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Tip revision: 6fd1a26809a4c754b73c1a645b48d7cda35b2cd6 authored by John Bradshaw on 24 October 2017, 10:29:09 UTC
Merge remote-tracking branch 'origin/GPflow-1.0-RC' into john-bradshaw/linear-features-for-kernels-gpflow1.0
Tip revision: 6fd1a26
from __future__ import print_function, absolute_import
import itertools

import tensorflow as tf
import numpy as np

from gpflow import settings

def hermgauss(n):
    x, w = np.polynomial.hermite.hermgauss(n)
    x, w = x.astype(settings.np_float), w.astype(settings.np_float)
    return x, w

def mvhermgauss(H, D):
    Return the evaluation locations 'xn', and weights 'wn' for a multivariate
    Gauss-Hermite quadrature.

    The outputs can be used to approximate the following type of integral:
    int exp(-x)*f(x) dx ~ sum_i w[i,:]*f(x[i,:])

    :param H: Number of Gauss-Hermite evaluation points.
    :param D: Number of input dimensions. Needs to be known at call-time.
    :return: eval_locations 'x' (H**DxD), weights 'w' (H**D)
    gh_x, gh_w = hermgauss(H)
    x = np.array(list(itertools.product(*(gh_x,) * D)))  # H**DxD
    w =*(gh_w,) * D))), 1)  # H**D
    return x, w

def mvnquad(f, 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
    chol_cov = tf.cholesky(covs)  # NxDxD
    Xt = tf.matmul(chol_cov, 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(f(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)
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