A MATLAB script is a text file with the extension .m containing a sequence of MATLAB commands. Scripts can be run from the Command Window, executing the entire sequence in a single step. Scripts can also contain comments, which is text that MATLAB ignores during execution. Comments are an excellent way to organize the script, leave notes about the sources of data or formulas, and include metadata about the script.

While scripts themselves are simple plain text files, MATLAB can create PDF files with formatted text, the code, and the outputs of the script. This process is called publishing the script, and can be useful for completing homework assignments. MATLAB live scripts work like published scripts, but have the benefit of showing the results instantly - live.

Example: Center of Mass

Question

The Boeing 737 airliner is made of several components: the empty weight, the crew and equipment, the passengers, the cargo, and the fuel.

  1. Given the weights and locations (measured from the nose) of these components, where is the center of mass of the aircraft?
  2. When the aircraft runs out of fuel, where will the center of mass be?
  3. If the aircraft needs to be ferried to another airport, with no passengers or cargo, where is the center of mass?
Component Mass (kg) Distance from nose (m)
Empty Weight 41,000 16.7
Crew and Equipment 340 5
Passengers 15,000 17.5
Cargo 1000 18.0
Fuel 20,000 13.5

Calculate the answers to these questions using a MATLAB script. Recall that the center of mass is mass-weighted average distance:

\[\bar{x} = \frac{\sum_i m_i x_i}{\sum_i m_i}\]

Solution

In a MATLAB script, the data in the table above are organized into sections with comments. The three center of mass values are then calculated using the equation above. The script center_of_mass_737.m contains:

%% Center of Mass of a 737
% *Dr. Kip Hart*
%
% 17 June 2025
%
% This script calculates the center of mass of a Boeing 737
% in several scenarios. Mass values are in kilograms.
% Distances are in meters from the nose of the aircraft.
%
% The center of mass equation is given by:
% $$ \bar{x} = \frac{\sum_i m_i x_i}{\sum_i m_i} $$

%% Givens
% The values below are taken from the table in the problem statement.

% Empty Weight
empty_mass = 41e3;
empty_dist = 16.7;

% Crew and Equipment
crew_equip_mass = 340;
cerw_equip_dist = 5;

% Passengers
pax_mass = 15e3;
pax_dist = 17.5;

% Cargo
cargo_mass = 1000;
cargo_dist = 18.0;

% Fuel
fuel_mass = 20e3;
fuel_dist = 13.5;

%% Question 1
% Where is the center of mass of the aircraft?
mass_total = empty_mass + crew_equip_mass + pax_mass + cargo_mass + fuel_mass;
weighted_sum = empty_mass*empty_dist + crew_equip_mass*cerw_equip_dist + pax_mass*pax_dist + cargo_mass*cargo_dist + fuel_mass*fuel_dist;

center_of_mass = weighted_sum / mass_total

%% Question 2
% When the aircraft runs out of fuel, where will the center of mass be?
mass_total_q2 = mass_total - fuel_mass;
weighted_sum_q2 = weighted_sum - fuel_mass*fuel_dist;

center_of_mass_q2 = weighted_sum_q2 / mass_total_q2

%% Question 3
% If the aircraft needs to be ferried to another airport,
% with no passengers or cargo, where is the center of mass?
mass_total_q3 = mass_total - pax_mass - cargo_mass;
weighted_sum_q3 = weighted_sum - pax_mass*pax_dist - cargo_mass*cargo_dist;

center_of_mass_q3 = weighted_sum_q3 / mass_total_q3

Running it in the Command Window produces:

>> center_of_mass_737

center_of_mass =

   15.9930


center_of_mass_q2 =

   16.8626


center_of_mass_q3 =

   15.5918

Note that the answers to questions 2 and 3 depend on the mass_total and weighted_sum variables defined as part of question 1. This saves time, but if there was an error in the solution to question 1 then it would propagate to 2 and 3. In this case, however, it is clear that the code is answering the question. With question 2, for example, the fuel mass contributions are subtracted from the total mass and weighted sum, which is clearer than if we repeated the sum but without the fuel terms.

Diary

MATLAB includes a built-in function named diary that will record your commands from the Command Window. If you prefer to work and develop in the Command Window, you can start with diary on or diary <filename>, type your commands into the Command Window, then save your work to a file with diary off. For example:

>> diary my_commands.diary
>> x = 3;
>> y = x^2

y =

     9

>> z = 2 + y;
>> z = 2 - y;

will write to a diary file named my_commands.diary that contains:

x = 3;
y = x^2

y =

     9

z = 2 + y;
z = 2 - y;

This file contains everything, including the printed output from lines missing a ; at the end. It also includes mistakes, old versions of commands, etc. Nonetheless, you can copy paste lines from the diary into a script.

Personally, I start with a script and never use diary. That being said, it is a tool and if you find it helpful please use it. The MATLAB documentation has more information about diary.

Comments

Comments are text in the script that MATLAB does not interpret as a command. Everything after the % symbol is not interpreted. This can be at the beginning of the line or in the middle. For example:

% Parachute parameters
chute_mass = 2;  % lbm
chute_area = 32; % m^2, from Table 6 in Chapter 3

To create a comment that spans multiple lines, you can either start each line with the % symbol or start the block comment with %{ and end it with %}. For example:

%{

The beam cross section geometry is defined as:

          B ------- D
        / |       / |
       /  |      /  |
      /   |     /   |
     /    |    /    |
    /     |   /     |
   /      |  /      |
  /       | /       |
A ------- C ------- E

%}

len_AC = 12;
len_CE = 15;
len_CB = 10;

In this script, the block comments contain a rough sketch of the geometry and provide context for the variable definitions.

Commenting your code is the best habit you can develop while learning to program. It gives you the opportunity to document what you’re doing, why it is being done this way, and where your numbers came from. You can also use comments like hashtags, then find all instances of that word in your file. For example:

width = 3; %TODO check this value, it was a wild guess

In MATLAB you can search for all instances of %TODO, which makes a to-do list. Another common keyword is %FIXME, for code you know needs to be fixed but you have not had the time.

Publishing

MATLAB scripts are written in plain text .m files, which can be difficult to read and do not contain any of the results from running the script. Publishing the script converts the plain text to rich text PDFs that are easy to read and contain the results. With the Boeing 737 example, the comments certainly clarify what the script is doing, but it would be easier to read as a PDF. A PDF is also easier to share with someone who does not have MATLAB installed, or does not have time to rerun your script if it contains slow operations.

To convert a script into a PDF (or other formats), use the publish command. For example:

publish('center_of_mass_737.m', 'pdf');

The PDF produced by this command is center_of_mass_737.pdf.

Unable to display PDF.

MATLAB provides more details on the publishing process on their publish page. For more information on formatting text in the comments, visit Publishing Markup.

Live Scripts

Live scripts in MATLAB are similar to published scripts, with the primary difference being the results are recalculated live. This is an interactive experience, where you can adjust the inputs to the script and see the effects on outputs in real time. More details about live scripts are on the Create Live Scripts in the Live Editor page.

Scripts Within Scripts

Since you can call scripts from the Command Window, and scripts contain commands, it is possible to call a script from within another script. For example, if I have an engine and want to analyze it to determine its efficiency, I could write a script called engine_1.m that contains:

% Engine Parameters
T_cold = 300; % Kelvin
T_hot  = 800; % Kelvin

% Efficiency Analysis
analyze_engine;

The analyze_engine.m script would assume that T_cold and T_hot are already defined. It would contain the formula for Carnot efficiency:

eff_carnot = (T_hot - T_cold) / T_hot

Then if I have a second engine, I could copy/paste engine_1.m to engine_2.m, update T_cold and T_hot, then call the same analyze_engine script. This guarantees that I’m using the exact same equation to analyze both engines. If I want to expand the analysis to include other metrics, I only have to make the changes to the analyze_engine.m file. This enables code reuse and reduces code duplication, which is much easier to maintain.

Another example of reusing code like this would be to run separate analyzes on the same set of inputs. For example, the design variables of a spacecraft may all be contained in a script called spacecraft_design.m. A stress engineer would run that script to populate the givens for a stress analysis, a thermal engineer would run it to populate the givens for a thermal analysis, and so on. Each member of the team can run their own separate analyzes, then when they discuss the results they are all talking about the same design.

While scripting is a necessary aspect of programming in MATLAB, it does have a couple drawbacks. They are mainly two assumptions: 1) that variables will be named exactly as you expect and 2) that scripts will not redefine any of your variables. In the case of analyze_engine.m, if you use T_H instead of T_hot then MATLAB will error out. It will not look for similarly named variables, so if you write analyze_engine.m assuming one naming convention and engine_1.m assuming another there will be errors. The second assumption is that the script you call does not redefine or overwrite values in variables you have defined. For example, if analyze_engine.m ended with the line T_hot=1000; then any code after analyze_engine will use a value of 1000 for T_hot instead of 800. This would be difficult to spot if both scripts defined many variables with similar names. To keep variable definitions contained and isolated from each other, it is better to write User Functions.

Reading Questions

  1. What is a MATLAB script?
  2. How do you run a MATLAB script from the Command Window?
  3. Why are comments useful in MATLAB scripts?
  4. What kinds of information are included in comments?
  5. Describe two ways to create comments in MATLAB.
  6. How can you publish a script to a PDF?
  7. Which built-in MATLAB function records activity from the Command Window?
  8. What are some advantages to calling scripts from within other scripts?
  9. What disadvantages are there to calling scripts within scripts?