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David Warne

By David Warne, a former QCIF eResearch Analyst at QUT.

MATLAB is a powerful programming environment for scientific applications. It is designed to be highly optimised for matrix and vector mathematical operations. Writing code in a way that leverages these matrix operations is known as vectorising code. There are many reasons why a particular piece of MATLAB code is running slow, but low usage of vectorised code is one of the most common ones that I see.

The differences between vectorised and non-vectorised code can be substantial. Consider a somewhat contrived example of matrix multiplication; a direct MATLAB implementation would be: 

function [C] = slowMatMul(A,B)
[N,M] = size(A); [Q,P] = size(B);
if M ~= Q
    error(‘Matrix dimension mismatch!’);
C = zeros(N,P);
for j=1:P
    for i=1:N
        for k=1:M
            C(i,j) = C(i,j) + A(i,k)*B(k,j);

Now, compare the runtime of the above code to MATLAB’s in-built matrix multiply for two 1000 x 1000 matrices (using a two-year-old Core i7 laptop):

>> tic; C = slowMatMul(A,B);toc;
Elapsed time is 9.948649 seconds.
>> tic; C = A*B;toc;
Elapsed time is 0.039372 seconds.

The in-built matrix mathematics is around 250x faster than direct MATLAB! There are lots of reasons for this, but for now, let’s just leave it at that. 

Admittedly, this example is a bit artificial, but the point is to emphasise the potential computational gain that can be achieved through ensuring your code is as vectorised as possible. This may require a little more coding effort, but the results are well worth it.

For more details and examples, check out the following MATLAB documentation page.

This article was first published on 09/11/2017.