Repeating With Loops

Overview

Teaching: 30 min
Exercises: 0 min
Questions
  • How can I repeat the same operations on multiple values?

Objectives
  • Explain what a for loop does.

  • Correctly write for loops that repeat simple commands.

  • Trace changes to a loop variable as the loops runs.

  • Use a for loop to process multiple files

Recall that we have to do this analysis for every one of our dozen datasets, and we need a better way than typing out commands for each one, because we’ll find ourselves writing a lot of duplicate code. Remember, code that is repeated in two or more places will eventually be wrong in at least one. Also, if we make changes in the way we analyze our datasets, we have to introduce that change in every copy of our code. To avoid all of this repetition, we have to teach MATLAB to repeat our commands, and to do that, we have to learn how to write loops.

Suppose we want to print each character in the word “lead” on a line of its own. One way is to use four disp statements:

word = 'lead';

disp(word(1));
disp(word(2));
disp(word(3));
disp(word(4));
l
e
a
d

But this is a bad approach for two reasons:

  1. It doesn’t scale: if we want to print the characters in a string that’s hundreds of letters long, we’d be better off typing them in.

  2. It’s fragile: if we change word to a longer string, it only prints part of the data, and if we change it to a shorter one, it produces an error, because we’re asking for characters that don’t exist.

word = 'tin';

disp(word(1));
disp(word(2));
disp(word(3));
disp(word(4));
error: A(I): index out of bounds; value 4 out of bound 3

There’s a better approach:

word = 'lead';

for letter = 1:4
    disp(word(letter))
end
l
e
a
d

This improved version uses a for loop to repeat an operation—in this case, printing to the screen—once for each element in an array.

The general form of a for loop is:

for variable = collection
    do things with variable
end

The for loop executes the commands in the loop body for every value in the array collection. This value is called the loop variable, and we can call it whatever we like. In our example, we gave it the name letter.

We have to terminate the loop body with the end keyword, and we can have as many commands as we like in the loop body. But, we have to remember that they will all be repeated as many times as there are values in collection.

Our for loop has made our code more scalable, and less fragile. There’s still one little thing about it that should bother us. For our loop to deal appropriately with shorter or longer words, we have to change the first line of our loop by hand:

word = 'tin';

for letter = 1:3
    disp(word(letter));
end
t
i
n

Although this works, it’s not the best way to write our loop:

Fortunately, MATLAB provides us with a convenient function to write a better loop:

word = 'aluminum';

for letter = 1:length(word)
    disp(word(letter));
end
a
l
u
m
i
n
u
m

This is much more robust code, as it can deal identically with words of arbitrary length. Here’s another loop that repeatedly updates the variable len:

len = 0
for vowel = 'aeiou'
    len = len + 1;
end

disp(['Number of vowels: ', num2str(len)])

It’s worth tracing the execution of this little program step by step.

The debugger

We can use the MATLAB debugger to trace the execution of a program.

The first step is to set a break point by clicking just to the right of a line number on the - symbol. A red circle will appear — this is the break point, and when we run the script, MATLAB will pause execution at that line.

A green arrow appears, pointing to the next line to be run. To continue running the program one line at a time, we use the step button.

We can then inspect variables in the workspace or by hovering the cursor over where they appear in the code, or get MATLAB to evaluate expressions in the command window (notice the prompt changes to K>>).

This process is useful to check your understanding of a program, in order to correct mistakes.

This process is illustrated below: debugger-demo

Since there are five characters in “aeiou”, the loop body will be executed five times. When we enter the loop, len is zero - the value assigned to it beforehand. The first time through, the loop body adds 1 to the old value of len, producing 1, and updates len to refer to that new value. The next time around, vowel is e, and len is 1, so len is updated to 2. After three more updates, len is 5; since there’s nothing left in aeiou for MATLAB to process, the loop finishes and the disp statement tells us our final answer.

Note that a loop variable is just a variable that’s being used to record progress in a loop. It still exists after the loop is over, and we can re-use variables previously defined as loop variables as well:

disp(vowel)
u

Performing Exponentiation

MATLAB uses the caret (^) to perform exponentiation:

disp(5^3)
125

You can also use a loop to perform exponentiation. Remember that b^x is just b*b*b*x times.

Let a variable b be the base of the number and x the exponent. Write a loop to compute b^x. Check your result for b = 4 and x = 5.

Solution

% Loop to perform exponentiation
b = 4;    % base
x = 5;    % exponent

result=1;
for i = 1:x
    result = result * b;
end

disp([num2str(b), '^', num2str(x), ' = ', num2str(result)])

Incrementing with Loops

Write a loop that spells the word “aluminum,” adding one letter at a time:

a
al
alu
alum
alumi
alumin
aluminu
aluminum

Solution

% spell a string adding one letter at a time using a loop

word = 'aluminium';

for letter = 1:length(word)
    disp(word(1:letter))
end

Looping in Reverse

In MATLAB, the colon operator (:) accepts a stride or skip argument between the start and stop:

disp(1:3:11)
1 4 7 10
disp(11:-3:1)
11 8 5 2

Using this, write a loop to print the letters of “aluminum” in reverse order, one letter per line.

m
u
n
i
m
u
l
a

Solution

% Spell a string in reverse using a loop

word = 'aluminium';

for letter = length(word):-1:1
    disp(word(letter))
end

We now have almost everything we need to process multiple data files with our analyze script.

We need to generate a list of data files to process, and then we can use a loop to repeat the analysis for each file.

We can use the dir command to return a structure array containing the names of the files in the data directory. Each element in this structure array is a structure, containing information about a single file in the form of named fields.

files = dir('data/inflammation-inflammation-*.csv')
files = 
  12×1 struct array with fields:
    name
    folder
    date
    bytes
    isdir
    datenum

To access the name field of the first file, we can use the following syntax:

filename = files(1).name;
disp(filename)
inflammation-01.csv

To get the modification date of the third file, we can do:

mod_date = files(3).date;
disp(mod_date)
26-Jul-2015 22:24:31

A good first step towards processing multiple files is to write a loop which prints the name of each of our files:

files = dir('data/inflammation-*.csv');

for i = 1:length(files)
	data_file = files(i).name;
	disp(data_file)
end
inflammation-01.csv
inflammation-02.csv
inflammation-03.csv
inflammation-04.csv
inflammation-05.csv
inflammation-06.csv
inflammation-07.csv
inflammation-08.csv
inflammation-09.csv
inflammation-10.csv
inflammation-11.csv
inflammation-12.csv

The final task is to generate the file names for the figures we’re going to save. Let’s name the output file after the data file used to generate the figure. So for the data set inflammation-01.csv we will call the figure inflammation-01.png. We can use the replace command for this purpose.

The syntax for the replace command is like this:

NEWSTR = replace(STR, OLD, NEW)

So for example if we have the string big_shark and want to get the string terror_shark, we can execute the following command:

new_string = replace('big_shark', 'big', 'terror');
disp(new_string)
terror_shark

Recall that we’re saving our figures to the results directory. The best way to generate a path to a file in MATLAB is by using the fullfile command. This generates a file path with the correct separators for the platform you’re using (i.e. forward slash for Linux and macOS, and backslash for Windows). This makes your code more portable which is great for collaboration.

We’re now ready to modify analyze.m to process multiple data files:

%ANALYSE Process first three inflammation data sets

files = dir('data/inflammation-*.csv');

% Process first three files only
for idx = 1:3
    file_name = files(idx).name;
	
    % Generate strings for image names:
    img_name  = replace(file_name, '.csv', '.png');

    % Generate path to data file and image file
    file_name = fullfile('data', file_name);
    img_name  = fullfile('results', img_name);
	
    patient_data = csvread(file_name);

    disp(['Maximum inflammation: ', num2str(max(patient_data(:)))]);
    disp(['Minimum inflammation: ', num2str(min(patient_data(:)))]);
    disp(['Standard deviation: ', num2str(std(patient_data(:)))]);

    ave_inflammation = mean(patient_data, 1);

    % Create figures
    figure('visible', 'off')

    subplot(2, 2, 1);
    plot(ave_inflammation);
    title('Average')
    ylabel('Inflammation')
    xlabel('Day')

    subplot(2, 2, 2);
    plot(max(patient_data, [], 1));
    title('Max')
    ylabel('Inflammation')
    xlabel('Day')

    subplot(2, 2, 3);
    plot(min(patient_data, [], 1));
    title('Min')
    ylabel('Inflammation')
    xlabel('Day')

    print('-dpng', img_name);
    close();
end

We run the modified script using its name in the Command Window:

analyze

The figures output to the results directory are as shown below:

Sure enough, the maxima of these data sets show exactly the same ramp as the first, and their minima show the same staircase structure.

We’ve now automated the analysis and have confirmed that all the data files show the same artifact. This is what we set out to test, and now we can just call one script to do it. With minor modifications, this script could be re-used to check all our future data files.

GNU Octave

Lastly, in the above trick using ls with the wildcard *, another small Octave/MATLAB difference shows up. In Octave, the value returned by filestr = ls('path/to/data/*.csv') is an array of strings, so we can loop over filestr directly without the need to split it with strsplit.

Key Points

  • Use for to create a loop that repeats one or more operations.