gemdbht.m

function [grad] = gemdbht(A,K,S,m,para,Obs,Kc)
% this calculate gradient step of objective function for MKC_emdb(ht) with respect to A^{(m)}
% Output :
% grad :  (\partial f / \partial A^{(m)})

grad=zeros(size(A,1),size(A,2));
eps=1E-10;
M=size(K,3); 
N=size(K,2);
  
for l =1:1:M
	temp(l).T=zeros(size(A,1),size(A,2));
	for l2=1:1:M
		if l2==l
		else
           		temp(l).T=S(l,l2)*A(:,:,l2);
		end
	end

	temp(l).D=A(:,Obs(l).id,l)*K(Obs(l).id,Obs(l).id,l);
	temp(l).hatk=temp(l).D*A(:,Obs(l).id,l)';
	temp(l).B=K(Obs(l).id,Obs(l).id,l)-temp(l).hatk(Obs(l).id,Obs(l).id);
	temp(l).E=temp(l).B*temp(l).D(Obs(l).id,:);
	temp(l).C=A(:,:,l)-temp(l).T;
end

Part1=zeros(N,N);

Part1=-temp(m).E;
grad(Obs(m).id,Obs(m).id)= grad(Obs(m).id,Obs(m).id) +4*para.c1*Part1/(M*length(Obs(m).id)^2);
                          
part= zeros(size(A,1),size(A,2));
for l =1:1:M
if l==m
   part=part+temp(m).C;
else
part=part-S(l,m)*temp(l).C;
end
end
grad= grad + 2*para.c2*part/(M*N);


clear temp part Part1;
             
    return;     
end