How to write vectorized functions in MATLAB

Question

I am just learning MATLAB and I find it hard to understand the performance factors of loops vs vectorized functions.

In my previous question: Nested for

Answer 1

Update 2 (to address your updated question)

MATLAB is optimized to work well with arrays. Once you get used to it, it is actually really nice to just have to type one line and have MATLAB do the full 4D looping stuff itself without having to worry about it. MATLAB is often used for prototyping / one-off calculations, so it makes sense to save time for the person coding, and giving up some of C[++|#]'s flexibility.

This is why MATLAB internally does some loops really well - often by coding them as a compiled function.

The code snippet you give doesn't really contain the relevant line of code which does the main work, namely

% Sort along given dimension
x = sort(x,dim);

In other words, the code you show only needs to access the median values by their correct index in the now-sorted multi-dimensional array x (which doesn't take much time). The actual work accessing all array elements was done by sort, which is a built-in (i.e. compiled and highly optimized) function.

Original answer (about how to built your own fast functions working on arrays)

There are actually quite a few built-ins that take a dimension parameter: min(stack, [], n), max(stack, [], n), mean(stack, n), std(stack, [], n), median(stack,n), sum(stack, n)... together with the fact that other built-in functions like exp(), sin() automatically work on each element of your whole array (i.e. sin(stack) automatically does four nested loops for you if stack is 4D), you can built up a lot of functions that you might need just be relying on the existing built-ins.

If this is not enough for a particular case you should have a look at repmat, bsxfun, arrayfun and accumarray which are very powerful functions for doing things "the MATLAB way". Just search on SO for questions (or rather answers) using one of these, I learned a lot about MATLABs strong points that way.

As an example, say you wanted to implement the p-norm of stack along dimension n, you could write

function result=pnorm(stack, p, n)
result=sum(stack.^p,n)^(1/p);

... where you effectively reuse the "which-dimension-capability" of sum.

Update

As Max points out in the comments, also have a look at the colon operator (:) which is a very powerful tool for selecting elements from an array (or even changing it shape, which is more generally done with reshape).

In general, have a look at the section Array Operations in the help - it contains repmat et al. mentioned above, but also cumsum and some more obscure helper functions which you should use as building blocks.