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function [margpot, comppot] = complement_pot(pot, keep)
% COMPLEMENT_POT complement means decompose of a potential into its strong marginal and
% its complement corresponds exactly to the decomposition of a probability distribution
% into its marginal and conditional
% [margpot, comppot] = complement_pot(pot, keep)
% keep can only include continuous head nodes and discrete nodes
% margpot is the stable CG potential of keep nodes
% comppot is the stable CG potential of others in corresponds exactly to
% the discomposition of a probability distribution of its marginal and conditional
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Calculation of the marginal requires integration over %
% all variables in csumover. Thus cheadkeep contains all %
% continuous variables in the marginal potential %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%keyboard;
csumover = mysetdiff(pot.cheaddom, keep);
cheadkeep = mysetdiff(pot.cheaddom, csumover);
nodesizes = zeros(1, max(pot.domain));
nodesizes(pot.ddom) = pot.dsizes;
nodesizes(pot.cheaddom) = pot.cheadsizes;
nodesizes(pot.ctaildom) = pot.ctailsizes;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Description of the variables in the marginal domain %
% For the calculation of a strong marginal first integration %
% over all continuous variables in the head takes place. %
% The calculation of the marginal over the head variables %
% might result in a smaller or empty tail %
% If there are no head variables, and therefore no tail %
% variables, left marginalisation over discrete variables %
% may take place %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
margdom = mysetdiff(pot.domain,keep);
% margddom = pot.ddom;
margcheaddom = cheadkeep;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Marginalisation over discrete variables is only allowed when %
% the tail is empty %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
margddom = myintersect(pot.ddom,keep); % Discrete domain of marginal
margctaildom = myintersect(pot.ctaildom,keep); % Tail domain
assert(isempty(mysetdiff(pot.ddom,margddom)) | isempty(margctaildom))
%margctaildom = pot.ctaildom;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Even if marginalisation over continuous variables is only defined %
% for head variables, the marginalisation over haed-variables might %
% result in a smaller tail %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
margctaildom = myintersect(pot.ctaildom,keep);
margcheadsizes = nodesizes(margcheaddom);
margcheadsize = sum(margcheadsizes);
margctailsizes = nodesizes(margctaildom);
margctailsize = sum(margctailsizes);
compdom = pot.domain;
compddom = pot.ddom;
compcheaddom = csumover;
compctaildom = myunion(pot.ctaildom, cheadkeep);
compcheadsizes = nodesizes(compcheaddom);
compcheadsize = sum(compcheadsizes);
compctailsizes = nodesizes(compctaildom);
compctailsize = sum(compctailsizes);
dkeep = myintersect(pot.ddom, keep);
%if dom is only contain discrete node
if isempty(pot.cheaddom)
dsumover = mysetdiff(pot.ddom, dkeep);
if isempty(dsumover)
margpot = pot;
comppot = scgpot([], [], [], []);
return;
end
I = prod(nodesizes(dkeep));
J = prod(nodesizes(dsumover));
sum_map = find_equiv_posns(dsumover, pot.ddom);
keep_map = find_equiv_posns(dkeep, pot.ddom);
iv = zeros(1, length(pot.ddom)); % index vector
p1 = zeros(I,J);
for i=1:I
keep_iv = ind2subv(nodesizes(dkeep), i);
iv(keep_map) = keep_iv;
for j=1:J
sum_iv = ind2subv(nodesizes(dsumover), j);
iv(sum_map) = sum_iv;
k = subv2ind(nodesizes(pot.ddom), iv);
potc = struct(pot.scgpotc{k}); % violate object privacy
p1(i,j) = potc.p;
end
end
p2 = sum(p1,2);
p2 = p2 + (p2==0)*eps;
margscpot = cell(1, I);
compscpot = cell(1, I*J);
iv = zeros(1, length(pot.ddom)); % index vector
for i=1:I
margscpot{i} = scgcpot(0, 0, p2(i));
keep_iv = ind2subv(nodesizes(dkeep), i);
iv(keep_map) = keep_iv;
for j=1:J
sum_iv = ind2subv(nodesizes(dsumover), j);
iv(sum_map) = sum_iv;
k = subv2ind(nodesizes(pot.ddom), iv);
q = p1(i,j)/p2(i);
compscpot{k} = scgcpot(0, 0, q);
end
end
margpot = scgpot(dkeep, [], [], nodesizes, margscpot);
comppot = scgpot(pot.ddom, [], [], nodesizes,compscpot);
return;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% head of the potential is not empty %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
dsize = pot.dsize;
compscpot = cell(1, dsize);
fmaskh = find_equiv_posns(margcheaddom, compctaildom);
fmaskt = find_equiv_posns(margctaildom, compctaildom);
fh = block(fmaskh, compctailsizes);
ft = block(fmaskt, compctailsizes);
if ~isempty(margcheaddom)
for i=1:dsize
potc = struct(pot.scgpotc{i});
q = 1;
p = potc.p;
[A1, A2, B1, B2, C11, C12, C21, C22] = partition_matrix_vec_3(potc.A, potc.B, potc.C, margcheaddom, compcheaddom, nodesizes);
if ~isempty(margcheaddom)
margscpot{i} = scgcpot(margcheadsize, margctailsize, p, A1, B1, C11);
else
margscpot{i} = scgcpot(margcheadsize, margctailsize, p);
end
if ~isempty(compcheaddom)
if ~isempty(margcheaddom)
E = A2 - C21*pinv(C11)*A1;
tmp1 = C21*pinv(C11);
tmp2 = B2 - C21*pinv(C11)*B1;
F = zeros(compcheadsize, compctailsize);
F(:, fh) = tmp1;
F(:, ft) = tmp2;
G = C22 - C21*pinv(C11)*C12;
else
E = A2;
F = B2;
G = C22;
end
compscpot{i} = scgcpot(compcheadsize, compctailsize, q, E, F, G);
else
compscpot{i} = scgcpot(compcheadsize, 0, q);
end
if isempty(margcheaddom)
margpot = scgpot(margddom, [], [], nodesizes, margscpot);
else
margpot = scgpot(margddom, margcheaddom, margctaildom, nodesizes, margscpot);
end
end
else
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Marginalisation took place over all head variables. %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Calculate the strong marginal %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
margpot = marginalize_pot(pot,keep);
mPot = struct(margpot);
for i =1:dsize
potc = struct(pot.scgpotc{i});
% Get the probability of the original potential %
q = potc.p;
% Get the configuration defined by the index i%
config = ind2subv(pot.dsizes,i);
% Calculate the corresponding configuration in the marginal potential
if isempty(margpot.dsizes)
% keep == []
indMargPot = 1;
else
equivPos = find_equiv_posns(dkeep,pot.ddom);
indMargPot = subv2ind(margpot.dsizes,config(equivPos));
end
% Figure out the corresponding marginal potential
mPotC = struct(mPot.scgpotc{indMargPot});
p = mPotC.p;
if p == 0
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The following assignment is correct as p is only zero if q is also zero %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
compscpot{i} = scgcpot(compcheadsize,compctailsize,0,potc.A,potc.B,potc.C);
else
compscpot{i} = scgcpot(compcheadsize,compctailsize,q/p,potc.A,potc.B,potc.C);
end
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Put all components in one potential %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if isempty(compcheaddom)
comppot = scgpot(compddom, [], [], nodesizes,compscpot);
else
comppot = scgpot(compddom, compcheaddom, compctaildom, nodesizes,compscpot);
end
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