Question

I’m wondering, what is faster for addressing a single Element of a vector:

1) direct access via

result = a(index)

or

2) access an element via a matrix multiplication e.g

a = [1 2 3 4]';
b = [0 0 1 0];
result = b*a;   % Would return 3

In my oppinion (which comes from “classic” programming like C++) the first method must be more performant, because of the direct access…the second method would need a iteration through both vectors(?).

The reason why I’m asking is, that matlab is very performant on matrix and vector operations, maybe I am missing any aspect and the second method is more effective…

Answer 1

A quick test:

function [] = fun1()
a = [1 2 3 4]';
b = [0 0 1 0];
tic;
for i=1:1000000
    r = a(3);
end
toc;
end

Elapsed time: 0.006 seconds

Change a(3) to b*a

Elapsed time: 0.9 seconds

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The performance difference is quite obvious(, and you should have done that yourself before asking this question).

Reason behind that:

No matter how efficient MATLAB’s calculation is, MATLAB still needs to fetch the number 1 by 1, and do multiplication 1 by 1, and sum up. There is no hope to be faster than a single access.

In your special case, there are all 0’s except 1, but it is useless to do optimization for single special case in my opinion, and the best optimization I can come up with still needs to access all the elements for at least once each.

---

EDIT:

_{It seems I am in quite good mood today….}

Change a(3) to a(1)*b(1)+a(2)*b(2)+a(3)*b(3)+a(4)*b(4)

Elapsed time: 0.02 seconds

It seems that boundary checking (and/or other errands) take more time than the access and calculation.