How to vectorize the given code?

u=[1 2 40 70];b=u;
[~,C]=size(b);
P=C/2;
M=2*C;
f=1e9;
c=3e8;
l=c/f;
K=(2*pi)/l;
M=10;
d_circular=l/2;
a=(M*d_circular)/(2*pi);

xo=zeros(1,M);
xe=zeros(1,M);
for k=1:M
    for i=1:P
        xo(1,k)=xo(1,k)+exp(-1i*K*a*sind(u(i))*cosd(u(P+i)-(2*pi*(k-1)/M)));
        xe(1,k)=xe(1,k)+exp(-1i*K*a*sind(b(i))*cosd(b(P+i)-(2*pi*(k-1)/M)));
     end 
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% (MSE)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
e = mean(abs(xo-xe).^2);

e = 0

Answer 1

[Torsten]

u = [1, 2, 30, 50];b=u; 
dim = length(u);
N=dim;
s_u = u(1:dim/2)';
angles_u = u((dim/2)+1:end)';
s_b = b(1:dim/2)';
angles_b = b(1+dim/2:end)';
lambda = 1;
d = lambda/2;
% Steering matrix
Ao = zeros(N, length(angles_u));
Ae = zeros(N, length(angles_b));
for i = 1:N
    for j = 1:length(angles_u)
        Ao(i, j) = exp(1j * 2 * pi * d * (i-1) / lambda * sind(angles_u(j)));
        Ae(i, j) = exp(1j * 2 * pi * d * (i-1) / lambda * sind(angles_b(j)));
    end
end
xo=Ao*s_u

xo = 
   3.0000 + 0.0000i
  -1.4837 + 2.3412i
  -0.7987 - 1.9898i
   1.1850 + 0.6111i

xe=Ae*s_b

xe = 
   3.0000 + 0.0000i
  -1.4837 + 2.3412i
  -0.7987 - 1.9898i
   1.1850 + 0.6111i

% MSE
e=mean(abs(xo-xe).^2)

e = 0

i = 1:N;
j = 1:length(angles_u);
Ao = (exp(1j * 2 * pi * d * (i-1) / lambda .* sind(angles_u(j)))).';
Ae = (exp(1j * 2 * pi * d * (i-1) / lambda .* sind(angles_b(j)))).';
xo=Ao*s_u

xo = 
   3.0000 + 0.0000i
  -1.4837 + 2.3412i
  -0.7987 - 1.9898i
   1.1850 + 0.6111i

xe=Ae*s_b

xe = 
   3.0000 + 0.0000i
  -1.4837 + 2.3412i
  -0.7987 - 1.9898i
   1.1850 + 0.6111i

% MSE
e=mean(abs(xo-xe).^2)

e = 0

[Sadiq Akbar]

Thanks a lot dear Torsten for your help.

Answer 2

[Sulaymon Eshkabilov]

One quick comment is that xe and xo have the same values and therefore, the error is "0".

u=[1 2 40 70];b=u;
[~,C]=size(b);
P=C/2;
M=2*C;
f=1e9;
c=3e8;
l=c/f;
K=(2*pi)/l;
M=10;
d_circular=l/2;
a=(M*d_circular)/(2*pi);

xo=zeros(1,M);
xe=zeros(1,M);
for k=1:M
    for i=1:P
        xo(1,k)=xo(1,k)+exp(-1i*K*a*sind(u(i))*cosd(u(P+i)-(2*pi*(k-1)/M)));
        xe(1,k)=xe(1,k)+exp(-1i*K*a*sind(b(i))*cosd(b(P+i)-(2*pi*(k-1)/M)));
     end 
end
plot(1:numel(xo),real(xo), 'bo-','LineWidth', 2.5, 'DisplayName', 'Re(x_o)')
hold on
plot(1:numel(xe),real(xe), 'r-','LineWidth', 1.5, 'DisplayName', 'Re(x_e)')
legend('show')

figure
plot(1:numel(xo),imag(xo), 'bo-','LineWidth', 2.5, 'DisplayName', 'Im(x_o)')
hold on
plot(1:numel(xe),imag(xe), 'r-','LineWidth', 1.5, 'DisplayName', 'Im(x_e)')
legend('show')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% (MSE)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
e = mean(abs(xo-xe).^2)

e = 0

[Sadiq Akbar]

@Sulaymon Eshkabilov

Thanks a lot for your kind response. But you haven't vectorized my code. You have dome something else. Yes, the value of b is equal to u.

[Torsten]

@Sadiq Akbar

Why do you ask the same questions again and again ?

https://uk.mathworks.com/matlabcentral/answers/2061487-how-to-vectorize-the-following-piece-of-code-by-removing-the-two-for-loops?s_tid=srchtitle

[Sadiq Akbar]

Thanks a lot dear @Torsten for your prompt response. You are right. I have done it but that is not correct and gives me error though I have tried many. I reproduce that here. You can run it, you will see the errors:

u = [1, 2, 30, 50];b=u; 
dim = length(u);
N=dim;

s_u = u(1:dim/2)';
angles_u = u((dim/2)+1:end)';
s_b = b(1:dim/2)';
angles_b = b(1+dim/2:end)';

lambda = 1;

% Distance between array elements (assumed to be 1 for simplicity)
d = lambda/2;%1;

% Steering matrix
Ao = zeros(N, length(angles_u));
Ae = zeros(N, length(angles_b));
%for i = 1:N
    %for j = 1:length(angles_u)
    i=(1:N).';
    j=(1:length(angles_u)).';
        Ao = sum(exp(1j * 2 * pi * d * (i-1) / lambda .* sind(angles_u(j))),2);
        Ae = sum(exp(1j * 2 * pi * d * (i-1) / lambda * sind(angles_b(j))),2);
xo=Ao*s_u;
xe=Ae*s_b;

e=mean(abs(xo-xe).^2)

[Torsten]

Please include the code you want to vectorize (the one with the working for-loops).

I doubt the result for Ao and Ae will be of dimension N x length(angles_u).

[Sadiq Akbar]

Thanks a lot dear @Torsten for your prompt response. The whole code is as below:

u = [1, 2, 30, 50];b=u; 
dim = length(u);
N=dim;
s_u = u(1:dim/2)';
angles_u = u((dim/2)+1:end)';
s_b = b(1:dim/2)';
angles_b = b(1+dim/2:end)';
lambda = 1;
d = lambda/2;

% Steering matrix
Ao = zeros(N, length(angles_u));
Ae = zeros(N, length(angles_b));
for i = 1:N
    for j = 1:length(angles_u)
        Ao(i, j) = exp(1j * 2 * pi * d * (i-1) / lambda * sind(angles_u(j)));
        Ae(i, j) = exp(1j * 2 * pi * d * (i-1) / lambda * sind(angles_b(j)));
    end
end
xo=Ao*s_u;
xe=Ae*s_b;

% MSE
e=mean(abs(xo-xe).^2)