function sketchpadaux
%tmpcheck % this shows why you really do need sublip
%betlp
%return  

global m n K K0
m=2
n=2
[Ainf,Binf] = lipab(m,n);

'rounding seems to matter -- investigate!!!'

dmin = 1;
while 1
  K = genK(m,n);  K1 = getK1(K,m,n); ksig = (K>0)';
  [A,B,LB,UB] = alfab(K,m,n);
  UB1 = UB + 1;

  [x,fval] = linprog(-K,A,B,[],[],LB,UB);  % fails(!!!) for UB1
  alf = x';
  alf = round(alf);
  
  [x,fval] = linprog(-K,A,B,[],[],LB,UB1);
  alf1 = x';
  alf1 = round(alf1);

  if ~tryfail(alf1*K,pl(sum(K))+alf*K,'basic SL ineq(1) fails')
    keyboard,
  end  

  if 0
  trymyalf(alf1,K,m,n);
  if 1,
    for t=1:10
      K0 = randn(size(K));
      [x,fval] = linprog(-K0,A,B,[],[],LB,UB1);
      alf1 = x';
      alf1 = round(alf1);
      % alf1 is a random element of B_n
      trymyalf(alf1,K,m,n);
    end
  end
  end
end
return

function [A,B,LB,UB] = alfab(K,m,n)
n1 = n-1;
MN  = repmat([m],[1 n ]);
MN1 = repmat([m],[1 n1]);
mn  = m^n;
mn1 = m^n1;

A=zeros(0,mn);
B=zeros(0,1);
rind = 0;
for ind1 = 1:mn
  for ind2 = ind1+1:mn
    x = ind2coord(ind1,MN);
    y = ind2coord(ind2,MN);
    d = rho(x,y);
    if (sign(K(ind1))==sign(K(ind2)))
      % signs equal -- ordinary Lip. cond
      if 1 % condition (ii).a
        for s = [-1,1]
          rind = rind+1;
          A(rind,ind1) =  s;
          A(rind,ind2) = -s;
          B(rind,1) = d;
        end
      end
    elseif d==1
      if (K(ind1)>0)
        pos = ind1;
        neg = ind2;
      else
        pos = ind2;
        neg = ind1;
      end
      if 0  % condition (ii).b  -- DO need this!!
        rind = rind+1;
        A(rind,neg) = -1;
        A(rind,pos) =  1;
        B(rind,1) = 0;
      end
    end
  end
end

LB = 0*K;
UB = LB + n - (~~pl(K));
%UB = LB + n + 1 - (~~pl(K));
%UB = LB + n + 1;
%UB = LB + n;
return


function alf = mungea(alf,K,m,n)
alf0 = alf;
%alf = round(alf);
% it's much simpler than I thought
[A,B,LB,UB] = alfab(K,m,n);
if ~all(alf < UB'+1e-8)
  alf = pl(alf-1); 
%alf = alf - min(min(alf),1);  % NOPE
end

b = all(LB'<=alf) & all(alf<=UB'+1e-9);
b = b & all(A*alf' <= B+1e-9);
if ~b
  'bad alf'
  keyboard
end
return


function alf = mungea1(alf,K,m,n)
[A,B,LB,UB] = alfab(K,m,n);
% DO seem to need this
if all(alf < UB'+1e-8)
  % we're already good
  return
end
alf = pl(alf-1); return
%don't seem to need this
%if min(alf)>1-1e-8
%  alf = pl(alf-1);
%  return
%end

%if alf*K <= 0
%  alf = alf*0;
%  return
%end

MN  = repmat([m],[1 n ]);
ii = find( K'<0 );
alf(ii) = pl(alf(ii)-1);
% force sublip property
while 1
  ii = find(A*alf' > B+1e-6);
  if isempty(ii)
    break; % we're done -- they all conform!
  else
    i = ii(1);
    inds = find(A(i,:));
    ind1 = inds(1);
    ind2 = inds(2);
    % simple idea: just make the bigger one smaller
    if alf(ind1)>alf(ind2)
      alf(ind1) = pl(alf(ind1) - 1);
    else
      alf(ind2) = pl(alf(ind2) - 1);
    end
  end
end

return


function trymyalf(alf,K,m,n)
betacheck(alf,K,m,n);
atil = mungea(alf,K,m,n);
del = alf - atil;
if ~tryfail(del*K,pl(sum(K)),'my alf ineq fails!!!!')
%if ~tryfail(alf*K,pl(sum(K))+atil*K,'my alf ineq fails!!!!')
  keyboard,
end  
return

function [A,B] = betab(K,m,n)
n1 = n-1;
MN  = repmat([m],[1 n ]);
MN1 = repmat([m],[1 n1]);
mn  = m^n;
mn1 = m^n1;

A=zeros(0,mn);
B=zeros(0,1);
rind = 0;
for ind1 = 1:mn
  for ind2 = 1:mn
    x = ind2coord(ind1,MN);
    y = ind2coord(ind2,MN);
    if (sign(K(ind1))>sign(K(ind2)))
        rind = rind+1;
        A(rind,ind2) = -1;
        A(rind,ind1) =  1;
        B(rind,1) = 0;
      end
  end
end
return



function betacheck(bet,K,m,n)
%[A,B,LB,UB] = alfab(K,m,n);
%UB1 = UB+1;
%if 1 % NO!!
%if ~all(bet < UB'+1e-8)
if max(bet)-min(bet) > n
  zind = find((K<0) & (~bet'));
  xind = find((K>0) & (bet'));
  if (~isempty(zind) & ~isempty(xind))
    'predicate fails'
    keyboard
  end
  if (~isempty(zind))
    'weaker predicate fails'
    keyboard
  end
  if 1
    % in fact, strong sublip is FALSE!!
    [A,B] = betab(K,m,n);
    %b = all(A*bet' < B+1e-9);
    b = all(A*(~~bet') < B+1e-9);
    if ~b
      'strong sublip fails'
      keyboard
    end
  end
end
return

function sketchpadaux3
global m n K K0
m=2
n=3
[Ainf,Binf] = lipab(m,n);


dmin = 1;
while 1
  K = genK(m,n);  K1 = getK1(K,m,n); ksig = (K>0)';
  [A,B,LB,UB] = alfab(K,m,n);
  UB1 = UB + 1;
  
  [x,fval] = linprog(-K,A,B,[],[],LB,UB);  % fails(!!!) for UB1
  alf = x';
  %alf = round(alf);
  
  [x,fval] = linprog(-K,A,B,[],[],LB,UB1);
  alf1 = x';
  %alf1 = round(alf1);

  if 0
    d = min(min(alf1),dmin);
    atil = alf1-d;
    b = all(LB'<=atil) & all(atil<=UB'+1e-6);
    b = b & all(A*atil' <= B+1e-9);
    if ~b
      'bad atil'
      keyboard
    end
  end
  
  if 1
    for t=1:20
      %K0 = genK(m,n);
      %K0 = K;
      %K0 = abs(randn(m^n,1)).*sign(K);
      K0 = randn(size(K));
      [x,fval] = linprog(-K0,A,B,[],[],LB,UB);
      alf = x';
      [x,fval] = linprog(-K0,A,B,[],[],LB,UB1);
      alf1 = x';

      % alf,alf1 are random elements of A_n and B_n, resp
      if ~tryfail(alf1*K,pl(sum(K))+alf*K,'basic SL ineq fails')
        keyboard,
      end  
           
      % nope
      %d0 = max(alf)-min(alf);
      %d1 = max(alf1)-min(alf1);
      %if ~tryfail(max(d0,d1),n,'diam fails'),
      %  keyboard,
      %end  
      
      %if ~tryfail(max(Ainf*alf1'),2,'Lip2 fails'),
      %  keyboard,
      %end  
    
      %phi = alf1+ksig;
      %if ~tryfail(max(Ainf*phi'),1,'Lip1 fails'),
      %  keyboard,
      %end 
      
      
    end
  end
  
end
return



function sketchpadaux2
global m n
m=2
n=3

while 1
  K = genK(m,n);  K1 = getK1(K,m,n); ksig = (K>0)';
  [A,B] = lipab(m,n); 
  [x,fval] = linprog(-K,A,B,[],[],0*K,n+0*K);  
  %phi = round(x'); 
  phi = (x'); 
  ptil = pl(phi-ksig);

  
  
  [A,B,LB,UB] = alfab(K,m,n);
  UB1 = UB + 1;
  
  [x,fval] = linprog(-K,A,B,[],[],LB,UB);  % fails(!!!) for UB1
  %[x,fval] = linprog(-K,[],[],[],[],LB,UB);  % fails(!!!) for UB1
  alf = x';
  %alf = round(alf);
  
  [x,fval] = linprog(-K,A,B,[],[],LB,UB1);
  %[x,fval] = linprog(-K,[],[],[],[],LB,UB1);
  alf1 = x';
  %alf1 = round(alf1);

  if ~tryfail(alf*K,Psi(K1,m,n-1),'(1) fails'),
    keyboard,
  end  
  
  %if ~tryfail(alf1*K,pl(sum(K))+alf*K,'(2) fails'),
  %this indeed fails
  if ~tryfail(alf1*K,pl(sum(K))+Psi(K1,m,n-1),'(2) fails'),
    keyboard,
  end

  
  if 1
    %K0 = genK(m,n);
    %K0 = K;
    K0 = abs(randn(m^n,1)).*sign(K);
    UB = UB+0;
    %dmin = 2;
    dmin = 1;
    UB1 = UB + dmin;
    [x,fval] = linprog(-K0,A,B,[],[],LB,UB);
    alf = x';
    [x,fval] = linprog(-K0,A,B,[],[],LB,UB1);
    alf1 = x';
  end
  if 1
    atil = ptil;
    b = all(LB'<=atil) & all(atil<=UB');
    b = b & all(A*atil' <= B+1e-9);
    if ~b
      'bad ptil'
      keyboard
    end
  end
  d = min(min(alf1),dmin);
  %atil = alf1-(min(alf1)>=1);
  atil = alf1-d;
  b = all(LB'<=atil) & all(atil<=UB'+1e-9);
  b = b & all(A*atil' <= B+1e-9);
  if ~b
    'bad atil'
    keyboard
  end
  'its ok',  keyboard
  
  %if ~tryfail(alf1*K,pl(sum(K))+atil*K,'alf ineq fails'),  keyboard,  end  
  %if ~tryfail(alf1*K,pl(sum(K))+alf*K,'BASIC alf ineq fails'),  keyboard,  end  
  % this basic one FAILS!!
  % see /home/lkontor/SKETCHFAIL1
  
  
end
return


function sketchpadaux1
global m n A B K K1 phi ksig ptil
m=3
n=3

while 1
  K = genK(m,n);  K1 = getK1(K,m,n); ksig = (K>0)';
  
  s = 0;
  for y=1:m
    Ky = getky(K,y,m,n);
    Ky1 = getky(K1,y,m,n-1);
    s = s + pl(sum(Ky)) + Psi(Ky1,m,n-2);
  end
  if ~tryfail(s,Psi(K1,m,n-1),'psi ineq(1) fails'),keyboard,end
  % seems to work
  
  s = 0;
  for y=1:m
    Ky = getky(K,y,m,n);
    s = s + pl(sum(Ky)) + Psi(Ky,m,n-1);
  end
  if ~tryfail(s,Psi(K,m,n),'psi ineq(2) fails'),keyboard,end
  % seems to work
  
  
  
  
  
  % NO
  if 0
    if flip
      alf = rand(size(K'))*n;
    else
      [x,fval] = linprog(-K,[],[],[],[],0*K,0*K+n);
      alf = x';
      if ~tryfail(alf*K,pl(sum(K))+pl(alf-1)*K,'(1) fails'),
        keyboard,
      end  
    end
  end
  
  %if flip
  %if 0
  %  randliphi
  %else
  %  optphi
  %end
  %advphi
  %alfconj

  [A,B,LB,UB] = alfab(K,m,n);
  UB1 = UB + 1;
  
  [x,fval] = linprog(-K,A,B,[],[],LB,UB);  % fails(!!!) for UB1
  alf = x';
  if ~tryfail(alf*K,Psi(K1,m,n-1),'(1) fails'),
    keyboard,
  end  
  
  [x,fval] = linprog(-K,A,B,[],[],LB,UB1);
  alf1 = x';
  %if ~tryfail(alf1*K,pl(sum(K))+alf*K,'(2) fails'),
  %this indeed fails
  if ~tryfail(alf1*K,pl(sum(K))+Psi(K1,m,n-1),'(2) fails'),
    keyboard,
  end


  if 0
    % NO
    s = [];
    for i=2:n
      s(i) = 0;
      for y=1:m
        %Ky = getky(K,y,m,n);
        Ky = project(K,y,m,n,i);
        s(i) = s(i) + pl(sum(Ky));
      end
    end
    ms = max(s);
    [x,fval] = linprog(-K,A,B,[],[],LB,UB); % fails(!!!) for UB1
    alf = x';
    %if ~tryfail(alf*K,pl(sum(K))+pl(alf-1)*K,'alf ineq fails'),
    if ~tryfail(alf*K,ms+pl(alf-1)*K,'alf ineq fails'),  
      keyboard,
    end  
  end
  

  if 1
    %if flip
    if 1
      %alf1 = rand(size(K'))*n - (~~pl(K'));
      alf1 = rand(size(K'))*100;
    else
      [x,fval] = linprog(-K,[],[],[],[],0*K,0*K+n);
      alf1 = x';
    end
  end
  
  ii = find(alf1==n+1);
  atil = alf1;
  atil(ii) = atil(ii)-1;
  %atil = pl(alf1-1); % this one don't work!!!
  if ~tryfail(alf1*K,pl(sum(K))+atil*K,'alf ineq fails'),  
    keyboard,
  end  
  
  
end
return




function [A,B,LB,UB] = alfab0(K,m,n)
n1 = n-1;
MN  = repmat([m],[1 n ]);
MN1 = repmat([m],[1 n1]);
mn  = m^n;
mn1 = m^n1;

A=zeros(0,mn);
B=zeros(0,1);
rind = 0;
rind = 0;
for ind1 = 1:mn
  for ind2 = ind1+1:mn
    x = ind2coord(ind1,MN);
    y = ind2coord(ind2,MN);
    %if rho(x,y)==1  % Hamming dist == 1
    if 1
      d = rho(x,y);
      if (sign(K(ind1))==sign(K(ind2)))
        % signs equal -- ordinary Lip. cond
        if 1 % condition (ii).a
          for s = [-1,1]
            rind = rind+1;
            A(rind,ind1) =  s;
            A(rind,ind2) = -s;
            B(rind,1) = d;
          end
        end
      else
        % try w/o this? -- not quite
        % try alternative
        % "neg" ind - "pos" ind <= 2
        % "pos" - "neg" <= 0
        if (K(ind1)>0)
          pos = ind1;
          neg = ind2;
        else
          pos = ind2;
          neg = ind1;
        end
        if 1  % condition (ii).b  -- DO need this!!
          rind = rind+1;
          A(rind,neg) = -1;
          A(rind,pos) =  1;
          B(rind,1) = 0;
        end
      end
    end
  end
end

LB = 0*K;
UB = LB + n - (~~pl(K));
%UB = LB + n + 1 - (~~pl(K));
%UB = LB + n + 1;
%UB = LB + n;
return



function [fval,alf] = alflp(K,m,n)
global ptil
[A,B,LB,UB] = alfab(K,m,n);
[x,fval] = linprog(-K,A,B,[],[],LB,UB);
alf = x';
fval = -fval;

%lhs = max(A*ptil' - B) ;
%rhs = 0;
%tryfail(lhs,rhs,'ptil glitch');
return

function alf = atil(alf,K,m,n)
alf0=alf;
% take off one for the negative K's
%ii = ~~(K<0);
%a1 = pl(alf - ii');
%a1 = min(alf,n-1);
%a1 = min(alf,n);
%ii = (~~(K'>0))&(alf>n-1);
%a1 = alf - ii;
%ii = ~~(K>0);
%a1 = pl(alf - ii');
%a1 = pl(alf-1);
[A,B,LB,UB] = alfab(K,m,n);
alf = round(alf);
alf = alf - (alf>UB');
ii = find(K<0)';
alf(ii) = min(alf(ii),n);
if sum(K)<=0
  alf = alf - min(alf);
end


b = all(LB'<=alf) & all(alf<=UB');
b = b & all(A*alf' <= B+1e-9);
if ~b
  'bad atil'
  keyboard
end


%[fval,a1] = alflp(K,m,n);

return

function alf = mungea0(alf,K,m,n)
% try the following simple algorithm
% 1. find smallest (most neg) value of K[x]
% 2. find all y within rho(1) of x
% 3. A[y] -= 1
% 4. enforce (ii)
% too complicated --> prob won't work!

% different idea
[A,B,LB,UB] = alfab(K,m,n);
if all(alf < UB'+1e-8)
  % we're already good
  return
end
if min(alf)>1-1e-8
  alf = pl(alf-1);
  return
end
if alf*K <= 0
  alf = alf*0;
  return
end

MN  = repmat([m],[1 n ]);
%ii = find(K'<0);
%ii = find( (alf > UB'+1e-6) );
%ii = find( (alf > UB'+1e-6) | (alf > n+1-1e-6) );
ii = find( (alf > UB'+1e-6) | (K'<0) );  % seems like really need this!!
alf(ii) = pl(alf(ii)-1);
% this takes care of the LB, UB condition
% force sublip property
while 1
  ii = find(A*alf' > B+1e-6);
  if isempty(ii)
    % we're done -- they all conform!
    break;
  else
    i = ii(1);
    inds = find(A(i,:));
    ind1 = inds(1);
    ind2 = inds(2);
    % simple idea: just make the bigger one smaller
    if alf(ind1)>alf(ind2)
      alf(ind1) = pl(alf(ind1) - 1);
    else
      alf(ind2) = pl(alf(ind2) - 1);
    end
    %x = ind2coord(ind1,MN);
    %y = ind2coord(ind2,MN);
    % it must be the case that sign(K(x))~=sign(K(y))
    if 0
      if (K(ind1)>0)
        pos = ind1;
        neg = ind2;
      else
        pos = ind2;
        neg = ind1;
      end
    end
    
  end
end

return


function checkay(alf)
global m n A B K K1 phi ksig ptil
%a1 = atil(alf,K,m,n);
%if ~tryfail(alf*K,pl(sum(K))+a1*K,'decomposition fails'),keyboard,end

s = 0;
for y=1:m
  %y
  Ky = getky(K,y,m,n);
  K1y = getky(K1,y,m,n-1);
  %ay = getky(a1,y,m,n);
  ay = getky(alf,y,m,n);
  %a1 = atil(0,Ky,m,n-1);  % force UB to hold
  a1 = atil(ay,Ky,m,n-1);  % force UB to hold
  
  if 0
    [A,B,LB,UB] = alfab(Ky,m,n-1);
    b = all(LB'<=ay) & all(ay<=UB');
    b = b & all(A*ay' <= B+1e-9);
    if ~b,    'A_n membership fails',    keyboard,  end
  end
  
  %if ~tryfail(ay*Ky,Psi(K1y,m,n-2),'inner ineq fails'),keyboard,end
  if ~tryfail(ay*Ky,pl(sum(Ky))+a1*Ky,'inner ineq fails'),keyboard,end
  %s = s + Psi(K1y,m,n-2);
  s = s + ay*Ky;
end
%if ~tryfail(alf*K,Psi(K1,m,n-1),'outer ineq fails'),keyboard,end
if ~tryfail(alf*K,pl(sum(K))+s,'outer ineq fails'),keyboard,end
return


function randliphi
global m n A B K K1 phi ksig ptil
phi = randlip(m,n);
ptil = pl(phi-ksig);
return

function advphi
global m n A B K K1 phi ksig ptil
% adversarial phi
phi = zeros(1,m^n);    
ii = find(K>0);    
phi(ii) = n*ones(size(ii));  
ptil = pl(phi-ksig);
return

function optphi
global m n A B K K1 phi ksig ptil
[A,B] = lipab(m,n); 
[x,fval] = linprog(-K,A,B,[],[],0*K,n+0*K);  
phi = round(x'); 
ptil = pl(phi-ksig);
return

function alfconj
global m n A B K K1 phi ksig ptil
[fval,alf] = alflp(K,m,n);
checkay(alf);

lhs = fval;
rhs = Psi(K1,m,n-1);
if ~tryfail(lhs,rhs,'alfconj FALSE')
keyboard,end
return

%a1 = min(alf,n-1);
a1 = atil(alf,K,m,n);

%tryfail(alf*K,sum(K)+a1*K                          ,'fail1');
%tryfail(      sum(K)+a1*K,pl(sum(K))+a1*K   ,'fail2');
%tryfail(alf*K,pl(sum(K))+a1*K   ,'fail2.1');

return

tryfail(alf*K,pl(sum(K))+sumkphiy(K,a1,m,n)   ,'fail2.5');

tryfail(pl(sum(K))+a1*K, Psi(K1,m,n-1)   ,'fail3');

tryfail(pl(sum(K))+a1*K, pl(sum(K1))+sumky(K1,m,n-1) ,'fail4');




lhs = alf*K;
rhs = pl(sum(K1)) + sumky(K1,m,n-1);
%tryfail(lhs,rhs,'huh?');

return


function Ky = project(K,y,m,n,i)
%global m n
MN = repmat([m],[1 n]);
Ky = [];
mn = m^n;
for ind = 1:mn
  z = ind2coord(ind,MN);
  %if z(end)==y
  %if z(1)==y
  if z(i)==y
    Ky(end+1) = K(ind);
  end
end
%Ky=Ky(:);
Ky = reshape(Ky,size(K(1:length(Ky))));
return




function S = sumky(K,m,n)
%global m n
S = 0;
for y=1:m
  Ky = getky(K,y,m,n);
  S = S + Psi(Ky,m,n-1);
end
return

function S = sumkphiy(K,phi,m,n)
%global m n
S = 0;
for y=1:m
  Ky = getky(K,y,m,n);
  phiy = getky(phi,y,m,n);
  S = S + phiy*Ky;
end
return


function Ky = getky(K,y,m,n)
%global m n
MN = repmat([m],[1 n]);
Ky = [];
mn = m^n;
for ind = 1:mn
  z = ind2coord(ind,MN);
  if z(end)==y
  %if z(1)==y
    Ky(end+1) = K(ind);
  end
end
%Ky=Ky(:);
Ky = reshape(Ky,size(K(1:length(Ky))));
return



function good = tryfail(lhs,rhs,failstr)
global m n A B K K1 phi ksig ptil
good = (lhs <= rhs+1e-6);
if ~good
  failstr
  %save SKETCHFAIL m n A B K K1 phi ksig ptil
  %keyboard
end
return


function betlp
global m n K K0
m=2
n=3
while 1
  K = genK(m,n);  K1 = getK1(K,m,n); ksig = (K>0)';
  
  if 1
    [Ad,Bd,LBd,UBd] = delab(K,m,n);
    [x,fval] = linprog(-K,Ad,Bd,[],[],0*K,0*K+1);
    oneb = x';
    oneb = round(oneb);
    if ~tryfail(oneb*K,pl(sum(K)),'oneb dont work!!!'),
      keyboard, 
    end
  end

  [A,B,LB,UB] = alfab(K,m,n);
  if flip
    [x,fval] = linprog(-K,A,B,[],[],LB,UB+1);
  else
    K0 = randn(size(K));
    [x,fval] = linprog(-K0,A,B,[],[],LB,UB+1);
  end
  bet = x';
  bet = round(bet);
  alf = mungea(bet,K,m,n);
  oneb = bet - alf;
  
  %b = all(Ad*oneb'<Bd+1e-9);
  %if ~b
  %  'bad oneb'
  %  keyboard
  %end
  
  
  if (any(oneb)&any(~oneb)&(sum(K)>1e-9))
  %if 1  % only works when oneb is nonhomogeneous!!!!
    %[K oneb']
    phitable(K,oneb,m,n)
    %[Ad,Bd,LBd,UBd] = delab(K,m,n);    
    b = all(Ad*oneb'<Bd+1e-9);
    if ~b
      'bad oneb'
      keyboard
    end
  end
    
end



return

function tmpcheck
global m n K K0
m=2
n=3

[Ainf,Binf] = lipab(m,n);

while 1
  K = genK(m,n);  K1 = getK1(K,m,n); ksig = (K>0)';

  [x,fval] = linprog(-K,Ainf,Binf,[],[],0*K,0*K+n);
  phi = x';
  phi = round(phi);
  
  %phi1 = pl(phi-1);
  phi1 = pl(phi-ksig);
  
  %if ~tryfail(phi*K,sum(pl(K))+phi1*K,'simple -1 dont work dude!!!'),
  if ~tryfail(phi*K,sum(pl(K))+phi1*K,'phi1 dont work dude!!!'),
    keyboard, end
    
    if 1
      % ok, so it's obv not sublip
      [A,B,LB,UB] = alfab(K,m,n);
      alf = phi1;
      b = all(LB'<=alf) & all(alf<=UB'+1e-9);
      b = b & all(A*alf' <= B+1e-9);
      if ~b
        'bad alf'
        keyboard
      end
    end
    
  if ~tryfail(phi1*K,Psi(K1,m,n-1),'psi bound fails for phi1'),
    keyboard, end
    
end
  
return





function [A,B,LB,UB] = delab(K,m,n)
n1 = n-1;
MN  = repmat([m],[1 n ]);
MN1 = repmat([m],[1 n1]);
mn  = m^n;
mn1 = m^n1;

A=zeros(0,mn);
B=zeros(0,1);
rind = 0;
for ind1 = 1:mn
  for ind2 = 1:mn
    x = ind2coord(ind1,MN);
    y = ind2coord(ind2,MN);
    % no need to enforce lip -- the range is [0,1]
    if (sign(K(ind1))>sign(K(ind2)))
      rind = rind+1;
      A(rind,ind2) = -1;
      B(rind,1) = -1;

      rind = rind+1;
      A(rind,ind2) = -1;
      A(rind,ind1) =  1;
      B(rind,1) = 0;
    end
  end
end

LB = 0*K;
UB = 0*K + 1;
return