relent.3

speech signal process tools

.\" Copyright (c) 1988 Entropic Speech, Inc. All rights reserved.
.\"@(#)relent.3	1.1	31 Aug 1989	ESI
.TH REL_ENT 3\-ESPSsp 31 Aug 1989
.ds ]W "\fI\s+4\ze\h'0.05'e\s-4\v'-0.4m'\fP\(*p\v'0.4m'\ Entropic Speech, Inc.
.if t .ds S \(*S
.if n .ds S \fRSUM\fP
.if t .ds f \fI
.if n .ds f \fR
.SH NAME
rel_ent \- compute relative entropy of two probability distributions
.SH SYNOPSIS
.ft B
.nf
double
rel_ent(q, p, n)
    double  *q, *p;
    int	    n;
.SH DESCRIPTION
.PP
Given two probability distributions
.I p
and
.I q,
this function returns the
.I relative entropy
.IP
\*f\*S\d\s-3j\s+3\u q\d\s-3j\s+3\u \fRlog\fP q\d\s-3j\s+3\u/p\d\s-3j\s+3\u\fR
.LP
of
.I q
with respect to
.I p.
Terms of the form 0 log 0 or 0 log 0/0 in this formula are taken to be 0 by
convention.
.PP
The arguments
.I q
and
.I p
should each be an array of
.I n
nonnegative numbers that sum to 1.
The argument
.I n
gives the array lengths.
.SH DIAGNOSTICS
The function does no error checking.
If
.I p
or 
.I q
is not a probability distribution \- that is,
if it has a negative element or if the sum of its elements is not 1,
.I rel_ent
simply applies the formula.
A floating exception will occur if
.IR log (3M)
is given a negative argument,
or if there is an index
.I j
for which
\*fp\d\s-3j\s+3\u\fR
is 0 but
\*fq\d\s-3j\s+3\u\fR
is not.
.SH SEE ALSO
min_rel_ent(3-ESPSsp)
.AUTHOR
Rodney W. Johnson, ESI