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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def rouwenhorst(rho, sigma, N):
 """ Approximate an AR1 process by a finite markov chain using Rouwenhorst's method. :param rho: autocorrelation of the AR1 process :param sigma: conditional standard deviation of the AR1 process :param N: number of states :return [nodes, P]: equally spaced nodes and transition matrix """


    from numpy import sqrt, linspace, array,zeros

    sigma = float(sigma)

    if N == 1:
      nodes = array([0.0])
      transitions = array([[1.0]])
      return [nodes, transitions]

    p = (rho+1)/2
    q = p
    nu = sqrt( (N-1)/(1-rho**2) )*sigma

    nodes = linspace( -nu, nu, N)
    sig_a = sigma
    n = 1
    #    mat0 = array( [[1]] )
    mat0 = array([[p,1-p],[1-q,q]])
    if N == 2:
        return [nodes,mat0]
    for n in range(3,N+1):
        mat = zeros( (n,n) )
        mat_A = mat.copy()
        mat_B = mat.copy()
        mat_C = mat.copy()
        mat_D = mat.copy()
        mat_A[:-1,:-1] = mat0
        mat_B[:-1,1:] = mat0
        mat_C[1:,:-1] = mat0
        mat_D[1:,1:] = mat0

        mat0 = p*mat_A + (1-p)*mat_B + (1-q)*mat_C + q*mat_D
        mat0[1:-1,:] = mat0[1:-1,:]/2
    P = mat0
    return [nodes, P]