04-func.md

layout	title	subtitle	minutes
page	Programming with MATLAB	Creating Functions	30

Learning Objectives {.objectives}

• Explain a Matlab function file.
• Define a function that takes parameters.
• Test a function.
• Explain what a call stack is, and trace changes to the call stack as functions are called.
• Set default values for function parameters.
• Know 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.

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,

kelvin_to_celsius(0.0)

we get, as expected:

ans = -273.15

This is our first taste of how larger programs are built: we define basic operations, then combine them in ever-large 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 {.challenge}

1. 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 and wrapper and appends wrapper before and after original:

   disp(fence('name', '*'))
   

   *name*
   

2. If the variable s refers to a string, then s(1) is the string's first character and s(end) is its last. Write a function called outer 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_celcius(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_celcius(original);

The diagram below shows what memory looks like after the first line has been executed:

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(:))])

-6.1487e+00  -2.2962e-14   1.3851e+01

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 {.challenge}

1. 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.

2. Run help linspace to see how to use this function to generate regularly-spaced values. Use arrays like this to test your rescale function.

3. 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:

1. Use arrays to store related values, and loops to repeat operations on them.

2. Use functions to make code easier to re-use and easier to understand.

We have one more big idea to introduce, and then we will be able to construct a better 'heat map', like the one we initially used to display our first data set.