Gaussian(3) User Contributed Perl Documentation Gaussian(3)NAMEPDL::Gaussian-- Gaussian distributions.
SYNOPSIS
$a = new PDL::Gaussian([3],[5]);
$a->set_covariance(...)
DESCRIPTION
This package provides a set of standard routines to handle sets
gaussian distributions.
A new set of gaussians is initialized by
$a = new PDL::Gaussian(xdims,gdims);
Where xdims is a reference to an array containing the dimensions in the
space the gaussian is in and gdimslist is a reference to an array
containing the dimensionality of the gaussian space. For example, after
$a = new PDL::Gaussian([2],[3,4]);
$b = new PDL::Gaussian([],[]);
The variable $a contains set of 12 (="3*4") 2-Dimensional gaussians and
$b is the simplest form: one 1D gaussian. Currently, xdims may
containe either zero or one dimensions due to limitations of PDL::PP.
To set the distribution parameters, you can use the routines
$a->set_covariance($cv); # covariance matrices
$a->set_icovariance($icv); # inverse covariance matrices
$a->set_mu($mu); # centers
The dimensions of $cv and $icv must be "(@xdims,@xdims,@gdims)" and the
dimensions of $mu must be "(@xdims,@gdims)".
Alternatively you can use the routines
$cv = $a->get_covariance(); # cv = reference to covariance matrix
... # Fuzz around with cv
$a->upd_covariance(); # update
and similarly for "icovariance" (inverse covariance). The last sub call
is important to update the other parts of the object.
To get a string representation of the gaussians (most useful for
debugging) use the routine
$string = $a->asstr();
It is possible to calculate the probability or logarithm of probability
of each of the distributions at some points.
$a->calc_value($x,$p);
$a->calc_lnvalue($x,$p);
Here, $x must have dimensions "(ndims,...)" and $p must have dimensions
"(gdimslist, ...)" where the elipsis represents the same dimensions in
both variables. It is usually advisable to work with the logarithms of
probabilities to avoid numerical problems.
It is possible to generate the parameters for the gaussians from data.
The function
$a->fromweighteddata($data,$wt,$small_covariance);
where $data is of dimensions "(ndims,npoints)" and $wt is of dimensions
"(npoints,gdimslist)", analyzes the data statistically and gives a
corresponding gaussian distribution. The parameter $small_covariance is
the smallest allowed covariance in any direction: if one or more of the
eigenvalues of the covariance matrix are smaller than this, they are
automatically set to $small_covariance to avoid singularities.
BUGS
Stupid interface.
Limitation to 1 x-dimensions is questionable (although it's hard to
imagine a case when more is needed). Note that this does not mean that
you can only have 1-dimensional gaussians. It just means that if you
want to have a 6-dimensional gaussian, your xs must be structured like
(6) and not (2,3). So clumping the dimensions should make things
workable.
Also, it limits you so that even if you have one variable, you need to
have the '1' dimensions explicitly everywhere.
Singular distributions are not handled. This should use SVD and be able
to handle both infinitely narrow and wide dimensions, preferably so
that infinitely narrow dimensions can be queried like "$a-"relations()>
or something like that.
The routines should, if the user requests for it, check all the
dimensions of the given arguments for reasonability.
AUTHOR
Copyright (C) 1996 Tuomas J. Lukka (lukka@fas.harvard.edu) All rights
reserved. There is no warranty. You are allowed to redistribute this
software / documentation under certain conditions. For details, see the
file COPYING in the PDL distribution. If this file is separated from
the PDL distribution, the copyright notice should be included in the
file.
perl v5.10.0 2000-04-29 Gaussian(3)
