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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 sinkhorn_lpl1_mm(a, labels_a, b, M, reg, eta=0.1, numItermax=10, numInnerItermax=200, stopInnerThr=1e-9, verbose=False, log=False, to_numpy=True):
 """ Solve the entropic regularization optimal transport problem with nonconvex group lasso regularization on GPU If the input matrix are in numpy format, they will be uploaded to the GPU first which can incur significant time overhead. The function solves the following optimization problem: .. math:: \gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega_e(\gamma) + \eta \Omega_g(\gamma) s.t. \gamma 1 = a \gamma^T 1= b \gamma\geq 0 where : - M is the (ns,nt) metric cost matrix - :math:`\Omega_e` is the entropic regularization term :math:`\Omega_e(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})` - :math:`\Omega_g` is the group lasso regulaization term :math:`\Omega_g(\gamma)=\sum_{i,c} \|\gamma_{i,\mathcal{I}_c}\|^{1/2}_1` where :math:`\mathcal{I}_c` are the index of samples from class c in the source domain. - a and b are source and target weights (sum to 1) The algorithm used for solving the problem is the generalised conditional gradient as proposed in [5]_ [7]_ Parameters a : np.ndarray (ns,) samples weights in the source domain labels_a : np.ndarray (ns,) labels of samples in the source domain b : np.ndarray (nt,) samples weights in the target domain M : np.ndarray (ns,nt) loss matrix reg : float Regularization term for entropic regularization >0 eta : float, optional Regularization term for group lasso regularization >0 numItermax : int, optional Max number of iterations numInnerItermax : int, optional Max number of iterations (inner sinkhorn solver) stopInnerThr : float, optional Stop threshold on error (inner sinkhorn solver) (>0) verbose : bool, optional Print information along iterations log : bool, optional record log if True to_numpy : boolean, optional (default True) If true convert back the GPU array result to numpy format. Returns ------- gamma : (ns x nt) ndarray Optimal transportation matrix for the given parameters log : dict log dictionary return only if log==True in parameters References .. [5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, "Optimal Transport for Domain Adaptation," in IEEE Transactions on Pattern Analysis and Machine Intelligence , vol.PP, no.99, pp.1-1 .. [7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). Generalized conditional gradient: analysis of convergence and applications. arXiv preprint arXiv:1510.06567. See Also -------- ot.lp.emd : Unregularized OT ot.bregman.sinkhorn : Entropic regularized OT ot.optim.cg : General regularized OT """


    a, labels_a, b, M = utils.to_gpu(a, labels_a, b, M)

    p = 0.5
    epsilon = 1e-3

    indices_labels = []
    labels_a2 = cp.asnumpy(labels_a)
    classes = npp.unique(labels_a2)
    for c in classes:
        idxc, = utils.to_gpu(npp.where(labels_a2 == c))
        indices_labels.append(idxc)

    W = np.zeros(M.shape)

    for cpt in range(numItermax):
        Mreg = M + eta * W
        transp = sinkhorn(a, b, Mreg, reg, numItermax=numInnerItermax,
                          stopThr=stopInnerThr, to_numpy=False)
        # the transport has been computed. Check if classes are really
        # separated
        W = np.ones(M.shape)
        for (i, c) in enumerate(classes):

            majs = np.sum(transp[indices_labels[i]], axis=0)
            majs = p * ((majs + epsilon)**(p - 1))
            W[indices_labels[i]] = majs

    if to_numpy:
        return utils.to_np(transp)
    else:
        return transp