{"id":41,"date":"2016-07-24T10:11:39","date_gmt":"2016-07-24T18:11:39","guid":{"rendered":"http:\/\/wonghoi.humgar.com\/blog\/?p=41"},"modified":"2018-08-20T19:50:44","modified_gmt":"2018-08-21T03:50:44","slug":"matlab-fundamentals-vectorization","status":"publish","type":"post","link":"https:\/\/wonghoi.humgar.com\/blog\/2016\/07\/24\/matlab-fundamentals-vectorization\/","title":{"rendered":"MATLAB Fundamentals: Vectorization"},"content":{"rendered":"

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,\u00a0asked me if he has two vectors,<\/p>\n

a = 0:32767;\r\nb = 0:32767;<\/pre>\n
and he want\u00a0all\u00a0combinations<\/span> of the elements in \"a\" and \"b\" so that for each index pair \"(i, j)\", he will get<\/p>\n
   <\/span>   <\/span>\"\[ 167\left(\frac{a_j+42}{b_j+17} \right)\]\"<\/p>\n
There are \"32768^2\" combinations out there. At first, I showed him the typical method shown in the MATLAB’s introduction materials:<\/p>\n
% Should have used ndgrid() for a more natural (column first) layout\r\n[B, A] = meshgrid(a, b);\r\n\r\nC = 167*(A+42).\/(B+17)<\/pre>\n
Then he asked, ‘This way I have to store the matrices \"A\" and \"B\". 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\u00a0get\u00a0sophisticated at the MATLAB language):<\/p>\n
C = 167*bsxfun(@rdivide, a'+42, b+17)<\/pre>\n
This one liner does not save intermediate input values, so it’s memory efficient as well.<\/p>\n
bsxfun<\/a>() is a function that takes two inputs (we call it a binary function) which any<\/span> of them can be a matrix, vector or scalar. It will conceptually<\/span> expand the dimensions\u00a0so the function handle (e.g. @rdivide) get to apply to all combinations as if the inputs are expanded (repeated)\u00a0to the\u00a0longer of each dimension supplied. I bet under the hood it’s just a pair of for-loops with the\u00a0loop increments managed so it doesn’t waste memory storing the intermediaries.<\/p>\n
In the example above, I have a column \"a^T+42\" and a\u00a0row \"b+17\". The output \"C\" is arranged as if\u00a0\"a^T+42\" is copied right to meet the length of \"b+17\", and \"b+17\" is copied down to meet the length of \"a^T+42\".<\/p>\n
This involves two major concepts one needs to\u00a0program the\u00a0MATLAB way : vectorization and anonymous functions. Not something you’d tell a\u00a0day-zero beginner (probably scare them off), but showing them a\u00a0Ninja trick\u00a0after they understand\u00a0the beginner’s method might motivate them to learn the true power of MATLAB.<\/p>\n
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Rik has pointed out in the comments below that TMW introduced implicit expansion<\/em><\/a> that makes the bsxfun() obsolete. This is an excellent move (readability), despite it won’t police matrix crimes<\/a> anymore so educators should teach about implicit expansion as the first thing as it’d be hard to debug is the user is not aware of the behavior. Thanks Rik!<\/p>\n
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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,\u00a0asked me if he has two vectors, … Continue reading →<\/span><\/a><\/p>\n
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