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College of EngineeringEngineering Education Innovation Center

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Functions 1 in MATLAB

Topics Covered:

1. Uses of Functions

• Organizational Tool

• User Function Library

2. Function Syntax

User Defined Functions / Chapter 6

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Why Not Use Script Files For Everything?

• Imagine that you’re heading a programming group supervising 10 programmers.

• Imagine that you have to allocate tasks to create a new application program.

• Imagine that everything is done with script files.

• What would you have to do?Create a table of all variable names to be used in every part of the program

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Why Not Use Script Files For Everything?• Imagine you created a useful set of code

two years ago and would like to use it again for a new program

• Wouldn’t it be nice to not have to remember exactly what you did?

• If back then you used a variable name you’d like to use for something else now – wouldn’t it be nice to not have to find all cases and change it?

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• Consider the built in functions like the sin(x) function

• Do you have to know every variable name used by the person who programmed it?

Wouldn’t it be nice to do the same with your own programming? Function files help solve these problems.

Why Not Use Script Files For Everything?

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Function FilesEvery programming language has a way

to do this.• In MATLAB it’s called a user-defined

function• In FORTRAN and BASIC it’s called a

subroutine• In PASCAL it’s called a procedure• In C it’s also called a function

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A USER-DEFINED FUNCTIONIN A FUNCTION FILE

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FunctionFile

Input data Output

A user-defined function is a program created by the user and can be used like a built-in function.

Its main feature is that it has an input and an output.

The function can be used many times with different values of the input data.

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FUNCTION FILE

A function file is a program that can be used in

two ways:

Perform tasks that are used frequently

Be a subprogram in a large program• In this way a large program can be made of

smaller “building blocks” that can be developed

independently.

141-142

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Programming Insight

• In practice, only the top level of a program is a script file. The script file interacts with the user and keeps track of calling the other routines (like a project manager).

• ALL other routines are functions.• Because of this, function files never use

the input command

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Programming Insight• User created function files can either be in

the current working directory or be placed into a user library whose location has been added to MATLAB’s search path.

• Add a folder to MATLAB’s search path by going to File > Set Path

• Click on the “Add a Folder” button and indicate the folder you want to add

• Don’t forget to “Save” if you want this folder used in future MATLAB sessions!

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FUNCTION FILE Once they are created, the functions can be

used in the Command Window, in script files, or inside other function files

Data is transferred to a function file by input variables and the results are transferred back by output variables.

All variables inside the function are local (NOT global), (they are not recognized by other parts of MATLAB – e.g. the command window or any script file)

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FUNCTION FILE User-defined Function files are used in the same way

as built-in functions, (i.e. once they are created, functions can be used in the Command Window, in script files, in equations, or inside other function files)

Data is transferred to a function file by input variables and the results are transferred back by output variables.

All the calculations and the variables that are used inside the function are local, (i.e. they are not recognized by, transferred to, or available to other parts of MATLAB)

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CREATING A FUNCTION FILEA function file is created in the Editor/Debugger Window (the same window that is used to create script files).

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The first line of the function file is typed here.It must be the function definition line.

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STRUCTURE OF A FUNCTION FILE 143

function [mPay, tPay] = loan(amount, rate, years)% loan() calculates monthly and total payment of loan% Input arguments:% amount = loan amount in $% rate = annual interest rate in percent% years = number of years% Output arguments:% mPay = monthly payment% tPay = total payment

ratePerMonth = rate * 0.01 / 12; rPM = (1 + ratePerMonth) ^ (years * 12);

mPay = amount * rPM * ratePerMonth / (rPM - 1); tPay = mPay * years * 12;

Function definition line

Help text

Function body(Program)

Assign values tooutput arguments

Output arguments Input arguments

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FUNCTION DEFINITION LINE

The function definition line:1. Defines that the M-file is a function2. Defines the name of the function3. Lists the input and output variables

function [output vars] = function_name(input vars)

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function [mpay, tpay] = loan(amount, rate, years)

The first line of a function file MUST be the functiondefinition line (without this line it will be a script file)

Example:

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THE FUNCTION DEFINITION LINE

The word function must be typed in lower case letters (if it is wrong, it won’t turn blue)

Square brackets are not required in the function definition line if the function has only one output variable:

function [A] = RectArea(a,b) function A = RectArea(a,b) If there are no output variables, the square brackets

and the equal sign can be omitted:function CirclePlot(r)

Either form is ok

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The names of the input and output variables given in the function definition line and in the body of the function are local.

The variables are assigned according to their position in the

output or input variables list in the function definition line.

Do not name a function file a name that is already used by MATLAB for a built-in function. To check if a function name is used by MATLAB type “help name” in the Command Window.

143-146

THE FUNCTION DEFINITION LINE

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FUNCTION EXAMPLEw = 5;h = 10;a = RectArea(w, h);<more commands>...

Memory (main) w h a 5

function area = RectArea(width, height)area = width * height;

Memory (local function)width height area 5 10 50 5010

Call a function to calculate thearea of a rectangle with sides w and h.

Script file

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SAVING A FUNCTION FILE(similar to saving a script file)

Once the script file is completed, it must be saved. In our class use Save As and save: (N:\, USB drive). Save it in the working directory.

The file MUST be saved with a name that is identical to the function name in the function definition line

“Save and Run” will not work, since the function needs to be called from somewhere with input values.

It is common to forget to save changes, in which case MATLAB will run the OLD version.

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EXAMPLES OF FUNCTION DEFINITION LINES

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Three input variables, two output variables, save as loan.m

Two input variables, one output variable, save as RectArea.m

One input variable, two output variables, save as SphereVolArea.m

Three input variables, no output variables, save as trajectory.m

function [mpay, tpay] = loan(amount, rate, years)

function trajectory(velocity, height, gravity)

function [volume, surfArea] = SphereVolArea(radius)

function [area] = RectArea(width, height)

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USING A USER-DEFINED-FUNCTION(FUNCTION FILE)

A user-defined function is used in the same way as a built-in function.

To use a function file, the directory where it was saved must either be in the current directory, or be in the search path (same as required for a script file).

A variable that is assigned a value in the code of the function file will be displayed in the Command Window, unless a semicolon is typed at the end of the command (always use semicolons in functions)

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EXAMPLE OF A FUNCTION FILE 143

function [mPay, tPay] = loan(amount, rate, years)% loan() calculates monthly and total payment of loan% Input arguments:% amount = loan amount in $% rate = annual interest rate in percent% years = number of years% Output arguments:% mPay = monthly payment% tPay = total payment

ratePerMonth = rate * 0.01 / 12; rPM = (1 + ratePerMonth) ^ (years * 12);

mPay = amount * rPM * ratePerMonth / (rPM - 1); tPay = mPay * years * 12;

Function definition line

Help text

Function body(Program)

Assign values tooutput arguments

Input argumentsOutput arguments

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>> [month total] = loan(25000, 7.5, 4)month = 600.72total = 28834.47

>> a = 70000; b = 6.5;>> [x y] = loan(a, b, 30)x = 440.06y = 158423.02

EXECUTING THE loan() FUNCTION

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First input argument is loan amountSecond is interest rateThird is the number of years

Define variables a and b.

Use a, b, and the number 30 for inputarguments and x (monthly pay) andy (total pay) for output arguments.