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MATLAB for Engineers:Speeding up your code

Alistair JohnsonAdapted from slides by Violeta Monasterio

31st May 2012

Centre for Doctoral Training in Healthcare Innovation

Institute of Biomedical Engineering

Department of Engineering ScienceUniversity of Oxford

Supported by the RCUK Digital Economy Programme grant number EP/G036861/1

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Speeding up your code

Why do you care?

Downtime slows down your research

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Speeding up your code

Easy:

1. Preallocate2. Vectorize

Harder:

3. Clever code4. Parallelization

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How to assess code's speed

Before we start optimizing your code, wehave to figure out how to time it!

Two main methods of timing code:

1. ticand toc2. Profiler (profile viewer)

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tic and toc

Quick calls to see how fast code runs

First call tic;

Then calling toc;outputs the elapsed time inseconds

ex6_1a.m ex6_1b.m

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Profiler

Sophisticated interface for seeing wherebottlenecks in your code are

Uses profilecommand to generate timings

Easy to use GUI... we will see this later

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Speeding up your code

Easy:

1.

Preallocate2. Vectorize

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What is pre-allocation?

Each variable requires continuous memory

Pre-allocation gives each variable the spaceit needs BEFOREyou fill it with data

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Preallocation

Every variable has a"pointer" - which tells it thevariable's location inmemory

If you don't preallocate,

MATLAB must repeat:1. Creating the pointer2. Finding a continuous

section of memory

Wikimedia commons, released under GFDL:http://en.wikipedia.org/wiki/File:Pointers.svg

http://en.wikipedia.org/wiki/File:Pointers.svg

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Preallocation

Useful functions: cell, zeros, ones

x = 0;for k = 2:1000000

x(k) = x(k-1) + 5;end

x = zeros(1, 1000000);for k = 2:1000000x(k) = x(k-1) + 5;

end

0.085

seconds

0.305

seconds

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Profiler

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Preallocation what if the final sizecan vary?

3 options: don't pre-allocate (bad)

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Preallocation

this code could be even faster!

block pre-allocate fully pre-allocate

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Vectorization

To vectorize a computation means toreplace serial operations (loops) withvector operations

MATLAB is a vectorized language (MATrixLABoratory) - it knows how to handlematrix multiplications the best

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Vectorization

Example vectorization: ex6_3.m

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Vectorization

Most of the time this is easy! The main trick is toconstantly think: "can I vectorize this?"

Helpful functions! (tutorials to follow)

bsxfun repmat filter cellfun arrayfun structfun

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bsxfun

Most commonly, you will use this to calculatesomething using a vector, across a matrix, e.g.:

More generally, this function applies a functionusing an N dimensional matrix across an N+1dimensional matrix

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repmat

In a nutshell:

repmat duplicates a vector across a givendimension

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Practice! Open exercise6_1.m

"Normalize" each column in a matrix of data, thisinvolves:a. Subtracting each column by its meanb. Dividing each column by its standard deviation

Tips:

a. mean(data,1) calculates column meansb. std(data,[],1) calculates column standard

deviationsc. Generate your data like this:

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Answers

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Exercise: vectorizing a loop that creates avector whose elements depend on the

previous element

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Example: vectorizing a loop that creates avector whose elements depend on the

previous element

L = 1000;A = filter([1],[1 -2],ones(1,L+1));

Solution:

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The FUN functions!

arrayfun, cellfun, structfun Used to evaluate a function across an array of

something

Let's look at ex6_5_funs.m

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Speeding up your code

Harder:

3. Clever code4. Parallelization

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Example cleverness

AUROC

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Example cleverness

AUROC

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How to handle the "hard" part

Clever code is case-specific, but always keepthese things in mind:a. Less operations in a loop == faster codeb. Built-in MATLAB functions == faster code

c. Less loops == faster coded. Nested for loops == probably vectorizablee. Using more memory ~~ using less time

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Practice time: QRS detector

rpeakdetect_spe.m

To get you started - let's use reports!

I have added in TODO comments wherethe code must be vectorized