Speed up matlab script

http://www-h.eng.cam.ac.uk/help/tpl/programs/Matlab/faster_scripts.html
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Matlab - faster scripts

Matlab is easy to use, but the easiest method might not be the fastest. Fortunately, some of the simpler ways to improve the speed of matlab programs are also amongst the most effective, leading to order-of-magnitude improvements.

Firstly, make sure you're not writing unnecessary code. Each new version of matlab has new functions that might be useful, and functions that have been made faster. Remember that some of matlab's commands are scripts and some are built-in functions which are going to be faster than anything you can write. Use the which command to find out whether or not a function is a script (cumsum for example, isn't).

Also make sure you're up to date with matlab's newer features: Some (like cells and structures) might make your code tidier but slower; others (like the newer visualisation routines) may speed up your code considerably.

Matlab 6.5 introduced the "JIT-Accelerator" which greatly speeds up some scripts with big simple "for" loops. If you have pre-2006 matlabs it might be worth use the profile routine to help you adapt your code to take advantage of it. See the JIT-Accelerator example. Newer matlabs don't show JIT information in the profile output.

Then go through this checklist of issues to consider

Matlab Routines

Some matlab routines are *.m files, others are compiled into matlab (built-in) and are much faster. Try to use built-ins where possible. Use type functionname to see if a function is a built-in.

Functions and Scripts

There are 2 sorts of M-files - functions and scripts. When you call an M-file function MATLAB parses it and stores it in memory, so that on subsequent calls it runs faster. The difference isn't much, but functions are better than scripts anyway - they make use of their own local variables and accept input arguments. Look up the function command to find out how to write functions.

You can convert a function into matlab's internal form yourself using the pcode command, but it's hardly worth it.

Matrix pre-allocation

Matlab has the ability to increase the size of a matrix on demand. If you know the maximum size of a matrix beforehand, it's worth creating the matrix with this size initially rather than making the matrix grow incrementally. Speed-up factors of 500 are possible using this method.

Sparse Arrays

Matlab has 2 ways of storing matrices - full and sparse. Full matrices store their all of their elements in a block of memory; sparse matrices keep a list of the non-zero elements. If matrices aren't dense, using sparse matrices saves memory and increases speed. If you save the following text as spdemo.m you can experiment with using different matrix sizes and densities. For example, spdemo(100,.1) compares multiplication for full and sparse matrices of size 100 by 100 and density .1.

function sp = spdemo(arg1, arg2)
% Comparison of sparse vs full matrices
if (nargin ~= 2)
    error('Give order and density');
    return
end
S = sprandn(arg1,arg1,arg2);
F = full(S);
 % Compare speed.

t0=cputime;
B = S * S;
stime=cputime-t0;

t0=cputime;
C = F * F;
ftime=cputime-t0;

sprintf('Order %d matrix, density %f: Full=%f, Sparse=%f', arg1, ...
	arg2, ftime, stime) 

Structures and Arrays

Structures of arrays are faster than arrays of structures.

Note that if you're processing a 2D array, it's faster to scan down the columns than along the rows.

Profiling

Before you start spending a lot of time on optimising it's useful to find out where the main bottlenecks are. The profile command can do this for you, providing text or graphical output. For example, this is how you could profile spdemo.m

  profile on 
  spdemo(100, .1)       
  profile off
  profile viewer

You'll need to click on the function names displayed by the viewer in order to get detailed information. Within the department one particular diagnostic session led to a speedup of 3000 times (to several hours to several seconds) when it turned out that the same huge .mat file was being loaded on every iteration of a loop.

Vectorisation

Matlab scripts can be written using fortran/C-style "for" loops, but to make the most of matlab's abilities you should try whenever possible to treat matrices as a single entity rather than a bundle of elements. A separate document deals with vectorisation tricks

Algorithms

Matlab routines deal with general cases. If your data has a special feature (matrices are symmetrical, for instance) you may be able to implement an algorithm which is tuned to your special case. See Mex files - an example.

Compilers

It's possible to combine the ease of writing M-files with the speed provided by writing in C or Fortran. Compilers (Mathworks' mcc or the free matcom) convert M-files into compiled C code. Our Signal Processing & Communications group have used mcc successfully. However, mcc isn't free. Also speed improvements depend strongly on the particular application. In some cases, performance improves by more than 200 times, while other files show little or no improvement. Whether or not you use a compiler, it's worth using other optimisation techniques too.