Matlab. A Practical Introduction to Programming and Problem Solving

541 Pages·2014·9.159 MB·English

by  Stormy Attaway (Auth.)

CHAPTER 1
Introduction to MATLAB
KEY TERMS CONTENTS
prompt characters logarithm 1.1 Getting into
MATLAB........4
programs strings commonlogarithm
scriptfiles casting natural logarithm 1.2 The MATLAB
Desktop Envi-
toolstrip typecasting constants
ronment
variable saturationarithmetic randomnumbers ........................5
assignment statement default seed
1.3 Variables and
assignment operator continuationoperator pseudorandom Assignment
user ellipsis openinterval Statements....6
initializing unary global stream 1.4 Numerical
incrementing operand character encoding Expressions
......................12
decrementing binary character set
identifier names scientific notation relational expression 1.5 Charactersand
Encoding.....21
reservedwords exponentialnotation Boolean expression
keywords precedence logical expression 1.6 Relational
mnemonic associativity relational operators Expressions
......................23
types nestedparentheses logical operators
classes innerparentheses scalars
double precision help topics short-circuit operators
floating point call afunction truth table
unsigned arguments commutative
range returningvalues
(cid:1)
MATLAB isaverypowerfulsoftwarepackagethathasmanybuilt-intoolsfor
solvingproblemsanddevelopinggraphicalillustrations.Thesimplestmethod
forusing the MATLAB product is interactively;anexpression isentered bythe
user and MATLAB responds immediately with a result. It is also possible to
3
MATLAB(cid:1).http://dx.doi.org/10.1016/B978-0-12-405876-7.00001-8
Copyright(cid:3)2013ElsevierInc.Allrightsreserved.
4 CHAPTER 1: Introduction to MATLAB
write scripts and programs in MATLAB, which are essentially groups of
commands that are executed sequentially.
This chapter will focus on the basics, including many operators and built-in
functions that can be used in interactive expressions.
1.1 GETTING INTO MATLAB
MATLAB is a mathematical and graphical software package with numerical,
graphical, and programming capabilities. It has built-in functions to
perform many operations, and there are toolboxes that can be added to
augment these functions (e.g., for signal processing). There are versions
available for different hardware platforms, in both professional and student
editions.
WhentheMATLABsoftwareisstarted,awindowopensinwhichthemainpart
is the Command Window (see Figure 1.1). In the Command Window, you
should see:
>>
FIGURE 1.1 MATLABcommandwindow
1.2 The MATLAB Desktop Environment 5
The >> is called the prompt. In the Student edition, the prompt instead is:
EDU>>
IntheCommandWindow,MATLABcanbeusedinteractively.Attheprompt,
any MATLAB command or expression can be entered, and MATLAB will
respond immediately with the result.
ItisalsopossibletowriteprogramsinMATLABthatarecontainedinscriptfiles
or M-files. Programs will be introduced in Chapter 3.
The following commands can serve as an introduction to MATLAB and allow
you to get help:
n demo will bring up MATLAB examples in the Help Browser, which has
examples of some of the features of MATLAB
n help will explain any function; help help will explain how help works
n lookfor searches through the help for a specific word or phrase (note: this
can take a long time)
n doc will bring up a documentation page in the Help Browser.
To exit from MATLAB, either type quit or exit at the prompt, or click on
MATLAB, then Quit MATLAB from the menu.
1.2 THE MATLAB DESKTOP ENVIRONMENT
In addition to the Command Window, there are several other windows that
can be opened and may be opened by default. What is described here is the
defaultlayoutforthesewindowsinVersionR2012b,althoughthereareother
possible configurations. Different versions of MATLAB may show other
configurationsbydefault,andthelayoutcanalwaysbecustomized.Therefore,
the main features will be described briefly here.
To the left of the Command Window is the Current Folder Window. The
folderthatissetastheCurrentFolderiswherefileswillbesaved.Thiswindow
shows the files that are stored in the Current Folder. These can be grouped in
manyways,forexample,bytype,andsorted,forexample,byname.Ifafileis
selected, information about that file is shown on the bottom.
TotherightoftheCommandWindowaretheWorkspaceWindowontopand
the Command History Window on the bottom. The Command History
Window shows commands that have been entered, not just in the current
session (in the current Command Window), but previously as well. The
Workspace Window will be described in the next section.
This default configuration can be altered by clicking the down arrow at the
top right corner of each window. This will show a menu of options
6 CHAPTER 1: Introduction to MATLAB
(different for each window), including, for example, closing that particular
window and undocking that window. Once undocked, bringing up the
menu and then clicking on the curled arrow pointing to the lower right will
dock the window again. To make any of these windows the active window,
click the mouse in it. By default, the active window is the Command
Window.
Beginning with Version 2012b, the look and feel of the Desktop Environ-
ment has been completely changed. Instead of menus and toolbars, the
Desktop now has a toolstrip. By default, three tabs are shown (“HOME”,
“PLOTS”, and “APPS”), although others, including “SHORTCUTS”, can be
added.
Underthe“HOME”tabtherearemanyusefulfeatures,whicharedividedinto
functional sectionsd“FILE”, “VARIABLE”, “CODE”, “ENVIRONMENT”, and
“RESOURCES” (these labels can be seen on the very bottom of the gray
toolstriparea).Forexample,under“ENVIRONMENT”,hittingthedownarrow
under Layout allows for customization of the windows within the Desktop
Environment. Other toolstrip features will be introduced in later chapters
when the relevant material is explained.
1.3 VARIABLES AND ASSIGNMENT STATEMENTS
TostoreavalueinaMATLABsession,orinaprogram,avariable isused.The
Workspace Window shows variables that have been created and their values.
Oneeasywaytocreateavariableistouseanassignmentstatement.Theformat
of an assignment statement is
variablename = expression
The variable is always on the left, followed by the ¼ symbol, which is the
assignment operator (unlike in mathematics, the single equal sign does not
mean equality), followed by an expression. The expression is evaluated and
thenthatvalueisstoredinthevariable.Hereisanexampleandhowitwould
appear in the Command Window:
>> mynum = 6
mynum =
6
>>
Here, the user (the person working in MATLAB) typed “mynum ¼ 6” at the
prompt, and MATLAB stored the integer 6 in the variable called mynum, and
then displayed the result followed by the prompt again. As the equal sign is
theassignmentoperator,anddoesnotmeanequality,thestatementshouldbe
read as “mynum gets the value of 6” (not “mynum equals 6”).
1.3 Variables and Assignment Statements 7
Notethatthevariablenamemustalwaysbeontheleft,andtheexpressionon
the right. An error will occur if these are reversed.
>> 6 = mynum
6 = mynum
j
Error: The expression to the left of the equals sign is not
a valid target for an assignment.
>>
Putting a semicolon at the end of a statement suppresses the output. For
example,
>> res = 9 e 2;
>>
Thiswouldassigntheresultoftheexpressionontherightside,thevalue7,to
the variable res; it just does not show that result. Instead, another prompt
appears immediately. However, at this point in the Workspace Window both
the variables mynum and res and their values can be seen. Note
Intheremainderofthe
The spaces in a statement or expression do not affect the result, but make it
text,thepromptthat
easier to read. The following statement, which has no spaces, would accom-
appearsaftertheresult
plish exactly the same result as the previous statement:
willnotbeshown.
>> res = 9-2;
MATLAB uses a default variable named ans if an expression is typed at the
prompt and it is not assigned to a variable. For example, the result of the
expression 6 þ 3 is stored in the variable ans:
>> 6 þ 3
ans =
9
This default variable is reused any time only an expression is typed at the
prompt.
Ashortcutforretypingcommandsistohittheuparrow[,whichwillgoback
tothepreviouslytypedcommand(s).Forexample,ifyoudecidedtoassignthe
result of the expression 6 þ 3 to a variable named result instead of using the
default variable ans, you could hit the up arrow and then the left arrow to
modify the command rather than retyping the entire statement:
>> result = 6 þ 3
result =
9
Thisisveryuseful,especiallyifalongexpressionisenteredanditcontainsan
error, and it is desired to go back to correct it.
8 CHAPTER 1: Introduction to MATLAB
Tochangeavariable,anotherassignmentstatementcanbeused,whichassigns
the value of a different expression to it. Consider, for example, the following
sequence of statements:
>> mynum = 3
mynum =
3
>> mynum = 4 þ 2
mynum =
6
>> mynum = mynum þ 1
mynum =
7
In the first assignment statement, the value 3 is assigned to the variable
mynum.Inthenextassignmentstatement,mynumischangedtohavethevalue
of the expression 4 þ 2, or 6. In the third assignment statement, mynum is
changed again, to the result of the expression mynum þ 1. Since, at that time,
mynum had the value 6, the value of the expression was 6 þ 1, or 7.
Atthatpoint,iftheexpressionmynumþ3isentered,thedefaultvariableansis
used as the result of this expression is not assigned to a variable. Thus, the
valueofansbecomes10,butmynumisunchanged(itisstill7).Notethatjust
typing the name of a variable will display its value (of course, the value can
also be seen in the Workspace Window).
>> mynum þ 3
ans =
10
>> mynum
mynum =
7
1.3.1 Initializing, Incrementing, and Decrementing
Frequently,valuesofvariableschange,asshownpreviously.Puttingthefirstor
initial value in a variable is called initializing the variable.
Adding to a variable is called incrementing. For example, the statement
mynum = mynum þ 1
increments the variable mynum by 1.
QUICK QUESTION!
How can1 be subtracted from the valueof a variable called Thisiscalleddecrementingthevariable.
num?
Answer
num = num e 1;
1.3 Variables and Assignment Statements 9
1.3.2 Variable names
Variablenamesareexamplesofidentifiernames.Wewillseeotherexamplesof
identifier names, such as function names, in future chapters. The rules for
identifier names are as follows.
n Thenamemustbeginwithaletterofthealphabet.Afterthat,thenamecan
contain letters, digits, and the underscore character (e.g., value_1), but it
cannot have a space.
n There is a limit to the length of the name; the built-in function
namelengthmax tells what this maximum length is (any extra characters
are truncated).
n MATLAB is case-sensitive, which means that there is a difference between
upper- and lowercase letters. So, variables called mynum, MYNUM, and
Mynumarealldifferent(althoughthiswouldbeconfusingandshouldnot
be done).
n Althoughunderscorecharactersarevalidinaname,theirusecancause
problemswithsomeprogramsthatinteractwithMATLAB,sosome
programmersusemixedcaseinstead(e.g.,partWeightsinsteadofpart_weights).
n There are certain words called reserved words, or keywords, that cannot be
used as variable names.
n Namesofbuilt-infunctions(describedinthenextsection)can,butshould
not, be used as variable names.
Additionally,variablenamesshouldalwaysbemnemonic,whichmeansthat
they should make some sense. For example, if the variable is storing the
radius of a circle, a name such as radius would make sense; x probably
wouldn’t.
The following commands relate to variables:
n who shows variables that have been defined in this Command Window
(this just shows the names of the variables)
n whos shows variables that have been defined in this Command Window
(this shows more information on the variables, similar to what is in the
Workspace Window)
n clear clears out all variables so they no longer exist
n clear variablename clears out a particular variable
n clear variablename1 variablename2 . clears out a list of variables (note:
separate the names with spaces).
If nothing appears when who or whos is entered, that means there aren’t any
variables!Forexample,inthebeginningofaMATLABsession,variablescould
be created and then selectively cleared (remember that the semicolon
suppresses output).
10 CHAPTER 1: Introduction to MATLAB
>> who
>> mynum = 3;
>> mynum þ 5;
>> who
Your variables are:
ans mynum
>> clear mynum
>> who
Your variables are:
ans
These changes can also be seen in the Workspace Window.
1.3.3 Types
Every variable has a type associated with it. MATLAB supports many types,
whicharecalledclasses.(Essentially,aclassisacombinationofatypeandthe
operationsthatcanbeperformedonvaluesofthattype,but,forsimplicity,we
will use these terms interchangeably for now.)
For example, there are types to store different kinds of numbers. For float or
real numbers, or, in other words, numbers with a decimal place (e.g., 5.3),
there are two basic types: single and double. The name of the type double is
short for double precision; it stores larger numbers than the single type.
MATLAB uses a floating point representation for these numbers.
There are many integer types, such as int8, int16, int32, and int64. The
numbersinthenamesrepresentthenumberofbitsusedtostorevaluesofthat
type. For example, the type int8 uses eight bits altogether to store the integer
anditssign.Asonebitisusedforthesign,thismeansthatsevenbitsareused
tostoreactualnumbers(0sor1s).Therearealsounsignedintegertypesuint8,
uint16, uint32, and uint64. For these types, the sign is not stored, meaning
that the integer can only be positive (or 0).
Therangeofatype,whichindicatesthesmallestandlargestnumbersthatcan
bestoredinthetype,canbecalculated.Forexample,thetypeuint8stores2^8
or256integers,rangingfrom0to255.Therangeofvaluesthatcanbestored
inint8,however,isfrome128toþ127.Therangecanbefoundforanytype
bypassing thename ofthetype asastring(whichmeansinsinglequotes)to
the functions intmin and intmax. For example,
>> intmin('int8')
ans =
-128
>> intmax('int8')
ans =
127
Thelargerthenumberinthetypename,thelargerthenumberthatcanbestored
init.Wewill,forthemostpart,usethetypeint32whenanintegertypeisrequired.
1.3 Variables and Assignment Statements 11
Thetypecharisusedtostoreeithersinglecharacters(e.g.,‘x’)orstrings,which
aresequencesofcharacters(e.g.,‘cat’).Bothcharactersandstringsareenclosed
in single quotes.
The type logical is used to store true/false values.
Variables that have been created in the Command Window can be seen in
the Workspace Window. In that window, for every variable, the variable
name, value, and class (which is, essentially, its type) can be seen. Other
attributes of variables can also be seen in the Workspace Window. Which
attributes are visible by default depends on the version of MATLAB.
However, when the Workspace Window is chosen, clicking on the down
arrow allows the user to choose which attributes will be displayed by
modifying Choose Columns.
By default, numbers are stored as the type double in MATLAB. There are,
however, many functions that convert values from one type to another. The
names of these functions are the same as the names of the types shown in
this section. These names can be used as functions to convert a value to that
type. This is called casting the value to a different type, or type casting. For
example,toconvertavaluefromthetypedouble,whichisthedefault,tothe
type int32, the function int32 would be used. Entering the assignment
statement
>> val = 6 þ 3;
wouldresultinthenumber9beingstoredinthevariableval,withthedefault
type of double, which can be seen in the Workspace Window. Subsequently,
the assignment statement
>> val = int32(val);
wouldchangethetypeofthevariabletoint32,butwouldnotchangeitsvalue.
Here is another example using two different variables.
>> num = 6 þ 3;
>> numi = int32(num);
>> whos
Name Size Bytes Class Attributes
num 1x1 8 double
numi 1x1 4 int32
Note that whos shows the type (class) of the variables, as well as the number
of bytes used to store the value of a variable. One byte is equivalent to eight
bits, so the type int32 uses four bytes. The function class can also be used to
see the type of a variable:
>> class(num)
ans =
double
12 CHAPTER 1: Introduction to MATLAB
One reason for using an integer type for a variable is to save space in
memory.
QUICK QUESTION!
Whatwouldhappenifyougobeyondtherangeforaparticular lowest value in the range, its value would be e128. This is
type? For example, the largest integer that can be stored in anexampleofwhatiscalledsaturationarithmetic.
int8 is 127, so what would happen if we type cast a larger
>> int8(200)
integertothetypeint8?
ans =
>> int8(200) 127
>> int8(-130)
Answer
ans =
Thevaluewouldbethelargestintherange,inthiscase127.If,
-128
instead, we use a negative number that is smaller than the
PRACTICE 1.1
n Calculatetherangeofintegersthatcanbestoredinthetypesint16anduint16.Useintmin
andintmaxtoverifyyourresults.
n EnteranassignmentstatementandviewthetypeofthevariableintheWorkspaceWindow.
Then,changeitstypeandviewitagain.Viewitalsousingwhos.
1.4 NUMERICAL EXPRESSIONS
Expressions can be created using values, variables that have already been
created,operators,built-infunctions,andparentheses.Fornumbers,thesecan
includeoperators,suchasmultiplication,andfunctions,suchastrigonometric
functions. An example of such an expression is:
>> 2 * sin(1.4)
ans =
1.9709
1.4.1 The Format Function and Ellipsis
The default in MATLAB is to display numbers that have decimal points with
four decimal places, as shown in the previousexample. (The default means if
youdonotspecifyotherwise,thisiswhatyouget.)Theformatcommandcan
be used to specify the output format of expressions.
There are many options, including making the format short (the default) or
long. For example, changing the format to long will result in 15 decimal
places. This will remain in effect until the format is changed back to short, as
demonstrated in the following: