function [logp, yhat, res] = tapas_logrt_linear_whatworld(r, infStates, ptrans)
% Calculates the log-probability of log-reaction times y (in units of log-ms) according to the
% linear log-RT model developed with Louise Marshall and Sven Bestmann
%
% --------------------------------------------------------------------------------------------------
% Copyright (C) 2014 Christoph Mathys, 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/>.
% Transform zetas to their native space
be0 = ptrans(1);
be1 = ptrans(2);
be2 = ptrans(3);
be3 = ptrans(4);
ze = exp(ptrans(5));
% Initialize returned log-probabilities, predictions,
% and residuals 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 responses and inputs
y = r.y(:,1);
y(r.irr) = [];
u = r.u(:,1);
u(r.irr) = [];
% Extract trajectories of interest from infStates
mu1hat = squeeze(infStates(:,1,:,:,1));
mu1 = squeeze(infStates(:,1,:,:,3));
mu2 = squeeze(infStates(:,2,:,:,3));
sa2 = squeeze(infStates(:,2,:,:,4));
mu3 = squeeze(infStates(:,3,1,1,3));
% Surprise
% ~~~~~~~~
% mu1 contains the actually occurring transition -> multiply with
% mu1hat to get probability of that transition (other elements are
% zero)
otp = mu1.*mu1hat; % observed transition probabilities (3-dim)
otps3 = nansum(otp,3); % sum over 3rd dim
otps23 = nansum(otps3,2); % sum over 2nd dim
surp = -log(otps23);
surp(r.irr) = [];
% Expected uncertainty
% ~~~~~~~~~~~~~~~~~~~~
euo = mu1.*sa2; % expected uncertainty of observed transition (3-dim)
euos3 = nansum(euo,3); % sum over 3rd dim
euos23 = nansum(euos3,2); % sum over 2nd dim
to = mu1.*mu2; % tendency of observed transition (3-dim)
tos3 = nansum(to,3); % sum over 3rd dim
tos23 = nansum(tos3,2); % sum over 2nd dim
eu = tapas_sgm(tos23,1).*(1-tapas_sgm(tos23,1)).*euos23; % transform down to 1st level
eu(r.irr) = [];
% Unexpected uncertainty
% ~~~~~~~~~~~~~~~~~~~~~~
ueu = tapas_sgm(tos23,1).*(1-tapas_sgm(tos23,1)).*exp(mu3); % transform down to 1st level
ueu(r.irr) = [];
% Calculate predicted log-reaction time
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
logrt = be0 +be1.*surp +be2.*eu +be3.*ueu;
% 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).*ze) -(y-logrt).^2./(2.*ze);
yhat(reg) = logrt;
res(reg) = y-logrt;
return;