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function pot = direct_combine_pots(pot1, pot2)
% DIRECTED_COMBINE_POTS The combination operation corresponds to ordinary composition of conditional distributions.
% In some sense is similar to that of forming disjoint union of set.
% pot = direct_combine_pots(pot1, pot2)
% directed combine can be performed under the conditon that the head node set of pot1 is disjoint from the domain of
% pot2 or vice versa. if the last conditon was satisfied we exchange the pot1 and pot2 firstly then perform the operation.
% If neither of them was satified the directed combine is undifined.
if isempty( myintersect(pot1.domain, pot2.cheaddom) )
pot1 = pot1;
pot2 = pot2;
elseif isempty( myintersect(pot2.domain, pot1.cheaddom))
temppot = pot1;
pot1 = pot2;
pot2 = temppot;
else
assert(0);
return;
end
domain = myunion(pot1.domain, pot2.domain);
nodesizes = zeros(1,max(domain));
nodesizes(pot2.ctaildom) = pot2.ctailsizes;
nodesizes(pot2.cheaddom) = pot2.cheadsizes;
nodesizes(pot2.ddom) = pot2.dsizes;
nodesizes(pot1.ctaildom) = pot1.ctailsizes;
nodesizes(pot1.cheaddom) = pot1.cheadsizes;
nodesizes(pot1.ddom) = pot1.dsizes;
dom_u = mysetdiff(pot2.ctaildom, pot1.cheaddom);
if ~isempty(dom_u) & ~mysubset(dom_u, pot1.ctaildom)
pot1 = extension_pot(pot1, [], [], dom_u, nodesizes(dom_u));
end
dom_u = myunion(pot1.cheaddom, pot1.ctaildom);
if ~isempty(dom_u) & ~mysubset(dom_u, pot2.ctaildom)
pot2 = extension_pot(pot2, [], [], dom_u, nodesizes(dom_u));
end
cheaddom = myunion(pot1.cheaddom, pot2.cheaddom);
ctaildom = mysetdiff(myunion(pot1.ctaildom, pot2.ctaildom), cheaddom);
cdom = myunion(cheaddom, ctaildom);
ddom = mysetdiff(domain, cdom);
dsizes = nodesizes(ddom);
dsize = prod(nodesizes(ddom));
cheadsizes = nodesizes(cheaddom);
cheadsize = sum(nodesizes(cheaddom));
ctailsizes = nodesizes(ctaildom);
ctailsize = sum(nodesizes(ctaildom));
r1 = pot1.cheadsize;
s1 = pot1.ctailsize;
scpot = cell(1, dsize);
mask1 = [];
mask2 = [];
if ~isempty(pot1.ddom)
mask1 = find_equiv_posns(pot1.ddom, ddom);
end
if ~isempty(pot2.ddom)
mask2 = find_equiv_posns(pot2.ddom, ddom);
end
cmask1 = [];
cmask2 = [];
if ~isempty(pot1.cheaddom)
cmask1 = find_equiv_posns(pot1.cheaddom, cheaddom);
end
if ~isempty(pot2.cheaddom)
cmask2 = find_equiv_posns(pot2.cheaddom, cheaddom);
end
u1 = block(cmask1, cheadsizes);
u2 = block(cmask2, cheadsizes);
fmaskh = find_equiv_posns(pot1.cheaddom, pot2.ctaildom);
fmaskt = find_equiv_posns(pot1.ctaildom, pot2.ctaildom);
fh = block(fmaskh, pot2.ctailsizes);
ft = block(fmaskt, pot2.ctailsizes);
for i=1:dsize
sub = ind2subv(dsizes, i);
sub1 = sub(mask1);
sub2 = sub(mask2);
ind1 = subv2ind(pot1.dsizes, sub1);
ind2 = subv2ind(pot2.dsizes, sub2);
if isempty(ind1)
ind1 = 1;
end
if isempty(ind2)
ind2 = 1;
end
potc1 = struct(pot1.scgpotc{ind1});
potc2 = struct(pot2.scgpotc{ind2});
p = potc1.p;
q = potc2.p;
ro = p*q;
A = potc1.A;
B = potc1.B;
C = potc1.C;
E = potc2.A;
F = potc2.B;
G = potc2.C;
F1 = F(:, fh);
F2 = F(:, ft);
if ~isempty(F1)
K1 = F1*A;
K2 = F1*B;
FCF = F1*C*F1';
FC = F1*C;
CFT = C*F1';
else
K1 = zeros(size(E));
K2 = zeros(size(F2));
FCF = zeros(size(G));
FC = zeros(size(C, 1), size(G, 2));
CFT = zeros(size(G, 2), size(C, 1));
end
U = zeros(cheadsize,1);
W = zeros(cheadsize,cheadsize);
V = zeros(cheadsize,ctailsize);
if cheadsize > 0
U(u1) = A;
U(u2) = E + K1;
W(u1, u1) = C;
W(u2, u2) = G + FCF;
W(u1, u2) = CFT;
W(u2, u1) = FC;
else
U = zeros(cheadsize,1);
W = zeros(cheadsize,cheadsize);
end
if cheadsize > 0 | ctailsize > 0
if ~isempty(u1)
V(u1, :) = B;
else
V(u1, :) = zeros(potc1.cheadsize, ctailsize);
end
if ~isempty(u2)
V(u2, :) = F2 + K2;
else
V(u2, :) = zeros(potc2.cheadsize, ctailsize);
end
else
V = zeros(cheadsize,ctailsize);
end
scpot{i} = scgcpot(cheadsize, ctailsize, ro, U, V, W);
end
pot = scgpot(ddom, cheaddom, ctaildom, nodesizes, scpot);
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