OverviewTeaching: 45 min
Exercises: 20 minQuestions
How can I teach MATLAB how to do new things?Objectives
Compare and contrast MATLAB function files with MATLAB scripts.
Define a function that takes arguments.
Test a function.
Recognize why we should divide programs into small, single-purpose functions.
If we only had one data set to analyze, it would probably be faster to load the file into a spreadsheet and use that to plot some simple statistics. But we have twelve files to check, and may have more in future. In this lesson, we’ll learn how to write a function so that we can repeat several operations with a single command.
Let’s start by defining a function
fahr_to_kelvin that converts temperatures from Fahrenheit to Kelvin:
function ktemp = fahr_to_kelvin(ftemp) %FAHR_TO_KELVIN Convert Fahrenheit to Kelvin ktemp = ((ftemp - 32) * (5/9)) + 273.15; end
A MATLAB function must be saved in a text file with a
The name of that file must be the same as the function defined
inside it. The name must start with a letter and cannot contain spaces.
So, you will need to save the above code in a file called
Remember to save your m-files in the current directory.
The first line of our function is called the function definition,
and it declares that we’re writing a function named
that has a single input parameter,
and a single output parameter,
Anything following the function definition line is called the body of the
function. The keyword
end marks the end of the function body, and the
function won’t know about any code after
A function can have multiple input and output parameters if required, but isn’t required to have any of either. The general form of a function is shown in the pseudo-code below:
function [out1, out2] = function_name(in1, in2) %FUNCTION_NAME Function description % This section below is called the body of the function out1 = something calculated; out2 = something else; end
Just as we saw with scripts, functions must be visible to MATLAB, i.e., a file containing a function has to be placed in a directory that MATLAB knows about. The most convenient of those directories is the current working directory.
In common with MATLAB, Octave searches the current working directory and the path for functions called from the command line.
We can call our function from the command line like any other MATLAB function:
ans = 273.15
When we pass a value, like
32, to the function, the value is assigned
to the variable
ftemp so that it can be used inside the function. If we
want to return a value from the function, we must assign that value to a
ktemp—in the first line of our function, we promised
that the output of our function would be named
Outside of the function, the variables
ktemp aren’t visible;
they are only used by the function body to refer to the input and
This is one of the major differences between scripts and functions: a script can be thought of as automating the command line, with full access to all variables in the base workspace, whereas a function can only read and write variables from the calling workspace if they are passed as arguments — i.e. a function has its own separate workspace.
Now that we’ve seen how to convert Fahrenheit to Kelvin, it’s easy to convert Kelvin to Celsius.
function ctemp = kelvin_to_celsius(ktemp) %KELVIN_TO_CELSIUS Convert from Kelvin to Celcius ctemp = ktemp - 273.15; end
Again, we can call this function like any other:
ans = -273.15
What about converting Fahrenheit to Celsius? We could write out the formula, but we don’t need to. Instead, we can compose the two functions we have already created:
function ctemp = fahr_to_celsius(ftemp) %FAHR_TO_CELSIUS Convert Fahrenheit to Celcius ktemp = fahr_to_kelvin(ftemp); ctemp = kelvin_to_celsius(ktemp); end
Calling this function,
we get, as expected:
ans = 0
This is our first taste of how larger programs are built: we define basic operations, then combine them in ever-larger chunks to get the effect we want. Real-life functions will usually be larger than the ones shown here—typically half a dozen to a few dozen lines—but they shouldn’t ever be much longer than that, or the next person who reads it won’t be able to understand what’s going on.
Concatenating in a Function
In MATLAB, we concatenate strings by putting them into an array or using the
>> disp(['abra', 'cad', 'abra'])
>> disp(strcat('a', 'b'))
Write a function called
fencethat has two parameters,
wrapperbefore and after
>> disp(fence('name', '*'))
function wrapped = fence(original, wrapper) %FENCE Return original string, with wrapper prepended and appended wrapped = strcat(wrapper, original, wrapper); end
Getting the Outside
If the variable
srefers to a string, then
s(1)is the string’s first character and
s(end)is its last. Write a function called
outerthat returns a string made up of just the first and last characters of its input:
function ends = outer(s) %OUTER Return first and last characters from a string ends = strcat(s(1), s(end)); end
Variables Inside and Outside Functions
Consider our function
fahr_to_kelvinfrom earlier in the episode:
function ktemp = fahr_to_kelvin(ftemp) %FAHR_TO_KELVIN Convert Fahrenheit to Kelvin ktemp = ((ftemp-32)*(5.0/9.0)) + 273.15; end
What does the following code display when run — and why?
ftemp = 0 ktemp = 0 disp(fahr_to_kelvin(8)) disp(fahr_to_kelvin(41)) disp(fahr_to_kelvin(32)) disp(ktemp)
259.8167 278.1500 273.1500 0
ktempis 0 because the function
fahr_to_kelvinhas no knowledge of the variable
ktempwhich exists outside of the function.
Once we start putting things in functions so that we can re-use them, we need to start testing that those functions are working correctly. To see how to do this, let’s write a function to center a dataset around a particular value:
function out = center(data, desired) out = (data - mean(data(:))) + desired; end
We could test this on our actual data, but since we don’t know what the values ought to be, it will be hard to tell if the result was correct, Instead, let’s create a matrix of 0’s, and then center that around 3:
>> z = zeros(2,2); >> center(z, 3)
ans = 3 3 3 3
That looks right, so let’s try out
center function on our real data:
>> data = readmatrix('data/inflammation-01.csv'); >> centered = center(data(:), 0)
It’s hard to tell from the default output whether the result is correct–this is often the case when working with fairly large arrays–but, there are a few simple tests that will reassure us.
Let’s calculate some simple statistics:
>> disp([min(data(:)), mean(data(:)), max(data(:))])
0.00000 6.14875 20.00000
And let’s do the same after applying our
to the data:
>> disp([min(centered(:)), mean(centered(:)), max(centered(:))])
-6.1487 -0.0000 13.8513
That seems almost right: the original mean was about 6.1, so the lower bound from zero is now about -6.1. The mean of the centered data isn’t quite zero–we’ll explore why not in the challenges–but it’s pretty close. We can even go further and check that the standard deviation hasn’t changed:
>> std(data(:)) - std(centered(:))
The difference is very small. It’s still possible that our function is wrong, but it seems unlikely enough that we should probably get back to doing our analysis. We have one more task first, though: we should write some documentation for our function to remind ourselves later what it’s for and how to use it.
function out = center(data, desired) %CENTER Center data around a desired value. % % center(DATA, DESIRED) % % Returns a new array containing the values in % DATA centered around the value. out = (data - mean(data(:))) + desired; end
Comment lines immediately below the function definition line
are called “help text”. Typing
help function_name brings
up the help text for that function:
>> help center
Center Center data around a desired value. center(DATA, DESIRED) Returns a new array containing the values in DATA centered around the value.
Testing a Function
Write a function called
normalisethat takes an array as input and returns an array of the same shape with its values scaled to lie in the range 0.0 to 1.0. (If L and H are the lowest and highest values in the input array, respectively, then the function should map a value v to (v - L)/(H - L).) Be sure to give the function a comment block explaining its use.
help linspaceto see how to use
linspaceto generate regularly-spaced values. Use arrays like this to test your
function out = normalise(in) %NORMALISE Return original array, normalised so that the % new values lie in the range 0 to 1. H = max(max(in)); L = min(min(in)); out = (in-L)/(H-L); end
a = linspace(1, 10); % Create evenly-spaced vector norm_a = normalise(a); % Normalise vector plot(a, norm_a) % Visually check normalisation
Convert a script into a function
Write a function called
plot_datasetwhich plots the three summary graphs (max, min, std) for a given inflammation data file.
The function should operate on a single data file, and should have two parameters:
plot_switch. When called, the function should create the three graphs produced in the previous lesson. Whether they are displayed or saved to the
resultsdirectory should be controlled by the value of
plot_dataset('data/inflammation-01.csv', 0)should display the corresponding graphs for the first data set;
plot_dataset('data/inflammation-02.csv', 1)should save the figures for the second dataset to the
You should mostly be reusing code from the
Be sure to give your function help text.
function plot_dataset(file_name, plot_switch) %PLOT_DATASET Perform analysis for named data file. % Create figures to show average, max and min inflammation. % Display plots in GUI using plot_switch = 0, % or save to disk using plot_switch = 1. % % Example: % plot_dataset('data/inflammation-01.csv', 0) % Generate string for image name: img_name = replace(file_name, '.csv', '.png'); img_name = replace(img_name, 'data', 'results'); patient_data = readmatrix(file_name); if plot_switch == 1 figure('visible', 'off') else figure('visible', 'on') end subplot(2, 2, 1) plot(mean(patient_data, 1)) ylabel('average') subplot(2, 2, 2) plot(max(patient_data, , 1)) ylabel('max') subplot(2, 2, 3) plot(min(patient_data, , 1)) ylabel('min') if plot_switch == 1 print(img_name, '-dpng') close() end end
Automate the analysis for all files
plot_allscript so that as it loops over the data files, it calls the function
plot_datasetfor each file in turn. Your script should save the image files to the ‘results’ directory rather than displaying the figures in the MATLAB GUI.
%PLOT_ALL Analyse all inflammation datasets % Create figures to show average, max and min inflammation. % Save figures to 'results' directory. files = dir('data/inflammation-*.csv'); for i = 1:length(files) file_name = files(i).name; file_name = fullfile('data', file_name); % Process each data set, saving figures to disk. plot_dataset(file_name, 1); end
We have now solved our original problem: we can analyze any number of data files with a single command. More importantly, we have met two of the most important ideas in programming:
Use arrays to store related values, and loops to repeat operations on them.
Use functions to make code easier to re-use and easier to understand.
Break programs up into short, single-purpose functions with meaningful names.
Define functions using the