How to aviod the following for loops

Hi, I want to perform the following calculations on Matlab

N=1000;

M=200;

K=256;

U=rand(N,M)+i*rand(N,M); % where i is complex

V=rand(N,M)+i*rand(N,M); % where i is complex

B=rand(N,K);

C=zeros(1,K);

D=zeros(1,K);

const_c=2;

const_d=0.5;

for m=1:M

ux=zeros(1,K);

vx=zeros(1,K);

for n=1:N

ux=ux+U(n,m)*B(n,:);

vx=vx+V(n,m)*B(n,:);

end

C=C+const_c*abs(vx).^2;

D=D+const_d*ux.*conj(vx);

end

There are two loops, for large M and N, the loops is very slowly. So How can I aviod the loops without using parallel computing? I think it may be realized by using 'reshape' function, but I do not know how to use it for this code.

Thanks very much!

Answer 1

[Voss]

N=1000;
M=200;
K=256;
U=rand(N,M)+1i*rand(N,M);
V=rand(N,M)+1i*rand(N,M);
B=rand(N,K);
const_c=2;
const_d=0.5;

% no loops
tic
ux = U.'*B;
vx = V.'*B;
C_new = const_c*sum(abs(vx).^2,1);
D_new = const_d*sum(ux.*conj(vx),1);
toc

Elapsed time is 0.013907 seconds.

% with loops
tic
C=zeros(1,K);
D=zeros(1,K);
for m=1:M
    ux=zeros(1,K);
    vx=zeros(1,K);
    for n=1:N
        ux=ux+U(n,m)*B(n,:);
        vx=vx+V(n,m)*B(n,:);
    end
    C=C+const_c*abs(vx).^2;
    D=D+const_d*ux.*conj(vx);
end
toc

Elapsed time is 1.765365 seconds.

% results are not exactly the same, but the differences are ~1e-8 out of ~1e7:
[max(abs(C-C_new)) max(abs(D-D_new))]

ans = 1×2

1.0e-07 * 0.5960 0.1677

% which is about as accurate as you can get for floating-point numbers around 1e7:
[max(eps(C)) max(eps(D))]

ans = 1×2

1.0e-08 * 0.7451 0.1863

% plots to inspect the differences:
subplot(3,1,1)
plot(C,'--b','LineWidth',2)
hold on
plot(C_new,'-c')
title('C,C\_new')
subplot(3,1,2)
plot(real(D),'--r','LineWidth',2)
hold on
plot(real(D_new),'-m')
title('real(D,D\_new)')
subplot(3,1,3)
plot(imag(D),'--r','LineWidth',2)
hold on
plot(imag(D_new),'-m')
title('imag(D,D\_new)')

[Qiu Xu]

Thanks very much for your helps