import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

a = 0.
b = 1.

N = 30

plt.hold(True)

while (N<31):
    A = np.zeros([N,N])
    eigval = np.zeros([N])
    eigvec = np.zeros([N,N])

    h = (b-a)/(N-1)
    #print h

    for i in range(len(A)):
        for j in range(len(A[0])):
            # loading A
            if i==j:
                A[i][j] = 2
            if abs(i-j) == 1:
                A[i][j] = -1

    #print a+i*h, b
    #print A, '\n', B, '\n'

    #print np.linalg.eig(A)
    (eigval, eigvec) = np.linalg.eig(A)
    #print B

    #print eigval

    idx = eigval.argsort()
    eigval = eigval[idx]
    eigvec = eigvec[:,idx]

    #print eigval

    #or np.linalg.inv(A)
    #print X, '\n', U

    plt.plot(np.linspace(0,1,N), np.abs(eigvec[0]/h**(1./2)), label=0)
    plt.plot(np.linspace(0,1,N), np.abs(eigvec[1]/h**(1./2)), label=1)
    plt.plot(np.linspace(0,1,N), np.abs(eigvec[2]/h**(1./2)), label=2)
    plt.plot(np.linspace(0,1,N), np.abs(eigvec[3]/h**(1./2)), label=3)
    plt.legend(loc='upper right')
    N = 2*N

plt.plot(eigval)