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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 barycenter(A, M, reg, weights=None, numItermax=1000, stopThr=1e-4, verbose=False, log=False):
 """Compute the entropic regularized wasserstein barycenter of distributions A The function solves the following optimization problem: .. math:: \mathbf{a} = arg\min_\mathbf{a} \sum_i W_{reg}(\mathbf{a},\mathbf{a}_i) where : - :math:`W_{reg}(\cdot,\cdot)` is the entropic regularized Wasserstein distance (see ot.bregman.sinkhorn) - :math:`\mathbf{a}_i` are training distributions in the columns of matrix :math:`\mathbf{A}` - reg and :math:`\mathbf{M}` are respectively the regularization term and the cost matrix for OT The algorithm used for solving the problem is the Sinkhorn-Knopp matrix scaling algorithm as proposed in [3]_ Parameters A : np.ndarray (d,n) n training distributions a_i of size d M : np.ndarray (d,d) loss matrix for OT reg : float Regularization term >0 weights : np.ndarray (n,) Weights of each histogram a_i on the simplex (barycentric coodinates) numItermax : int, optional Max number of iterations stopThr : float, optional Stop threshol on error (>0) verbose : bool, optional Print information along iterations log : bool, optional record log if True Returns ------- a : (d,) ndarray Wasserstein barycenter log : dict log dictionary return only if log==True in parameters References .. [3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. (2015). Iterative Bregman projections for regularized transportation problems. SIAM Journal on Scientific Computing, 37(2), A1111-A1138. """


    if weights is None:
        weights = np.ones(A.shape[1]) / A.shape[1]
    else:
        assert(len(weights) == A.shape[1])

    if log:
        log = {'err': []}

    # M = M/np.median(M) # suggested by G. Peyre
    K = np.exp(-M / reg)

    cpt = 0
    err = 1

    UKv = np.dot(K, np.divide(A.T, np.sum(K, axis=0)).T)
    u = (geometricMean(UKv) / UKv.T).T

    while (err > stopThr and cpt < numItermax):
        cpt = cpt + 1
        UKv = u * np.dot(K, np.divide(A, np.dot(K, u)))
        u = (u.T * geometricBar(weights, UKv)).T / UKv

        if cpt % 10 == 1:
            err = np.sum(np.std(UKv, axis=1))

            # log and verbose print
            if log:
                log['err'].append(err)

            if verbose:
                if cpt % 200 == 0:
                    print(
                        '{:5s}|{:12s}'.format('It.', 'Err') + '\n' + '-' * 19)
                print('{:5d}|{:8e}|'.format(cpt, err))

    if log:
        log['niter'] = cpt
        return geometricBar(weights, UKv), log
    else:
        return geometricBar(weights, UKv)