mech_pid_from_ped.m

function pid = mech_pid_from_ped(lat)
% calculate full PID (including ambiguous terms) from a PED

if lat.Nx ~= 3
    error('only 2 variable PID supported')
end

pid = zeros(1,5);
n = lat.nodes;

mech = abs( min( lat.PI(n('{1}{2}')), 0) );
% source redundancy
pid(1) = lat.PI(n('{1}{2}{3}')) - mech;
% mechanistic redundancy
pid(2) = mech ...
       - lat.PI(n('{13}{23}')) ...
       - lat.PI(n('{12}{13}{23}'));
   
% unique info
pid(3) = lat.PI(n('{1}{3}')) ...
       - lat.PI(n('{13}')) ...
       - lat.PI(n('{12}{13}')) ...
       - lat.PI(n('{2}{13}'));
   
pid(4) = lat.PI(n('{2}{3}')) ...
       - lat.PI(n('{23}')) ...
       - lat.PI(n('{12}{23}')) ...
       - lat.PI(n('{1}{23}'));

% synergy
pid(5) = lat.PI(n('{3}{12}')) ...
       + lat.PI(n('{12}{13}')) ...
       + lat.PI(n('{12}{23}')) ...  
       + lat.PI(n('{12}{13}{23}')) ...       
       + lat.PI(n('{1}{23}')) ...
       + lat.PI(n('{2}{13}')) ...
       - lat.PI(n('{123}'));