function [A,gam,fval] = s1check(n,d,h)

%n=1;
m=2;
Hn = sum(h.^(0:n-1));
c1 = d*Hn;
c2 = d*h^(n-1);

global nstate lenseq
nstate = m;
lenseq = n;

T = 1;

adim = m^2*T;
gdim = m^2;
xdim = adim + gdim;


% 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;

for t=1:T
  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;


rind=0;
% gamma sum constraint
for i=1:m
  for s=[-1 1]
    rind = rind+1;
    for j=1:m
      cind = coord2ind([i j],[m m]);
      Aing(rind,cind) = s;
    end
    Bing(rind,1) = c1;
  end
end

for s=[-1 1]
  rind = rind+1;
  cind1 = coord2ind([1 1],[m m]);
  cind2 = coord2ind([2 2],[m m]);
  Aing(rind,cind1) = s;
  Aing(rind,cind2) = s;
  Bing(rind,1) = c1+h*c2;
  rind = rind+1;
  cind1 = coord2ind([1 2],[m m]);
  cind2 = coord2ind([2 1],[m m]);
  Aing(rind,cind1) = s;
  Aing(rind,cind2) = s;
  Bing(rind,1) = c1+h*c2;
end

Ain = assembleblock({Aina,Aing});
Bin = [Bina;Bing];

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

G0 = randn(m,m);

x0 = [A0(:); G0(:)];

[x,fval] = fmincon(@myobjm,x0,Ain,Bin,Aeq,Beq,LB,UB);
fval = sqrt(abs(fval));

y = myobjm(x);

global A FN

A = reshape(x(1:adim),[m m T]);
gam = reshape(x(adim+1:end),[m m]);
return


function y = myobjm(x)
global nstate lenseq

m = nstate;
n = lenseq;
T = 1;

adim = m^2*T;
gdim = m^2;
xdim = adim + gdim;

A = reshape(x(1:adim),[m m T]);
gam = reshape(x(adim+1:end),[m m]);

g00 = gam(1,1);
g10 = gam(1,2);
g01 = gam(2,1);
g11 = gam(2,2);

a0 = A(1,1);
a1 = A(2,1);
b0 = A(1,2);
b1 = A(2,2);

s = (a0-b0)*(g00-g10) + (a1-b1)*(g01-g11);


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