MATLAB: Please help me to rewrite the following codes

code generation

%% Calculation of phi and f
 
    a11 =  ai(1);
    a12 = ((ai(1)*ai(2))^0.5)*(1-bin_PR(1,2));
    a13 = ((ai(1)*ai(3))^0.5).*(1-bin_PR(1,3));
    
    a21 = a12;
    a22 = ai(2);
    a23 = ((ai(2)*ai(3))^0.5)*(1-bin_PR(2,3));
    
    a31 = a13;
    a32 = a23;
    a33 = ai(3);
    
    sum_xa(1) = x(1)*a11 + x(2)*a12 +x(3)*a13;
    sum_xa(2) = x(1)*a21 + x(2)*a22 +x(3)*a23;
    sum_xa(3) = x(1)*a31 + x(2)*a32 +x(3)*a33;
  
    sum_ya(1) = y(1)*a11 + y(2)*a12 +y(3)*a13;
    sum_ya(2) = y(1)*a21 + y(2)*a22 +y(3)*a23;
    sum_ya(3) = y(1)*a31 + y(2)*a32 +y(3)*a33;
 
    phi_L=exp((bi./b_L).*(ZLt-1)-log(ZLt-B_L)-(A_L./(B_L.*(-2*sqrt(2)))).*(log((ZLt+(1-sqrt(2)).*B_L)/(ZLt+(1+sqrt(2)).*B_L)))*((2*sum_xa/a_L)-(bi./b_L)));
    
 
    phi_G=exp((bi./b_G).*(ZGt-1)-log(ZGt-B_G)-(A_G./(B_G.*(-2*sqrt(2)))).*(log((ZGt+(1-sqrt(2)).*B_G)/(ZGt+(1+sqrt(2)).*B_G)))*((2*sum_ya/a_G)-(bi./b_G)));
  
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I want to write the above coding like this (below one):
for i=1:3
        for j=1:3
            el_L(i,j)=x(i).*x(j)*((ai(i).*ai(j)).^0.5).*(1-bin_PR(i,j));
            el_G(i,j)=y(i).*y(j)*((ai(i).*ai(j)).^0.5).*(1-bin_PR(i,j));
        end
    end
 
    a_L=sum(el_L(:));
    b_L=sum(x.*bi);

Best Answer

YOu need not to use a loop for your code. YOu can achieve it by simple matrix multiplication. Check the below code. 
a11 =  ai(1);
a12 = ((ai(1)*ai(2))^0.5)*(1-bin_PR(1,2));
a13 = ((ai(1)*ai(3))^0.5).*(1-bin_PR(1,3));
a21 = a12;
a22 = ai(2);
a23 = ((ai(2)*ai(3))^0.5)*(1-bin_PR(2,3));
a31 = a13;
a32 = a23;
a33 = ai(3);
A = [a11 a12 a13 ; a21 a22 a23;a31 a32 a33] ;
b1 = x ;   % this should be a 3X1 array

b2 = y ;   % this should be a 3X1 array
sum_xa = A*b1 ;
sum_ya = A*b2 ;
phi_L=exp((bi./b_L).*(ZLt-1)-log(ZLt-B_L)-(A_L./(B_L.*(-2*sqrt(2)))).*(log((ZLt+(1-sqrt(2)).*B_L)/(ZLt+(1+sqrt(2)).*B_L)))*((2*sum_xa/a_L)-(bi./b_L)));
phi_G=exp((bi./b_G).*(ZGt-1)-log(ZGt-B_G)-(A_G./(B_G.*(-2*sqrt(2)))).*(log((ZGt+(1-sqrt(2)).*B_G)/(ZGt+(1+sqrt(2)).*B_G)))*((2*sum_ya/a_G)-(bi./b_G)));
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