MATLAB Fundamentals: Vectorization

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 a and b so that for each index pair (i, j), he will get

    \[ 167\left(\frac{a_j+42}{b_j+17} \right)\]

There are 32768^2 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 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 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 a^T+42 and a row b+17. The output C is arranged as if 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.

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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Structuring your MATLAB code base

When your MATLAB project gets large, or when you have a lot of projects, it’s time to consider restructuring your code and libraries so you can focus on what matters the most instead of plowing through the mess you just created.

For my projects, I usually create a file called ‘managedPathAndFiles_{myProjectName}.m’ at the top-level folder. The comments in the demo code below highlight the techniques used:

function [file, folder] = managedPathAndFile_myProject(isRegenerated)
% isRegenerated: set to 'false' to skip addpath() (which is slow)

 % Optional default input arguments by name instead of couting nargin
 if( ~exist('isRegenerated', 'var') )
   isRegenerated = true;
 end

 % Note the use of nested structures (like replacing _ with .)
 % You can use the hierarchy to group folders/files in a way you can 
 % operate on them in one-shot

 % Use the location of this file as anchor 
 % 'pwd' is unreliable because you can call this from other folders if
 % it's in MATLAB's path
 folder.root = fileparts( mfilename('fullpath') );
 
 % Include your project specific subroutines in the MATLAB path
 % Use fullfile() to generate platform independent folder structures
 folder.core.root = fullfile(folder.root, 'core');
 folder.core.helper = fullfile(folder.core.root, 'helper'); 
 % Add all the paths under the folder in one shot
 if( isRegenerated )
   % '-end' avoids name conflict by yielding to the incumbent paths 
   addpath( genpath(folder.core.root), '-end' );
 end
 
 % Automatically create data storage folder
 folder.data.root = fullfile(folder.root, 'data');
 folder.data.cache = fullfile(folder.data.cache, 'data');
 if( isRegenerated )
   % Outputting something will absorb the error if the path alreayd
   % exist. I made a mkdir_silent() in my libraries, but used the
   % native call here for demo.
   [~, ~] = structfun(@mkdir, folder.data);
 end
 
 % Sometimes you might have config or external files to load
 file.data.statistics = fullfile(folder.data.root, 'statistics.mat');
 
end

Many people don’t know about the function genpath() so they ended up lumping all their dependencies in one folder which makes my eyes bleed. Organize your files into a tree that makes sense now!

I’d recommend any serious MATLAB developer build their own library folder with a consistent naming and a sensible tree hierarchy. After looking into FEX and what’s natively available in MATLAB and you still need to roll out your own code, you’re likely to rediscover what you’ve already built just by establishing a new .m file/function you are about to write in the folder you’d most naturally put it in (like people with like mind: self, tend to pick the same names).

Sometimes you have to whip up some ‘crappy’ code that doesn’t generalize (or can be reused) in other contexts. Consider putting them in a /private folder under the caller so it won’t be visible to everybody else. Of course, I encourage people spend a little more time to write the code properly so it can be put in your own MATLAB library.

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How I learned MATLAB inside out

Back when I was in struggling graduate student working 3 university jobs to stay afloat, one of the job was to build a multi-center data collection system that take cares of remote data upload, store it in a database and visualize the waveforms and records.

I surveyed other platforms and languages for a couple of months and finally settled on MATLAB because at the time MATLAB had the most convenient data types (cells), data loading/saving (‘.mat’ files so I don’t have to manage the datatypes/format), external interfaces, and most importantly MATLAB FileExchange (FEX) pretty much cover every generic idea I can think of. With MATLAB, my work is pretty much down to coding the high level ‘business’ logic.

And no, I wasn’t biased towards MATLAB at the time because I have a signal processing background. I didn’t know much about MATLAB’s programming support back then other than number crunching (just like the 90% of the public who misundestood the power of the language), so I wouldn’t choose it for a software project at that level of complexity without much research.

Learning the guts of MATLAB, architecturing and coding the entire system took me only 3 months (well, it included a 1 month non-stop 16 hours a day, 7-days a week shut-in programming). Not a shabby platform for a project that is supposed to take 4 years. In fact, the rest of the time was spent

  1. reading the last owners *#@&ed up perl code and fighting to get the fragile linux setup to work on other machines, then reverse the entire project requirements from the source code because there wasn’t any documentation and the previous owners graduated.
  2. reconstruct Guidant’s half-finished (done by a 3rd party then abandoned) binary data reader by finishing the hardest part of the incomplete XSLT code.

The rest that has to do with MATLAB was relatively easy once I learned the main ideas through their documentation, newsgroups, Loren’s blog and the official support.

To understand and appreciate the beauty of MATLAB and use it effectively, you have to get past the following hurdles:

  1. Basic data structures: cell, struct and language features.
  2. Vectorization: use for-loops only in limited cases
  3. Anonymous function (Lambdas), cellfun(), arrayfun(), bsxfun(), structfun()
  4. Overloading and OOP
  5. Tables (Heterogeneous data structures) and Categorical objects (Nominal, Ordinal)

or else you are coding it like a C programmer: a complete waste of MATLAB’s license fees. If you know these 5 aspects of MATLAB well and would say there are strictly superior options out there, please let me know in the comments section and I’ll look into it.

 

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MATLAB Quirks: cellfun() high-performance trap

cellfun() is a powerful function in MATLAB which mirrors the idea of applying a ‘map’ operation (as in functional programming) to monads (cells: a datatype that holds any arbitrary data type, including itself).

One common use is to identify which cells are empty so you can ignore them. Typically, you can do

index.emptyCells = cellfun(@isempty, C);

According to the help (H1) page, there is a limited set of strings that you can use in place of the function handle (functor) for backward compatibility:

 
A = CELLFUN('fun', C), where 'fun' is one of the following strings,
returns a logical or double array A the elements of which are computed 
from those of C as follows:
 
   'isreal'     -- true for cells containing a real array, false
                   otherwise 
   'isempty'    -- true for cells containing an empty array, false 
                   otherwise 
   'islogical'  -- true for cells containing a logical array, false 
                   otherwise 
   'length'     -- the length of the contents of each cell 
   'ndims'      -- the number of dimensions of the contents of each cell
   'prodofsize' -- the number of elements of the contents of each cell
 
A = CELLFUN('size', C, K) returns the size along the K-th dimension of
the contents of each cell of C.
 
A = CELLFUN('isclass', C, CLASSNAME) returns true for each cell of C
that contains an array of class CLASSNAME.  Unlike the ISA function, 
'isclass' of a subclass of CLASSNAME returns false.

Turns out these functions have their native implementation and runs super-fast. But I got burned once when I tried to use this on cells containing table() objects:

index.emptyCells = cellfun('isempty', cellsOfTables);

I meant to find out if I have zero-row or zero-column (empty) table objects with that. It gave me all false even when my cells have these 0-by-0 tables. What a Terrible Failure?! Turns out these ‘backward compatibility’ native implementations (I guess they already have cellfun() before having function handles) looks at the raw data stream like PODs (Plain Old Datatypes) as a C program would do.

A table() object has lots of stuff stored in it like variable (column) names, so there’s no way a program looking at an arbitrary binary stream without accounting for such data type will consider that object empty. It’s up to the overloaded isempty() or numel() of the class to tell what is empty and what’s not, but it needs to be called by the function handle to establish which method to call.

Lesson learned: don’t use those special string based functor in cellfun() unless you know for sure it’s a POD. Otherwise it will get you the wrong answer at the speed of light.

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Make your MATLAB code work everywhere

MATLAB is used in many different setups that it’s hard to expect every line of your code you write generalizes to all other versions, platform and deployments. The following code examples helps you identify what envirnoment you are in and so you can branch accordingly:

% 32 bit vs 64 bit MATLAB
% This exploits the fact that mex is on the same platform as your MATLAB
is64bit = strcmpi( mexext(), 'mexw64');

% Handling different MATLAB versions
if( verLessThan('matlab', yourVersionString) )
  error('This code requires %s or above to run!', yourVersionString);
end

% Headless (Parallel) workers
% This exploits the fact that JVM is not loaded for parallel workers. 
% Starting MATLAB with '/nojvm' will be considered headless
isHeadless = ~usejava('desktop');

% DCOM / ActiveX /Automation Server
isDCOM = enableservice('AutomationServer');

% Test for compiled MATLAB:
isdeployed()

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