function permsketch
global m n
m = 2; n = 3;

X = rand(m^n,1); X = X/sum(X);
zz = X*0 + 1e-12; oo = X*0+1;

[Aeq,Beq] = permdif(m,n);
Aeq = [Aeq;oo'];
Beq = [Beq;1];

global maxH
maxH = 0;
while 1

  X = rand(m^n,1); X = X/sum(X);

  y = fmincon(@myobj1,X,[],[],Aeq,Beq,zz,oo);

  fprintf(' maxH = %1.9f \n',maxH);
end
return

function y = myobj1(X)
global m n
global maxH maxP
[hhx,Hx,H] = gethhn(X,m,n);
if H > maxH
  maxP = X;
  maxH = H;
  fprintf(' maxH = %1.9f \n',maxH);
end
y = -H;
return



function permsketch0
global m n
m = 2; n = 3;

global PERMS
PERMS = generate_perms(n);

global maxrxy maxryx
maxrxy=0; maxryx=0;
while 1

  X = rand(m^n,1); X = X/sum(X);

  if 0
    Y = randpermswap(X);
    [hhx,Hx,H] = gethhn(X,m,n);
    [hhy,Hy,H] = gethhn(Y,m,n);
    %rxy = max(max(hhx./(hhy+eps)));
    %ryx = max(max(hhy./(hhx+eps)));
    rxy = max(Hx)/max(Hy);
    ryx = max(Hy)/max(Hx);
    maxrxy = max(maxrxy,rxy);
    maxryx = max(maxryx,ryx);
  else
    zz = X*0 + 1e-12; oo = X*0+1;
    y = fmincon(@myobj,X,[],[],oo',1,zz,oo);
  end

  %fprintf('maxrxy = %1.9f        maxryx = %1.9f \n',maxrxy,maxryx);
  fprintf(' maxryx = %1.9f \n',maxryx);
end
return

function y = myobj(X)
global m n
global maxrxy maxryx
Y = randpermswap(X);
[hhx,Hx,H] = gethhn(X,m,n);
[hhy,Hy,H] = gethhn(Y,m,n);
ryx = max(Hy)/max(Hx);
if ryx > maxryx
  maxryx = ryx;
  fprintf(' maxryx = %1.9f \n',maxryx);
end
y = -ryx;
return


function Y = randpermswap(X)
global m n
global PERMS
nP = size(PERMS,1);
MN = repmat([m],[1 n]);
mn = m^(n);
Y = zeros(m^n,1);
for yind = 1:mn
  y = ind2coord(yind,MN);
  for pind = 1:nP
    sig = PERMS(pind,:);
    isig = invperm(sig);
    x = y(isig);
    xind = coord2ind(x,MN);
    Y(yind) = Y(yind) + X(xind)/nP;
  end
end
return