A coworker whose background is in embedded systems (with a C background and no MATLAB at all), after hearing my rants that people are coding MATLAB like C using way more for-loops than necessary, asked me if he has two vectors,

a = 0:32767; b = 0:32767;

and he want all combinations of the elements in and so that for each index pair , he will get

There are combinations out there. At first, I showed him the typical method shown in the MATLAB’s introduction materials:

% Should have used ndgrid() for a more natural (column first) layout [B, A] = meshgrid(a, b); C = 167*(A+42)./(B+17)

Then he asked, ‘This way I have to store the matrices and . Wouldn’t it be memory intensive? Is there a better way to do it like with functional programming?’ Now I have to show him a more advanced trick that requires some mental leaps (the ones necessary to get sophisticated at the MATLAB language):

C = 167*bsxfun(@rdivide, a'+42, b+17)

This one liner does not save intermediate input values, so it’s memory efficient as well.

bsxfun() is a function that takes two inputs (we call it a binary function) which any of them can be a matrix, vector or scalar. It will conceptually expand the dimensions so the function handle (e.g. @rdivide) get to apply to all combinations as if the inputs are expanded (repeated) to the longer of each dimension supplied. I bet under the hood it’s just a pair of for-loops with the loop increments managed so it doesn’t waste memory storing the intermediaries.

In the example above, I have a column and a row . The output is arranged as if is copied right to meet the length of , and is copied down to meet the length of .

This involves two major concepts one needs to program the MATLAB way : vectorization and anonymous functions. Not something you’d tell a day-zero beginner (probably scare them off), but showing them a Ninja trick after they understand the beginner’s method might motivate them to learn the true power of MATLAB.

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