How to reduce its execution time?

I have the following piece of code. It works but takes time. How can we reduce its time to a very minimum value?

u=[1 3 5 7 20 30 40 50];
b=u;
Noise=5;
[R,C]=size(b);
P=C/2;
M=2*C;

%%%%%%%%%%%%%%%%%%%%
% Swapping vector b 
%%%%%%%%%%%%%%%%%%%%
[~, ix] = sort(u); % u is my desired vector
[~, ix1(ix)] = sort(b); 
b = b(ix1);

%%%%%%%%%%%%%%%%%%%%%%%%%%
% calculate xo
%%%%%%%%%%%%%%%%%%%%%%%%%%
xo=zeros(1,M);
for k=1:M 
    for i=1:P 
        xo(1,k)=xo(1,k)+u(i)*exp(-1i*(k-1)*pi*cosd(u(P+i)));
    end 
end

xo=awgn(xo,Noise);% add Noise
%%%%%%%%%%%%%%%%%%%%%
% Calculate xe
%%%%%%%%%%%%%%%%%%%%%
xe=zeros(1,M);
for k=1:M
        for i=1:P
            xe(1,k)=xe(1,k)+b(i)*exp(-1i*(k-1)*pi*cosd(b(P+i)));
        end
end

%%%%%%%%%%%%%%%%%
% MSE
%%%%%%%%%%%%%%%%%
abc=0.0;
for m1=1:M
  abc=abc+(abs(xo(1,m1)-xe(1,m1))).^2;  
end
abc=abc/M;
e=abc

Answer 1

[Voss]

u=[1 3 5 7 20 30 40 50];
b=u;
Noise=5;
[R,C]=size(b);
P=C/2;
M=2*C;

%%%%%%%%%%%%%%%%%%%%
% Swapping vector b 
%%%%%%%%%%%%%%%%%%%%
[~, ix] = sort(u); % u is my desired vector
[~, ix1(ix)] = sort(b); 
b = b(ix1);

% not sure why you sort b and u, since you have b=u above. seems like you
% can just sort one of them. anyway, I don't know what the "swapping vector
% b" code is supposed to do, so I left it alone. see below for the rest of
% it:


%%%%%%%%%%%%%%%%%%%%%%%%%%
% calculate xo
%%%%%%%%%%%%%%%%%%%%%%%%%%
% xo=zeros(1,M);
% for k=1:M 
%     for i=1:P 
%         xo(1,k)=xo(1,k)+u(i)*exp(-1i*(k-1)*pi*cosd(u(P+i)));
%     end 
% end

xo = sum(u(1:P).*exp(-1i.*(0:M-1).'.*pi.*cosd(u(P+1:C))),2).';

xo=awgn(xo,Noise);% add Noise


%%%%%%%%%%%%%%%%%%%%%
% Calculate xe
%%%%%%%%%%%%%%%%%%%%%
% xe=zeros(1,M);
% for k=1:M
%         for i=1:P
%             xe(1,k)=xe(1,k)+b(i)*exp(-1i*(k-1)*pi*cosd(b(P+i)));
%         end
% end

xe = sum(b(1:P).*exp(-1i.*(0:M-1).'.*pi.*cosd(b(P+1:C))),2).';


%%%%%%%%%%%%%%%%%
% MSE
%%%%%%%%%%%%%%%%%
% abc=0.0;
% for m1=1:M
%   abc=abc+(abs(xo(1,m1)-xe(1,m1))).^2;  
% end
% abc=abc/M

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

[Sadiq Akbar]

Thanks a lot to both of you dear Karim and Voss.

Answer 2

[Karim]

Hi, I vectorized your code. Using tic/toc procedure the run time is about 0.04 seconds.

Hope it helps.

tic

% transpose u and b
% we want these to be column vectors for easy vectorization
u = [1 3 5 7 20 30 40 50]';
b = u;
Noise = 5;
[R,~] = size(b);
P = R/2;
M = 2*R;

I commented the lines below, since they don't do anything. You start with u=b and you end up with u=b. Hence these steps do nothing, you will need to provide details on what you mean with "swapping b"

% % Swapping vector b 
% [~, ix] = sort(u); % u is my desired vector
% [~, ix1(ix)] = sort(b); 
% b = b(ix1);

% calculate xo
u1 = u(    1:P );
u2 = u( P+(1:P));
k = 1:M;

xo = sum( u1.*exp( -1i.*pi*cosd(u2).*(k-1) ) , 1);

% add Noise
xo = awgn(xo,Noise);

% Calculate xe
b1 = b(    1:P );
b2 = b( P+(1:P));

xe = sum( b1.*exp( -1i.*pi*cosd(b2).*(k-1) ) , 1);

% MSE
e = mean( abs( xo(1,:) - xe(1,:) ) .^2 )

e = 0.2862

toc

Elapsed time is 0.040369 seconds.

[Voss]

Don't forget about this:

abc=abc/M;

[Karim]

yes indeed, thank you for pointing it out!