()