mat lab intro elmer

CEE15 Introduction to Computing for Civil Engineers !

An Introduction to MATLAB (Version 4.61 Release 1;)

Chapter 1 Introduction to MATLAB

1.1. MATLAB Windows Table 1.1 MATLAB Windows

Window Purpose "o$$a&'!(i&'o*! +ai&!*i&'o*,!e&ters!1aria2les,!ru&s!5ro6ra$s!7i6ure!(i&'o*!! "o&tai&s!out5ut!fro$!6ra59ic!co$$a&'s!E'itor!(i&'o*! "reates!a&'!'e2u6s!scri5t!a&'!fu&ctio&!files!au&c9!Pa'!(i&'o*! Pro1i'es!access!to!tools,!'e$os,!a&'!'ocu$e&tatio&!"o$$a&'!GH!Ki&!case!of!i&fi&ite!loo5PE !" help #!a!9el5!$e&u!a55earsE !" To!6et!9el5!o&!a!5articular!to5ic,!use!help to5ic!

7or!eDa$5le,!help dispE!!" +GT>GH! is! a! caseJse&siti1e! la&6ua6e,! for! eDa$5le,! TIME a&'! time are! t*o! 'iffere&t!

1aria2lesE!!!" T9e!co$$a&'!who lists!t9e!1aria2les!t9at!?ou!9a1e!'efi&e'E!!" T9e!co$$a&'!whos lists! t9e!1aria2les!alo&6!*it9! t9eir! siQes!a&'!*9et9er! t9e?!9a1e!&o&Qero!

i$a6i&ar?!5artE!

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!" Glso!who a&'!whos *ill!list!a!1aria2le!&a$e'!ans Ki&!co$$a&'!*i&'o*PE!Ans!stores!t9e!1alue!of!t9e!eD5ressio&!t9at!*as!last!co$5ute'!2ut!&ot!assi6&e'!!a!&a$eE!7or!eDa$5le,!

! !!!!!a=[2 3]; b=[3 5]; a+b; a.*b; who;

T9e!a2o1e!5ro6ra$!*ill!9a1e!a&!out5ut!as!t9e!follo*i&6!Kif!?ou!t?5e!t9e$!i&!co$$a&'!*i&'o*P:!Sour!1aria2les!are:!

! a!!!!!a&s!!!!!2!*9ere!a&s!stores!t9e!1alue!of!aET2E!!!" M-files!K!TestRE$,!TestUE$,VetcP!are!use'!to!eDecute!seIue&ce!of!co$$a&'s!t9at!are!store'!i&!

t9e!file!i&!a''itio&!to!eDecuti&6!co$$a&'s!e&tere'!t9rou69!t9e!@e?!2oar'E!M-file!Kalso!@&o*&!as! t9e! script fileP! is! a! file! of! GB"NN! c9aracters! a&'! is! 6e&erate'! usi&6! a&! e'itor! or! *or'!5rocessorE!To!eDecute!t9e!co$$a&'s!i&!t9e!M-file!sa?!Test1.m,!*e!&ee'!to!e&ter!t9e!co$$a&'!Test1 i&!t9e!co$$a&'!*i&'o*!or!ru&!t9e!M-file fro$!t9e!$e&uE!Sou!ca&!create!a!&e*!M-file or!e'it!a&!eDisti&6!M-file fro$!t9e!$e&uE!Glso!for!t9e!eDisti&6!file,!?ou!ca&!use!t9e!co$$a&'!edit to!e'it!t9at!fileE!

!" % i&'icates!co$$e&t!li&e!i&!t9e!5ro6ra$E!!" (ellipsisP!i&'icates!t9at!t9e!ro*!is!to!2e!co&ti&ue'E!!" T9e!co$$a&'!echo Ki&!t9e!co$$a&'!*i&'o*P!causes M-files to!2e!1ie*e'!as!t9e?!eDecuteE!

echo on!tur&s!o&!ec9oi&6!of!co$$a&'s!i&si'e!Bcri5tJfilesE!!!!!!! echo off!tur&s!off!ec9oi&6E! Ec9oi&6!ca&!2e!tur&e'!o&!a&'!off!*it9!t9e!co$$a&'!echoE!!!!!! a=[2,3]; b=[3 5]; c=[1:4;10:13]; a+b; a.*b; disp(a) disp(ans) disp(c) !T9e!a2o1e!M-file *ill!6i1e!us!a&!out5ut!*it9out!t9e!co$$a&'!echo as,!! U!!!!!W!!!!!!X!!!!RY!!!!!!R!!!!!U!!!!!W!!!!!Z!!!!!R[!!!!RR!!!RU!!!RW!!a&'!a&!out5ut!*it9!t9e!co$$a&'!echo as,!a\]U,W^_!2\]W!Y^_!c\]R:Z_R[:RW^_!a`2_!aET2_!'is5KaP!!!!!!U!!!!!W!'is5Ka&sP!!!!!!X!!!!RY!

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'is5KcP!!!!!!R!!!!!U!!!!!W!!!!!Z!!!!!R[!!!!RR!!!!RU!!!!RW!!!" T9e!co$$a&'!what is!t9e!'irector?!listi&6s!of!all!t9e!M-files!a&'!mat-files.!!" T9e!co$$a&'!type Test1.m or type Test1!lists!t9e!co&te&ts!of!a!s5ecifie'!file!&a$eE !" To!9alt!a!5ro6ra$!te$5oraril?,!*e!ca&!use!t9e!co$$a&'!pauseE!T9e!co$$a&'!pause (30) *ill!

9alt!t9e!5ro6ra$!for!W[!seco&'sE!To!co&ti&ue!*it9!our!5ro6ra$!*e!&ee'!to!9it!t9e!enter @e?!o&!our!@e?2oar'E!!

% This program reads the values of the matrices a and b % and computes and displays their addition and subtraction. a = input('Enter the value of a'); b = input('Enter the value of b'); pause c = a + b; d = a - b; disp('c=') disp(c) pause(5) disp('d=') disp(d)

!" +atla2!*ill!acce5t!$a&?!of!t9e!sa$e!co$$a&'s!as!u&iDE!!7or!eDa$5le,!ls!*ill!list!t9e!curre&t!'irector?,!c'!*ill!c9a&6e!itE!!5*'!6i1es!?ou!t9e!5rese&t!*or@i&6!'irector?E!!!

!" T9e!curre&t!'irector?!is!also!liste'!i&!t9e!tool2ar!a2o1e!t9e!co$$a&'!*i&'o*E!!!!" T?5i&6!path!*ill!6i1e!?ou!$atla2as!curre&t!searc9!5at9E!!T9is!is!*9ere!it!loo@s!for!co$$a&'s!

a&'!scri5ts!to!ru&!*9e&!?ou!t?5e!so$et9i&6!i&to!t9e!co$$a&'!*i&'o*E!!! 1.3. Basic Built In Functions in MALAB!1.3.1. Elementary Math Functions

Table 1.2 Math functions in MATLAB Function Description a2sKP! G2solute!1alue!eD5KP! ED5o&e&tial!

factorialKP! T9e!factorial!fu&ctio&!lo6KP! Matural!lo6arit9$!lo6R[KP! Hase!R[!lo6arit9$!sIrtKP! BIuare!root!

1.3.2. Trigonometric Math Functions Table 1.3 Trigonometric functions in MATLAB

Function Description Function Description acosKP! N&1erse!cosi&e! cosKP! "osi&e!acotKP! N&1erse!cota&6e&t! cotKP! "ota&6e&t!asi&KP! N&1erse!si&e! si&KP! Bi&e!ata&KP! N&1erse!ta&6e&t! ta&KP! Ta&6e&t!

1.3.3. Hyperbolic Math Functions Table 1.4 Hyperbolic functions in MATLAB

Function Description Function Description cos9KP!


!Note:!all!t9e!c9aracters!i&!fu&ctio&!&a$e!s9oul'!2e!i&!t9e!lo*er!caseE

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Chapter 2 Scalar, Vector and Matrix Operations

2.1. Scalars 2.1.1. Special Values pi: $!KUUbc!or!WERZRXP!i, j: R% !inf: &!KN&fi&it?,!for!eDa$5le,!it!*ill!2e!t9e!result!for!a&?!&u$2er!'i1i'e'!2?!QeroP!nan: Mot!a!&u$2er,!for!eDa$5le,!it!*ill!2e!t9e!result!for!t9e!'i1isio&!of!Qero!2?!Qero!clock: T9is!ele$e&t!retur&s!t9e!curre&t!ti$e!i&!a!siDJele$e&t!ro*!1ector!co&tai&i&6!?ear,!$o&t9,!'a?,!

9our,!$i&ute!a&'!seco&'sE!date: T9is!fu&ctio&!retur&s!t9e!curre&t!'ate!i&!a!c9aracter!stri&6!for$at,!suc9!as!U[Jdu&JeUE!!

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!Precedence in Arithmetic Operations: Precedence! ! Operation!

R! Pare&t9esis!U! ED5o&e&tiatio&,!left!to!ri69t!W! +ulti5licatio&!a&'!'i1isio&,!left!to!ri69t!Z! G''itio&!a&'!su2tractio&,!left!to!ri69t!

!Arithmetic operation between two scalars: Operation Algebraic form MATLAB expression G''itio&! ! ! a!`!2! ! ! a!`!2!Bu2tractio&! ! ! a!i!2! ! ! a!i!2!+ulti5licatio&!! ! a!'!2! ! ! a!T!2!

Ri69t!'i1isio&!!!!!!!!!!!!!!! !!ba !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!a!b!2!

ED5o&e&tiatio&! !!!! !! ! !!!!!!!!!!!!!!!!!!!!!!!!!a!h!2!ba

>eft!'i1isio&!!!!!!!!!!!!!!!!! !!ab !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!a!g!2!

!EDa$5le!R:!"o&si'er!t9e!follo*i&6!5ro6ra$:!a=2; b=3; x=a+b; fprintf('a=%1.0f\n',x) count=1; count=count+1; count time=0.0; time=5.0; disp('time') disp(time) !T9e!a2o1e!5ro6ra$!*ill!6i1e!us!t9e!follo*i&6!out5ut:!a=5 count = 2 time 5 EDa$5le!U:!"o&si'er!t9e!follo*i&6!5ro6ra$:!%area of a trapezium 1/2 * height * (base1 +base2) h=2; b1=3; b2=5; area=0.5*h*(b1+b2); disp('area') disp(area) !T9e!out5ut!*ill!2e:!area 8

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!KDhWJUTDhU`DJXEWPbKDhU`[E[Y[[YTDJWERZP!

2.2. Matrices and Vectors!G!$atriD!is!a!set!of!&u$2ers!arra&6e'!i&!a!recta&6ular!6ri'!of!ro*s!a&'!colu$&sE!Bcalar!#!a!\!WEY_!or!a!\!]WEY^_!jector!#!2!\!]REY!,!WER^_!or!2!\!]REY!!WER^_!!T9e!5re1ious!eDa$5le!is!a!ro*!1ectorE!Nt!ca&!2e!a!colu$&!1ector!as!*ell,!suc9!as,!2!\!]REY! or!! 2!\!]REY!_!WER^_!!!!!!!!WER^_!

+atriD!#!c!\! !ca&!also!2e!*ritte&!as!c!\!]JR![![_!R!R![_!R!iR![_![![!U^_!

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or!c!\!]JR,![,![_!R,!R,![_!R,!iR,![_![,![,!U^_!or!c!\!]JR!![!![!!!!or!!c!\!]JR,![,!![!!!!!! ! ! ! ! ! !!!!!!R!!R!![!! !!!!!!!!!!R,!R,!![!! ! ! ! ! ! !!!!!!R!iR![!! !!!!!!!!!!R,!JR,![!! ! ! ! ! ! !!!!!![!![!!U^_!!!!!!!!!!!!!!!![,![,!!U^_!!T9e!a2o1e!$atriD!9as!Z!ro*s!a&'!W!colu$&sE!G&?!ele$e&t!of!t9e!$atriD!is!'e&ote'!2?!cKi,!kP!*9ere!i!is!t9e!ro*!l!a&'!k!is!t9e!colu$&!lE!!

!" T9e!co$$a&'!size(a) 6i1es!t9e!siQe!of!a!s5ecific!$atriD!aE!a\]R:Z_R[:RW^_!!size(a) *ill!6i1e!us!t9e!follo*i&6!out5ut:!a&s!\!

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T9e!Mu$2er!of!Ro*s!is!co&si'ere'!t9e!first!'i$e&sio&!K9e&ce!UP!a&'!t9e!&u$2er!of!colu$&s!is!co&si'ere'!t9e!seco&'!'i$e&sio&!K9e&ce!ZPE!!T9e!'i$e&sio&!!!

!" T9e!co$$a&'!length(a)!retur&s!t9e!le&6t9!of!a!1ector!or!t9e!lo&6est!'i$e&sio&!of!a!UJA!arra?!a\]R:Z_R[:RW^_!length(a)!*ill!6i1e!us!t9e!follo*i&6!out5ut:!a&s!\!!Z!!2\]R:Y^_!length(b)!*ill!6i1e!us!t9e!follo*i&6!out5ut:!a&s!\!!Y!!

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Table 2.2 Special symbols related to array operations Character Description

:! "olo&_!creates!1ectors!*it9!eIuall?!s5ace'!ele$e&ts,!!re5rese&ts!ra&6e!of!ele$e&ts!i&!arra?s!\! Gssi6&$e&t!o5erator!KP! Bu2scri5tio&s!of!arra?s!]^! Hrac@ets_!for$s!arra?s,!e&closes!out5ut!ar6u$e&ts!i&!fu&ctio&s!

,! "o$$a_!se5arates!arra?!su2scri5tio&s!a&'!fu&ctio&!ar6u$e&ts,!!se5arates!co$$a&'s!i&!t9e!sa$e!li&e!_! Be$icolo&_!su55resses!'is5la?,!e&'s!ro*!i&!arra?!m! Bi&6le!Iuote_!$atriD!tra&s5ose,!creates!stri&6!

2.3. Special Matrices: magic: T9e!magic fu&ctio&!6e&erates!a&!&!'!&!$atriD!co&structe'!fro$!t9e!i&te6ers!fro$!R!t9rou69!&UE!T9e!i&te6ers!are!or'ere'!i&!suc9!a!*a?!t9at!all!t9e!ro*!su$s!a&'!all!t9e!colu$&!su$s!are!eIual!to!t9e!sa$e!&u$2erE!zeros: T9e!zeros fu&ctio&!6e&erates!a!$atriD!co&tai&i&6!all!QerosE!ones: T9e ones fu&ctio& 6e&erates!a!$atriD!co&tai&i&6!all!o&esE!!eye: T9e eye fu&ctio&!6e&erates!a&!i'e&tit?!$atriDE! "o&si'er!t9e!follo*i&6!5ro6ra$:!disp(magic(3)) disp('matrix of zeros') a=zeros(3) b=zeros(3,2) c=[1 2 3 ; 4 2 5] d=zeros(size(c)) disp('matrix of ones') a=ones(3) b=ones(3,2) c=[1 2 3;4 2 5] d=ones(size(c)) disp('identity matrix') a=eye(3) b=eye(3,2) d=eye(size(c)) T9e!out5ut!*ill!2e:! 8 1 6 3 5 7 4 9 2 matrix of zeros a = 0 0 0 0 0 0 0 0 0 b = 0 0 0 0 0 0

! n


c = 1 2 3 4 2 5 d = 0 0 0 0 0 0 matrix of ones a = 1 1 1 1 1 1 1 1 1 b = 1 1 1 1 1 1 c = 1 2 3 4 2 5 d = 1 1 1 1 1 1 identity matrix a = 1 0 0 0 1 0 0 0 1 b = 1 0 0 1 0 0 d = 1 0 0 0 1 0 2.4. Initializing Matrices T9ere!are!Z!$et9o's:!

!" ED5licit!lists!!" Aata!file!!" "olo&!o5erator!!" Lser!i&5ut!

2.4.1. Explicit Lists!c!\!]JR![![_!R!R![_!R!iR![_![![!U^_!!

!" The name of the matrix must start with a letter!a&'!ca&!co&tai&!u5!to!Re!c9aracters!t9at!are!'i6its,!letters!a&'!t9e!u&'erscore!c9aracterE!

!" (9e&!*e! 'efi&e! a!$atriD,!+GT>GH!*ill! 5ri&t! t9e! 1alue! of! t9e!$atriD! o&! t9e! &eDt! li&e!u&less!*e!su55ress!t9e!5ri&ti&6!*it9!t9e!se$icolo&!after!t9e!'efi&itio&E!

!Nf!a!si&6le!ro*!1ector!is!too!lo&6!t9e&!*e!ca&!use!ellipsis () *9ic9!is!si$5l?!t9ree!5erio'sE!!!Examples:!7!\!]R!YU!XZ!Rec!ZU!iZU!YY!nU!UU!R[e^_!!ca&!2e!*ritte&!as,!7!\!]R!YU!XZ!Rec!ZU!iZU!V!! YY!nU!UU!R[e^_!!

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N&!fact,!ellipsis ca&!2e!use'!i&!a&?!li&e!of!a!+GT>GH!5ro6ra$!i&!or'er!to!s9o*!t9e!co&ti&uatio&E!!Concatenation: Nf!2!\!]REY!WER^!a&'!s!\!]WE[!2^!t9e&!s!$atriD!is!eIui1ale&t!to!]WE[!REY!WERÊ!!!!!!!!!!!!(9at!a2out!6\]2a!2a^!a&'!6\]2a_2aô!"o&si'er!t9e!follo*i&6!U!+GT>GH!state$e&ts:!!s!\!]WE[!REY!WER^_!sKUP!\!JRE[_!!T9e!&e*!s!$atriD!is!]WE[!iRE[!WERÊ!!More examples: s!\!]WE[!iRE[!WER^_!sKZP!\!YEY_!sKnP!\!eEY_!!T9e!resulta&t!s!$atriD!is!s!\!]WE[!iRE[!WER!YEY![![![!eEYÊ!T9is!eDa$5le!s9o*s!t9at!if!a''itio&al!e&tries!are!co&cate&ate'!2e?o&'!t9e!ori6i&al!ra&6e!of!t9e!$atriD,!t9e!&e*!$atriD!is!5a''e'!*it9!Qeros!i&!2et*ee&!t9ose!e&triesE!!!!2.4.2. Data File: +atrices!ca&!2e!'efi&e'!fro$!i&for$atio&!t9at!9as!2ee&!store'!i&!a!data fileE!+GT>GH!ca&!i&terface!to!U!'iffere&t!t?5es!of!data filesE!!

!" MAT files: Aata!store'!i&!a!$e$or?Jefficie&t!2i&ar?!for$atE!T9e?!are!5refera2le!for!'ata!t9at!are!6oi&6!to!2e!6e&erate'!a&'!use'!2?!+GT>GH!5ro6ra$s!o&l?E!

!" ASCII files: Aata!store'!i&!GB"NN!c9aractersE!T9e?!are!&ecessar?!if! t9e!'ata!are!to!2e!s9are'!Ki$5orte'!or!eD5orte'P!*it9!5ro6ra$s!ot9er!t9a&!+GT>GHE!

2.4.2.1. Generating MAT Files: "o&si'er!t9e!follo*i&6!5ro6ra$E!a = [2 3]; b = [4 5]; c = a + b; d = a - b; save data c d; disp('c=') disp(c) disp('d=') disp(d) !T9e!a2o1e!5ro6ra$!*ill!auto$aticall?!6e&erate!a!data.mat fileE!T9e!out5ut!of!t9e!a2o1e!5ro6ra$!is:!c\!!!!!!X!!!!!n!'\!!!!!JU!!!!JU!!Mo*!co&si'er!a&ot9er!5ro6ra$!*9ic9!*ill!use!t9e!sa1e'!1alue!fro$!t9e!data.mat file!load data.mat; %Now data is a matrix c=data(1,:); d=data(2,:);

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e = c + d; disp('e=') disp(e) !T9e!out5ut!of!t9e!a2o1e!5ro6ra$!*ill!2e:!e\!!!!!!Z!!!!!X!!!!!!

!" save!filename!x y z!!-append!!a''s!t9e!1aria2les!to!a&!eDisti&6!MAT fileE! 2.4.2.2. Generating ASCII Files: Rules:

!" The ASCII files $ust!co&tai&!o&l?!&u$eric!i&for$atio&E!(e!ca&!use!% i&!t9e!ASCII file for!co$$e&ts!li&esE

!" Eac9! ro*! of! t9e!ASCII files $ust! co&tai&! t9e! sa$e! l! of! 'ata! 1alues! to! 2e! rea'! 2?! a&ot9er!5ro6ra$!i&!+GT>GHE

!" ASCII files are!6e&erate'!i&!W!*a?s: 2.4.2.2.1. By a MATLAB program: "o&si'er!t9e!follo*i&6!5ro6ra$:!a = [2 3]; b = [4 5]; c = a + b; d = a - b; save data.dat c d -ascii; disp('c=') disp(c) disp('d=') disp(d) Nt!*ill!create!t9e!follo*i&6!out5ut:!c\!!!!!!X!!!!!n!'\!!!!!JU!!!!JU!!Nt!*ill!also!create!a&!ASCII file calle'!data.dat!as!t9e!follo*i&6:!6.0000000e+000 8.0000000e+000 -2.0000000e+000 -2.0000000e+000!!"o&si'er!a&ot9er!5ro6ra$!*9ic9!*ill!use!t9e!'ata!store'!i&!t9e!data.dat fileE!load data.dat; x = data(1,:); y = data(2,:); e = x + y; disp('e=') disp(e) !T9e!out5ut!of!t9e!a2o1e!5ro6ra$!is:!e\!!!!!!Z!!!!!X!

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!Note:

!" H?!loa'i&6!t9e!ascii!file,!t9e!'ata!1alue!*ill!2e!auto$aticall?!store'!i&!a!$atriD!data K*it9!t9e!sa$e!&a$e!as!t9e!'ata!fileP!*9ic9!*ill!9a1e!t9e!sa$e!siQe!as!t9e!'ataE

!" T9ou69!1alues!of!t9e!1aria2les!c a&'!d *ere!store'!i&!t9e!data.dat file,!t9e?!ca&!2e!rea'!as!a!1aria2le!$atriD!Kdata)!for!our!caseE

2.4.2.2.2. By a Text Editor or Word Processor: Lsi&6!a!teDt!e'itor,!create!a!&e*!file!as!follo*s:!X! n!JU! JU!!Ba1e!t9e!file!as!data1.datE!Mo*!*rite!t9e!follo*i&6!+GT>GH!5ro6ra$:!load data1.dat; disp(data1) x = data1(1,:); disp(x) y = data1(2,:); disp(y) e = x + y; disp('e=') disp(e) !Nt!*ill!6i1e!us!a&!out5ut!of:!!!!!!!X!!!!!n!!!!!JU!!!!JU!!!!!!!X!!!!!n!!!!!JU!!!!JU!!e\!!!!!!Z!!!!!X!!2.4.2.2.3. ASCII files ca&! also! 2e! 6e&erate'! 2?! a! Fortran or! C 5ro6ra$! a&'! it! ca&! 2e! use'! 2?!+GT>GH!5ro6ra$sE!!!2.4.2.3. Colon Operator: Array Indexing T9e!colo&!o5erator!creates!1ectors!fro$!a!$atriD!2?!selecti1el?!re$o1i&6!ro*s!a&'!colu$&sE!!Nt!sta&'s!for!pGll!Ro*sq!or!pGll!"olu$&sEq!!Nt!also!9as!ot9er!usesE! load data1.dat; disp(data1) x = data1(1,:); disp(x) y = data1(2,:); disp(y) e = x + y; disp('e=') disp(e) !T9e!colo&!o5erator!create'!x a&'!y 1ectors!fro$!t9e!data1 $atriDE!9!\!R:n_!is!eIui1ale&t!to!t9e!follo*i&6!ro*!1ector!]R!U!W!Z!Y!X!c!n^E!

! RU


9!\!R:U:e_!is!eIui1ale&t!to!]R!W!Y!c!e^!*it9!t9e!middle value K\UP!i&!t9e!eD5ressio&!9!\!R:U:e_!is the step incrementE!!!" T9e!colo&!o5erator!ca&!also!select!a!su2!$atriD!fro$!a&ot9er!$atriDE!7or!eDa$5le,!c = [-1 0 0; 1 1 0; 1 -1 0; 0 0 2]; disp('c=') disp(c) c1 = c(:,2:3); c2 = c(3:4,1:2); disp('c1=') disp(c1) disp('c2=') disp(c2)

!T9e!a2o1e!5ro6ra$!*ill!9a1e!t9e!follo*i&6!out5ut:!c\!!!!!JR!!!!![!!!!![!!!!!!R!!!!!R!!!!![!!!!!!R!!!!JR!!!!![!!!!!![!!!!![!!!!!U!cR\!!!!!![!!!!![!!!!!!R!!!!![!!!!!JR!!!!![!!!!!![!!!!!U!cU\!!!!!!R!!!!JR!!!!!![!!!!![!!

!" a!\! ]^_!*9ere!a is!a&!e$5t?!$atriDE!E$5t?!$atriD! is!'iffere&t! fro$!$atriD! t9at!co&tai&s!o&l?!QerosE!

"o&si'er!t9e!follo*i&6!5ro6ra$:!c = [-1 0 0; 1 1 0; 1 -1 0; 0 0 2]; disp('c=') disp(c) x = c(:); disp('x=') disp(x)

!Nt!*ill!6i1e!us!t9e!follo*i&6!out5ut:!c\!!!!!JR!!!!![!!!!![!!!!!!R!!!!!R!!!!![!!!!!!R!!!!JR!!!!![!!!!!![!!!!![!!!!!U!!D\!!!!!JR!!!!!!R!!!!!!R!

! RW


!!!!![!!!!!![!!!!!!R!!!!!JR!!!!!![!!!!!![!!!!!![!!!!!![!!!!!!U!!


Eb! Ele$e&tJ2?Jele$e&t!ri69t!'i1isio&!Eg! Ele$e&tJ2?Jele$e&t!left!'i1isio&!Eh! Ele$e&tJ2?Jele$e&t!eD5o&e&tiatio&!

Precedence (higher to lower): RE!tra&s5ose!K.P,!5o*er!K.^P,!co$5leD!co&ku6ate!tra&s5ose!K'P,!$atriD!5o*er!K^P!UE!u&ar?!o5erator:!lo6ical!&e6atio&!K~P!WE!$ulti5licatio&!K.*P,!ri69t!'i1isio&!K./P,!left!'i1isio&!K.\P,!$atriD!$ulti5licatio&!K*P,!$atriD!ri69t!'i1isio&!

K/P,!$atriD!left!'i1isio&!K\P!ZE!a''itio&!K+P,!su2tractio&!K-P!YE!colo&!o5erator!K:P!!"7or!t9e!o5erators!*it9!t9e!sa$e!5rece'e&ce,!t9e!eDecutio&s!5rocee'!fro$!left!to!ri69tE!!"o&si'er!t9e!follo*i&6!5ro6ra$:!a=[1 3 2; 3 5 4; 2 5 4]; b=[2 3 1;6 8 1; 9 7 5]; c=a.*b d=a*b (e!*ill!9a1e!t9e!follo*i&6!out5ut:!c = 2 9 2 18 40 4 18 35 20 d = 38 41 14 72 77 28 70 74 27 !" (e!9a1e! to!2e!1er?!careful! so! t9at! t9e!$atriD!'i$e&sio&s!a6ree! i&!2ot9! t9e!arra?!a&'! t9e!$atriD!

o5eratio&sE!!" G&! arra?! o5eratio&! ca&! 2e! 2et*ee&! a! scalar! a&'! a! &o&scalar! K1ector! or! $atriDP! 2ut! t9e! $atriD!

o5eratio&!9as!to!2e!2et*ee&!&o&scalarsE!!"o&si'er!t9e!follo*i&6!5ro6ra$:!a=[2 4 7]; b=3*a b=3.*a c=a/5 c=a./5 Nt!*ill!6i1e!us!t9e!follo*i&6!out5ut:!b = 6 12 21 b = 6 12 21 c = 0.4000 0.8000 1.4000 c = 0.4000 0.8000 1.4000 !" T9e!5oi&t!to!&ote!i&!t9e!a2o1e!5ro6ra$!is!t9at!*9e&!*e!co&si'er!o5eratio&s!2et*ee&!a!scalar!a&'!a!

$atriD,!t9e!result!is!sa$e!for!2ot9!t9e!arra?!K.* a&'!./P!a&'!$atriD!K* a&'!/P!co$$a&'sE!!" T9e! arra?! o5eratio&s! for! t9e! 1ectors! a&'! t9e!$atrices! are! al$ost! si$ilarE!"o&si'er! t9e! follo*i&6!

5ro6ra$:!

! RY


a=[2 5 6] b=[2 3 5] c=a.*b d=a./b e=a.\b f=a.^2 g=a.^b h=3.0.^a k=[1:5;-1:-1:-5] l=ones(size(k)) m=k-l n=k.*m o=k.^3 T9e!out5ut!s9oul'!loo@!li@e!t9e!follo*i&6:!a = 2 5 6 b = 2 3 5 c = 4 15 30 d = 1.0000 1.6667 1.2000 e = 1.0000 0.6000 0.8333 f = 4 25 36 g = 4 125 7776 h = 9 243 729 k = 1 2 3 4 5 -1 -2 -3 -4 -5 l = 1 1 1 1 1 1 1 1 1 1 m = 0 1 2 3 4 -2 -3 -4 -5 -6 n = 0 2 6 12 20 2 6 12 20 30 o = 1 8 27 64 125 -1 -8 -27 -64 -125 2.5.2. Common Functions: "o&si'er!t9e!follo*i&6!+GT>GH!state$e&t:!2!\!si&KDP_!!sin(x):!calculates!t9e!si&e!of!t9e!!a&6le!x!Kra'ia&sPE!!" T9e!a2o1e!state$e&t!is!1ali'!if!a&!a&6le!is!a!scalar!or!if!a&!a&6le!is!a!$atriDE!If angle is a matrix,

then the function will be applied element by element to the values in the matrixE!!" G!fu&ctio&!ca&!9a1e!&o!ar6u$e&ts!KpiP,!o&e!ar6u$e&t!Ksin(angle)P!or!$ore!ar6u$e&ts!Krem(x,y)PE!!" G!fu&ctio&!ca&!also!2e!&este'!as,!?!\!lo6Ka2sKDPPE!!"o&si'er!t9e!follo*i&6!5ro6ra$:!x=[2.4 0.0 5.5; -1.2 -0.3 -1.7]

! RX


abs_x=abs(x) %It computes the absolute value of x. sqrt_x=sqrt(x) %It computes the square root of x. round_x=round(x) %It rounds x to nearest integer. fix_x=fix(x) %It rounds x to the nearest integer toward zero. floor_x=floor(x) %It rounds x to the nearest integer toward minus infinity. ceil_x=ceil(x) %It rounds x to the nearest integer toward infinity. sign_x=sign(x) %It returns -1 if x0. exp_x=exp(x) %It returns the value of e to the power x. log_x=log(x) %It returns the natural logarithm of x to the base e. log10_x=log10(x) %It returns the common logarithm of x to the base 10. a=[4 5];b=[2 2]; rem_ab=rem(a,b) %It returns the remainder of a/b. rut5ut:!x = 2.4000 0 5.5000 -1.2000 -0.3000 -1.7000 abs_x = 2.4000 0 5.5000 1.2000 0.3000 1.7000 sqrt_x = 1.5492 0 2.3452 0 + 1.0954i 0 + 0.5477i 0 + 1.3038i round_x = 2 0 6 -1 0 -2 fix_x = 2 0 5 -1 0 -1 floor_x = 2 0 5 -2 -1 -2 ceil_x = 3 0 6 -1 0 -1 sign_x = 1 0 1 -1 -1 -1 exp_x = 11.0232 1.0000 244.6919 0.3012 0.7408 0.1827 Warning: Log of zero. > In C:\matlab_sv12\work\Untitled1.m at line 10 log_x = 0.8755 -Inf 1.7047 0.1823 + 3.1416i -1.2040 + 3.1416i 0.5306 + 3.1416i Warning: Log of zero. > In C:\matlab_sv12\toolbox\matlab\elfun\log10.m at line 13 In C:\matlab_sv12\work\Untitled1.m at line 11 log10_x = 0.3802 -Inf 0.7404 0.0792 + 1.3644i -0.5229 + 1.3644i 0.2304 + 1.3644i rem_ab =

0 1 2.5.3. Transpose of a Matrix: T9e!tra&s5ose!of!a!$atriD!is!a!&e*!$atriD!i&!*9ic9!t9e!ro*s!of!t9e!ori6i&al!$atriD!are!t9e!colu$&s!of!t9e!&e*!$atriDE! Nf! a!$atriD!co&tai&s!a!co$5leD!1alue! t9e&!*e!ca&!9a1e!2ot9! t9e!co$5leD!co&ku6ate!tra&s5ose! a&'! co$5leD! &o&co&ku6ate! tra&s5oseE! T9e! follo*i&6! 5ro6ra$! s9oul'! eD5lai&! t9ese! ter$s!$ore!clearl?E!

!Program:

! Rc


disp('The original Matrices') a = [ 2i+3 3; 5 4i-5] aa = [2 3;5 -4] disp('The nonconjugated transpose :') disp('There are three ways to compute this.') b = transpose(a) %complex c = a.' %complex d = conj(a') %complex e = aa.' %noncomplex disp('The conjugated transpose :') disp('There are two ways to compute this.') f = a' %complex g = ctranspose(a) %complex h = aa.' %noncomplex Output: The original Matrices a = 3.0000 + 2.0000i 3.0000 5.0000 -5.0000 + 4.0000i aa = 2 3 5 -4 The nonconjugated transpose : There are three ways to compute this. b = 3.0000 + 2.0000i 5.0000 3.0000 -5.0000 + 4.0000i c = 3.0000 + 2.0000i 5.0000 3.0000 -5.0000 + 4.0000i d = 3.0000 + 2.0000i 5.0000 3.0000 -5.0000 + 4.0000i e = 2 5 3 -4 The conjugated transpose : There are two ways to compute this. f = 3.0000 - 2.0000i 5.0000 3.0000 -5.0000 - 4.0000i g = 3.0000 - 2.0000i 5.0000 3.0000 -5.0000 - 4.0000i h = 2 5 3 -4

2.5.4. Dot Product ---- dot(a,b): T9e!'ot!5ro'uct!is!t9e!scalar!co$5ute'!fro$!t*o!1ectors!of!t9e!sa$e!siQeE!

R

s K , Pn

i ii

do t product do t a b a b/

/ / 0N&!+GT>GH,!'ot!5ro'uct!ca&!2e!also!co$5ute'!as,!sum(a.*b),!*9ere!2ot9!a!a&'!b are!eit9er!ro*!or!colu$&!1ectorsE!Nf!a is!a!ro*!1ector!a&'!b is!a!colu$&!1ector,!t9e&!t9e!co$5utatio&!coul'!2e!'o&e!*it9!eit9er!of!t9e!follo*i&6!co$$a&'s:!!!sum(a.*b) or!!

! Rn


b

sum(a.*b)E!!or!if!a!a&'!2e!are!2ot9!colu$&!1ectors!?ou!$a?!*rite!aaT2E!!T9is!is!t9e!mi&&er!5ro'ucta!a&'!5ro'uces!a!scalar!result!o&!t9e!ot9er!9a&':!aT2a!!!6i1es!t9e!mruter!5ro'ucta!a&'!5ro'uces!a!$atriD!resultE!!2.5.5. Cross Product ---- cross(a,b): T9e! co$$a&'!cross(a,b)! retur&s! t9e! cross! 5ro'uct! of! t9e! 1ectors!a! a&'!bE!Hot9!a! a&'!b!$ust! 2e! W!ele$e&t!1ectorsE!!2.5.6. Matrix Multiplication ---- a*b:

R

Tn

ij ik k jk

c a b

c a/

/

/ 0T9e!first!$atriD!a $ust!9a1e!t9e!sa$e!&u$2er!of!ele$e&ts!i&!eac9!ro*!as!t9ere!are!i&!t9e!colu$&s!of!t9e!seco&'!$atriD!bE!T9e!resulta&t!$atriD!*ill!9a1e! t9e!sa$e!&u$2er!of!ro*s!of! t9e!first!$atriD!a&'!sa$e!&u$2er!of!colu$&s!as!t9e!seco&'!$atriDE! !(e!&ote!t9at! t9e!mi&&er!'i$e&sio&a!of!2ot9!$atrices!$ust!2e!t9e!sa$eE!!G&!eDa$5le!is!G]WDY^!T!H]YDR[^!\!"]WDR[^E!Note: Nf! f a&'! g are! t*o! ro*! 1ectors,! t9e! 'ot! 5ro'uct! $a?! also! 2e! co$5ute'! as! f*g K+atriD!

$ulti5licatio&PE! 2.5.7. Matrix Powers ---- a^n: T9e!co$$a&'!for!t9e!5o*er!of!a!$atriD!a is!a^2!K*9ere,!5o*er!is!eIual!to!UPE!a^2 is!eIui1ale&t!to!a*aE!Bi$ilarl?,!a^4 is! eIui1ale&t! to!a*a*a*aE!To! raise! a!$atriD! to! a! 5o*er,! t9e!$atriD!$ust! 2e! a! sIuare!$atriDE!!2.5.8. Matrix Inverse ---- inv(a): H?!'efi&itio&,! if!b is! a&! i&1erse!of! a! sIuare!$atriD!a,! t9e&!a*b or!b*a! are!2ot9!eIual! to!a&! i'e&tit?!$atriD!*it9!o&l?!t9e!'ia6o&al!ele$e&ts!2ei&6!R!a&'!ot9er!ele$e&ts!2ei&6![E!

Program: a = [4 -1 3] b = [-2 5 2] dot_ab1 = dot(a,b) dot_ab2 = a*b' cross_ab = cross(a,b) c = [2 5 1;0 3 -1] d = [1 0 2;-1 4 -2;5 2 1] mult_cd = c*d matrix_power1 = d^2 matrix_power2 = d*d matrix_inverse = inv(d) matrix_invmatrix = d*matrix_inverse Output: a = 4 -1 3 b = -2 5 2

! Re


dot_ab1 = -7 dot_ab2 = -7 cross_ab = -17 -14 18 c = 2 5 1 0 3 -1 d = 1 0 2 -1 4 -2 5 2 1 mult_cd = 2 22 -5 -8 10 -7 matrix_power1 = 11 4 4 -15 12 -12 8 10 7 matrix_power2 = 11 4 4 -15 12 -12 8 10 7 matrix_inverse = -0.2222 -0.1111 0.2222 0.2500 0.2500 0.0000 0.6111 0.0556 -0.1111 matrix_invmatrix = 1.0000 0 0.0000 -0.0000 1.0000 0.0000 -0.0000 -0.0000 1.0000

2.5.9. Determinants ---- det(a): Program: a = [2 4 5;1 2 3;0 2 4] det_a = det(a) Output: a = 2 4 5 1 2 3 0 2 4 det_a = -2

2.6. Formatted Printing of Matrices 2.6.1. Long-Short format N&!+GT>GH! t9e! 'eci$al! fractio&s! are! 5ri&te'! usi&6! a! 'efault! for$at! Kshort formatP! t9at! s9o*s! Y!si6&ifica&t!'eci$al!'i6itsE! Nf!*e!*a&t!1alues! to!2e!'is5la?e'! i&!a!'eci$al! for$at!*it9!RY!si6&ifica&t!'i6its,! *e! use! t9e! co$$a&'! format longE! T9e! for$at! ca&! 2e! retur&e'! to! a! 'eci$al! for$at! *it9! Y!si6&ifica&t!'i6its!usi&6!t9e!co$$a&'!format shortE!7or!eDa$5le:!a = [1.23456789 2.34567891]; disp(a); !(it9!format short,!t9e!a2o1e!5ro6ra$!*ill!5ri&t,!REUWZX! UEWZYc!

! U[


!a&'!*it9!format long,!REUWZYXcne[[[[[[!!!UEWZYXcneR[[[[[[!!Mo*!co&si'er!a!si$ilar!5ro6ra$!as!t9e!follo*i&6:!a = [1.23456789 2.34567891]; disp(a); format long; disp(a); The output will be: !REUWZX!!!!UEWZYc!REUWZYXcne[[[[[[!!!UEWZYXcneR[[[[[[! ! !!

!" format short e co$$a&'!*ill!5ri&t!t9e!1alues!i&!scie&tific!&otatio&!*it9!Y!si6&ifica&t!'i6its!a&'!format long e 5ri&ts!t9e!sa$e!2ut!*it9!RY!si6&ifica&t!'i6itsE!7or!eDa$5le:!

a = [1234.5678934567 234.56789198]; disp(a);

The above program will print (with the format short e command) 1.2346e+003 2.3457e+002

and the same will print with the format long e command. 1.234567893456700e+003 2.345678919800000e+002

!!" Format + co$$a&'!K5ri&t!t9e!si6&!o&l?P:!

c = [-1 0 1; 1 1 0; 1 -1 0; 0 0 2];disp(c) format +; disp(c) The output of the above program will be: -1 0 1 1 1 0 1 -1 0 0 0 2 - + ++ +- +!!(9e&!a!$atriD! is!5ri&te'!*it9! t9e! format + co$$a&',! t9e!o&l?!c9aracter!5ri&te'! is!5lus!a&'!$i&us!si6&sE!Nf!a!1alue!is!5ositi1e!a!5lus!si6&!*ill!2e!5ri&te'_!if!a!1alue!is!Qero,!a!s5ace!*ill!2e!5ri&te'_!if!a!1alue!is!&e6ati1e,!a!$i&us!si6&!*ill!2e!5ri&te'E!!

Table 2.4 Display formats Command Description 7or$at!2a&@! T*o!'eci$al!'i6its!

7or$at!co$5act! Eli$i&ates!e$5t?!li&es!7or$at!lo&6! 7iDe'J5oi&t!for$at!*it9!RZ!'eci$al!'i6its!7or$at!lo&6!e! Bcie&tific!&otatio&!*it9!RY!'eci$al!'i6its!7or$at!lo&6!6! Hest!of!RYJ'i6it!fiDe'!or!floati&6!5oi&t!

! UR


7or$at!loose! G''s!e$5t?!li&es!7or$at!s9ort! 7iDe'J5oi&t!for$at!*it9!Z!'eci$al!'i6its!7or$at!s9ort!e! Bcie&tific!&otatio&!*it9!Z!'eci$al!'i6its!7or$at!s9ort!6! Hest!of!YJ'i6it!fiDe'!or!floati&6!5oi&t!

2.6.2. Prescribed Formatted Printing

!" disp co$$a&':!!

disp('Total # of students in the class =') n = 20; disp(n) !T9e!5ro6ra$!a2o1e!*ill!6i1e!us!t9e!follo*i&6!out5ut:!Total # of students in the class = 20 !

!" 7or$atte'!out5ut!Kfprintf co$$a&'P:!T9e!s5ecifiers:!!!%e #!ED5o&e&tial!&otatio&!%f #!7iDe'!5oi&t!or!'eci$al!&otatio&!%g #!T9e!1alues!*ill!eit9er!use!%e or!%f,!'e5e&'i&6!o&!*9ic9!is!s9orter!!

"o&si'er!t9e!follo*i&6!5ro6ra$:!temp = 78.234567989; fprintf('The temperature is %f degrees',temp); Nt!*ill!5ri&t!The temperature is 78.234568 degrees Mo*!co&si'er!t9is:!temp = 78.234567989; fprintf('The temperature is %e degrees',temp); Nt!*ill!5ri&t!The temperature is 7.823457e+001 degrees Mo*,!!temp = 78.234567989; fprintf('The temperature is %g degrees',temp); *ill!6i1e!us!a&!out5ut!!The temperature is 78.2346 degrees Note:!Nf!t9e!stri&6!\n!a55ears!i&!t9e!for$at,!t9e!li&e!s5ecifie'!u5!to!t9at!5oi&t!is!5ri&te',!a&'!t9e!rest!of!t9e!i&for$atio&!*ill!2e!5ri&te'!i&!t9e!&eDt!li&eE! temp = 78.234567989; fprintf('The temperature is %g degrees.',temp) fprintf('It is warm.') T9e!5ro6ra$!a2o1e!*ill!6i1e!us!a&!out5ut!as!t9e!follo*i&6:!

! UU


The temperature is 78.2346 degrees.It is warm. (9ere!as,!!temp = 78.234567989; fprintf('The temperature is %g degrees.\n',temp) fprintf('It is warm.') *ill!5ri&t:!The temperature is 78.2346 degrees. It is warm. G&',!fprintf('The temperature is %g degrees.\nIt is warm.',temp) *ill!5ri&t:!The temperature is 78.2346 degrees. It is warm. !Note:!T9e!for$at!s5ecifiers!%f,!%e a&'!%g ca&!also!co&tai&!i&for$atio&!to!s5ecif?!t9e!&u$2er!of!'eci$al!5laces!to!5ri&t!a&'!t9e!&u$2er!of!5ositio&s!to!allot!for!t9e!corres5o&'i&6!1alueE!!temp = 78.234567989; fprintf('The temperature is %4.1f degrees.\n',temp) fprintf('It is warm.') !T9e!5ro6ra$!a2o1e!*ill!6i1e!us!t9e!follo*i&6!out5ut:!The temperature is 78.2 degrees. It is warm. N&!t9e!a2o1e!5ro6ra$!t9e!out5ut!*ill!co&tai&!t9e!1alue!of!temp 5ri&te'!*it9!Z!5ositio&s,!o&e!of!*9ic9!*ill!2e!a!'eci$al!5ositio&!as!s9o*&!a2o1eE!

! UW


Chapter 3 Branching Statements

3.1. Relational Operators +GT>GH!9as!siD!relational operators for!co$5ari&6!t*o!$atrices!of!eIual!siQe!or!t*o!scalarsE!

Table 3.1 Relational operators!Relational Operator Interpretation

t! >ess!t9a&!t\! >ess!t9a&!or!eIual!to!u! vreater!t9a&!u\! vreater!t9a&!or!eIual!to!\\! EIual!to!w\! Mot!eIual!to!

!"o&si'er!t9e!follo*i&6!5ro6ra$:!a = input('a ='); b = input('b ='); if a > b disp('a is greater than b') end if a < b disp('b is greater than a') end if a == b disp('a is equal to b') end rut5ut!R:!a =3 b =4 b is greater than a rut5ut!U:!a =4 b =2 a is greater than b rut5ut!W:!a =5 b =5 a is equal to b rut5ut!Z:!a =[2 3 5] b =[3 7 9] b is greater than a !rut5ut!Y:!a = [2 4 5] b = [1 3 6] !!" (9e&!*e! co$5are! t*o!$atrices! or! 1ectors! usi&6! a! relatio&al! o5erator,! t9e! logical expression is!

o&l?!true!if!all! t9e!ele$e&ts!satisf?!t9e!co&'itio&!i&'i1i'uall?E!7or!eDa$5le,!2ot9!a a&'!b 1ectors!9a1e!W!ele$e&tsE!N&!or'er! to!9a1e!t9e!lo6ical!eD5ressio&!a > b to!2e!true,!all! t9e!W!ele$e&ts!of!a $ust!2e!6reater!t9a&!t9e!corres5o&'i&6!ele$e&ts!of!bE!

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!" Gll!t9e!relatio&al!o5erators!9a1e!t9e!sa$e!5rece'e&ceE!!"o&si'er!t9e!follo*i&6!5ro6ra$!a&'!its!out5ut!!!a = input('a ='); b = input('b ='); if a > b disp('a is greater than b') end if a < b disp('b is greater than a') end if a == b disp('a is equal to b') end rut5ut!:!a = [2 3] b = [4 5] b is greater than a 3.2. Logical Operators (e!ca&!also!co$2i&e!t*o!lo6ical!eD5ressio&s!usi&6!t9e!logical operatorsE!

Table 3.2 Logical Operators Logical Operator Symbol

a&'! x!or! y!&ot! w!

!!" T9e!9ierarc9?!fro$!9i69est!to!lo*est,!is!not,!and, a&'!orE!

Table 3.3 Result of Logical Operators A B ~A A | B A & B

false! false! true! false! false!false! true! true! true! false!true! false! false! true! false!true! true! false! true! true!

3.3. Simple if Statement: if lo6ical!eD5ressio&! state$e&t!6rou5!a!end "o&si'er!t9e!follo*i&6!5ro6ra$!:!n = input('n=') count = 0; if n < 50 count = count + 1; disp('count') disp(count) end disp('count') disp(count) Output 1:!

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n=30 n = 30 count 1 count 1 Output 2:!n=100 n = 100 count 0 3.4. Nested if Statement: if lo6ical!eD5ressio&!R! state$e&t!6rou5!a!! if lo6ical!eD5ressio&!U! state$e&t!6rou5!2!! end state$e&t!6rou5!c!end

!!"o&si'er!t9e!follo*i&6!5ro6ra$:!n = input('Enter the value n = '); count = 0; if n < 50 count = count + 1; disp('count') disp(count) if n < 25 disp('n is less than 25') end disp('n is less than 50') end disp('count') disp(count) Output 1: Enter the value n = 100 count 0 Output 2: Enter the value n = 30 count 1 n is less than 50 count 1 Output 3: Enter the value n = 20 count 1 n is less than 25 n is less than 50 count

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1 3.5. else Clause: if lo6ical!eD5ressio&!! state$e&t!6rou5!a!else ! state$e&t!6rou5!2!end Nf!t9e!lo6ical!eD5ressio&!is!true,!t9e&!state$e&t!6rou5!a!is!eDecute'E!Nf!t9e!lo6ical!eD5ressio&!is!false,!t9e&!state$e&t!6rou5!2!is!eDecute'E!!Example: a = input('a='); b = input('b='); counta=0;countb=0; if a > b disp('a is greater than b') counta = counta + 1; else disp('b is greater than or equal to a') countb = countb + 1; end counta countb disp('end of program') Output 1:!a=5 b=3 a is greater than b

counta = 1 countb = 0 end of program

Output 2:!a=4 b=6 b is greater than or equal to a counta = 0 countb = 1 end of program 3.6. elseif Clause: if lo6ical!eD5ressio&!R! state$e&t!6rou5!a!elseif lo6ical!eD5ressio&!U!! state$e&t!6rou5!2!elseif lo6ical!eD5ressio&!W! state$e&t!6rou5!c!end

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Nf!lo6ical!eD5ressio&!R!is!true,!t9e&!o&l?!state$e&t!6rou5!a!is!eDecute'E!Nf!lo6ical!eD5ressio&!R!is!false!a&'!lo6ical!eD5ressio&!U!is!true,!t9e&!o&l?!state$e&t!6rou5!2!is!eDecute'E!Nf!lo6ical!eD5ressio&s!R!a&'!U!are!false!a&'!lo6ical!eD5ressio&!W!is!true,!t9e&!o&l?!state$e&t!6rou5!c!is!eDecute'E!Nf!2ot9!t9e!lo6ical!eD5ressio&s!R!a&'!U!are!true,!t9e&!o&l?!state$e&t!6rou5!a!is!eDecute'E!Nf!&o&e!of!t9e!lo6ical!eD5ressio&s!is!true,!t9e&!&o&e!of!t9e!state$e&ts!*it9i&!t9e!if!structure!is!eDecute'E!!!Example: a = input('a='); b = input('b='); if a > b disp('a is greater than b') elseif a < b disp('b is greater than a') elseif a ==b disp('a is equal to b') end disp('end of program') T9e!5ro6ra$!a2o1e!*ill!6i1e!us!t9e!follo*i&6!out5uts:!Output 1: a=3 b=5 b is greater than a end of program !Output 2: a=5 b=2 a is greater than b end of program !Output 3: a=5 b=5 a is equal to b end of program "o&si'er!t9e!5ro6ra$!2elo*:!a = input('a='); b = input('b='); c = input('c='); if a > b disp('a is greater than b') elseif b > c disp('b is greater than c') elseif c > a disp('c is greater than a') end disp('end of program') Output 1:!a=3 b=6 c=2 b is greater than c end of program Output 2:!

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a=3 b=2 c=1 a is greater than b end of program 3.7. elseif else Clause: if lo6ical!eD5ressio&!R! state$e&t!6rou5!a!elseif lo6ical!eD5ressio&!U!! !!!!!!!!!!!!!state$e&t!6rou5!2!elseif lo6ical!eD5ressio&!W! state$e&t!6rou5!c!else state$e&t!6rou5!'!end !Nf!lo6ical!eD5ressio&!R!is!true,!t9e&!o&l?!state$e&t!6rou5!a!is!eDecute'E!Nf!lo6ical!eD5ressio&!R!is!false!a&'!lo6ical!eD5ressio&!U!is!true,!t9e&!o&l?!state$e&t!6rou5!2!is!eDecute'E!Nf!lo6ical!eD5ressio&s!R!a&'!U!are!false!a&'!lo6ical!eD5ressio&!W!is!true,!t9e&!o&l?!state$e&t!6rou5!c!is!eDecute'E!Nf!2ot9!t9e!lo6ical!eD5ressio&s!R!a&'!U!are!true,!t9e&!o&l?!state$e&t!6rou5!a!is!eDecute'E!Nf!t9e!lo6ical!eD5ressio&s!R,!U!a&'!W!are!false,!t9e&!state$e&t!6rou5!'!is!eDecute'E!!Example: a = 5; b = 5; if a > b disp('a is greater than b') elseif b > a disp('b is greater than a') else disp('a is equal to b') end disp('end of program') Output: a is equal to b end of program

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Chapter 4 Loops

4.1. for Loops: for i&'eD!\!eD5ressio&! state$e&t!6rou5!a!end !Rules for for Loops: !" T9e!i&'eD!for!t9e!for loo5!$ust!2e!a!1aria2leE !" Nf! t9e! eD5ressio&! $atriD! is! a! scalar,! t9e&! t9e! loo5! *ill! 2e! eDecute'! o&e! ti$e,! *it9! t9e! i&'eD!

co&tai&i&6!t9e!1alue!of!t9e!scalarE !" Nf!t9e!eD5ressio&!$atriD!is!a!ro*!1ector,!t9e&!eac9!ti$e!t9rou69!t9e!loo5,!t9e!i&'eD!*ill!co&tai&!t9e!

&eDt!1alue!i&!t9e!1ectorE !" Nf!t9e!eD5ressio&!$atriD!is!a!$atriD,!t9e&!eac9!ti$e!t9rou69!t9e!loo5,!t9e!i&'eD!*ill!co&tai&!t9e!&eDt!

colu$&!i&!t9e!$atriDE !" L5o&!co$5letio&!of!t9e!loo5,!t9e!i&'eD!co&tai&s!t9e!last!1alue!use'E !" Nf!t9e!colo&!o5erator!is!use'!to!'efi&e!t9e!eD5ressio&!$atriD!usi&6!t9e!follo*i&6!for$at: for k = i&itial:i&cre$e&t:li$it!!t9e&!t9e!&u$2er!of!ti$es!t9e!loo5!*ill!2e!eDecute'!ca&!2e!co$5ute'!usi&6!t9e!follo*i&6!eIuatio&:!floorKKli$itJi&itialPbi&cre$e&tP`R!!Nf!t9e!1alue!is!&e6ati1e,!t9e!loo5!is!&ot!eDecute'E!!!Example: for!@!\!Y:Z:nW! T9e!loo5!*oul'!2e!eDecute'!U[!ti$es!*it9!t9e!fi&al!1alue!of!k 2ei&6!nRE!!Example: for k = 5 k = k*3 end !Output: k = 15 !Example:!for k = [5 4 9] x = k*3 end k Output: x = 15 x = 12 x =

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27 k = 9 Program: for k = [5 4 9;1 2 3] x = k*3 end k Output: x = 15 3 x = 12 6 x = 27 9 k = 9 3 Example:!for k = 2:5 x = k*3 end k !Output: x = 6 x = 9 x = 12 x = 15 k = 5 Example:!for k = 2:3:11 k x = k*3 end Output: k k = 2 x = 6 k = 5 x = 15 k = 8 x = 24 k =

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11 x = 33 k = 11 !" T9e!i&cre$e&t!ca&!also!2e!&e6ati1e,!for!eDa$5le,!for k = 5:-1:2! Example:!d = [2 4 7 9 13 20]; for k = 1:6 k if d(k)


4.2. while loop: while eD5ressio&! state$e&t!6rou5!a!!end Nf! t9e! eD5ressio&! is! true,! t9e! state$e&t! 6rou5 a is eDecute'E! Gfter! t9e! state$e&ts! are! eDecute',! t9e!co&'itio&!is!reteste'E!Nf!t9e!eD5ressio&!is!still!true,!t9e!6rou5!of!state$e&ts!is!eDecute'!a6ai&E!(9e&!t9e!co&'itio&!is!false,!t9e!co&trol!s9ifts!to!t9e!state$e&ts!follo*i&6!t9e!end state$e&tE!Nf!t9e!eD5ressio&!is!al*a?s!true,!t9e!loo5!2eco$es!a&!i&fi&ite!loo5!a&'!*e!&ee'!to!use!t9e!Ctrl-C!@e?!to!a2ort!itE!!T9e!follo*i&6!5ro6ra$!a''s! t9e!1alues! i&!a!1ector!x to!a!scalar!1aria2le!calle'!sum u&til!a!&e6ati1e!1alue!is!reac9e'E!!sum = 0; x = [2 5 7 5 9 0 -2 5 4] k = 1 while k = 0 sum = sum + x(k) k = k+1 end disp('The last value of k') k T9e!out5ut!of!t9e!5ro6ra$!a2o1e!is!as!follo*s:!x = 2 5 7 5 9 0 -2 5 4 k = 1 sum = 2 k = 2 sum = 7 k = 3 sum = 14 k = 4 sum = 19 k = 5 sum = 28 k = 6 sum = 28 k = 7 The last value of k k = 7 !Example:

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sum = 0; x = [2 5 7] k = 1 while x(k) >= 0 sum = sum + x(k) k = k+1 end disp('The last value of k') k Output: k = 1 sum = 2 k = 2 sum = 7 k = 3 sum = 14 k = 4 ??? Index exceeds matrix dimensions. Error in ==> C:\matlabR12\work\Untitled.m On line 4 ==> while x(k) >= 0 !Example: sum = 0; x = [2 5 7] k = 1 while k = 0 sum = sum + x(k) k = k+1 end disp('The last value of k') k Output: k = 1 sum = 2 k = 2 sum = 7 k = 3 sum = 14 k = 4 The last value of k k = 4

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Chapter 5 Plotting Capabilities

5.1. X Y Plot!rur!o2kecti1e!is!to!6e&erate!DJ?!5lot!fro$!'ata!store'!i&!U!1ectorsE!D!\!ti$e,!s! ! ?!\!te$5,!17!

[! YZEU!R! YnEY!

! U! ! ! XWEn!W! ! ! XZEU!

!T9ere!are!W!*a?s!to!rea'!t9is!'ataE!!

!" T9e!'ata!ca&!2e!rea'!eD5licitl?E!7or!eDa$5le,!!x=[0 1 2 3]; y=[54.2 58.5 63.8 64.2]; disp(x); disp(y); plot(x,y),... title('Temperature Measurement'),... xlabel('time, s'),... ylabel('temp, F'),... grid !*ill!6i1e!t9e!follo*i&6!out5ut!i&!t9e!co$$a&'!*i&'o*:!0 1 2 3 54.2000 58.5000 63.8000 64.2000 a&'!t9e!follo*i&6!fi6ure!i&!t9e!6ra59ic!*i&'o*:!!

!!

!" T9e!'ata!ca&!2e!rea'!usi&6!t9e!user!i&5utE!7or!eDa$5le!co&si'er!t9e!follo*i&6!5ro6ra$:!!

x=input('give the values of time'); y=input('give the values of temperature'); disp(x); disp(y); plot(x,y),... title('Temperature Measurement'),... xlabel('time, s'),... ylabel('temp, F'),... grid T9e!a2o1e!5ro6ra$!*ill!6i1e!us!t9e!follo*i&6!out5ut!i&!t9e!co$$a&'!*i&'o*:!

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give the values of time [0 1 2 3] give the values of temperature [54.2 58.5 63.8 64.2] 0 1 2 3 54.2000 58.5000 63.8000 64.2000 Nt!*ill!also!6i1e!us!t9e!sa$e!5lot!i&!t9e!6ra59ic!*i&'o*E!

!" T9e!'ata!ca&!2e! rea'! fro$!a&!ASCII file i&to!a!$atriD!a&'!store'! i&! t9e!1ectors!usi&6!colon operatorE!!

!7or!eDa$5le,!let!us!co&si'er!t9e!follo*i&6!file!Kdata.datP:![!R!U!W!YZEU!YnEY!XWEn!XZEU!!a&'!t9e!follo*i&6!5ro6ra$:!load data.dat; disp(data); x=data(1,:); y=data(2,:); plot(x,y),... title('Temperature Measurement'),... xlabel('time, s'),... ylabel('temp, F'),... grid T9e!out5ut!i&!t9e!co$$a&'!*i&'o*!*ill!2e!:![!!!!RE[[[[!!!!UE[[[[!!!!WE[[[[!YZEU[[[!!!YnEY[[[!!!XWEn[[[!!!XZEU[[[!!a&'!t9e!5lot!re$ai&s!t9e!sa$eE!!

!" (e!coul'!9a1e!also!store'!t9e!'ata!i&!a!mat file a&'!rea'!t9e!1alues!of!ti$e a&'!te$5erature!fro$!t9ereE!

!(e!ca&!also!9a1e!t*o!6ra59ic!*i&'o*s!at!t9e!sa$e!ti$eE!7or!eDa$5le,!!!load data.dat; disp(data); x=data(1,:); y=data(2,:); plot(x,y),... title('Temperature Measurement'),... xlabel('time, s'),... ylabel('temp, F'),... grid plot(y,x),... title('Temperature Measurement'),... ylabel('time, s'),... xlabel('temp, F'),... grid *ill!6i1e!us!o&l?!seco&'!5lot!2ut!!load data.dat; disp(data); x=data(1,:);

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y=data(2,:); figure(1) plot(x,y),... title('Temperature Measurement'),... xlabel('time, s'),... ylabel('temp, F'),... grid figure(2) plot(y,x),... title('Temperature Measurement'),... ylabel('time, s'),... xlabel('temp, F'),... grid *ill!6i1e!us!2ot9!t9e!5lotsE!!5.2. 2-D Plot Labels title(text)!#!T9is!co$$a&'!*rites!t9e!teDt!as!a!title!at!t9e!to5!of!t9e!curre&t!5lotE!xlabel(textP!#!T9is!co$$a&'!*rites!t9e!teDt!2e&eat9!t9e!DJaDis!o&!t9e!curre&t!5lotE!ylabel(text)!#!T9is!co$$a&'!*rites!t9e!teDt!2esi'e!t9e!?JaDis!o&!t9e!curre&t!5lotE!text(x,y,text)!#!T9is!co$$a&'!*rites!t9e!teDt!o&!t9e!6ra59ics!scree&!at!t9e!5oi&ts!s5ecifie'!2?!t9e!

coor'i&ates! KD,?P!usi&6! t9e! aDes! fro$! t9e! curre&t!5lotE! Nf!x! a&'!y! are!1ectors! t9e&! t9e! teDt! is!*ritte&!i&!eac9!5oi&tE!

gtext(text)!!#!T9is!co$$a&'!*rites!t9e!teDt!at!t9e!5ositio&!o&!t9e!6ra59ics!scree&!i&'icate'!2?!t9e!$ouse!or!arro*!@e?sE!

grid !#!T9is!co$$a&'!a''s!6ri'!li&es!to!t9e!curre&t!5lotE! 5.3. Plot Commands plot(x,y)!#!T9e!co$$a&'!6e&erates!a! li&ear!5lot!*it9!x!2ei&6!t9e!i&'e5e&'e&t!1aria2le!a&'!y!2ei&6!

t9e!'e5e&'e&t!1aria2leE!semilogx(x,y)!#!T9is!co$$a&'!6e&erates!a!5lot!*it9!lo6arit9$ic!scale!for!x!a&'!li&ear!scale!for!yE!semilogy(x,y) #!T9is!co$$a&'!6e&erates!a!5lot!*it9!lo6arit9$ic!scale!for!y!a&'!li&ear!scale!for!xE!loglog(x,y)!#!T9is!co$$a&'!6e&erates!a!5lot!*it9!lo6arit9$ic!scales!for!2ot9!x!a&'!yE! Program: time = [1 2 3 4 5] temp = [2 5 9 14 20] figure(1) plot(time,temp),xlabel('time (min)'),ylabel('temp (c)'),text([1 3],[2 9],... 'critical point'),gtext('current point1'),grid,gtext('current point2') figure(2) semilogy(time,temp),xlabel('time (min)'),ylabel('temp (c)'),text([1 3],[2 9],... 'critical point'),gtext('current point1'),grid,gtext('current point2') Output: Command Window # time = 1 2 3 4 5 temp = 2 5 9 14 20 Graphics Window # Figure No. 1:

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Figure No. 2:

!" G&?!fi6ure!ca&!2e!sa1e'!as!.fig eDte&sio&E!7or!eDa$5le,!figure1.figE!!5.4. Histograms (SKIPPED) hist(x) # T9e!co$$a&'!5lots!a!9isto6ra$!*it9!R[!i&ter1als!for!t9e!'ata!store'!i&!1ector!xE!hist(x,n) # T9e!co$$a&'!5lots!a!9isto6ra$!*it9!n i&ter1als!*it9!'ata!store'!i&!1ector!xE!hist(x,y) # Nt!5lots!a!9isto6ra$!for! t9e!'ata!i&!1ector!x *it9!t9e!i&ter1als!'efi&e'!2?!t9e!1ector!y,!a!1ector!*it9!ele$e&ts!i&!asce&'i&6!or'erE!

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Program: x = [2 5 7 9 8 3 2 6 9 3 5 4 7 6 5 9 2 4 6 8 5 3 4 6 1 3] figure(1) hist(x),title('Scores in midterm') figure(2) hist(x,[1 2 4 6]) figure(3) hist(x,5) Output in Graphics Window: Figure No. 1:

!Figure No. 2:

Figure No. 3:

5.5. Plotting Options 5.5.1. Multiple Plots T9ere!are!t9ree!*a?s!to!5lot!$ulti5le!cur1es!o&!t9e!sa$e!6ra59E!!" Nf!2ot9!x a&'!y are!$atrices!of!t9e!sa$e!siQe,!t9e!colu$&s!of!x!are!5lotte'!*it9!t9e!colu$&s!of!y!i&!

case!of!plot(x,y)E!

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!" (e!ca&!5lot!$ulti5le!cur1es!o&!t9e!sa$e!6ra59!2?!usi&6!$ulti5le!ar6u$e&ts!i&!t9e!5lot!co$$a&',!as!i&!t9e!follo*i&6:!!plot(x,y,w,z)!!

#"


figure(1) plot(time,temp,':+g'),legend('timetemp1','timetemp2'),xlabel('time'),... ylabel('temp') figure(2) plot(x,y,':g',a,b,'-.xb'),legend('xy','ab',2),title('multiple curves') hold plot(c,d,'-rO'),legend('xy','ab','cd',2) Output: Command Window: time = 1 0 2 2 3 4 4 6 5 8 temp = 2 12 5 15 9 18 14 32 20 57 x = 1 2 3 4 5 y = 2 5 11 17 26 a = 2 4 6 b = 12 17 19 c = 0 1 2 d = 7 11 42 Current plot held Graphics Window: Figure No. 1:

Figure No. 2:

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5.5.2. Sub Plots T9e! subplot co$$a&'! allo*s! us! to! s5lit! t9e! 6ra59ics! *i&'o*! i&to! su2*i&'o*sE! T9e! co$$a&'!subplot(m,n,p) s5lits! t9e! 6ra59ics! *i&'o*! i&to!m ro*s,! n colu$&s! a&'! sets! su2*i&'o*! p as! t9e!curre&tE!T9e!su2*i&'o*s!are!&u$2ere'!2?!ro*!fro$!left!to!ri69t,!to5!to!2otto$E!!Program: time = [1 2 3 4 5 6] temp = [13 16 20 29 40 48] x = [1 2 3 4 5] y = [2 5 11 17 26] a = [2 4 6] b = [12 17 19] c = [0 1 2] d = [7 11 42] subplot(2,2,1),plot(time,temp,':+g'),legend('timetemp'),... xlabel('time'),ylabel('temp') subplot(2,2,2),plot(x,y,':g',a,b,'-.xb'),legend('xy','ab',2),... title('multiple curves') subplot(2,2,3),plot(c,d,'-rO'),legend('cd',1) Output: Command Window : time = 1 2 3 4 5 6 temp = 13 16 20 29 40 48 x = 1 2 3 4 5 y = 2 5 11 17 26 a = 2 4 6 b = 12 17 19 c = 0 1 2 d = 7 11 42 Graphics Window:

! ZU


5.5.3. Special Symbols in Labels "o&si'er!t9e!follo*i&6!5ro6ra$:!clear!all_!clc_!close!all_!te$5\JRYER_!for!i\R:W[[!!!!!te$5\te$5`[ER_!!!!!DKiP\te$5_!!!!!if!a2sKDKiPPuWE[!!!!!!!!!?KiP\si6&KDKiPP_!!!!!else!!!!!!!!!?KiP\DKiPbWE[_!!!!!e&'!!!!!if!DKiPtJR!!!!!!!!!QKiP\JRE[JRbDKiP_!!!!!elseif!DKiPuR!!!!!!!!!QKiP\RJRbDKiP_!!!!!else!!!!!!!!!QKiP\[E[_!!!!!e&'!!!!!*KiP\cot9KDKiPPJRbDKiP_!e&'!5lotKD,?,!{r{P_!9ol'!o&!5lotKD,Q,{2{,{>i&e(i't9{,WP_!9ol'!o&!5lotKD,*,{EJ6{P!9\le6e&'K{Gs?$5totic{,{"ritical{,{r5ti$al{,UP_!Dla2elK{gal59a{P_!?la2elK{gDi{P_!T9e!out5ut!*ill!2e!Ki&!6ra59ic!*i&'o*P:!

! ZW


-15 -10 -5 0 5 10 15-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

2

3

AsymptoticCriticalOptimal

!+ore!c9aracter!seIue&ces!for!la2els!are!liste'!i&!ta2le!YEWE!

Table 5.3 Character sequence for labels in plots Character sequence Symbol Character sequence Symbol Character sequence symbol

gal59a! !! gu5silo&! "! gsi$! w!g2eta! #! g59i! 4 ! gle6! 5 !

g6a$$a! $! gc9i! %! gi&ft?! & !g'elta! &! g5si! '! gclu2suit! (!ge5silo&! )! go$e6a! *! g'ia$o&'suit! +!gQeta! ,! gva$$a! -! g9eartsuit! .!geta! /! gAelta! 0! gs5a'esuit! 1!gt9eta! 2! gT9eta! 3! gleftri69tarro*! 4!

g1art9eta! 6 ! g>a$2'a! 5! gleftarro*! 6!giota! 7! gOi! 8! gu5arro*! 9!g@a55a! :! gPi! ;! gri69tarro*! gsi6$a! H! geDists! < ! g2ullet! $"!g1arsi6$a! I! g&i! = ! g'i1! > !

gtau! J! gco&6! ? ! g&eI! @ !geIui1! A ! ga55roD! B ! gale59! C !gN$! D ! gRe! E ! g*5! F!

goti$es! G ! go5lus! H ! goslas9! I !gca5! J ! gcu5! K ! gsu5seteI! L !

gsu5set! M ! gsu2seteI! N ! gsu2set! O !gi&t! P ! gi&! Q ! go! R !

grfloor! K! glceil! L! g&a2la! S !

! ZZ


glfloor! M! gc'ot! }! gl'ots! ! !g5er5! T ! g&e6! U ! g5ri$e! ~!g*e'6e! V ! gti$es! ' ! g[! !grceil! N! gsur'! O! g$i'! y!g1ee! W ! g1ar5i! X ! gco5?ri69t! !

gla&6le! Y ! gra&6le! Z ! ! ! 5.6. 3-D plots T9e!plot co$$a&'!for!t9e!UJA!*orl'!ca&!2e!eDte&'e'!i&to!WJA!*it9!plot3E!T9e!for$at!is!t9e!sa$e!as!t9e!UJA!5lot,!eDce5t!t9e!'ata!are!i&!tri5les!rat9er!t9a&!i&!5airsE!

Program: x = [0 1 2 3 4 5 6 7 8 9]; y = [1 3 6 9 13 17 20 25 32 40]; height = [ 2 8 9 3 14 6 8 4 19 17]; plot3(x,y,height,'-xb'), title('Elevation above mean sea level'),... xlabel('x axis'),ylabel('yaxis'),zlabel('zaxis'),... legend('Height in meter'),grid Output: Command Window: x = 0 1 2 3 4 5 6 7 8 9 y = 1 3 6 9 13 17 20 25 32 40 height = 2 8 9 3 14 6 8 4 19 17 end of program Graphics Window:

!5.7. Mesh Plots and Surface Plots (SKIPPED) G!$es9!surface!is!6e&erate'!2?!a!set!of!1alues!i&!a!$atriDE!Eac9!5oi&t!i&!t9e!$atriD!re5rese&ts!t9e!1alue!of!a!surface!t9at!corres5o&'s!to!t9e!5oi&t!i&!t9e!6ri'E!G!surface!5lot!loo@s!li@e!t9e!$es9!5lot!eDce5t!t9at!t9e!s5aces!2et*ee&!t9e!li&es!are!fille'!i&E!!Program: [xgrid,ygrid] = meshgrid(1:1:10,1:1:10); xgrid ygrid z = sqrt(abs(1-xgrid.^2-ygrid.^2)) mesh(z), title('mesh plot')

! ZY


Output: Command Window : xgrid = 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 ygrid = 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 z = Columns 1 through 7 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 2.0000 2.6458 3.4641 4.3589 5.2915 6.2450 7.2111 3.0000 3.4641 4.1231 4.8990 5.7446 6.6332 7.5498 4.0000 4.3589 4.8990 5.5678 6.3246 7.1414 8.0000 5.0000 5.2915 5.7446 6.3246 7.0000 7.7460 8.5440 6.0000 6.2450 6.6332 7.1414 7.7460 8.4261 9.1652 7.0000 7.2111 7.5498 8.0000 8.5440 9.1652 9.8489 8.0000 8.1854 8.4853 8.8882 9.3808 9.9499 10.5830 9.0000 9.1652 9.4340 9.7980 10.2470 10.7703 11.3578 10.0000 10.1489 10.3923 10.7238 11.1355 11.6190 12.1655 Columns 8 through 10 8.0000 9.0000 10.0000 8.1854 9.1652 10.1489 8.4853 9.4340 10.3923 8.8882 9.7980 10.7238 9.3808 10.2470 11.1355 9.9499 10.7703 11.6190 10.5830 11.3578 12.1655 11.2694 12.0000 12.7671 12.0000 12.6886 13.4164 12.7671 13.4164 14.1067 Graphics window:

! ZX


Program: z = [1 4 6;5 7 13;12 15 23] mesh(z) Output: Command Window : z = 1 4 6 5 7 13 12 15 23 Graphics Window:

Program: [xgrid,ygrid] = meshgrid(1:1:10,1:1:10); z = sqrt(abs(1-xgrid.^2-ygrid.^2)); surf(z), title('surface plot') Output: Graphics Window:

! Zc


5.8. Contour Plots (SKIPPED) "o&tour!5lots!s9o*!li&es!of!co&sta&t!ele1atio&!or!9ei69tE!

!" T9e!co$$a&'!contour(z) 'ra*s!a!co&tour!5lot!of!$atriD!zE!T9e!&u$2er!of!co&tour!li&es!a&'!t9eir!1alues!are!c9ose&!auto$aticall?!2?!+GT>GHE!

!" T9e!co$$a&'!contour(z,n) 5ro'uces!a!co&tour!5lot!of!$atriD!z *it9!n!co&tour!le1elsE!!" T9e! co$$a&'! contour(z,v) 5ro'uces! a! co&tour! 5lot! of! z *it9! co&tour! le1els! at! t9e! 1alues!

s5ecifie'!2?!1ector!vE!!" T9e! co$$a&'!pcolor(z) fu&ctio&!$a5s! t9e! 9ei69t! to! a! set! of! colors! a&'! 5rese&ts! t9e! sa$e!

i&for$atio&!as!t9e!contour(z)!5lotE!!" T9e!co$$a&'!contour3(z) *ill!6i1e!us!WJA!co&tour!5lotsE!

!Program: [xgrid,ygrid] = meshgrid(-0.5:0.1:0.5,-0.5:0.1:0.5); z = sqrt(abs(1-xgrid.^2-ygrid.^2)); figure(1) contour(z),title('Contour plot with default number of control levels') figure(2) contour(z,10),title('Contour plot with 10 control levels') figure(3) contour(z,[0.8 0.85 0.9]),title('Contour plot with 3 specified interval') figure(4) pcolor(z),title('Contour plot with color mapping') Output: Figure No. 1:

!Figure No. 2:

! Zn


Figure No. 3:

Figure No. 4:!

! 5.9. Polynomial Regression 5.9.1 Polyfit Function T9e!+GT>GH! fu&ctio&! for! co$5uti&6! t9e!2est! fit! to! a! set!of!'ata!*it9!5ol?&o$ial!*it9! a! s5ecifie'!'e6ree!is!t9e!polyfit fu&ctio&E!T9is!fu&ctio&!9as!t9ree!ar6u$e&ts:!!T9e!x!a&'!y!coor'i&ates!of!t9e!'ata!5oi&ts!a&'!'e6ree!N of!t9e!5ol?&o$ialE!


Program: x = [1 2 3 4 5 6 7 8 9] y = [2 4 7 11 16 23 32 45 60] coef = polyfit(x,y,2) ybest = polyval(coef,x) z = [1 -2 -3 10] root = roots(z) Output: x = 1 2 3 4 5 6 7 8 9 y = 2 4 7 11 16 23 32 45 60 coef = 0.9405 -2.4548 4.7143 ybest = Columns 1 through 7 3.2000 3.5667 5.8143 9.9429 15.9524 23.8429 33.6143 Columns 8 through 9 45.2667 58.8000 z = 1 -2 -3 10 root = -2.0000 2.0000 + 1.0000i 2.0000 - 1.0000i

! Y[


Chapter 6 M-File Functions

function output arguments = name of the function (input arguments) T9e! li&e! a2o1e! 'efi&es! t9e! i&5ut! a&'! out5ut! ar6u$e&ts! a&'! 'isti&6uis9es! t9e! fu&ctio&! file! fro$! t9e!scri5t!fileE!

!" T9e!first!fe*!li&es!s9oul'!2e!co$$e&ts!2ecause!t9e?!*ill!2e!'is5la?e'!if!9el5!is!reIueste'!for!t9e!fu&ctio&!&a$e,!for!eDa$5le,!help circle K*9ere!circle!is!t9e!fu&ctio&!&a$ePE!

!" T9e!o&l?!i&for$atio&!retur&e'!fro$!t9e!fu&ctio&!is!co&tai&e'!i&!t9e!out5ut!ar6u$e&tsE!Gl*a?s!c9ec@! to! 2e! sure! t9at! t9e! fu&ctio&! i&clu'es! a! state$e&t! t9at! assi6&s! a! 1alue! to! t9e! out5ut!ar6u$e&tE!

!" T9e! sa$e! i&5ut! a&'! out5ut! ar6u$e&ts! or! $atrices! ca&! 2e! use'! i&! 2ot9! a! fu&ctio&! a&'! t9e!5ro6ra$!t9at!refere&ces!it,!alt9ou69!*e!ca&!use!se5arate!i&5ut!ar6u$e&tsE!G&?!1alues!co$5ute'!i&!t9e!fu&ctio&,!ot9er!t9a&!t9e!out5ut!ar6u$e&ts,!are!&ot!accessi2le!fro$!t9e!5ro6ra$E!

!" G!fu&ctio&!t9at!is!6oi&6!to!retur&!$ore!t9a&!o&e!1alue!s9oul'!s9o*!all!1alues!to!2e!retur&e'!as!a!1ector!i&!t9e!fu&ctio&!state$e&t,!as!i&!t9is!eDa$5le,!*9ic9!*ill!retur&!t9ree!1alues:!function [dist, vel, accel] = motion(x)

!" G!fu&ctio&!t9at!9as!$ulti5le!i&5ut!ar6u$e&ts!$ust!list!t9e!ar6u$e&ts!i&!t9e!fu&ctio&!state$e&t,!as!s9o*&!i&!t9e!eDa$5le,!*9ic9!9as!t*o!i&5ut!ar6u$e&ts:

function error = mse(w,d) !" T9e!s5ecial!1aria2les!nargin a&'!nargout ca&!2e!use'!to!'eter$i&e!t9e!&u$2er!of!i&5ut!a&'!

out5ut!ar6u$e&ts!res5ecti1el?E!

Case 1: (single input and single output) Program: r = [0 1 2] volume = vol(r); fprintf('The volumes of the spheres are = ') disp(volume) Function (vol.m): function volume = vol(r) %This function calculates the volume of spheres volume = 4/3*pi*r.^3 Output: r = 0 1 2 volume = 0 4.1888 33.5103 The volumes of the spheres are = 0 4.1888 33.5103 Case 2: (multiple inputs and single output) Program: r = [0 1 2]; h = [1 3 5]; volume = vol(r,h); fprintf('The volumes of the spheres are = ') disp(volume) Function (vol.m): function volume = vol(r,h) %This function calculates the volume of cylinders

! YR


volume = pi*r.^2.*h Output: volume = 0 9.4248 62.8319 The volumes of the spheres are = 0 9.4248 62.8319 Case 3: (single input and multiple outputs) Program: r = [0 1 2]; [sarea,volume] = survol(r); fprintf('The volumes of the spheres are = ') disp(volume) fprintf('The surface areas of the spheres are = ') disp(sarea) Function (survol.m): function [sarea,volume] = survol(r) %This function calculates the volume and surface area of spheres volume = 4/3*pi*r.^3 sarea = 4*pi*r.^2 Output: volume = 0 4.1888 33.5103 sarea = 0 12.5664 50.2655 The volumes of the spheres are = 0 4.1888 33.5103 The surface areas of the spheres are = 0 12.5664 50.2655 Case 4: (multiple inputs and multiple outputs) Program: r = [3 1 2]; h = [2 4 6]; [volcylinder,volsphere] = vol(r,h); fprintf('The volumes of the spheres are = ') disp(volsphere) fprintf('The volumes of the cylinders are = ') disp(volcylinder) Function (vol.m): function [volcylinder,volsphere] = vol(r,h) %This function calculates the volume and surface area of spheres volsphere = 4/3*pi*r.^3 volcylinder = pi*r.^2.*h Output: volsphere = 113.0973 4.1888 33.5103 volcylinder = 56.5487 12.5664 75.3982 The volumes of the spheres are = 113.0973 4.1888 33.5103 The volumes of the cylinders are = 56.5487 12.5664 75.3982

Chapter 7 Input/Output Functions

7.1. Opening the Files fid = fopen(filename,permission) *9ere!5er$issio&s!are:!

! YU


{r{!!!!!!!!r5e&!file!for!rea'i&6!K'efaultPE!{*{!!!!!!r5e&!file,!or!create!&e*!file,!for!*riti&6_!'iscar'!eDisti&6!co&te&ts,!if!a&?E!{a{!!!!!!!r5e&!file,!or!create!&e*!file,!for!*riti&6_!a55e&'!'ata!to!t9e!e&'!of!t9e!fileE!{r`{!!!!!r5e&!file!for!rea'i&6!a&'!*riti&6E!{*`{!!!!r5e&!file,!or!create!a!&e*!file,!for!rea'i&6!a&'!*riti&6_!'iscar'!eDisti&6!co&te&ts,!if!a&?E!{a`{!!!!!r5e&!file,!or!create!&e*!file,!for!rea'i&6!a&'!*riti&6_!a55e&'!'ata!to!t9e!e&'!of!t9e!fileE!!Example: fid = fopen('exp.txt','w'); 7.2. Closing the Files fclose(fid) or fclose('all') 7.3. Writing the Output Files To!*rite!for$atte'!'ata!to!a!file,!*e!ca&!use!t9e!follo*i&6!co$$a&':!fprintf(fid,format,A,...) !*9ere! fid! is! t9e! file! i'e&tificatio&! use'! i&! t9e! o5e&! co$$a&',! format! is! t9e! 'escri5tor! fiel'! a&'!A!'e&otes!t9e!out5ut!ar6u$e&tsE!!7.3.1. Useful Switches e!!!!!!!ED5o&e&tial!&otatio&!Kusi&6!a!lo*ercase!e!as!i&!WERZRYe`[[P!E!!!!!!ED5o&e&tial!&otatio&!Kusi&6!a&!u55ercase!E!as!i&!WERZRYE`[[P!f!!!!!!!7iDe'J5oi&t!&otatio&!6!!!!!!T9e!$ore!co$5act!of!e!or!f,!as!'efi&e'!i&!]U^E!N&si6&ifica&t!Qeros!'o!&ot!5ri&tE!s!!!!!!!Btri&6!of!c9aracters!!g&!!!!!!!!Me*!li&e!gt!!!!!!!!!


Output:!A unit circle has circumference 6.283186. !Example: B = [8.8 7.7; 8800 7700] L = fopen('exp.txt','w'); fprintf(L,'X is %6.2f meters or %8.3f mm\n',9.9,9900,B) fclose(L) Output:!X is 9.90 meters or 9900.000 mm X is 8.80 meters or 8800.000 mm X is 7.70 meters or 7700.000 mm 7.4. Reading the Input Files A = fscanf(fid,format,size) (9ere!size!is!a&!ar6u$e&t!t9at!'eter$i&es!9o*!$uc9!'ata!is!rea'E!jali'!o5tio&s!are:!&!!!!!!!!Rea'!&!ele$e&ts!i&to!a!colu$&!1ectorE!N&f!!!!!Rea'!to!t9e!e&'!of!t9e!file,!resulti&6!i&!a!colu$&!1ector!co&tai&i&6!t9e!sa$e!&u$2er!of!ele$e&ts!

as!are!i&!t9e!fileE!]$,&^!Rea'!e&ou69!ele$e&ts!to!fill!a&!$J2?J&!$atriD,!filli&6!t9e!$atriD!i&!colu$&!or'erE!&!ca&!2e!N&f,!

2ut!&ot!$E!!Example: G&!GB"NN!teDt!file!calle'!eD5EtDt!loo@s!li@e:!0.00 1.00000000 0.10 1.10517092 ... 1.00 2.71828183 !+atla2!rea's!t9is!GB"NN!file!2ac@!i&to!a!t*oJcolu$&!+GT>GH!$atriD:!fid = fopen('exp.txt'); a = fscanf(fid,'%g %g',[2 inf]) % It has two rows now. a = a'; fclose(fid) !

! YZ


Appendix: Statistical Measurements:

A.1. Simple Analysis!!" max(x) #!Nf!x is!a!1ector!t9e&!t9e!fu&ctio&!retur&s!t9e!lar6est!1alue!i&!xE!Nf!x is!a!$atriD!t9e&!t9e!

fu&ctio&!retur&s!a!ro*!1ector!co&tai&i&6!t9e!$aDi$u$!ele$e&t!fro$!eac9!colu$&E!!" max(x,y) #!T9is!fu&ctio&!retur&s!a!$atriD!t9e!sa$e!siQe!as!x a&'!yE!Eac9!ele$e&t! i&! t9e!$atriD!

co&tai&s! t9e!$aDi$u$!1alue! fro$! t9e!corres5o&'i&6!5ositio&s! i&!x a&'!yE!


!" prod(x,1) #! T9e! fu&ctio&! retur&s! a! ro*! 1ector! co&tai&i&6! t9e! 5ro'uct! of! ele$e&ts! fro$! eac9!colu$&E!

!" prod(x,2) #!T9e!fu&ctio&!retur&s!a!colu$&!1ector!co&tai&i&6!t9e!5ro'uct!of!ele$e&ts!fro$!eac9!ro*E!

!" cumsum(x) #! Nf!x is! a!$atriD,! t9is! fu&ctio&! retur&s! a!$atriD!of! t9e! sa$e! siQe! t9at! co&tai&s! t9e!cu$ulati1e!su$!of!1alues!i&!eac9!colu$&!till!t9at!5oi&t!i&!colu$&E!

!" cumsum(x,1) #!Ba$e!as!cumsum(x)E!!" cumsum(x,2) #!Nf!x is!a!$atriD,!t9is!fu&ctio&!retur&s!a!$atriD!of!t9e!sa$e!siQe!t9at!co&tai&s!t9e!

cu$ulati1e!su$!of!1alues!i&!eac9!ro*!till!t9at!5oi&t!i&!ro*E!!" cumprod(x) #! Nf!x is!a!$atriD,! t9is! fu&ctio&! retur&s!a!$atriD!of! t9e! sa$e!siQe! t9at!co&tai&s! t9e!

cu$ulati1e!5ro'uct!of!1alues!i&!eac9!colu$&!till!t9at!5oi&t!i&!colu$&E!!" cumprod(x,1) #!Ba$e!as!cumprod(x)E!!" cumprod(x,2) #!Nf!x is!a!$atriD,!t9is!fu&ctio&!retur&s!a!$atriD!of!t9e!sa$e!siQe!t9at!co&tai&s!t9e!

cu$ulati1e!5ro'uct!of!1alues!i&!eac9!ro*!till!t9at!5oi&t!i&!ro*E!!Program: x = [7 4 5 2] y = [7 4 5 2; 3 5 9 6] z = [1 2 3 4; 5 6 7 8] max_vector = max(x) max_matrix = max(y) max_yz = max(y,z) [a,b] = min(x) [c,d] = min(y) max1 = max(y,[],1) min2 = max(z,[],2) mean_vector = mean(x) mean_matrix = mean(y) mean1 = mean(y,1) mean2 = mean(z,2) med_vector = median(x) med_matrix = median(y) med1 = median(z,1) med2 = median(y,2) sum_vector = sum(x) prod_matrix = prod(y) cumprod_vector = cumprod(x) cumsum_matrix = cumsum(y) sumsum = sum(sum(x)) Output : x = 7 4 5 2 y = 7 4 5 2 3 5 9 6 z = 1 2 3 4 5 6 7 8 max_vector = 7 max_matrix = 7 5 9 6 max_yz = 7 4 5 4 5 6 9 8 a =

! YX


2 b = 4 c = 3 4 5 2 d = 2 1 1 1 max1 = 7 5 9 6 min2 = 4 8 mean_vector = 4.5000 mean_matrix = 5.0000 4.5000 7.0000 4.0000 mean1 = 5.0000 4.5000 7.0000 4.0000 mean2 = 2.5000 6.5000 med_vector = 4.5000 med_matrix = 5.0000 4.5000 7.0000 4.0000 med1 = 3 4 5 6 med2 = 4.5000 5.5000 sum_vector = 18 prod_matrix = 21 20 45 12 cumprod_vector = 7 28 140 280 cumsum_matrix = 7 4 5 2 10 9 14 8 sumsum = 18

!" sort(x) # Nf!x is!a!1ector!t9e&!t9is!fu&ctio&!sorts!t9e!1alues!i&to!asce&'i&6!or'erE!Nf!x is!a!$atriD!t9e&!t9is!fu&ctio&!sorts!eac9!colu$&!i&to!asce&'i&6!or'erE!

!" sort(x,1) #!T9is!fu&ctio&!retur&s!a!$atriD!of!siQe!x!*it9!sorti&6!eac9!colu$&!i&to!asce&'i&6!or'erE!!" sort(x,2) #!T9is!fu&ctio&!retur&s!a!$atriD!of!siQe!z!*it9!sorti&6!eac9!ro*!i&to!asce&'i&6!or'erE!!" [a, b] = sort(x) #!T9e!sorte'!1alues!are!retur&e'!to!t9e!$atriD!a a&'!reor'ere'!i&'ices!are!store'!i&!

t9e!$atriD!bE!(e!ca&!also!use!t9e!follo*i&6!eD5ressio&,!! [a, b] = sort(x, 2),! i&! *9ic9! eac9! ro*! is! sorte'! i&to! asce&'i&6! or'er! a&'! store'! i&! a *it9! t9e!

reor'ere'!i&'ices!2ei&6!store'!i&!bE!!

Program: x = [7 4 5 2] y = [7 4 5 2; 3 5 9 6] z = [1 2 3 4; 8 6 7 5] sortx = sort(x) sorty = sort(y) sort1 = sort(y,1) sort2 = sort(z,2) [a,b] = sort(y) [c,d] = sort(z,2)

! Yc


!Output: x = 7 4 5 2 y = 7 4 5 2 3 5 9 6 z = 1 2 3 4 8 6 7 5 sortx = 2 4 5 7 sorty = 3 4 5 2 7 5 9 6 sort1 = 3 4 5 2 7 5 9 6 sort2 = 1 2 3 4 5 6 7 8 a = 3 4 5 2 7 5 9 6 b = 2 1 1 1 1 2 2 2 c = 1 2 3 4 5 6 7 8 d = 1 2 3 4 4 2 3 1

A.2. Variance and Standard Deviation

[ \UR

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x

n

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%/0


! Ye

!" var(x) a&'!var(x,1) co$5ute!t9e!sa$e!t9i&6!as!sta&'ar'!'e1iatio&!2ut!all!t9e!1alues!are!sIuare'E!!" var(x,w)! co$5utes! t9e! 1aria&ce! usi&6! t9e!*ei69t! 1ector,!wE! T9e! &u$2er! of! ele$e&ts! i&!w!$ust!

eIual!t9e!&u$2er!of!ro*s!i&!xE! Program: x = [7 4 5 2] y = [7 4 5 2; 3 5 9 6] w = [1 2] std_vector = std(x) std_matrix = std(y) std_n = std(y,1) std_n2 = std(y,1,2) varrw = var(y,w) Output: x = 7 4 5 2 y = 7 4 5 2 3 5 9 6 w = 1 2 std_vector = 2.0817 std_matrix = 2.8284 0.7071 2.8284 2.8284 std_n = 2.0000 0.5000 2.0000 2.0000 std_n2 = 1.8028 2.1651

varrw = 3.5556 0.2222 3.5556 3.5556

mat lab intro elmer

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