function kl = kl_nats(pp, qq)
%KL_NATS divergence between two discrete distributions measured in nats
%
% kl = kl_divergence(pp, qq)
%    = pp(:)'*log(pp(:)./qq(:)), but with zeros from pp removed.
%
% See also, KL_BITS, HBITS, HNATS

% Iain Murray, September 2008

if nargin < 2
    error('Not enough input arguments.');
end
if ~isequal(size(pp), size(qq))
    error('Input probability arrays must have the same size.');
end

mask = (pp(:)~=0);
m = @(x) x(mask);
s = @(x) m(x(:));

kl = s(pp)'*reallog(s(pp)./s(qq));