# Repeating With Loops

## Overview

### 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:

### MATLAB

%LOOP_DEMO   Demo script to explain loops

disp(word(1))
disp(word(2))
disp(word(3))
disp(word(4))

### OUTPUT

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.

### MATLAB

%LOOP_DEMO   Demo script to explain loops

word = 'tin';

disp(word(1))
disp(word(2))
disp(word(3))
disp(word(4))

### ERROR

error: A(I): index out of bounds; value 4 out of bound 3

There’s a better approach:

### MATLAB

%LOOP_DEMO   Demo script to explain loops

for letter = 1:4
disp(word(letter))
end

### OUTPUT

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:

### MATLAB

%LOOP_DEMO   Demo script to explain loops

word = 'tin';

for letter = 1:3
disp(word(letter))
end

### OUTPUT

t
i
n

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

• We might update word and forget to modify the loop to reflect that change.

• We might make a mistake while counting the number of letters in word.

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

### MATLAB

%LOOP_DEMO   Demo script to explain loops

word = 'aluminum';

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

### OUTPUT

a
l
u
m
i
n
u
m

This is much more robust code, as it can deal identically with words of arbitrary length. Loops are not only for working with strings, they allow us to do repetitive calculations regardless of data type. Here’s another loop that calculates the sum of all even numbers between 1 and 10:

### MATLAB

%LOOP_DEMO   Demo script to explain loops

total = 0;
for even_number = 2 : 2 : 10
total = total + even_number;
end

disp('The sum of all even numbers between 1 and 10 is:')
disp(total)

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:

Since we want to sum only even numbers, the loop index even_number starts at 2 and increases by 2 with every iteration. When we enter the loop, total is zero - the value assigned to it beforehand. The first time through, the loop body adds the value of the first even number (2) to the old value of total (0), and updates total to refer to that new value. On the next loop iteration, even_number is 4 and the initial value of total is 2, so the new value assigned to total is 6. After even_number reaches the final value (10), total is 30; since this is the end of the range for even_number the loop finishes and the disp statements give us the 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:

### MATLAB

>> disp(even_number)

10

### Performing Exponentiation

MATLAB uses the caret (^) to perform exponentiation:

>> disp(5^3)

### OUTPUT

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.

### MATLAB

% 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

### MATLAB

% 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)

### OUTPUT

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

### MATLAB

% Spell a string in reverse using a loop

word = 'aluminium';

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

## Analyzing patient data from multiple files

We now have almost everything we need to process multiple data files using a loop and the plotting code in our plot_patient1 script.

We still 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.

### MATLAB

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

### OUTPUT

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:

### MATLAB

>> filename = files(1).name;
>> disp(filename)

### OUTPUT

inflammation-01.csv

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

### MATLAB

>> mod_date = files(3).date;
>> disp(mod_date)

### OUTPUT

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. Let’s write this in a script plot_all.m which we will then develop further:

### MATLAB

%PLOT_ALL	Developing code to automate inflammation analysis

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

for i = 1:length(files)
file_name = files(i).name;
disp(file_name)
end

>> plot_all

### OUTPUT

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

Another 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:

### MATLAB

NEWSTR = replace(STR, OLD, NEW)

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

### MATLAB

>> new_string = replace('big_shark', 'big', 'little');
>> disp(new_string)

little_shark

### GNU Octave

In Octave, the replace function doesn’t exist, but the strrep function is a direct replacement. The above example becomes

### MATLAB

>> new_string = strep('big_shark', 'big', 'little')
little_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.

Putting these concepts together, we can now generate the paths for the data files, and the image files we want to save:

### MATLAB

%PLOT_ALL	Developing code to automate inflammation analysis

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

for i = 1:length(files)
file_name = files(i).name;

% Generate string for image name
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);

disp(file_name)
disp(img_name)
end

### OUTPUT

data/inflammation-01.csv
results/inflammation-01.png
data/inflammation-02.csv
results/inflammation-02.png
data/inflammation-03.csv
results/inflammation-03.png
data/inflammation-04.csv
results/inflammation-04.png
data/inflammation-05.csv
results/inflammation-05.png
data/inflammation-06.csv
results/inflammation-06.png
data/inflammation-07.csv
results/inflammation-07.png
data/inflammation-08.csv
results/inflammation-08.png
data/inflammation-09.csv
results/inflammation-09.png
data/inflammation-10.csv
results/inflammation-10.png
data/inflammation-11.csv
results/inflammation-11.png
data/inflammation-12.csv
results/inflammation-12.png

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

### MATLAB

%PLOT_ALL   Print statistics for all patients.
%           Save plots of statistics to disk.

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

% Process each file in turn
for i = 1:length(files)
file_name = files(i).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);

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

subplot(2, 2, 1)
plot(mean(patient_data, 1))
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(img_name, '-dpng')
close()
end

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

### MATLAB

>> plot_all

The first three 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 we have looked at 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.

### Key Points

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