    NET-DVAR:  Find the variance of a difference in function values.

    Usage:

        net-dvar log-file range / centre n-pairs [ low ] high [ "hidden" ]

    This program evaluates the variance of the difference in the (first)
    outputs of networks at pairs of input points (differing in the first
    input), over the set of networks in the given range, stored in the
    given log file.  The variance of the difference is evaluated for
    n-pairs+1 pairs of points, with the points in each pair being
    equidistant from `centre'.  If only 'high' is present, the separations
    of the pairs form an arithmetic progression from zero to 'high'; if
    'low' is present, they form a geometric progression from 'low' to
    'high'. The separations of the points and the corresponding values of
    the variance are written one per line to standard output.

    For networks drawn from a prior distribution, the variance is expected
    to increase as some power, p, of the distance between points.  For a
    prior over smooth functions, we should have p=2.  For a Brownian
    prior, we should have p=1.  Values of p between 1 and 2 correspond to
    "fractional Brownian" priors.

    If a final argument of "hidden" is given, the program evaluates the
    variance of the values of hidden units in the final layer, using all
    hidden units in each network.  This is similar to the result using the
    output, but gives better statistics.

                Copyright (c) 1995-2004 by Radford M. Neal