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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 binormalize(A, tol=1e-5, maxiter=10):
 """Binormalize matrix A. Attempt to create unit l_1 norm rows. Parameters A : csr_matrix sparse matrix (n x n) tol : float tolerance x : array guess at the diagonal maxiter : int maximum number of iterations to try Returns ------- C : csr_matrix diagonally scaled A, C=DAD Notes ----- - Goal: Scale A so that l_1 norm of the rows are equal to 1: - B = DAD - want row sum of B = 1 - easily done with tol=0 if B=DA, but this is not symmetric - algorithm is O(N log (1.0/tol)) Examples -------- References .. [1] Livne, Golub, "Scaling by Binormalization" Tech Report SCCM-03-12, SCCM, Stanford, 2003 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679 """

    if not isspmatrix(A):
        raise TypeError('expecting sparse matrix A')

    if A.dtype == complex:
        raise NotImplementedError('complex A not implemented')

    n = A.shape[0]
    it = 0
    x = np.ones((n, 1)).ravel()

    # 1.
    B = A.multiply(A).tocsc()  # power(A,2) inconsistent in numpy, scipy.sparse
    d = B.diagonal().ravel()

    # 2.
    beta = B * x
    betabar = (1.0/n) * np.dot(x, beta)
    stdev = rowsum_stdev(x, beta)

    # 3
    while stdev > tol and it < maxiter:
        for i in range(0, n):
            # solve equation x_i, keeping x_j's fixed
            # see equation (12)
            c2 = (n-1)*d[i]
            c1 = (n-2)*(beta[i] - d[i]*x[i])
            c0 = -d[i]*x[i]*x[i] + 2*beta[i]*x[i] - n*betabar
            if (-c0 < 1e-14):
                print('warning: A nearly un-binormalizable...')
                return A
            else:
                # see equation (12)
                xnew = (2*c0)/(-c1 - np.sqrt(c1*c1 - 4*c0*c2))
            dx = xnew - x[i]

            # here we assume input matrix is symmetric since we grab a row of B
            # instead of a column
            ii = B.indptr[i]
            iii = B.indptr[i+1]
            dot_Bcol = np.dot(x[B.indices[ii:iii]], B.data[ii:iii])

            betabar = betabar + (1.0/n)*dx*(dot_Bcol + beta[i] + d[i]*dx)
            beta[B.indices[ii:iii]] += dx*B.data[ii:iii]

            x[i] = xnew

        stdev = rowsum_stdev(x, beta)
        it += 1

    # rescale for unit 2-norm
    d = np.sqrt(x)
    D = spdiags(d.ravel(), [0], n, n)
    C = D * A * D
    C = C.tocsr()
    beta = C.multiply(C).sum(axis=1)
    scale = np.sqrt((1.0/n) * np.sum(beta))
    return (1/scale)*C