function [logp, yhat, res] = tapas_bayes_optimal(r, infStates, ptrans)
% Calculates the log-probabilities of the inputs given the current prediction
% and its precision
%
% --------------------------------------------------------------------------------------------------
% Copyright (C) 2012-2013 Christoph Mathys, TNU, UZH & ETHZ
%
% This file is part of the HGF toolbox, which is released under the terms of the GNU General Public
% Licence (GPL), version 3. You can redistribute it and/or modify it under the terms of the GPL
% (either version 3 or, at your option, any later version). For further details, see the file
% COPYING or <http://www.gnu.org/licenses/>.

% Initialize returned log-probabilities as NaNs so that NaN is
% returned for all irregualar trials
n = size(infStates,1);
logp = NaN(n,1);
yhat = NaN(n,1);
res  = NaN(n,1);

% Weed irregular trials out from inputs and predictions
%
% Inputs
u = r.u(:,1);
u(r.irr) = [];

% Predictions
mu1hat = infStates(:,1,1);
mu1hat(r.irr) = [];

% Variance (i.e., inverse precision) of predictions
sa1hat = infStates(:,1,2);
sa1hat(r.irr) = [];

% Calculate log-probabilities for non-irregular trials
% Note: 8*atan(1) == 2*pi (this is used to guard against
% errors resulting from having used pi as a variable).
reg = ~ismember(1:n,r.irr);
logp(reg) = -1/2.*log(8*atan(1).*sa1hat) -(u-mu1hat).^2./(2.*sa1hat);
yhat(reg) = mu1hat;
res(reg) = u-mu1hat;

return;