MATLAB

Functions – Part I

Greg Reese, Ph.D

Research Computing Support Group

Academic Technology Services

Miami University

September 2013

MATLAB Functions – Part I

© 2010-2013 Greg Reese. All rights reserved

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M-files

M-file• Text file that holds MATLAB

commands or code • File ends in .m (for MATLAB)• Can hold a script or a function• Portable across platforms

Scripts

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Scripts

A script is a sequence of MATLAB commands stored in an m-file• Type in file as you would enter on

command line – Don't type prompt (>>)

• Scripts are simplest m-files because they have no input or output passed to or from them

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Scripts

To call a script is to execute (run) the commands in the script file• Call a script by typing its file's name

(the .m is optional)

A script can be called from:• The MATLAB command line• Another script• A function (to be discussed later)

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Scripts

When you run a script from the command line• All variables created in the script remain in

your workspace• The script can access all variables that were

in the workspace before it ran

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Scripts

Scripta = 3;c = 9;

BEFOREa = 7b = 5

No other variables

AFTERa = 3b = 5c = 9

Note: a changedb unchanged c added

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Scripts

Running a script can change the value of variables you have stored, or even erase the variables!

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Scripts

Scripts useful for:• Automating series of MATLAB commands,

e.g., ones you have to perform repeatedly from the command line

• Initializing workspace

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ScriptsTry It – automating commands

1. Remove all variables in your workspace by typing clear all and confirm by typing whos

2. Download the script petals.m and run it

3. Type whos to see if there are any variables

>> whos Name Size Bytes Class Attributes k 1x1 8 double rho 4x629 20128 double theta 1x629 5032 double

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Scripts

MATLAB runs startup.m when it starts. Put commands in file to set up your environment• Set working directory• Store often-used variables• Add directory of group functions to

MATLAB path

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Scripts

Try It – initialize environment

1. Type edit startup– Add the three lines

cd some_directoryhbar = 6.6262e-27 / ( 2*pi);mileToKm = 1.6;

2. At the command line type startup3. Verify that you're in the right directory

and the two variables are set

Put in name of directory on your machine

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Scripts

Questions?

Using MATLAB Functions

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Functions

You’re likely to want to compute functions of a variable, e.g.,

MATLAB has a large number of standard mathematical functions. To compute the function of a variable write the function name followed by the variable in parentheses.

x kxe )ln(x

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Functions

Exampleexp(x)

sqrt(x)• Usually store result in a variable,

e.g., root_x=sqrt(x)• Can pass constants too,

e.g., root_2=sqrt(2)

xe

x

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Functions

You can make complicated expressions by combining variables, functions, and arithmetic, e.g.,

5*exp(-k*t)+17.4*sin(2*pi*t/T)

Note how similar math and MATLAB are.

Tte kt 2sin4.175 Math

MATLAB

“*” means “×”

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Functions

Try It• Compute these

• The sine of 90° is 1. Use the MATLAB function sin to compute the sine of 90°.

Waz up?

2 4 8for2.0 xxe

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Functions

The MATLAB function sin is not doing what we expect. To get more information on a MATLAB function function_name, type

>> help function_name(Don’t include any parentheses.)

Try ItFind out more about sin

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Getting help

The help information explains that the argument is in radians, not degrees.

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Getting help

The help information often has links to related functions. Type help sin again and click on the link sind. It tells you that sind computes the sine of an argument that is in degrees.

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Getting help

What if you don’t know the MATLAB name of a mathematical function? Use

>> lookfor word

to search in the basic help information for “word”.

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Getting help

Example – what MATLAB function computes the inverse tangent?

>> lookfor tangent

produces 13 results of which three also say inverse – ATAN, ATAN2, and ATAND

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Getting help

Questions?

Writing Functions

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Writing Functions

A function is a MATLAB program that can accept inputs and produce outputs. Some functions don't take any inputs and/or produce outputs.

A function is called or executed (run) by another program or function. That program can pass it input and receive the function's output.

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Writing Functions

Why use functions?• Use same code in more than one place in

program• Reuse code by calling in different programs• Make debugging easier by putting all of one

kind of functionality in one place

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Writing Functions

Think of a function as a black box. • Calling program can't see (access) any of the variables inside the function• Function can't see any variables in the calling program

Function a = 5 b = ?Input Output

Calling Program a = ? b = 9

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Writing Functions

The code for a function is in an m-file. You can make the file in any text editor but it's easiest to do it with the MATLAB editor. To do this, at the command prompt type edit followed optionally by a filename not in quotes

• if file in current directory, MATLAB opens it• if not in current directory, MATLAB creates it

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Writing Functions

• What path does the baseball take?• How far does it go?• What's the best angle to throw it at?

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Writing Functions

y(t) = v sinθ t – ½ gt2

• v is initial speed (velocity)• g is 32 feet/sec2

• t is time• θ is throw angle

t

y(t)

Time

Hei

ght

θ

V

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Writing Functions

As soon as you make an m-file, give it a name (if needed) and save it. Do this by choosing “Save” or “Save as” under the file menu.

Try ItMake an m-file to compute the baseball height at a given time and call the file height.m>> edit height.mChoose File menu, Save

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Writing Functions

Function names• Must begin with a letter• Can contain any letters, numbers,

or an underscore• Name of file that contains function

should be function name with “.m” appended

– Example: the function compute_area should be in the file called compute_area.m

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Writing Functionsfunction y = fname( v1, v2 )

First line of function is called the function line• “function” – keyword that tells MATLAB function

starts with this line. Must be the word “function”• “y” – output variable(s). Can be any variable name• “fname” – any function name• “v1”, “v2” – input variable(s). Can be any variable name

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Writing Functions

function y = fname( v1, v2 )• Function ends when:

1. Another function line appears

2. An end-statement that matches the function line appears

3. There's no more code in file

• If function has outputs, must declare variables with output variable names and compute their values before function ends

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Writing Functions

Try ItMake the first line of your function be

function h = height( time )

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Writing Functions Pitcher #1

Greg (G-Dog) Reese

Fastball = 40 mph*

= 44 feet/sec

* with strong tailwind

function h = height( time )g = 32;speed = 44;angle = 70;h = ?

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Writing FunctionsTry ItWrite a function called height that accepts a time as an argument and returns the height at that time. Use the MATLAB function sind() to calculate the sine of an angle in degrees y(t) = v sinθ t – ½ gt2

function h = height( time )g = 32;speed = 44;angle = 70;h = speed*sind(angle)*time - 0.5*g*time^2;

Can be any name, but must be same name

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Writing FunctionsTo make the code clearer you can write comments, text that MATLAB ignores. If MATLAB sees a percent sign (%) it ignores the sign and everything after it on the rest of the line

function h = height( time )g = 32; % feet/sec^2speed = 44; % feet/secangle = 70; % degreesh = speed*sind(angle)*time - 0.5*g*time^2;

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Writing Functions

CAREFUL! You MUST save the file for any changes you made to go into effect. If you've fixed an error but your function still doesn't seem to work, make sure you saved the file.

TIP

If all changes to a file have been saved, the “save-icon”, a diskette, will be disabled (grayed-out)

Grayed-out “save” icon

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Writing FunctionsTo call a function type its name followed by the arguments in parentheses. If no arguments, can omit parentheses

Try It>> height(1)ans = 25.3465>> height(2.5)ans = 3.3662

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Writing FunctionsOften save result in a variable

Try It>> h1 = height(1)h1 = 25.3465>> h2 = height(2)h2 = 18.6930>> h1h1 = 25.3465

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Writing FunctionsMany functions require other functions to be passed to them. For example:• quad() – integration• fminbnd() – finding minimum• ezplot() – quick plot of function

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Writing FunctionsTo pass one function to another, use a function handle

Function handle– MATLAB data type that contains all info

needed to evaluate function– Make a function handle by putting the @

character in front of the function name

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Writing FunctionsCan see your function over range of values by using MATLAB function ezplot()

To use:

ezplot( @myFunction, [ t1 t2 ] )• Must include @• myFunction can have any name but must accept one and only one argument• t1 and t2 are starting and ending plotted values of argument

ez=easy

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Writing FunctionsTry ItPlot the baseball's height from when it's thrown to 2½ seconds later

>> ezplot( @height, [0 2.5] )Ignore the message Warning: Function failed to evaluate on array inputs;

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Writing Functions

Distance d that ball travels is

d = v2 sin(2θ) / g• v is initial speed (velocity)• g is 32 feet/sec2

• θ is throw angle

xDistance

θ

V

function distance = distance( speed )g = 32; % feet/sec^2angle = 70; % degreesdistance = ?;

function distance = distance( speed )g = 32; % feet/sec^2angle = 70; % degreesdistance = speed^2 * sind(2*angle) / g;

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Writing FunctionsTry ItWrite a function called distance that accepts a speed as an argument and returns the distance the ball was thrown.

d = v2 sin(2θ) / g

>> speed1 = 44;>> distance( speed1 )ans = 38.8887

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Writing Functions

Try ItStore pitcher 1's speed (44 ft/sec) in a variable and find out how far he threw the ball

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Writing FunctionsPitcher #2

Nolan (The Ryan Express) Ryan

Fastball = over 100 mph* = 147 feet/sec

* even after he turned 40!

>> speed2 = 147;>> distance( speed2 )ans = 434.0624

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Writing Functions

Try ItStore pitcher 2's speed (147 ft/sec) in a variable and find out how far he threw the ball

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Writing FunctionsTry ItMake a graph of how the distance the ball flies depends on the speed at which it's thrown. Plot the results from 40 to 140 feet/sec>> ezplot( @distance, [40 140] )

function distance = distance2( speed, angle )g = 32; % feet/sec^2distance = speed^2 * sind(2*angle) / g;

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Writing Functions

Try ItThe distance depends on both the velocity and the angle. Write a function called distance2 that takes both those arguments and computes the distance d = v2 sin(2θ)/g

>> distance2(speed1,20)ans = 38.8887>> distance2(speed2,20)ans = 434.0624>> distance2(speed1,50)ans = 59.5809>> distance2(speed2,50)ans = 665.0222

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Writing Functions

Try It d = v2 sin(2θ) / g

Compute how far both pitchers throw the ball at a 20o angle and at a 50o

angle

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Writing Functions

Want to find "best" angle, i.e., angle that makes the ball go the farthest. One way to do this is to plot

distance2( speed, angle)

over the range of angles from 0o to 90o

Problem: ezplot requires that the function passed to it have exactly one argument, but distance2 has two arguments

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Writing Functions

One solution – write another function that accepts only the angle and has the speed stored in it. This function calls distance2

function distance = distance1( angle )speed = 44;distance = distance2( speed, angle );

>> ezplot( @distance1, [0 90] )

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Writing Functions

Drawbacks• Have to make another m-file• When speed changes, have to edit the

m-file

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Writing Functions

Better solution

Use an anonymous function to convert distance2 to a function that accepts only one argument

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Writing Functions

Anonymous function – a quick way to write a simple function without having to make an m-file

@(arguments) expression• arguments – list of arguments separated

by commas• expression – a single MATLAB

expression. Can be a call of another function!

Try It

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Writing Functions

>> ezplot( @(angle)distance2(speed1,angle),[0 90] )

anonymous function

expression

"frozen"

varies

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Writing Functions

>> ezplot( @(angle)distance2(speed1,angle),[0 90] )

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Writing FunctionsTry ItWhat angle should pitcher 1 throw the ball at to make it go as far as possible?

45o

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Writing FunctionsTry ItRepeat for pitcher2

45o

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Writing FunctionsCan plot more than one data set on a graph. To do so:

1. Type the hold on command

2. Type the various ezplot calls

3. Type the hold off command

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Writing Functions

Try ItDraw the angle-distance plots for both pitchers on the same graph

>> hold on>> ezplot( @(angle)distance2(speed1,angle),[0 90] )>> ezplot( @(angle)distance2(speed2,angle),[0 90] )>> hold off

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Writing FunctionsIn other words…For the greatest distance throw the ball at a 45o angle, regardless of how strong your arm is!

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Writing FunctionsWhat angle should you throw the ball at to make it go as far as possible?

Another solution – use a MATLAB optimization function to find the angle that maximizes the distance

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Writing Functionsfminbnd finds the minimum of a single-variable function on a specified interval

>> x = fminbnd( @fun, x1, x2 )• fun is a function that has exactly one argument• x1 and x2 are the starting and ending points of the interval

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Writing Functions

Tipfminbnd finds the minimum of a function fun(x). To find the maximum, use the negative of the function, i.e., -fun(x)

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Writing Functions

Try ItUse fminbnd to find the best angle for both pitchers

>> fminbnd( @(angle) -distance2(speed1,angle),0,90 )ans = 45>> fminbnd( @(angle) -distance2(speed2,angle),0,90 )ans =45

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Writing Functions

Questions?

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The End