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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 factor_aug(z, DPhival, G, A):
 r"""Set up augmented system and return. Parameters z : (N+P+M+M,) ndarray Current iterate, z = (x, nu, l, s) DPhival : LinearOperator Jacobian of the variational inequality mapping G : (M, N) ndarray or sparse matrix Inequality constraints A : (P, N) ndarray or sparse matrix Equality constraints Returns ------- J : LinearOperator Augmented system """

    M, N = G.shape
    P, N = A.shape
    """Multiplier for inequality constraints"""
    l = z[N+P:N+P+M]

    """Slacks"""
    s = z[N+P+M:]

    """Sigma matrix"""
    SIG = diags(l/s, 0)
    # SIG = diags(l*s, 0)

    """Convert A"""
    if not issparse(A):
        A = csr_matrix(A)

    """Convert G"""
    if not issparse(G):
        G = csr_matrix(G)

    """Since we expect symmetric DPhival, we need to change A"""
    sign = np.zeros(N)
    sign[0:N//2] = 1.0
    sign[N//2:] = -1.0
    T = diags(sign, 0)

    A_new = A.dot(T)
    
    W = AugmentedSystem(DPhival, G, SIG, A_new)
    return W