ekernels.py 文件源码

def quad_eKzx1Kxz2(self, Ka, Kb, Z, Xmu, Xcov):
        # Quadrature for Cov[(Kzx1 - eKzx1)(kxz2 - eKxz2)]
        self._check_quadrature()
        warnings.warn("gpflow.ekernels.Sum: Using numerical quadrature for kernel expectation cross terms.")
        Xmu, Z = self._slice(Xmu, Z)
        Xcov = self._slice_cov(Xcov)
        N, M, HpowD = tf.shape(Xmu)[0], tf.shape(Z)[0], self.num_gauss_hermite_points ** self.input_dim
        xn, wn = mvhermgauss(self.num_gauss_hermite_points, self.input_dim)

        # transform points based on Gaussian parameters
        cholXcov = tf.cholesky(Xcov)  # NxDxD
        Xt = tf.matmul(cholXcov, tf.tile(xn[None, :, :], (N, 1, 1)), transpose_b=True)  # NxDxH**D

        X = 2.0 ** 0.5 * Xt + tf.expand_dims(Xmu, 2)  # NxDxH**D
        Xr = tf.reshape(tf.transpose(X, [2, 0, 1]), (-1, self.input_dim))  # (H**D*N)xD

        cKa, cKb = [tf.reshape(
            k.K(tf.reshape(Xr, (-1, self.input_dim)), Z, presliced=False),
            (HpowD, N, M)
        ) - k.eKxz(Z, Xmu, Xcov)[None, :, :] for k in (Ka, Kb)]  # Centred Kxz
        eKa, eKb = Ka.eKxz(Z, Xmu, Xcov), Kb.eKxz(Z, Xmu, Xcov)

        wr = wn * nppi ** (-self.input_dim * 0.5)
        cc = tf.reduce_sum(cKa[:, :, None, :] * cKb[:, :, :, None] * wr[:, None, None, None], 0)
        cm = eKa[:, None, :] * eKb[:, :, None]
        return cc + tf.transpose(cc, [0, 2, 1]) + cm + tf.transpose(cm, [0, 2, 1])