def generate_dataset(d, k, mode, nframes):
    """Generate a dataset useful for EM anf GMM testing.
    
    returns:
        data : ndarray
            data from the true model.
        tgm : GM
            the true model (randomly generated)
        gm0 : GM
            the initial model
        gm : GM
            the trained model
    """
    # Generate a model
    w, mu, va = GM.gen_param(d, k, mode, spread=2.0)
    tgm = GM.fromvalues(w, mu, va)

    # Generate data from the model
    data = tgm.sample(nframes)

    # Run EM on the model, by running the initialization separetely.
    gmm = GMM(GM(d, k, mode), 'test')
    gmm.init_random(data)
    gm0 = copy.copy(gmm.gm)

    gmm = GMM(copy.copy(gmm.gm), 'test')
    em = EM()
    em.train(data, gmm)

    return data, tgm, gm0, gmm.gm