function mequiv3
global m
n = 3;
m = 3;

global A C XX PPM
A = pnormdim(rand(m,m),1)
C = pnormdim(rand(m,1),1)

dims = repmat([2],[1 n]);
XX = list_all_ind(dims)-1;
nx = size(XX,1);
PPM = zeros(nx,1);
PROGstart(nx,'computing collapsed probs...');
for j=1:nx
    X = XX(j,:);
    Pm = PM(X,A,C);
    PPM(j) = Pm;
    PROGupdate(j);
end
PROGend;
return


function x=hinv(y)
global m
if y==0
    x = 0;
else
    x = 1:m-1;
end
return

function XX=HINV(Y)
x={};
for i=1:length(Y)
    x{i} = hinv(Y(i));
end
XX = list_all_ind_g(x);
return

function p = PM(Y,A,C)
XX = HINV(Y);
p = 0;
[N,n] = size(XX);
for j=1:N
    X = XX(j,:);
    p = p + P(X,A,C);
end
return

function p = P(x,A,C)
x=x+1;
if isempty(x)
  p = 1;
else
  p = C(x(1));
end
for j=2:length(x)
  p = p * A(x(j),x(j-1)); % markov case
end
return



function [A,C] = collapse(A,C,th)
%th = rand;  % mixing coeff
[n,n] = size(A);
% collapse states n-1 and n
A(n-1,:) = A(n-1,:) + A(n,:);
A(:,n-1) = th*A(:,n-1) + (1-th)*A(:,n);
A = A(1:n-1,1:n-1);
C(n-1) = C(n-1) + C(n);
C=C(1:n-1);
return


function h = strict(A)
[n,n] = size(A);
d = 0;
for i=1:n
  for j=i+1:n
    x = A(:,i);
    y = A(:,j);
    d = max(d,.5*sum(abs(x-y)));
    % this stricture has the VERY NICE property
    % of not increasing after state collapse
    %d = max(d,max(abs(x-y)));
    % this is the OLD, BAD stricture def.
    % that's the problem that Sinai was so quick to point out
    % in my terminology, this stricture might increase after collapse
  end
end
h=d;
return

function b=compallpairs(A,B)
global n
[n,n] = size(A);
b = 1;
for i=1:n
  for j=i+1:n
      for k=1:n
          a1 = A(k,i);
          a2 = A(k,j);
          da = abs(a1-a2);
          
          b1 = B(ci(k),ci(i));
          b2 = B(ci(k),ci(j));
          db = abs(b1-b2);

          b = b & (db <= da);
      end
  end
end
return

function i = ci(i)
global n
if i==n
    i=n-1;
end
return