quadrature.py 文件源码

def mvnquad(func, means, covs, H, Din, Dout=()):
    """
    Computes N Gaussian expectation integrals of a single function 'f'
    using Gauss-Hermite quadrature.
    :param f: integrand function. Takes one input of shape ?xD.
    :param means: NxD
    :param covs: NxDxD
    :param H: Number of Gauss-Hermite evaluation points.
    :param Din: Number of input dimensions. Needs to be known at call-time.
    :param Dout: Number of output dimensions. Defaults to (). Dout is assumed
    to leave out the item index, i.e. f actually maps (?xD)->(?x*Dout).
    :return: quadratures (N,*Dout)
    """
    xn, wn = mvhermgauss(H, Din)
    N = tf.shape(means)[0]

    # transform points based on Gaussian parameters
    cholXcov = tf.cholesky(covs)  # 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(means, 2)  # NxDxH**D
    Xr = tf.reshape(tf.transpose(X, [2, 0, 1]), (-1, Din))  # (H**D*N)xD

    # perform quadrature
    fX = tf.reshape(func(Xr), (H ** Din, N,) + Dout)
    wr = np.reshape(wn * np.pi ** (-Din * 0.5),
                    (-1,) + (1,) * (1 + len(Dout)))
    return tf.reduce_sum(fX * wr, 0)