Comparison for/vectorization- some general advice

Hi, i'm trying to vectorize my code. But i have recently found this:

clear all;
tic
k=zeros([1,10000]);
a=1:10000;
k(a)=rand;
toc

tic
g=zeros([1,10000]);
for i=1:10000;
    g(i)=rand;
    end
toc

Elapsed time is 0.030372 seconds.
Elapsed time is 0.013857 seconds.

(Obviously) Every time tic/toc time changes a bit but there is always this kind of gap. In Matlab a vectorized code is faster than a loop code so i dont understand this result.

On the contrary i have also found:

clear all;
tic
k=zeros([1,1000000]);
a=1:1000000;
k(a)=rand;
toc

tic
g=zeros([1,1000000]);
for i=1:1000000;
    g(i)=rand;
    end
toc

Elapsed time is 0.034189 seconds.
Elapsed time is 0.045542 seconds.

Maybe the for loop with preallocation is not so bad but the difference between them rises when the length of the array grows. Tell me what u think and please give me some advice for a good vectorization

Answer 1

[Ramnarayan Krishnamurthy]

The result you observe could be because preallocation the second time appears to be faster than the first. So, timing each allocation separately I found a slightly different result (over 1000 runs)

clear all

tic
k=zeros([1,10000]);
toc;

tic;
a=1:10000;
k(a)=rand;
toc

tic
g=zeros([1,10000]);
toc;

tic;
for i=1:10000;
    g(i)=rand;
    end
toc

Elapsed time is 0.000250 seconds. % pre allocation 1

Elapsed time is 0.000238 seconds.

Elapsed time is 0.000035 seconds. % pre-allocation 2

Elapsed time is 0.000730 seconds.

Here, Vectorization appears to be faster, though, the difference is definitely pronounced when the array length is larger (10000000)

I would suggest going through the following answers and questions on vectorization:

https://www.mathworks.com/matlabcentral/answers/160161-why-vectorized-calculations-are-faster-than-for-loops

https://www.mathworks.com/matlabcentral/answers/8461-double-summation-with-vectorized-loops

https://www.mathworks.com/matlabcentral/answers/12504-is-vectorized-code-always-faster-than-loops-any-exceptions

[Damiano Capocci]

Thank you,I'll meditate about it.Just one thing,could you see this other ask of mine

https://it.mathworks.com/matlabcentral/answers/374557-arrayfun-for-a-particukar-nested-loop-in-gpu-computing?s_tid=prof_contriblnk

Thank you