# Author: Alex Gezerlis

# Numerical Methods in Physics with Python (CUP, 2020)

from qrmet import qrmet

import numpy as np

def matsetup(q,n):

h = 2*np.pi/n

xs = np.arange(n)*h

A = np.zeros((n,n))

np.fill_diagonal(A, -2 - 2*h**2*q*np.cos(2*xs))

np.fill_diagonal(A[1:,:], 1)

np.fill_diagonal(A[:,1:], 1)

A[0,-1] = 1

A[-1,0] = 1

return A

def mathieu(q,n):

A = matsetup(q, n)

qreigvals = qrmet(A,200)

h = 2*np.pi/n

qreigvals = np.sort(-qreigvals/h**2)

return qreigvals

if __name__ == '__main__':

q, n = 1.5, 200

qreigvals = mathieu(q, n)

print(qreigvals[:6])