m = 3
n = 3

phi = zeros(m^n,1);
%combs = generate_combs(m^n,n);
%nc = size(combs,1);

LBK = -ones(size(phi));
UBK =  ones(size(phi));

LBg =   zeros(size(phi));
UBg = n+zeros(size(phi));

[Aing,Bing] = gradab(m^n);
[Ainl,Binl] = lipab(m,n);

GG = gengray(n,m);
iif = invperm(GG+1);

good = 1;

loop = 1;

while good
  %rp = randperm(nc);
  %rc = rp(1);
  %for rc=1:nc
  %com = combs(rc,:);
    
  if 0  
    com = zeros(m^n,1);
    rp = randperm(m^n);
    rp = rp(1:m);
    com(rp) = ones(m,1);
    phi = cumsum(com');
  end

  if 1  % generate legit K & derive phi from it
    global cc
    A0=pnormdim(rand(m,m,n-1),1);
    C0 = pnormdim(rand(m,1),1);
    %C0 = zeros(m,1); C0(2)=1;
    x = optmasklp(A0,C0);
    K = cc;
    [x,fval] = linprog(-K,Ainl,Binl,[],[],LBg,UBg);
    %[x,fval] = linprog(-K,[],[],[],[],LBg,UBg);
    %**** need Lipschitz!!!
    phi = round(x'-min(x));
    if round(rand)
        phi = randlip(m,n)';
    end
    if phi*K < 0,  K = -K;  end
  end
  
  
  if 0
    b = round(rand);
    b = 1;
    if b
      K = randn(m^n,1);
    else
      [x,fval] = linprog(-phi,[],[],[],[],LBK,UBK);
      K = x;
    end
    
    %if phi*K<0
    %  K = -K;
    %end    
    ip = find(K>=0);
    in = find(K<0);
    K(ip) = K(ip)/sum(K(ip));
    K(in) = K(in)/abs(sum(K(in)));
  end


  if 0
    [sK,iik] = sort(K);
    iif = invperm(iik);
    [x,fval] = linprog(-sK,Aing,Bing,[],[],LBg,UBg);
    phi = x(iif)'-min(x);
  end
  
  if 0
    [x,fval] = linprog(-K,Ainl,Binl,[],[],LBg,UBg);
    phi = round(x'-min(x));
  end
  
  
  if 0
    [K,fval] = linprog(-phi',[],[],ones(1,m^n),0,LBK,UBK);
    if phi*K < 0,  K = -K;  end
    ip = find(K>=0);
    in = find(K<0);
    K(ip) = K(ip)/sum(K(ip));
    K(in) = K(in)/abs(sum(K(in)));
  else
    [K,fval] = linprog(-phi',[],[],[],[],LBK,UBK);
  end
  
  b=round(rand);
  if b
    if round(rand)
      [K,fval] = linprog(-phi',[],[],[],[],LBK,UBK);
    else
      [K,fval] = linprog(-phi',[],[],ones(1,m^n),0,LBK,UBK);
    end
  else
    K = randn(m^n,1);
  end


  
  b=round(rand);
  if b
    ip = find(K>=0);
    in = find(K<0);
    K(ip) = K(ip)/sum(K(ip));
    K(in) = K(in)/abs(sum(K(in)));
  end
  
  if phi*K < 0,  K = -K;  end
  
  
  [MU,S] = k2mask(K,m,n);
  %S = randk2mask(K,m,n);
  phim = fillgmask(MU,m);
    
  
 
  
  good = (phi*K <= S + 1e-9);
  if ~good
    'rats'
    keyboard
  end
  
  if phi*K > sum(K.*(K>0))
      'vindication!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'
  end
  
  %fprintf('...........................loop %d: completed %d out of %d \n',loop,rc,nc);
  %end
end