function mcd_collapsesc
N = 10;
for t=1:100000
  A = pnormdim(rand(N),1);
  [h0,i0,j0] = SC(A);
  merge = setdiff(1:N,i0);
  %i = round(randinseg(1,N-1));
  %tha = pnormdim(rand(i,1),1);
  tha = pnormdim(rand(N-1,1),1);
  %A1 = collapse(A,1:i,tha);
  A1 = collapse(A,merge,tha);
  g = (SC(A1)<=SC(A)+1e-10);
  fprintf('T=%d \n',t);
  if ~g
    'problem!!!!'
    keyboard
  end
end
return


function [h,i0,j0] = SC(AA)
% the "stricture coefficient" of AA
[n,n,T] = size(AA);
h = 0;
for t=1:T
  A = AA(:,:,t);
  for i=1:n
    for j=i+1:n
      x = A(:,i);
      y = A(:,j);
      hxy = max(abs(x-y));
      if (hxy>h)
        i0=i;j0=j;h=hxy;
      end
    end
  end
end
return