Obj_PSO.m

%%______________________________________________________________________________
%% This function is to build the GP objective - maximimum likelihood estimation
%% This function is created by Kai Zhou 7/31/2019
%%______________________________________________________________________________
function Pos = Obj_PSO(b)
global x1;
global y1;
global k1
global numInp
x = x1;
y = y1;
num = length(x(:,1));
C = zeros(num,num);
fi = b(end);
b(end) = [];

for i = 1:num
    for j= 1:num
        C(i,j) = k1(x(i, :)',x(j, :)',b,fi);
    end
end


perb2_2 = 1e-6;
P1 = zeros(num,1) + 1;
H = [P1, x];

if rcond(C)>1e-20 
    signn = 1;
else
    signn = 0;
end

if signn == 1
Beta = zeros(numInp+1,1);
Temp1 = inv(C+perb2_2*eye(size(C)));
Temp2 = y-H*Beta;
Temp2 = reshape(Temp2,[],1);
end

part2 = 0;

      
      if signn == 1
        sig = det(C);  
        if sig<0
            part2 = 1e50;
            signn = 0;
        elseif sig == 0
            [tt1,tt2]=eig(C);
            if min(diag(tt2))<0
                part2 = 1e50;
                signn = 0;
            else
                for i = 1:length(C)
                    part2 = part2+log(tt2(i,i));
                end
            end
        else
            part2 = log(det(C));
        end
      else
          part2 = 1e50;
          signn = 0;
      end    

if signn == 1
    Pos = part2 + Temp2'*Temp1*Temp2;
else
    Pos = 2e50;
end

end