Why vectorized calculations are faster than for loops?

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Mikhail on 26 Oct 2014
Commented: Keldon Alleyne on 1 Oct 2018
Why it's faster in Matlab? Is it because better memory treating, or paralleling? If this is only due parallel computation, on single-core laptop it will be now difference between? Thanks<

Answers (1)

Jan on 26 Oct 2014
Edited: Jan on 26 Oct 2014
At first: There is no evidence that vectorized code is faster in general.
If a build-in function can be applied to a complete array, a vectorization is much faster than a loop appraoch. When large temporary arrays are required, the benefits of the vectorization can be dominated by the expensive allocation of the memory, when it does not match into the processor cache.
A secondray effect of vectorizing is that the code looks more clear, at least as a rule of thumb. A trivial example:
% Loops:
A = rand(10);
B = rand(10);
C = zeros(size(A));
for i2 = 1:size(A, 2)
for i1 = 1:size(A, 1) % Columns in the inner loop
C(i1, i2) = A(i1, i2) + B(i1, i2);
% Vectorized:
C = A + B;
The 2nd method is faster concerning the runtime, but also for the programming and debug time. There is almost no chance to create a bug and it will be very easy to understand the code, when the program needs changes in the future.
Keldon Alleyne
Keldon Alleyne on 1 Oct 2018
Multiplying matrices in loops is O(N^3), while the fastest algorithms using other methods are O(N^2.3) - O(N^2.8), which can easily explain the differences in performance.
On my laptop with Matlab 2018b I get:
Elapsed time is 0.112362 seconds.
Elapsed time is 0.214544 seconds.
Elapsed time is 0.007935 seconds.

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