# Kullback-Leibler Divergence

### Nima Razavi (view profile)

13 Jul 2008 (Updated )

Calculates the Kullback-Leibler Divergence between two probability distributions

dist=KLDiv(P,Q)
```function dist=KLDiv(P,Q)
%  dist = KLDiv(P,Q) Kullback-Leibler divergence of two discrete probability
%  distributions
%  P and Q  are automatically normalised to have the sum of one on rows
% have the length of one at each
% P =  n x nbins
% Q =  1 x nbins or n x nbins(one to one)
% dist = n x 1

if size(P,2)~=size(Q,2)
error('the number of columns in P and Q should be the same');
end

if sum(~isfinite(P(:))) + sum(~isfinite(Q(:)))
error('the inputs contain non-finite values!')
end

% normalizing the P and Q
if size(Q,1)==1
Q = Q ./sum(Q);
P = P ./repmat(sum(P,2),[1 size(P,2)]);
temp =  P.*log(P./repmat(Q,[size(P,1) 1]));
temp(isnan(temp))=0;% resolving the case when P(i)==0
dist = sum(temp,2);

elseif size(Q,1)==size(P,1)

Q = Q ./repmat(sum(Q,2),[1 size(Q,2)]);
P = P ./repmat(sum(P,2),[1 size(P,2)]);
temp =  P.*log(P./Q);
temp(isnan(temp))=0; % resolving the case when P(i)==0
dist = sum(temp,2);
end

```