function psisketch0(m0,n0)
global Ainf Binf m n mylinopt maxr
%warning off
warning on

%m = 2;
%n = 3;
m = m0; n=n0;

mylinopt = optimset('Diagnostics','off');
mylinopt = optimset('Display','off');

K = randn(m^n,1);
phi = randlip(m,n)';

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

LBf =   zeros(size(K));
UBf =  n*ones(size(K));

LB = [LBK];
UB = [UBK];


global w

maxr = 0;
while 1
  
  w = rand(n,1);
  %w = n*w/sum(w); % this is important!!!
  %w = 0*w+1;
  %wsum = sum(w)
  [Ainf,Binf] = lipabw(m,n,w); 
  %keyboard
  
  x = randn(m^n,1);
  [x,fval] = fmincon(@myobj_ratio,x,[],[],[],[],LB,UB);
  r = abs(fval);
  if r > maxr
    global maxalf maxK
    maxalf = w;
    maxK = x;
    maxr = r;
  end
  fprintf('m=%d   n=%d                      maxr = %1.9f \n',m,n,maxr);
end
return


function y = myobj_ratio(x)
global m n maxr w
%phi = x(1:m^n)';
%K = x(m^n+1:end);
K = x;

yPhi = phinorm(K);
yPsi = psinorm(K,m,n)+realmin;

%[yPhi yPsi]

r = yPhi/yPsi;
if r > maxr
  global maxalf maxK
  maxalf = w;
  maxK = x;
  maxr = r;
  fprintf('m=%d   n=%d                      maxr = %1.9f \n',m,n,maxr);
end

y = -r;
return


function y = phinorm(K)
global Ainf Binf m n mylinopt w

W = sum(w);

[x,fvalp] = linprog( K,Ainf,Binf,[],[],0*K,0*K+W,0,mylinopt);
[x,fvaln] = linprog(-K,Ainf,Binf,[],[],0*K,0*K+W,0,mylinopt);
y = max(abs(fvalp),abs(fvaln));
return

function y = psinorm(K,m,n)
y = max(Psi(K,m,n),Psi(-K,m,n));
return

function y = psiwnorm(K,w)
global m n
y = max(Psiw(K,m,n,w),Psiw(-K,m,n,w));
return


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