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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 predict_magnification(self, Xnew, kern=None, mean=True, covariance=True, dimensions=None):
 """ Predict the magnification factor as sqrt(det(G)) for each point N in Xnew. :param bool mean: whether to include the mean of the wishart embedding. :param bool covariance: whether to include the covariance of the wishart embedding. :param array-like dimensions: which dimensions of the input space to use [defaults to self.get_most_significant_input_dimensions()[:2]] """

        G = self.predict_wishart_embedding(Xnew, kern, mean, covariance)
        if dimensions is None:
            dimensions = self.get_most_significant_input_dimensions()[:2]
        G = G[:, dimensions][:,:,dimensions]
        from ..util.linalg import jitchol
        mag = np.empty(Xnew.shape[0])
        for n in range(Xnew.shape[0]):
            try:
                mag[n] = np.sqrt(np.exp(2*np.sum(np.log(np.diag(jitchol(G[n, :, :]))))))
            except:
                mag[n] = np.sqrt(np.linalg.det(G[n, :, :]))
        return mag