Home > wafo > markov > klcmat.m

# klcmat

## PURPOSE

Kullback-Leibler distance of cycle matrix.

## SYNOPSIS

kl = klcmat(Fobs,F)

## DESCRIPTION

```  KLCMAT  Kullback-Leibler distance of cycle matrix.

comuptes the Kullback-Leibler distance between the observed
cycle matrix Fobs and the expected cycle matrix F.

The Kullback-Leibler distance is defined as
K.L. = sum( f_ij * log(N*f_ij/N_ij) )

kl = klcmat(Fobs,F)

Fobs  = Observation of cycle matrix
F     = Expected cycle matrix```

## CROSS-REFERENCE INFORMATION

This function calls:
This function is called by:
 f_smctp Auxiliary function used by ESTSMCTP

## SOURCE CODE

```01 function kl = klcmat(Fobs,F)
02 % KLCMAT  Kullback-Leibler distance of cycle matrix.
03 %
04 % comuptes the Kullback-Leibler distance between the observed
05 %   cycle matrix Fobs and the expected cycle matrix F.
06 %
07 % The Kullback-Leibler distance is defined as
08 %   K.L. = sum( f_ij * log(N*f_ij/N_ij) )
09 %
10 % kl = klcmat(Fobs,F)
11 %
12 % Fobs  = Observation of cycle matrix
13 % F     = Expected cycle matrix
14
15 F = flipud(F)';       % Convert to PJ-def
16 Fobs = flipud(Fobs)'; % Convert to PJ-def
17
18 n = length(F);
19 N = sum(sum(Fobs));
20
21 F = F / sum(sum(F));
22
23 FF = F(:);
24 FFobs = Fobs(:);
25 FI = find( (Fobs>0) & (F>0) );
26
27 % Compute Kullback-Leibler distance
28
29 kl = sum( FF(FI) .* log(N*F(FI)./Fobs(FI)) );
30
31```

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

Comments or corrections to the WAFO group

Generated on Thu 06-Oct-2005 02:21:16 for WAFO by m2html © 2003