Speed up nested for loop

Hi,

I have to speed up the following code.

N is an integer of the order 10^4, l is of the order of (N)^(1/4), c and v are column complex vectors with N elements.

B = 0;
for m = 1:l
    for n = m+1 : N
        B = B + 2*real(c(n)*conj(v(n))* conj(c(n-m))*v(n-m)); 
    end
end

Thank you for your help.

Francesco

[Jan]

Please provide some inputs values, maybe produced by rand(). It is hard to improve the code without running it. And inveting default inputs might be misleading, if we oversee an important detail.

Answer 1

[Jan]

Maybe:

% [UNTESTED CODE] Please provide inputs for testing
B = 0;
for m = 1:l
   B = B + sum(2 * real(c(m+1 : N) .* conj(v(m+1 : N)) .* ...
               conj(c(1 : N-m)) .* v(1 : N-m)));
end

Does this work? Then:

B = 0;
c_cv = c .* conj(v);
cc_v = conj(c_cv);
for m = 1:l
   B = B + 2 * sum(real(c_cv(m+1 : N) .* cc_v(1 : N-m)));
end

[Francesco Lisi]

Thank you Jan for your fast reply!

The code you provided is faster indeed. Here is the updated script

y=c.*conj(v);
yc=conj(y);

B_est = sum(abs(y).^2);
for m = 1:l
    B_est = B_est + 2*sum(real(y(m+1:N) .* yc(1:N-m)));
end

Is there a way to speed up this one?

As input you can use complex arrays generated as randn(N,1)+1i*randn(N,1). I use this function in a Monte Carlo simulation with 10^3 iteration and this function is the slowest one.

Thank you again for your help.

Francesco

[Jan]

A further improvement:

c_cv = c .* conj(v);
cc_v = conj(c_cv);
B    = 0;   % sum(abs(y).^2) did not appear in the original question
for m = 1:l
   B = B + real(c_cv(m+1 : N).' * cc_v(1 : N-m));
end
B = B * 2;

Letting the sum() be done by the dot product saves some time, because the optimized BLAS library is used.