ekernels.py 文件源码

def eKzxKxz(self, Z, Xmu, Xcov):
        """
        Also known as Phi_2.
        :param Z: MxD
        :param Xmu: X mean (NxD)
        :param Xcov: X covariance matrices (NxDxD)
        :return: NxMxM
        """
        # use only active dimensions
        Xcov = self._slice_cov(Xcov)
        Z, Xmu = self._slice(Z, Xmu)
        M = tf.shape(Z)[0]
        N = tf.shape(Xmu)[0]
        D = tf.shape(Xmu)[1]
        lengthscales = self.lengthscales if self.ARD else tf.zeros((D,), dtype=settings.float_type) + self.lengthscales

        Kmms = tf.sqrt(self.K(Z, presliced=True)) / self.variance ** 0.5
        scalemat = tf.expand_dims(tf.eye(D, dtype=settings.float_type), 0) + 2 * Xcov * tf.reshape(lengthscales ** -2.0, [1, 1, -1])  # NxDxD
        det = tf.matrix_determinant(scalemat)

        mat = Xcov + 0.5 * tf.expand_dims(tf.matrix_diag(lengthscales ** 2.0), 0)  # NxDxD
        cm = tf.cholesky(mat)  # NxDxD
        vec = 0.5 * (tf.reshape(tf.transpose(Z), [1, D, 1, M]) +
                     tf.reshape(tf.transpose(Z), [1, D, M, 1])) - tf.reshape(Xmu, [N, D, 1, 1])  # NxDxMxM
        svec = tf.reshape(vec, (N, D, M * M))
        ssmI_z = tf.matrix_triangular_solve(cm, svec)  # NxDx(M*M)
        smI_z = tf.reshape(ssmI_z, (N, D, M, M))  # NxDxMxM
        fs = tf.reduce_sum(tf.square(smI_z), [1])  # NxMxM

        return self.variance ** 2.0 * tf.expand_dims(Kmms, 0) * tf.exp(-0.5 * fs) * tf.reshape(det ** -0.5, [N, 1, 1])