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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 posterior_samples_f(self, X, size=10, full_cov=True, **predict_kwargs):
 """ Samples the posterior TP at the points X. :param X: The points at which to take the samples. :type X: np.ndarray (Nnew x self.input_dim) :param size: the number of a posteriori samples. :type size: int. :param full_cov: whether to return the full covariance matrix, or just the diagonal. :type full_cov: bool. :returns: fsim: set of simulations :rtype: np.ndarray (D x N x samples) (if D==1 we flatten out the first dimension) """

        mu, var = self._raw_predict(X, full_cov=full_cov, **predict_kwargs)
        if self.normalizer is not None:
            mu, var = self.normalizer.inverse_mean(mu), self.normalizer.inverse_variance(var)

        def sim_one_dim(m, v):
            nu = self.nu + 2 + self.num_data
            v = np.diag(v.flatten()) if not full_cov else v
            Z = np.random.multivariate_normal(np.zeros(X.shape[0]), v, size).T
            g = np.tile(np.random.gamma(nu / 2., 2. / nu, size), (X.shape[0], 1))
            return m + Z / np.sqrt(g)

        if self.output_dim == 1:
            return sim_one_dim(mu, var)
        else:
            fsim = np.empty((self.output_dim, self.num_data, size))
            for d in range(self.output_dim):
                if full_cov and var.ndim == 3:
                    fsim[d] = sim_one_dim(mu[:, d], var[:, :, d])
                elif (not full_cov) and var.ndim == 2:
                    fsim[d] = sim_one_dim(mu[:, d], var[:, d])
                else:
                    fsim[d] = sim_one_dim(mu[:, d], var)
        return fsim