How to vectorize this piece of code by replacing all the for-loops?

I want to vectorize the following piece of code so that it becomes fast. But M and N can be only coprime numbers and N < M always. I tried but failed badly.

th=pi/180;
u=[40*th 50*th 60*th 70*th];
b=u;
K=length(u);
% Note that  N<M coprime No
N=3; M=4;   
NE=(N+M-1); %   Total 
x=0; y=0; z=1;    %   Initialization
Sto=zeros(NE,K);    % matrix initialization
    for ii=1:NE           
                if (x==0);
                 distance=0;
                 x=x+1;
                    elseif (y==0);
                        distance=z*pi*N;
                         y=y+1;
                        else
                         distance=z*pi*M;
                          y=0;
                         z=z+1;
                end
                 for jj=1:K
    Sto(ii,jj)=exp(-1i*distance*cos(u(jj)));    % matrix equation 
            
                end 
    end
y_act_sum=sum(Sto,2);
y_act_abs=abs(y_act_sum);
xx=(y_act_abs);

x=0;y=0;z=1;
Ste=zeros(NE,K);
    for kk=1:NE           
                if (x==0);
                 distance=0;
                 x=x+1;
                    elseif (y==0);
                        distance=z*pi*N;
                         y=y+1;
                        else
                         distance=z*pi*M;
                          y=0;
                         z=z+1;
                end
                 for i=1:K
    Ste(kk,i)=exp(-1i*distance*cos(b(i)));
    
                 end 
    end
 %%%%%%%%%%%%%%%%%%%%%%%%
 %   MSE
 %%%%%%%%%%%%%%%%%%%%%%%%
y_est_sum=sum(Ste,2);
y_est_abs=abs(y_est_sum);
yy=(y_est_abs);
correlation=corr(xx,yy);
mse1=zeros(1,NE);
for pp=1:NE
mse1=(xx(pp)-yy(pp));
end
mse2=sum(mse1,2);
mse3=mse2.^2;
mse=mse3/NE;
mse_corr=mse+norm(correlation-1);

Answer 1

[Voss]

Here is a vectorized code that doesn't have to be modified if you change M or N:

th=pi/180;
u=[40*th 50*th 60*th 70*th];
b=u;
K=length(u);
% Note that  N<M coprime No
N=3;
M=4;
NE = N+M-1; %   Total 

distance = [0; reshape((1:floor(NE/2))*pi.*[N; M],[],1)];
distance(NE+1:end) = [];

Sto = exp(-1i*distance.*cos(u));
Ste = exp(-1i*distance.*cos(b));

xx = abs(sum(Sto,2));
yy = abs(sum(Ste,2));

Note that you have b=u above, so that Sto == Ste, xx == yy, correlation is 1, and mse is 0. I suspect that your mse calculation is not what you really want (see comments in the code below, and maybe test with a case where b ~= u, so that mse is not zero, e.g., b = u+1, to see the difference between the two mse calculations).

%%%%%%%%%%%%%%%%%%%%%%%%
%   MSE
%%%%%%%%%%%%%%%%%%%%%%%%
correlation = corr(xx,yy)

correlation = 1

% mse1 = zeros(1,NE);
% for pp=1:NE
%     mse1=(xx(pp)-yy(pp)); % I assume you meant "mse1(pp)" here instead of "mse1"
% end

mse = sum(xx-yy,1).^2/NE % this is equivalent to what you had (with the mse1(pp) correction in the loop above) ...

mse = 0

mse = mean((xx-yy).^2,1) % ... but this is MSE

mse = 0

mse_corr = mse + correlation-1 % note that correlation is a real scalar, so norm(correlation) == correlation (i.e., norm() does nothing)

mse_corr = 0

Answer 2

[Sulaymon Eshkabilov]

Here is the vectorized code without any loops:

th=pi/180;
u=[40*th 50*th 60*th 70*th];
b=u;
K=length(u);
% Note that  N<M coprime No
N=3; M=4;
NE=(N+M-1); %   Total
distance = [0*pi*N; 1*pi*N; 1*pi*M; 2*pi*N; 2*pi*M; 3*pi*N];
STO_1 = exp(-1i*distance(:)*cos(u));
y_act_sum=sum(Sto,2);
y_act_abs=abs(y_act_sum);
xx=(y_act_abs);
STE_1 = exp(-1i*distance(:)*cos(b));

%%%%%%%%%%%%%%%%%%%%%%%%
%   MSE
%%%%%%%%%%%%%%%%%%%%%%%%%
y_est_sum=sum(Ste,2);
y_est_abs=abs(y_est_sum);
yy=(y_est_abs);
correlation=corr(xx,yy);
mse1=(xx-yy);
mse2=sum(mse1,2);
mse3=mse2.^2;
mse=mse3/NE;
mse_corr=mse+norm(correlation-1);