Code optimization by way of selective computations

I have the following code:

clc; clearvars;

Ts = 1e-1; t = 0:Ts:1-Ts

flag = mod(1:length(t),2)

s_t = exp(1i*2*pi*t)

I am looking to only execute the computation only when the corresponding value for is logical 1. I wish to do this without iterating as the final vector to process is long and is about 97% zero values in the result.

Answer 1

[Jiri Hajek]

Hi, you need to convert your flags to logical array, initialize the results with zeros and then apply the function to the flagged positions like this:

flag = logical(mod(1:length(t),2));
s_t = zeros(size(t));
s_t(flag) = exp(1i*2*pi*t(flag));

[Howard Wilton]

This definitely works, but the computation time ends up being longer... I thought that if I avoid the computaitons I could reduce overall processing time.

clc; clearvars;

Ts = 1e-7; t = 0:Ts:1-Ts;

tic
s_t = exp(1i*2*pi*t);
toc

Elapsed time is 0.174337 seconds.

tic
flag = logical(mod(1:length(t),2));
s_t = zeros(size(t));
s_t(flag) = exp(1i*2*pi*t(flag));
toc

Elapsed time is 0.732422 seconds.

[Jiri Hajek]

Yes, the logical indexing probably does add to the execution time, as basic functions are quite optimized... But you mentioned that your non-zeros should be only about 3% of the array size, whereas in this test you have 50% nonzeros... So the test dis not really fair, I think.

Perhaps you can also look at sparse arrays, but truth is, their usefullness is also limited by the fraction of zero elements.

[Howard Wilton]

Yeah. That is a good point. I did it again with just 1% of the flags set, but the overall processing was comparable to the unconditioned version. I shall have a look at sparse arrays. Thanks.

Answer 2

[Torsten]

Ts = 1e-7; t = 0:Ts:1-Ts;
tic
s_t = exp(1i*2*pi*t(1:2:end));
toc

Elapsed time is 0.111464 seconds.

or if your condition is more complicated:

tic
s_t = exp(1i*2*pi*t(mod(1:length(t),2)==1));
toc

Elapsed time is 0.431624 seconds.