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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 sinkhorn2(a, b, M, reg, method='sinkhorn', numItermax=1000, stopThr=1e-9, verbose=False, log=False, **kwargs):
 u""" Solve the entropic regularization optimal transport problem and return the loss The function solves the following optimization problem: .. math:: W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma) s.t. \gamma 1 = a \gamma^T 1= b \gamma\geq 0 where : - M is the (ns,nt) metric cost matrix - :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})` - a and b are source and target weights (sum to 1) The algorithm used for solving the problem is the Sinkhorn-Knopp matrix scaling algorithm as proposed in [2]_ Parameters a : np.ndarray (ns,) samples weights in the source domain b : np.ndarray (nt,) or np.ndarray (nt,nbb) samples in the target domain, compute sinkhorn with multiple targets and fixed M if b is a matrix (return OT loss + dual variables in log) M : np.ndarray (ns,nt) loss matrix reg : float Regularization term >0 method : str method used for the solver either 'sinkhorn', 'sinkhorn_stabilized' or 'sinkhorn_epsilon_scaling', see those function for specific parameters 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 ------- W : (nt) ndarray or float Optimal transportation matrix for the given parameters log : dict log dictionary return only if log==True in parameters Examples -------- array([ 0.26894142]) References .. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013 .. [9] Schmitzer, B. (2016). Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems. arXiv preprint arXiv:1610.06519. .. [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816. [21] Altschuler J., Weed J., Rigollet P. : Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration, Advances in Neural Information Processing Systems (NIPS) 31, 2017 See Also -------- ot.lp.emd : Unregularized OT ot.optim.cg : General regularized OT ot.bregman.sinkhorn_knopp : Classic Sinkhorn [2] ot.bregman.greenkhorn : Greenkhorn [21] ot.bregman.sinkhorn_stabilized: Stabilized sinkhorn [9][10] ot.bregman.sinkhorn_epsilon_scaling: Sinkhorn with epslilon scaling [9][10] """


    if method.lower() == 'sinkhorn':
        def sink():
            return sinkhorn_knopp(a, b, M, reg, numItermax=numItermax,
                                  stopThr=stopThr, verbose=verbose, log=log, **kwargs)
    elif method.lower() == 'sinkhorn_stabilized':
        def sink():
            return sinkhorn_stabilized(a, b, M, reg, numItermax=numItermax,
                                       stopThr=stopThr, verbose=verbose, log=log, **kwargs)
    elif method.lower() == 'sinkhorn_epsilon_scaling':
        def sink():
            return sinkhorn_epsilon_scaling(
                a, b, M, reg, numItermax=numItermax,
                stopThr=stopThr, verbose=verbose, log=log, **kwargs)
    else:
        print('Warning : unknown method using classic Sinkhorn Knopp')

        def sink():
            return sinkhorn_knopp(a, b, M, reg, **kwargs)

    b = np.asarray(b, dtype=np.float64)
    if len(b.shape) < 2:
        b = b.reshape((-1, 1))

    return sink()