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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 plot2D_samples_mat(xs, xt, G, thr=1e-8, **kwargs):
 """ Plot matrix M in 2D with lines using alpha values Plot lines between source and target 2D samples with a color proportional to the value of the matrix G between samples. Parameters xs : ndarray, shape (ns,2) Source samples positions b : ndarray, shape (nt,2) Target samples positions G : ndarray, shape (na,nb) OT matrix thr : float, optional threshold above which the line is drawn **kwargs : dict paameters given to the plot functions (default color is black if nothing given) """

    if ('color' not in kwargs) and ('c' not in kwargs):
        kwargs['color'] = 'k'
    mx = G.max()
    for i in range(xs.shape[0]):
        for j in range(xt.shape[0]):
            if G[i, j] / mx > thr:
                pl.plot([xs[i, 0], xt[j, 0]], [xs[i, 1], xt[j, 1]],
                        alpha=G[i, j] / mx, **kwargs)