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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 relaxation_vectors(A, R, k, alpha):
 """Generate test vectors by relaxing on Ax=0 for some random vectors x. Parameters A : csr_matrix Sparse NxN matrix alpha : scalar Weight for Jacobi R : integer Number of random vectors k : integer Number of relaxation passes Returns ------- x : array Dense array N x k array of relaxation vectors """

    # random n x R block in column ordering
    n = A.shape[0]
    x = np.random.rand(n * R) - 0.5
    x = np.reshape(x, (n, R), order='F')
    # for i in range(R):
    #     x[:,i] = x[:,i] - np.mean(x[:,i])
    b = np.zeros((n, 1))

    for r in range(0, R):
        jacobi(A, x[:, r], b, iterations=k, omega=alpha)
        # x[:,r] = x[:,r]/norm(x[:,r])

    return x