How to vectorize this piece of code and why doesn't e come out to be zero though it must come out to be zero because u and b are equal?

u=[30 50 75  -30 -50 -75];
b=u;

Noise=5;

M = 6;%Constant1
N = 6;%Constant2
d = 0.5;%Constant3
K = length(u)/2; %Constant4
alpha=ones(1,K);%[1 1 1 1 1];
a=zeros(M,K);%aTx
f=zeros(N,K);%fRx
c=zeros(M*N, length(u)-K);% Extended Matrix

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

%%%%%%%%%%%%%%%%%%%%
% Observed response
%%%%%%%%%%%%%%%%%%%
for i=1:K
    for h=1:M
        a(h,i)=exp(j*2*pi*(h-1)*d*sind(u(i))); %%%%% a
    end
    for p=1:N
        f(p,i)=exp(j*2*pi*(p-1)*d*sind(u(K+i))); %%%%% f
    end
end

for g= 1:K
c(:,g)=kron(a(:,g),f(:,g));% Extended vector 
end
yo=c*alpha'; % Observed Response (Noise Free)
yo=awgn(yo,Noise);% Uncomment for Noise consideration

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Estimated response
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
ae=zeros(M,K);
fe=zeros(N,K);
ce=zeros(M*N, length(u)-K);

for i=1:K
    for h=1:M
        ae(h,i)=exp(j*2*pi*(h-1)*d*sind(b(i))); %%%%% ae
    end
    for p=1:N
        fe(p,i)=exp(j*2*pi*(p-1)*d*sind(b(K+i))); %%%%% fe
    end
end

for g= 1:K
    ce(:,g)=kron(ae(:,g),fe(:,g));
end
ye=ce*alpha';% Estimated Response

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

Answer 1

[Bruno Luong]

Not tested but this

for i=1:K
    for h=1:M
        ae(h,i)=exp(j*2*pi*(h-1)*d*sind(b(i))); %%%%% ae
    end
    for p=1:N
        fe(p,i)=exp(j*2*pi*(p-1)*d*sind(b(K+i))); %%%%% fe
    end
end

can be replaced by

h=(1:M)';
p=(1:N)';
i=1:K;
br = b(:).';
ae=exp(j*2*pi*(h-1)*d.*sind(br(i)));
fe=exp(j*2*pi*(p-1)*d.*sind(br(K+i))); 

And

for g= 1:K
    ce(:,g)=kron(ae(:,g),fe(:,g));
end

By

ce = reshape(reshape(ae,K,1,[]).*fe,K,[]);

[Sadiq Akbar]

Thanks a lot dear Bruno Luong for your kind response. I inserted your vectorized code in the given code as below:

clear all
clc
global u
global Noise
% format long g
u=[30 50 75  -30 -50 -75];
b=u;
% Noise=5;
M = 6;%Constant1
N = 6;%Constant2
d = 0.5;%Constant3
K = length(u)/2; %Constant4
alpha=ones(1,K);%[1 1 1 1 1];
a=zeros(M,K);%aTx
f=zeros(N,K);%fRx
c=zeros(M*N, length(u)-K);% Extended Matrix
%%%%%%%%%%%%%%%%%%%%
% Swapping vector b 
%%%%%%%%%%%%%%%%%%%%
[~, ix] = sort(u); % u is my desired vector
[~, ix1(ix)] = sort(b);  
b = b(ix1);
%%%%%%%%%%%%%%%%%%%%
% Observed response
%%%%%%%%%%%%%%%%%%%
for i=1:K
    for h=1:M
        a(h,i)=exp(j*2*pi*(h-1)*d*sind(u(i))); %%%%% a
    end
    for p=1:N
        f(p,i)=exp(j*2*pi*(p-1)*d*sind(u(K+i))); %%%%% f
    end
end

for g= 1:K
c(:,g)=kron(a(:,g),f(:,g));% Extended vector 
end
yo=c*alpha'; % Observed Response (Noise Free)
% yo=awgn(yo,Noise);% Uncomment for Noise consideration
%%%%%%%%%%%%%%%%%%%%%%
% By Bruno Luong for Estimated Response
%%%%%%%%%%%%%%%%%%%%%%
h=(1:M)';
p=(1:N)';
i=1:K;
br = b(:).';
ae=exp(j*2*pi*(h-1)*d.*sind(br(i)));
fe=exp(j*2*pi*(p-1)*d.*sind(br(K+i))); 

ce = reshape(reshape(ae,K,1,[]).*fe,K,[]);
%%%%%%%5 End  Bruno Luong %%%%%%%%%%%%%%%%%%
ye=ce*alpha';% Estimated Response
%%%%%%%%%%%%%%%%%
% MSE
%%%%%%%%%%%%%%%%%
e2 = sum( (yo - ye).^2 );
e=abs(e2) % By Me 

But it gives error on this line:

ce = reshape(reshape(ae,K,1,[]).*fe,K,[]);

The error is: Arrays have incompatible sizes for this operation.

[Bruno Luong]

Ops try

ce = reshape(reshape(ae,1,[],K).*reshape(fe,[],1,K),[],K);

[Sadiq Akbar]

Thank you very uch dear Bruno Luong and Walter Roberson for your kind responses. But:

@Bruno Luong

Can't you convert the observed response part also in vectorized form i.e.,

%%%%%%%%%%%%%%%%%%%%
% Observed response
%%%%%%%%%%%%%%%%%%%
for i=1:K
    for h=1:M
        a(h,i)=exp(j*2*pi*(h-1)*d*sind(u(i))); %%%%% a
    end
    for p=1:N
        f(p,i)=exp(j*2*pi*(p-1)*d*sind(u(K+i))); %%%%% f
    end
end
for g= 1:K
c(:,g)=kron(a(:,g),f(:,g));% Extended vector 
end
yo=c*alpha'; % Observed Response (Noise Free)

can it be converted into vectorized form also? If yes, then how?

[Bruno Luong]

I just show you with almost the same code. Only variable names change. Don't you know to adapt the code with different variable names?

[Sadiq Akbar]

Thanks a lot for your kind response dear Bruno Luong. Ok I am trying.

[Sadiq Akbar]

@Bruno Luong thank you very much for your guidance and help. I did it.

[Bruno Luong]

You are welcome.

Answer 2

[Walter Roberson]

format long g

u=[30 50 75  -30 -50 -75];
b=u;

Noise=5;

M = 6;%Constant1
N = 6;%Constant2
d = 0.5;%Constant3
K = length(u)/2; %Constant4
alpha=ones(1,K);%[1 1 1 1 1];
a=zeros(M,K);%aTx
f=zeros(N,K);%fRx
c=zeros(M*N, length(u)-K);% Extended Matrix

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

%%%%%%%%%%%%%%%%%%%%
% Observed response
%%%%%%%%%%%%%%%%%%%
for i=1:K
    for h=1:M
        a(h,i)=exp(j*2*pi*(h-1)*d*sind(u(i))); %%%%% a
    end
    for p=1:N
        f(p,i)=exp(j*2*pi*(p-1)*d*sind(u(K+i))); %%%%% f
    end
end

for g= 1:K
c(:,g)=kron(a(:,g),f(:,g));% Extended vector 
end
yo=c*alpha'; % Observed Response (Noise Free)
yo=awgn(yo,Noise);% Uncomment for Noise consideration

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Estimated response
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
ae=zeros(M,K);
fe=zeros(N,K);
ce=zeros(M*N, length(u)-K);

for i=1:K
    for h=1:M
        ae(h,i)=exp(j*2*pi*(h-1)*d*sind(b(i))); %%%%% ae
    end
    for p=1:N
        fe(p,i)=exp(j*2*pi*(p-1)*d*sind(b(K+i))); %%%%% fe
    end
end

for g= 1:K
    ce(:,g)=kron(ae(:,g),fe(:,g));
end
ye=ce*alpha';% Estimated Response

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

e2 = sum( abs(yo - ye).^2 )

e2 = 
          11.7479934461356

yo - ye

ans = 
          0.334761462628025 -     0.251604299511244i
          0.178519020660132 -      0.11790756943532i
          0.284315581572755 -     0.408074305354306i
          0.436075962283236 +    0.0206136540004817i
          0.148113323815692 -       0.1129397164173i
          0.148601229842305 -     0.684227855074489i
         -0.045229189659987 +      1.06816976506834i
         0.0449597505407739 +    0.0474860403089703i
         -0.117067171711324 -     0.335272836828924i
         -0.170838058879666 -     0.485416275775231i
          -1.01036972409615 +    0.0987920670194429i
           0.17724058327333 +     0.358430065054272i
         -0.296057798011593 +     0.268159218550655i
          0.219874574050923 -     0.303912184656327i
         -0.196397184200888 +     0.579342311435272i
          0.362391793015109 -   0.00637536507210101i
         -0.198930152531317 +      0.17081587160563i
        0.00126195142908353 +     0.196629724720236i
          0.451323400274059 -      0.19338404893942i
         0.0163549272291462 +     0.211263099020562i
          0.153134628152902 -     0.360072343716162i
          0.125618160624793 -     0.447663575852295i
           0.18682261208064 -     0.440681989383234i
           0.56658020901609 -    0.0413352507512756i
          0.216864956628124 +     0.402128673330828i
         -0.650894787871801 +     0.195828199364969i
          0.526482743315456 +     0.161261991699198i
        -0.0222655470394779 -     0.303132876336713i
          0.249479128033312 -     0.125089115081018i
           0.23011373904232 +     0.168827365022589i
           0.37643644331261 +   0.00726229738016904i
         -0.933652368281796 -     0.958904637492813i
         -0.552407757174997 -     0.128690424103339i
         0.0864282827509827 +     0.565038735206412i
          0.617124996371567 -      1.11650348178558i
          0.390001758508875 +     0.358139661751764i

[Sadiq Akbar]

Thanks a lot for your kind response dear Walter Roberson. But still there are the following thee issues:

1-You didn't vectorize it. Still it contains for-loops.

2-Still the error is not zero.

3-The error comes out to be a complex number now though we don't want it to be a complex number, rather its magnitude. However we want it to be zero.

Regards,

[Walter Roberson]

I thought I had canceled that post...

I do not see any reason why the values should be the same. awgn() applies randomness, but your ye has not had any randomness applied to it (certainly not exactly the same randomness). There is no reason for them to be the same.

[Sadiq Akbar]

Thanks dear Walter Roberson for your kind response. Yes, you are right that awgn() has been added to yo and not to ye. So that's the reason. But what about vectorization of the code? Can you replace all the for loops by vectorization?

Regards,