% messed up w/the n, T, nn ...

function [A,phi,fval,diamX] = gamcheck2(m,n,h)
% conjecture:
% Suppose $\g_k[x]$ is such that
%\beq
%\sum_k \g_k[x^{(k)}] &\leq&
%C_1 + C_2\diam\{x^{(k)}\}.
%\eeq
%Then
%\beq
%\sum_k \sum_{k'} a_{kk'} \g_{k'}[x^{(k)}] &\leq&
%C_1 + C_2\h(1+\diam\{x^{(k)}\}).
%\eeq

global C
C = zeros(m,1); C(2)=1;

% searching over A and gam
global XX


global nstate lenseq
nstate = m;
lenseq = n;

lx = 1;
XX = cell(m,1);
for i=1:m
 XX{i} = ceil(rand(1,lx)*m);
end
XX{:}
diamX = diam(XX);

T = n-1;
n = n + length(XX{1});

adim = m^2*T;
fdim = m^n;
xdim = adim + fdim;


% box constraints
%LB = zeros(adim,1)+1e-10;
%UB = ones(adim,1);
LB = zeros(xdim,1)+1e-10;
LB(adim+1:end) = LB(adim+1:end) - Inf;  % no box constraints on phi
UB = ones(xdim,1);
UB(adim+1:end) = UB(adim+1:end) + Inf;  % no box constraints on phi


% normalization constraints
Aeq = zeros(m*T,xdim);
for i=1:m*T
  for j=1:m
    Aeq(i,m*(i-1)+j) = 1;
  end
end
Beq = ones(m*T,1);


% stricture constraints
SIGNS = 2*list_all_ind(repmat([2],[1 m]))-3;
Aina = zeros(size(SIGNS,1)*m*(m-1)/2*T,m^2*T);
rind = 0;

ii1 = 1;
ii2 = setdiff([1:m],ii1);

for t=1:T
  %if (T==1)
  %  ii1 = 1:m;
  %  %ii2 = setdiff([1:m],ii1);
  %  ii2 = 1:m;
  %else
  %  %ii1 = 1:m;
  %  %ii2 = 1:m;
  %  ii1 = 2;
  %  ii2 = setdiff([1:m],ii1);
  %end
  for i1 = ii1
    for i2 = ii2
      %for i1=1:m
      %  for i2=i1+1:m
      for s = 1:size(SIGNS,1)
        rind = rind+1;
        ss = SIGNS(s,:);
        for j=1:m
          ind1 = coord2ind([j i1 t],[m m T]);
          ind2 = coord2ind([j i2 t],[m m T]);
          Aina(rind,ind1) =  ss(j);
          Aina(rind,ind2) = -ss(j);
        end
      end
    end
  end
end
Bina = ones(size(Aina,1),1)*h*2;

d=1;
Ainf = zeros(0,m^n);
Binf = zeros(0,1);
mn = repmat([m],[1 n]);
rind = 0;
for ind1 = 1:m^n
  for ind2 = ind1+1:m^n
    x = ind2coord(ind1,mn);
    y = ind2coord(ind2,mn);
    if length(find(x~=y))==1  % Hamming dist == 1
      for s = [-1,1]
        rind = rind+1;
        Ainf(rind,ind1) =  s;
        Ainf(rind,ind2) = -s;
        Binf(rind,1) = d;
      end
    end
  end
end

Ain = assembleblock({Aina,Ainf});
Bin = [Bina;Binf];

A0 = pnormdim(ones(m,m,T),1);
A0 = A0+randn(size(A0))*1e-2;
A0 = pnormdim(A0,1);

FN = randFN(m,n,d,'not');
phi0 = FN{n};
x0 = [A0(:); phi0(:)];

[x,fval] = fmincon(@myobjm,x0,Ain,Bin,Aeq,Beq,LB,UB);
fval = sqrt(abs(fval));
A = reshape(x(1:adim),[m m T]);
phi = reshape(x(adim+1:end),[1 m^n]);

return


function y = myobjm(x)
global nstate lenseq
m = nstate;
n = lenseq;
T = n-1;
global XX

n = n + length(XX{1});
adim = m^2*T;
fdim = m^n;
xdim = adim + fdim;

global A
%A = reshape(x,[m m T]);
A = reshape(x(1:adim),[m m T]);
phi = reshape(x(adim+1:end),[1 m^n]);
global FN
FN{n} = reshape(x(adim+1:end),[1 m^n]);

s = 0;
for k=1:m
  gamk = gamma(n-1,XX{k});
  for k1=1:m
    s = s + A(k,k1,T) * gamk(k1);
  end
end
  
y = -s^2;
return




function r = F(x)
%r = length(find(x~=1));
%return
global nstate
lenseq = length(x);
global FN
FF = FN{lenseq};
ind = coord2ind(x,(repmat(nstate,1,lenseq)));
r = FF(ind);
return


function p = p_0(x)
global C
p = C(x);
return

function p = p_n(i,j,n)
% primitive cond prob
global A
if i
  p = A(i,j,n);
else
  p = 1;
end
return





function gam = gamma(n,x)
%global nstate
global A
[m,m,t] = size(A);
nstate = m;
gam = zeros(nstate,1);
if (n==2)
  for k=1:nstate
    for x1=1:nstate
      gam(k) = gam(k) + p_0(x1)*(p_n(k ,1 ,1)*F([1 k x]) - p_n(k ,x1,1)*F([x1 k x]));
    end
  end
else
  for k=1:nstate
    gamkx = gamma(n-1,[k x]);
    for k1=1:nstate
      gam(k) = gam(k) + p_n(k,k1,n-1) * gamkx(k1);
    end
  end
end  
return