#!/usr/bin/env python
import numpy as np
import matplotlib.pyplot as plt
N = 500
M = np.diag(np.ones((N-1,)),1) + np.diag(np.ones((N-1,)),-1)
v = np.ones((N,))*-2
M += np.diag(v)
vec = np.linalg.inv(M).dot(np.ones((N,)))
x = np.linspace(1/(N+1), 1 - 1/(N+1), N)
plt.plot(x,vec,'r', linewidth=3)
plt.xlabel('x values')
plt.ylabel('vector')
plt.grid()
plt.savefig('parabola.png', bbox_inches='tight', pad_inches=0.1)
plt.show()
