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?

Question

Sadiq Akbar 2022-12-10

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1875207-how-to-vectorize-this-piece-of-code-and-why-doesn-t-e-come-out-to-be-zero-though-it-must-come-out-t

评论： Bruno Luong 2022-12-11

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; 

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Answer 1

Bruno Luong 2022-12-10

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1875207-how-to-vectorize-this-piece-of-code-and-why-doesn-t-e-come-out-to-be-zero-though-it-must-come-out-t#answer_1124772

在 MATLAB Online 中打开

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,[]);

7 个评论
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Sadiq Akbar 2022-12-10

编辑：Sadiq Akbar 2022-12-10

在 MATLAB Online 中打开

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.

Sadiq Akbar 2022-12-11

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

Bruno Luong 2022-12-11

You are welcome.

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Answer 2

Walter Roberson 2022-12-10

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1875207-how-to-vectorize-this-piece-of-code-and-why-doesn-t-e-come-out-to-be-zero-though-it-must-come-out-t#answer_1124677

编辑：Walter Roberson 2022-12-10

在 MATLAB Online 中打开

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

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Walter Roberson 2022-12-10

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 2022-12-10

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,

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