function B = collapseA
global A
global C
[n,n,T] = size(A);
B = zeros(2,2,T);
for t=1:T
  B(:,:,t) = collapse_t(A(:,:,t),0);  
end
B = B + realmin;
return

function B = collapse_t(A,pi)
[n,n] = size(A);
p1 = A(:,1);
P1 = repmat(p1,[1 n]);
dd = sum(abs(A-P1),1);
[a,b] = max(dd);
% cluster states as closer to either 1 or b
S1 = [];
S2 = [];
for i=1:n
  d1 = sum(abs(A(:,1)-A(:,i)));
  d2 = sum(abs(A(:,b)-A(:,i)));
  if d1 < d2
    S1(end+1) = i;
  else
    S2(end+1) = i;
  end
end
B = zeros(2,2);

top = sum(A(S1,:),1);
bot = sum(A(S2,:),1);
%keyboard
B(1,1) = top(1);
B(2,1) = 1-B(1,1);
B(1,2) = mean(top(b));
B(2,2) = 1-B(1,2);
return


function B = OLD3collapse_t(A,pi)
global h0
[n,n] = size(A);
p1 = A(:,1);
P1 = repmat(p1,[1 n]);
dd = sum(abs(A-P1),1);
[a,b] = max(dd);
B = zeros(2,2);
B(1,1) = A(1,1);
B(2,1) = 1-B(1,1);
p11 = B(1,1);
if p11>.5
  p10 = max(0,p11-h0);
else
  p10 = min(1,p11+h0);
end
B(1,2) = p10;
B(2,2) = 1-B(1,2);
return


function B = OLD2collapse_t(A,pi)
[n,n] = size(A);
p1 = A(:,1);
P1 = repmat(p1,[1 n]);
dd = sum(abs(A-P1),1);
[a,b] = max(dd);
% cluster states as closer to either 1 or b
S1 = [];
S2 = [];
for i=1:n
  d1 = sum(abs(A(:,1)-A(:,i)));
  d2 = sum(abs(A(:,b)-A(:,i)));
  if d1 < d2
    S1(end+1) = i;
  else
    S2(end+1) = i;
  end
end
B = zeros(2,2);

top = sum(A(S1,:),1);
bot = sum(A(S2,:),1);
%keyboard
B(1,1) = mean(top(S1));
B(2,1) = 1-B(1,1);
B(1,2) = mean(top(S2));
B(2,2) = 1-B(1,2);
return


function B = OLDcollapse_t(A,pi)
[n,n] = size(A);
p1 = A(:,1);
P1 = repmat(p1,[1 n]);
dd = sum(abs(A-P1),1);
[a,b] = max(dd);
B(1,1) = A(1,1);
%B(2,1) = 1-B(1,1);
B(2,1) = A(b,1);
B(1,2) = A(1,b);
%B(2,2) = 1-B(1,2);
B(2,2) = A(b,b);
B=pnormdim(B,1);
return