% w: width of connection needs
% thred: if CI<thred -> connect
function [CI,dCI] = connectConstraint(microx,microy,xi,connEle,allx,w,thred)
    
    xi = reshape(xi,microy,microx);

    CI = zeros(4,1);
    dCI = zeros(4,microy*microx);
    
    % down, right, up, left
    for i = 1:4
        conn = zeros(microy,microx);
        dconn = zeros(microy,microx);
        connMeas = zeros(microy,microx);
        dconnMeas = zeros(microy,microx);
        
        if connEle(i)>0
            xj = reshape(allx(:,connEle(i)),microy,microx);

            switch i
            case 1 % down
                for ii = 1:microx
                    for jj = (microy-w+1):microy
                        % opposite
                        jj1 = microy-jj+1;
                        ii1 = ii;
                        % orthog, 45 degree left and right, 
                        % NOTE: don't forget border
                        ii2 = ii-(microy-jj)*2; ii2(ii2<1) = 1;
                        ii3 = ii+(microy-jj)*2; ii3(ii3>microx) = microx;
                        
                        tmp = xj(jj1,ii1);
%                         tmp = max(xj(jj1,ii1), max(xj(jj1,ii2), xj(jj1,ii3)));
                        conn(jj,ii) = exp(xi(jj,ii) .* (1-tmp));
                        dconn(jj,ii) = exp(xi(jj,ii)*(1-tmp))*(1-tmp);
                    end
                end                
                connMeas((microy-w+1):microy,1:microx) = exp(xi((microy-w+1):microy,1:microx));
                CI(i,1) = sum(sum(conn((microy-w+1):microy,1:microx)))/...
                    (sum(sum(connMeas((microy-w+1):microy,1:microx)))+1e-9);
                
%                 if CI(i,1)>thred
                    % bad connection                    
                    dconnMeas((microy-w+1):microy,1:microx) = exp(xi((microy-w+1):microy,1:microx));
                    tmp = (dconn*sum(connMeas(:)) - sum(conn(:))*dconnMeas)/(sum(connMeas(:))+1e-9)^2;            
                    dCI(i,:) = tmp(:);
%                 else
%                     CI(i,1) = 0;
%                 end                    
                
            case 2 % right
                for ii = (microx-w+1):microx
                    for jj = 1:microy
                        % opposite
                        jj1 = jj;
                        ii1 = microx-ii+1;
                        % orthog, 45 degree left and right, 
                        % NOTE: don't forget border
                        jj2 = jj-(microx-ii)*2; jj2(jj2<1) = 1;
                        jj3 = jj+(microx-ii)*2; jj3(jj3>microy) = microy;
                        
                        tmp = xj(jj1,ii1);
%                         tmp = max(xj(jj1,ii1), max(xj(jj2,ii1), xj(jj3,ii1)));
                        conn(jj,ii) = exp(xi(jj,ii) .* (1-tmp));
                        dconn(jj,ii) = exp(xi(jj,ii)*(1-tmp))*(1-tmp);
                    end
                end                          
                connMeas(1:microy,(microx-w+1):microx) = exp(xi(1:microy,(microx-w+1):microx));
                CI(i,1) = sum(sum(conn(1:microy,(microx-w+1):microx)))/...
                    (sum(sum(connMeas(1:microy,(microx-w+1):microx)))+1e-9);
                
%                 if CI(i,1)>thred
                    % bad connection                    
                    dconnMeas(1:microy,(microx-w+1):microx) = exp(xi(1:microy,(microx-w+1):microx)); 
                    tmp = (dconn*sum(connMeas(:)) - sum(conn(:))*dconnMeas)/(sum(connMeas(:))+1e-9)^2;            
                    dCI(i,:) = tmp(:);
%                 else
%                     CI(i,1) = 0;
%                 end

            case 3 % up
                for ii = 1:microx
                    for jj = 1:w
                        % opposite
                        jj1 = microy-jj+1;
                        ii1 = ii;
                        % orthog, 45? left and right, 
                        % NOTE: don't forget border
                        ii2 = ii-jj*2; ii2(ii2<1) = 1;
                        ii3 = ii+jj*2; ii3(ii3>microx) = microx;
                        
                        tmp = xj(jj1,ii1);
%                         tmp = max(xj(jj1,ii1), max(xj(jj1,ii2), xj(jj1,ii3)));
%                         conn(jj,ii) = xi(jj,ii) .* (1-tmp);
%                         dconn(jj,ii) = xi(jj,ii)*(1-tmp);
                        conn(jj,ii) = exp(xi(jj,ii) .* (1-tmp));
                        dconn(jj,ii) = exp(xi(jj,ii) .* (1-tmp))*(1-tmp);
                        
%                         connMeas(jj,ii) = tmp;
                    end
                end
                connMeas(1:w,1:microx) = exp(xi(1:w,1:microx));
%                 connMeas(1:w,1:microx) = xi(1:w,1:microx).^2;                                
                CI(i,1) = (sum(sum(conn(1:w,1:microx)))/...
                    (sum(sum(connMeas(1:w,1:microx)))+1e-9));
                
%                 if CI(i,1)>thred
                    % bad connection                    
%                     dconnMeas(1:w,1:microx) = xi(1:w,1:microx);
                    dconnMeas(1:w,1:microx) = exp(xi(1:w,1:microx));
                    tmp = (dconn*sum(connMeas(:)) - sum(conn(:))*dconnMeas)/(sum(connMeas(:))+1e-9)^2;            
                    dCI(i,:) = tmp(:);
%                 else
%                     CI(i,1) = 0;
%                 end

            case 4 % left
                for ii = 1:w
                    for jj = 1:microy
                        % opposite
                        jj1 = jj;
                        ii1 = microx-ii+1;
                        % orthog, 45 degree left and right, 
                        % NOTE: don't forget border
                        jj2 = jj-ii*2; jj2(jj2<1) = 1;
                        jj3 = jj+ii*2; jj3(jj3>microy) = microy;
                        
                        tmp = xj(jj1,ii1);
%                         tmp = max(xj(jj1,ii1), max(xj(jj2,ii1), xj(jj3,ii1)));
                        conn(jj,ii) = exp(xi(jj,ii) .* (1-tmp));
                        dconn(jj,ii) = exp(xi(jj,ii)*(1-tmp))* (1-tmp);
                    end
                end
                connMeas(1:microy,1:w) = exp(xi(1:microy,1:w));
                CI(i,1) = sum(sum(conn(1:microy,1:w)))/...
                    (sum(sum(connMeas(1:microy,1:w)))+1e-9);
                
%                 if CI(i,1)>thred
                    % bad connection                    
                    dconnMeas(1:microy,1:w) = exp(xi(1:microy,1:w));
                    tmp = (dconn*sum(connMeas(:)) - sum(conn(:))*dconnMeas)/(sum(connMeas(:))+1e-9)^2;            
                    dCI(i,:) = tmp(:);
%                 else
%                     CI(i,1) = 0;
%                 end

            end            
        end
    end
end