function myrade30(m0,n0,lb)
randomize
global m n
n = n0;
m = m0;

p0 = ones(m,1); p0 = p0/sum(p0);
zz = p0*0 + lb; oo = p0*0+1;

  Aeq = assembleblock({oo',oo'});
  Beq = ones(size(Aeq,1),1);
    
zz = [zz;zz];
oo = [oo;oo];
  
global maxr
maxr = 0;
while 1
  p0 = rand(m,1); p0=p0/sum(p0);
  p1 = rand(m,1); p1=p1/sum(p0);
  
  x = [p0(:);p1(:)];
  
  y = fmincon(@radrat,x,[],[],Aeq,Beq,zz,oo);
  
  fprintf('n=%d;  maxr = %1.9f \n',n,maxr);
end

return



function y = radrat(pp)
global n m maxr
p0 = makepos(pp(1:m));
p1 = makepos(pp(m+1:end));

P0 = p0;
P1 = p1;
for i=1:n-1
    P0 = tensprod(P0,p0);
    P1 = tensprod(P1,p1);
end

%[hh,Ht,H0] = gethhn(P0,2,n);
%[hh,Ht,H1] = gethhn(P1,2,n);

v1 = Psi(P0-P1,2,n);
%v2 = Ht(1)+1;
r = v1;

y = -r;

if r > maxr
  global optP0 optP1
  optP0 = P0;
  optP1 = P1;
  maxr = r;
  fprintf('n=%d;  maxr = %1.9f \n',n,maxr);
end


return

function R = radave(A,P)
global SIGMA
[n,m] = size(A);
R = P'*max(abs(SIGMA * A),[],2);
%R = P'*max((SIGMA * A),[],2); % w/o abs it's zero!!!
return



function B = radbound(A)
[n,N] = size(A);
ma = max(sqrt(sum(A.^2)));
B = ma * sqrt(2*log(N))/n;
return

function w = A2w(A)
%w = max(sum(abs(A)));
w = max(abs(A),[],2);
return
[n,N] = size(A);
w = zeros(n,1);
A = abs(A);
for i=1:N
    for j=i+1:N
        a = A(:,i);
        b = A(:,j);
        %d = abs(a-b);
        d = a+b;
        w = max(w,d);
    end
end
return