Overview
Teaching: 30 min
Exercises: 0 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 parameters.
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:
% file fahr_to_kelvin.m
function ktemp = fahr_to_kelvin(ftemp)
ktemp = ((ftemp - 32) * (5/9)) + 273.15;
end
A Matlab function must be saved in a text file with a .m
extension.
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
fahr_to_kelvin.m
.
The first line of our function:
function ktemp = fahr_to_kelvin(ftemp)
is called the function definition, and it declares that we’re
writing a function named fahr_to_kelvin
, that accepts a single parameter,
ftemp
, and outputs a single value, ktemp
. 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 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.
GNU Octave
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:
fahr_to_kelvin(32)
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
variable named ktemp
—in the first line of our function, we promised
that the output of our function would be named ktemp
.
Outside of the function, the names ftemp
and ktemp
don’t matter,
they are only used by the function body to refer to the input and
output values.
Now that we’ve seen how to turn Fahrenheit to Kelvin, it’s easy to turn Kelvin to Celsius.
% file kelvin_to_celsius.m
function ctemp = kelvin_to_celsius(ktemp)
ctemp = ktemp - 273.15;
end
Again, we can call this function like any other:
kelvin_to_celsius(0.0)
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:
% file fahr_to_celsius.m
function ctemp = fahr_to_celsius(ftemp)
ktemp = fahr_to_kelvin(ftemp);
ctemp = kelvin_to_celsius(ktemp);
end
Calling this function,
fahr_to_celsius(32.0)
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
strcat
function:disp(['abra', 'cad', 'abra'])
abracadabra
disp(strcat('a', 'b'))
ab
Write a function called
fence
that takes two parameters,original
andwrapper
and appendswrapper
before and afteroriginal
:disp(fence('name', '*'))
*name*
Getting the Outside
If the variable
s
refers to a string, thens(1)
is the string’s first character ands(end)
is its last. Write a function calledouter
that returns a string made up of just the first and last characters of its input:disp(outer('helium'))
hm
Let’s take a closer look at what happens when we call
fahr_to_celsius(32.0)
.
To make things clearer, we’ll start by putting the initial value 32.0
in a variable and store the final result in one as well:
original = 32.0;
final = fahr_to_celsius(original);
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 = csvread('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 center
function
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(:))
5.3291e-15
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 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 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
rescale
that 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.Run
help linspace
to see how to uselinspace
to generate regularly-spaced values. Use arrays like this to test yourrescale
function.Write a function
run_analysis
that accepts a filename as parameter, and displays the three graphs produced in the previous lesson, i.e.,run_analysis('inflammation-01.csv')
should produce the corresponding graphs for the first data set. Be sure to give your function help text.
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.
Key Points
Break programs up into short, single-purpose functions with meaningful names.
Define functions using the
function
keyword.