ee 2300 matlab tutorial - utdallas.edu

1

Matlab Basic

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MATLAB Basic

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MATLAB Basic (cont.)

matfun help

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matrices matlab demo

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5)(3/4)(2

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5.7500

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power 2.

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3.0000i + 2.0000

= ans

i*3+2

j.or i byeither denoted is 1- unit imaginary Theform.

r rectangula in drepresente are MATLAB in numbers Complex

numbers complex 3.

point) decimal with (Numbers numbers real 2.

point. decimal the without enterd are Integers

integers 1.

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:Numbers

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7

Matlab Basic (cont.)

. - or 0.0/0.0 as such operations undefined

allymathematic the of result a as obtained is andnumber -a-not

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ned.predetermi are valuestheir as

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statement. assignment an of side

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name. variable a of

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numbers letters, by followed letter, a with begins name Variable

user. the by chosen

are names whose variables in saved are nscomputatio of Results

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9


Save. onclick next and

.m)(or atfilename.m e.g. file,your for name a Chose

menu. File the from

as Workspace Save select workspace currentyour save To

session.

current in used variables all of list a creates who command

prompt. command from variable acheck also can You

variable. the tab.Choose workspace onClick

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in saved are session MATLAB current the in used variables All

:work reloading & Saving

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10


on grid

grid dotted a add to

,....)data2'',data1'legend('

legend put to

)axis'-yylabel('),axis'-xxlabel('

axes label to

) Title'Figuretitle('

title a put to

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axis.-x the along isvector first :Note

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codes. matlab from figure creates plot command

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11


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1

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0

0.2

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1sine & cosine wave

x-axis

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x);*cos(pi=z

x);*sin(pi=y

2;:.01:0=x

:Example

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12


on; grid

,0);cosine'',sine'legend('


);wave' cosine & sinetitle('

off; hold

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on; hold

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1

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0

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1sine & cosine wave

x-axis

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13


on; grid

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0 0.5 1 1.5 2-1

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1cosine wave

x-axis

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sine

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14


required. where paste and nsapplicatioother or word to Go

figure. copy choose menu, edit figure From

:nsapplicatioother & word to Copy

menu. Edit figure from modified be

also can properties Axis & properties FigureHowever

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15

Vectors & Matrices

3

2

1

b

[1;2;3] b

(matrix))vector in row of end marks (Semicolon :vector 2.Column

3 2 1

a

3] 2 [1 a

element) (matrix)vector diff.mark gapor (Comma :vector Row.1

:vectors column & row Creating

=

=>>

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16

Vectors & Matrices (Cont.)

same. is operation .' & ' both )matrix( vector real For

2.0000i + 2.0000

1.0000i + 1.0000

= ans

c.'

2.0000i - 2.0000

1.0000i - 1.0000

= ans

c'

i];*2+ 2 i+[1=c

(matrix).vector of transpose the createoperator quote) (dot .' The

3 2 1

= ans

b'

3

2

1

= ans

a'

(matrix).vector of transpose conjugate the createoperator (quote) ' The

:(rows) columns into (columns) rows Transfrom•

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17


9 4 1

= ans

a.^2

9 4 1

= ans

a*a.

opeartor. dot the follows thatopeartor the of

napplicatio isecomponentwfor used is operator) (dot . The

3

= ans

length(a)

vector. of components of no. the esminerdet:length

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18


5 8- 1

= ans

b)cross(a,

[-2,1,2];=b

[1;2;3];=a

3. be mustvector gthlength.Len same of be must B &A

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6

= ans

b)dot(a,

[-2,1,2];=b

[1;2;3];=a

length. same of be must B &A

B. and A vectors of productscalar the returns:dot

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19


value numerical indicares[]

address indicates()

8 7

2 1

= b

)2] [1,3] [1a(=b

:2&1 columns and

3 &1 rows of consisting b submatrix a extract to examplefor

:Submatrix Extracting

9 8 7

6 5 4

3 2 1

= a

9] 8 6;7 5 3;4 2 [1=a

:Matrix Creating

columnsrows

→

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321321

20


value indicates j][i,

position indicates j)(i,

9 7

6 4

3 1

= a

[]=a(:,2) >>

9]; 8 6;7 5 3;4 2 [1=a

[]operator vector empty use :(column) row a delete To

3] 2 [1order in (columns) rows all indicates :

9 7 8

6 4 5

3 1 2

= d

3]) 1 [2a(:,=d

3 2 1

6 5 4

9 8 7

= c

1],:) 2 a([3=c

:ns)rows(colum einterchang To

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21


5 7 3

= ans

7):2:a(2

3 4 5 6 7 5 3 1

= a

3]:-1:8,6:2:[1=a

order.regular a in bits extarctor build to used be (colon)can :

8

= ans

a(3,2)

10]; 8 6;7 5 3;4 2 [1=a

.position/s specific a of bit/s extarct to used race)is(bracket/b ()

:(matrix)vector of bits gExatractin

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22


1 4 9

9 4 1

= ans

a*a.

1]; 2 3;3 2 [1=a

matices.for works alsooperator .(dot) the

9 7

8 5

6 4

3 1

= a

a(3,:)]8]; a(2,:);[5[a(1,:);=a

9]; 6;7 3;4 [1=a

9 8 7

6 5 4

3 2 1

= a

a(:,2)] 8]' 5 [2 [a(:,1)=a

9]; 6;7 3;4 [1=a

:(column) row new a Inserting

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23


1 2 4

4- 2- 3

8 1 0

= c

b] [a=c

[8;-4;1];=b

2]; 2;4- 1;3 [0=a

matrices.smaller from from build be can matrix Large

:ionConcatenat Matrix

columns ofnumber

indicates second while rows, of

number indicatesinteger first

matrix. 3-by -3 a its

3 3

= ans

size(a) >>

10]; 8 6;7 5 3;4 2 [1=a

matrix) the of (dimension size the get size

:Matrix a of Size

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24


1 0 0

0 1 0

0 0 1

= I

eye(3)=I

matrix identity mm an gives eye(m)

0 0 0

0 0 0

0 0 0

= b

zeros(3,3)=b

s0' of matrix nm gives n)zeros(m,

1 1 1

1 1 1

= a

ones(2,3)=a

s1' of matrix nm an gives n)ones(m,

:Matrices Special

>>

×

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×

×

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25


37 21

47 23

= ans

b*a

9]; 3 8; 4;6 [2=b

1]; 2 3;3 2 [1=a

B in rows of no. to equal be must A of columns of no.

agree. must dimensions matrixInner

* ==> usingError ???

b*a

8]; 4;6 [2=b

1]; 2 3;3 2 [1=a

:tionMultiplica Matrix

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26


9

5

1

= b

diag(a)=b

9]; 8 7 6; 5 4 3; 2 [1=a

matrix. that ofvector diagonal main creates diag matrix a given

:matrix a of diagonal Main

3 0 0

0 2 0

0 0 1

= b

diag(a)=b

3]; 2 [1=a

diagonal. main asvector that with matrix a creates diagvector a given

:matrix Diagonal

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27


12

11

10

2

= i

4)==find(a=i

4]; 7 6 4;5 6 5 4;4 3 2 [1=a

condition. given a satisfying matrixor vector

a of (indices) positions the of list a returns find function

:Matrices & Vectorsfor Find

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⇒

28

Solving System of Linear Equations

0.0491

0.5849

= x

b\a=x

ones(3,1);=b

2]; 10;1 1;1- [2=a

)solution Square Least(

system edminerdetOver

nm :2 case

0.0000

1.0000

1.0000-

= x

b\a=x

ones(3,1);=b

10]; 8 6;7 5 3;4 2 [1=a

solution) (Exact

nm :1 case

vector. column ldimensiona m is b & nm size of is A

where b,ax symtemlinear solve to have weConsider

division. left as

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29

Solving System of Linear Equations (Cont.)

inv(b)*ac means a/bc

b*inv(a)c means b\ac

matrixfor :Note

0.5000

0

0.5000-

= x

b\a=x

ones(2,1);=b

6]; 5 3;4 2 [1=a

)consistent is system the if solutionr (particula

system minedunderdeter

nm:3 case

==

==

→

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30

Solving System of Linear Equations (Cont.)

column pivotted zero-non of indices the holds case, second in array c

3

= ans

length(c)

3 2 1

= c

0 1 0 0

1 0 1 0

1- 0 0 1

= x

b]) rref([a=c] [x

ones(3,1);=b

10]; 8 6;7 5 3;4 2 [1=a

0

1

1-

= x

x(:,4)=x

0 1 0 0

1 0 1 0

1- 0 0 1

= x

b]) rref([a=x

ones(3,1);=b

10]; 8 6;7 5 3;4 2 [1=a

b.ax system solve to

want we previous, As etc. ncalculatiorank matrix system,linear of solution as such

nsapplicatio manyfor used be can:)form echelon row reduced( rref Function

→

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31

Inverse of a Matrix

matrix. a of inverse find to used be also can rref Function

1.0000 2.0000- 1.0000

2.0000- 3.6667 0.6667-

1.0000 1.3333- 0.6667-

= ans

inv(a)

10]; 8 6;7 5 3;4 2 [1=a

matrix given a of inverse the calculates :inv

⇒

>>

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32

Inverse of a Matrix (Cont.)

1.0000 2.0000- 1.0000

2.0000- 3.6667 0.6667-

1.0000 1.3333- 0.6667-

= b

6):b(:,4=b

1.0000 2.0000- 1.0000 1.0000 0 0

2.0000- 3.6667 0.6667- 0 1.0000 0

1.0000 1.3333- 0.6667- 0 0 1.0000

= b

))])eye(size(a rref([a=b

10]; 8 6;7 5 3;4 2 [1=a

))]);eye(size(a rref([a=b

10]; 8 6;7 5 3;4 2 [1=a

:rref function using matrix a of Inverse⇒

33

Determinants

3-

= ans

det(a)

10]; 8 6;7 5 3;4 2 [1=a

ts.determinan gcalculatinfor designed is det Function

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34

Eigenvalues & Eigenvectors

{ {

seigenvalue are These

0.2599

1.3510-

17.0911

= ans

diag(d)

0.2599 0 0

0 1.3510- 0

0 0 17.0911

= d

0.3158 0.4557 0.8252-

0.8128- 0.1245 0.4978-

0.4895 0.8814- 0.2670-

= v

eig(a)=]d,v[ >>

10]; 8 7 6; 5 4 4; 2 [1=a

matrix. given a of rseigenvecto &

eigenvalus computingfor designed is eig function

vector eigenan is

column each

values eigen as elements

diagonalwith matrix

vectorseigen

of matrix

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43421

35

Programming in Matlab

arguments. output return &

arguments take may files function Thearguments. output

the returnor arguments input take not do files Script

files Function 2.

files Script 1.

files. .m of type two in contained are codes Matlab

file-M Select

New Choose

window command from menu file to Go

file .m new a open To

files (mat) .m The

→

→

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36

Programming in Matlab (Cont.)

grid

y);plot(x,

sin(x)./x;=y

pi;*10:pi/100:pi/100=x

:file script of Example

>>

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0 5 10 15 20 25 30 35-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

37


size same of not are matrix

dotprod ==> usingError ???

b)dotprod(a,

5]; [4=b

3]; 2 [1=a

18 10 4

= ans

b)dotprod(a,

[4;5;6];=b

3]; 2 [1=a

function, the access To

end

);size' same of not are matrixerror('

else

q;*p.dp

,length(q))(length(p) if

q)dotprod(p, dp function

:file Function of Example

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38


{

body Functuion

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);size' same of not are matrixerror('

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3214342143421

39


dotprod.m

as saved be must file example previous in : examplefor

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40


10

= ans

f(6,8) »

y^2)+sqrt(x^2 = y)f(x,

:function Inline

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functions. inline use to handy is it

session, Matlab currentfor only function a use to have we If

:Functions Inline

quote between

arguments

quote between expression function

keyword321

444 8444 76

321 +>>

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41

Programming in Matlab (cont.)

5050

= sum

sum »

end

i;+sum=sum

100,:1:0=ifor

0;=sum

:Example

end

commands

arraykfor

Structure

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42


s(k)sin(k)'*co=a

10;:1:1=k

:ionvectorizat By

end

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43


0.0061

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43421

48476

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44


end;

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M

44 844 76

44 844 76

44 844 76

K

45


}

{

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46


required.

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47


4 4 4

= ans

a(ind) >>

0 1 1 0 1 0 0

= ind

4)==(a=ind

1]; 4 4 3 4 1 [0=a

false'.' if 0 and true'' are

they when 1 returns and variables

two compares operators These

to) equal (Not ~

to) (Equal

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(Greater)

to) equalor than (Less

than) Less (

operators following the with performed are MATLAB in sComparison

:Operator Logical & Relations

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==

>=

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48


isempty[]. :like

functions. logical in-built several are there Matlab In

2.5000 2.0000 1.0000

= ans

a(ind) >>

1 0 0 0 1 1 0 0

= ind

3)<(a&1)>=(a=ind

2.5]; 3 4 3.5 2 1 0.5 [0=a

(not) ~

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(or) |

MATLAB. in available operators logical three are There

:operator Logical

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49


48 48

24 through 23 Columns

51 50 45 69 69 32 102 111 32 115 115


97 108 99 32 101 109 111 99 108 101 87


= ans

ouble(str)d

2300-EE of class Welcome

=str

2300'-EE of class Welcome='str

:string of Example

value. ASCII the from a''letter returns char(s)

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50


Matlab. learning are 2300.We-EE of class Welcome

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functions. string many are There:Functions String

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51


r);isspace(st

otherwise. 0or whitespace a ischaracter if 1 returns :isspace 2.

0 0 0


0 0 0 1 1 0 1 1 0 1 1


1 1 1 0 1 1 1 1 1 1 1


= ans

tr)isletter(s >>

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