function checkpsi(m,n)

n1 = n-1;
phi = zeros(m^n,1);
phi1 = zeros(m^n1,1);

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

LBg =   zeros(size(phi));
%UBg = n+zeros(size(phi));
%LBg = -n*ones(size(phi));
UBg =  n*ones(size(phi));

LBg1 =    zeros(size(phi1));
UBg1 = n1+zeros(size(phi1));


[Aing,Bing] = gradab(m^n);
[Ainl,Binl] = lipab(m,n);
[Ain1,Bin1] = lipab(m,n1);

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

good = 1;

%load PSIV

while good

  K = genK(m,n);
  
  [x,fval] = linprog(-K,Ainl,Binl,[],[],LBg,UBg);
  %if phi*K < 0,  K = -K;  end
  fs = abs(fval);
  
  S = Psi(K,m,n);
  
  %good = (phi*K <= S + 1e-9);
  good = (fs <= S + 1e-9);
  if ~good
    'rats'
    save PSIFAIL K phi
    keyboard
  end

  if 1
    if flip
      phi = round(x');
    else
      phi = randlip(m,n);
    end

    %[x,fval] = linprog(-K,[],[],[],[],LBg,UBg);
    %phi = x';

    if phi*K < 0,  K = -K;  end
    ksig = (K>0)';
    phi1 = max(phi-ksig,0);
    %phi1 = max(phi-1,0);
    % CAN!! subtract 1 from phi uniformly!!!
    % BUT, it's too crude a bound
    %good = (phi*K <= Psit(K,m,n,1) + phi1*K + 1e-9);
    %good = (phi*K <= Psit(K,m,n,n) + 1e-9);
    [x,fval] = linprog(-K,Ainl,Binl,[],[],0*K,n1+0*K);
    phi1 = x';
    
    K1 = getK1(K,m,n);
    [x,fval] = linprog(-K1,Ain1,Bin1,[],[],0*K1,n1+0*K1);
    phi11 = x';
    good = (phi1*K <= phi11*K1 + 1e-7);

    if ~good
    %if 1
      'blah'
      keyboard
    end
    if 0
      %iim = find(phi1==n);
      %phi1(iim) = phi1(iim)-1;
      %[phi1m,phi1M] = collapsephi(K,phi1,m,n);
      %phi11 = collapsephi(K,phi1,m,n);
      %phi11 = ceil(phi11);
      %islip = (max(abs(Ain1*phi11'))<=1);
      %islipm = (max(abs(Ain1*phi1m'))<=1);
      %islipM = (max(abs(Ain1*phi1M'))<=1);
      %if ~(islipm & islipM)
      %if ~islip
      %  'oh well, no lip'
      %  keyboard
      %  save NOTLIP K phi
      %end
    end
  end

  if 0
    %ksig = (K>0)';
    %phi1 = max(phi-ksig,0);
    K1 = getK1(K,m,n);
    %[x,fval] = linprog(-K1,Ain1,Bin1,[],[],LBg1,UBg1);
    %phi11 = x';
    %phi11 = round(phi11-min(phi11));
    %s2 = max(phi1m*K1,phi1M*K1);
    s2 = phi11*K1;
    good = (phi1*K <= s2+1e-9);
    %good = (phi1*K <= phi11*K1);
    %good = (phi*K <= Psit(K,m,n,1)+phi11*getK1(K,m,n) + 1e-9);
    if ~good
      'wtf'
      save WTF K phi
      keyboard
    end
  end


  if 0
    St = PsiT(K,m,n,n-1);
    if phi*K > St
      'vindication!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'
      nv = size(VIND,1)+1;
      VIND{nv,1} = K;
      VIND{nv,2} = phi;
      save PSIV VIND
    end
  end
  
  %fprintf('...........................loop %d: completed %d out of %d \n',loop,rc,nc);
  %end
end
  


return


function S = Psi(K,m,n)
S = 0;
for t=1:n
  S = S + sum(K.*(K>0));  
  K = getK1(K,m,n-t+1);
end
return

function S = PsiT(K,m,n,T)
S = 0;
for t=1:T
  S = S + sum(K.*(K>0));  
  K = getK1(K,m,n-t+1);
end
return