How to remove all for-loops with vectorization?

I have the following piece of code. I have posted similar codes earlier also and therefore 1st I tried myself to vectorize it but coudn't succeed. How can we replace all for-loops by making it vectorized code?

u=[35 75 -35 -75 0.3 0.5]; 
b=u;
K=length(u)/3;% Constant1
u1=u(1:2*K);
alpha=u(2*K+1:end);
M = 10; % Consatn2
N = 6;  % Consatn3

s1=zeros(M,K);
s2=zeros(N,K);
C=zeros(M*N, length(u1)-K);

%%%%%%%%%%%%%%%%%%%
% Xo Calculation
%%%%%%%%%%%%%%%%%%%

for i=1:K
    for h=1:M
      s1(h,i)=exp(j*2*pi*(h-1)*0.5*sind(u1(i)));
    end
    for p=1:N
      s2(p,i)=exp(j*2*pi*(p-1)*0.5*sind(u1(K+i)));
    end
end

for g= 1:K
C(:,g)=kron(s1(:,g),s2(:,g));
end
Xo=C*alpha';

%%%%%%%%%%%%%%%%%%%
% Xe Calculation
%%%%%%%%%%%%%%%%%%%
bu=b(1:2*K); alphab=b(2*K+1:end);
s1_e=zeros(M,K);
s2_e=zeros(N,K);
C_e=zeros(M*N, length(u1)-K);

for i=1:K
    for h=1:M
      s1_e(h,i)=exp(j*2*pi*(h-1)*0.5*sind(bu(i)));
    end
    for p=1:N
      s2_e(p,i)=exp(j*2*pi*(p-1)*0.5*sind(bu(K+i))); 
    end
end

for g= 1:K
C_e(:,g)=kron(s1_e(:,g),s2_e(:,g));
end
Xe=C_e*alphab';


%%%%%%%%%%%%%%%%%%
% MSE
%%%%%%%%%%%%%%%%%%
e=0.0;
for s=1:M*N
   e=e+(abs(Xo(s,1)-Xe(s,1))).^2;
end
e=e/M*N  

Answer 1

[Askic V]

This code should give you a pretty good idea how to do this:

clear
clc

u=[35 75 -35 -75 0.3 0.5]; 
b=u;
K=length(u)/3;% Constant1
u1=u(1:2*K);
%alpha=u(2*K+1:end);
M = 10; % Consatn2
N = 6;  % Consatn3
s1=zeros(M,K);
s2=zeros(N,K);
C=zeros(M*N, length(u1)-K);
%%%%%%%%%%%%%%%%%%%
% Xo Calculation
%%%%%%%%%%%%%%%%%%%
for i=1:K
    for h=1:M
      s1(h,i)=exp(j*2*pi*(h-1)*0.5*sind(u1(i)));
    end
    for p=1:N
      s2(p,i)=exp(j*2*pi*(p-1)*0.5*sind(u1(K+i)));
    end
end
% Vectorization approach
i = 1:K;
s1_n=zeros(M,K);
s2_n=zeros(N,K);
h = 1:M;
s1_n(h,i)=exp(j*2*pi*(h-1).'*0.5*sind(u1(i)));
p = 1:N;
s2_n(p,i)=exp(j*2*pi*(p-1).'*0.5*sind(u1(K+i)));

% check if there is a difference
norm(s1-s1_n)

ans = 0

norm(s2-s2_n)

ans = 0

[Sadiq Akbar]

Thank you very much dear Askic V for your kind response. I have some obervations:

1-1st you have not considered the last two values of u=[35 75 -35 -75 0.3 0.5]; but these values are must. Also you have commented alpha and have not included it in calculation but it is must.

2-You have not calculated C(:,g)=kron(s1(:,g),s2(:,g)); which is also must.

3-Calculation of both Xo and Xe are must, but you have not calculated them.

4-I don't want just error but I want mean sqaure error which you have not calculated.

[Askic V]

Helo Sadiq. The code snippet was just to show you how it is done. I have commented alpha because I did not use it in the code.

I'm pretty sure you won't have any problems completing the rest by yourself.

[Sadiq Akbar]

Thank you very much dear Askic V for your kind response. Yes, I do agree that you have not used the last two values of u and alpha but as I requested, these are must in calculation. Please, do include these two values also, after that I will try to convert the rest of the code myself in sha Allah.

[Sadiq Akbar]

Sorry one thing more. Please also calculate MSE instead of just difference. Regards,

[Sadiq Akbar]

I included the last two values and alpha and tried like this:

clear
clc

u=[35 75 -35 -75 0.3 0.5]; 
b=u;
K=length(u)/3;% Constant1
u1=u(1:2*K); b1=b(1:2*K);
alpha=u(2*K+1:end);alphab=b(2*K+1:end);
M = 10; % Consatn2
N = 6;  % Consatn3
s1=zeros(M,K);
s2=zeros(N,K);
C=zeros(M*N, length(u1)-K);
%%%%%%%%%%%%%%%%%%%
% Xo Calculation
%%%%%%%%%%%%%%%%%%%
i = 1:K;
s1=zeros(M,K);
s2=zeros(N,K);
C=zeros(M*N, length(u1)-K);% By Me
h = 1:M;
s1(h,i)=exp(j*2*pi*(h-1).'*0.5*sind(u1(i)));
p = 1:N;
s2(p,i)=exp(j*2*pi*(p-1).'*0.5*sind(u1(K+i)));
for g= 1:K
C(:,g)=kron(s1(:,g),s2(:,g));
end
Xo=C*alpha';


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Xe Calculation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
i = 1:K;
s1_n=zeros(M,K);
s2_n=zeros(N,K);
h = 1:M;
s1_n(h,i)=exp(j*2*pi*(h-1).'*0.5*sind(u1(i)));
p = 1:N;
s2_n(p,i)=exp(j*2*pi*(p-1).'*0.5*sind(u1(K+i)));
%%%%%%%%%%%%%%%5555
% Below is mine
%%%%%%%%%%%%%%%%%%%
for g= 1:K
C_e(:,g)=kron(s1_n(:,g),s2_n(:,g));
end
Xe=C_e*alphab';

%%%%%%%%%%%%%%%%%%
% MSE
%%%%%%%%%%%%%%%%%%
e=norm(Xo-Xe).^2/(M*N);

But I cannot replace the sinlge for-loop in each of Xo and Xe sections. Further, I don't know whether it is corret or not?

[Askic V]

Hello Sadiq,

I have used _n (n as new) to get results using vectorization approach, so I can compare with original arrays and determine if there is a difference.

Regarding the last for loop, do you want to eliminate for loop or you need to make this as efficient as it can be?

I can provide the solution without for loop but it wouldn't be much efficient (maybe even worse than for loop). I hope someone more knowledgeable can jump in and help.

clear
clc
a = rand(3, 2);
b = rand(4, 2);

for k = 1:2
    C(:,k) = kron(a(:,k), b(:,k));
end

k = 1:2;
D = kron(a(:,k),b(:,k));
D(:,2:end-1)=[];

C-D

ans = 12×2

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

[Sadiq Akbar]

Thank you very much dear Askic V for your kind response. This code works only for 3x2 and 4x2 matrices a and b. If we want to increase their order to 3x4 and 4x4, then it fails to work.

[Askic V]

Then a little adjustment is needed:

clear
clc

N = 4;
a = rand(3, N);
b = rand(4, N);

for k = 1:N
    C(:,k) = kron(a(:,k), b(:,k));
end

k = 1:N;
D = kron(a(:,k),b(:,k));
col_ind = mod(0:size(D,2)-1, 1+N) < 1;
D(:, ~col_ind) = [];

C-D

ans = 12×4

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

[Sadiq Akbar]

Thank you very much dear Askic V for your kind response. Ok I am going to accept your answer but fore that let me confirm from you 1st. Have I vectorized the code correctly like you which I have shared above i.e.:

clear
clc

u=[35 75 -35 -75 0.3 0.5]; 
b=u;
K=length(u)/3;% Constant1
u1=u(1:2*K); b1=b(1:2*K);
alpha=u(2*K+1:end);alphab=b(2*K+1:end);
M = 10; % Consatn2
N = 6;  % Consatn3
s1=zeros(M,K);
s2=zeros(N,K);
C=zeros(M*N, length(u1)-K);
%%%%%%%%%%%%%%%%%%%
% Xo Calculation
%%%%%%%%%%%%%%%%%%%
i = 1:K;
s1=zeros(M,K);
s2=zeros(N,K);
C=zeros(M*N, length(u1)-K);% By Me
h = 1:M;
s1(h,i)=exp(j*2*pi*(h-1).'*0.5*sind(u1(i)));
p = 1:N;
s2(p,i)=exp(j*2*pi*(p-1).'*0.5*sind(u1(K+i)));
for g= 1:K
C(:,g)=kron(s1(:,g),s2(:,g));
end
Xo=C*alpha';


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Xe Calculation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
i = 1:K;
s1_n=zeros(M,K);
s2_n=zeros(N,K);
h = 1:M;
s1_n(h,i)=exp(j*2*pi*(h-1).'*0.5*sind(u1(i)));
p = 1:N;
s2_n(p,i)=exp(j*2*pi*(p-1).'*0.5*sind(u1(K+i)));

for g= 1:K
C_e(:,g)=kron(s1_n(:,g),s2_n(:,g));
end
Xe=C_e*alphab';

%%%%%%%%%%%%%%%%%%
% MSE
%%%%%%%%%%%%%%%%%%
e=norm(Xo-Xe).^2/(M*N);

[Askic V]

Well, two for loops are correctly replaced with vectorization. However it seems that you have a lot of unnecessary (redundant) code.

You repeat calculations for s1 and s2 just to calculate Xe, signals b and u are the same, alpha and alphab have the same values. Therefore Xe and Xo have the same values.

Once gain, this is correct, change the code with for loops:

for i=1:K
    for h=1:M
      s1_e(h,i)=exp(j*2*pi*(h-1)*0.5*sind(bu(i)));
    end
    for p=1:N
      s2_e(p,i)=exp(j*2*pi*(p-1)*0.5*sind(bu(K+i))); 
    end
end

to vectorized version:

i = 1:K;
h = 1:M;
s1(h,i)=exp(j*2*pi*(h-1).'*0.5*sind(u1(i)));
p = 1:N;
s2(p,i)=exp(j*2*pi*(p-1).'*0.5*sind(u1(K+i)));

[Sadiq Akbar]

Thank you very much dear Askic V for your kind response.