How and when does MatLab support symatrical vector operations?

Hello,

my question is following?

I want to do a vector operation and I want to be sure that MatLab takes advantage of symmetrie.

Actually I want to get the nearest neighbour of points, so i have to calculate the distance from every point to each oter point. Since I am only interest about the order and not the distance, I neglect the sqrt since its only time consuming.

So my code loooks like following:

A=rand(10000,2);

Dista=(A(:,1)-A(:,1)').^2+(A(:,2)-A(:,2)').^2

The operation

A(:,1)-A(:,1)').^2

and

(A(:,2)-A(:,2)').^2

are symmetric, since (Ai-Aj)^2==(Aj-Ai)^2.

ans i want to take advantage of this.

I read about the fact that Matlab uses a differen BLAS when detecting symmetric operations, as you can read here:

https://de.mathworks.com/matlabcentral/answers/319587-is-it-possible-to-declare-the-matrix-is-symmetric-in-advance-before-multiplication

So i did the same with my code:

A = rand(10000);
B = rand(10000);

timeit(@()(A-B').^2)

timeit(@()(A-A').^2)

It shows that the difference is nearly 0, maybe 0.001%, sometimes also the asymetric one is the "faster" one.

So is there a possibility to get the advantage of the symmetrie? Or do i have to malually do it and try to linearize the problem and do some logic indexing and hopefully save some time? I mean its clearly a logical operation and MatLab supports them, but how can i benefit from it in my case??

Many thanks in advance,

Best regards

Marc