fisika komputasi matlab

7/23/2019 fisika komputasi matlab

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Introduction to Matlab



Outline:

What is Matlab? Matlab Screen Variables, array, matrix, indexing Operators (Arithmetic, relational, logical ) Display Facilities Flo !ontrol "sing o# M$File

Writing "ser De#ined F%nctions !oncl%sion



What is Matlab? Matlab is basically a high le&el lang%age

hich has many speciali'ed toolboxes #or

maing things easier #or %s

o high?

Assembly

High LevelLanguages such as

C, Pascal etc.

Matlab



What are we interested in?

Matlab is too broad #or o%r p%rposes in thisco%rse*

+he #eat%res e are going to re%ire is

Matlab

CommandLine

m-fles

unctions

mat-fles

Commandexecution like !"command #indo#

"e$ies oMatlab

commands

%n&ut!ut&ut

ca&ability

atasto$age

'loading



Matlab Screen

!ommand Windo type commands

!%rrent Directory

Vie #olders and m$#iles

Worspace Vie program &ariables

Do%ble clic on a &ariable

to see it in the Array -ditor

!ommand istory

&ie past commands

sa&e a hole session

%sing diary



Variables

.o need #or types* i*e*,

All &ariables are created ith do%ble precision %nlessspeci#ied and they are matrices*

A#ter these statements, the &ariables are /x/ matrices

ith do%ble precision

int a(double b()oat c(

*xam&le+x(

x/0(



Array, Matrix

a &ector x = [1 2 5 1]

x =

1 2 5 1

a matrix x = [1 2 3; 5 1 4; 3 2 -1]

x =

1 2 3

5 1 4

3 2 -1

transpose y = x’ y =

1

2

5

1



Long Array, Matrix

t =1:10

t =

1 2 3 4 5 6 7 8 9 10

k =2:-0.5:-1

k =

2 1.5 1 0.5 0 -0.5 -1

B = [1:4; 5:8]

x =

1 2 3 4

5 6 7 8



Generating Vectors ro!unctions 'eros(M,.) Mx. matrix o# 'eros

ones(M,.) Mx. matrix o# ones

rand(M,.) Mx. matrix o# %ni#ormly

distrib%ted randomn%mbers on (0,/)

x = zeros(1,3x =

0 0 0

x = o!es(1,3x =

1 1 1

x = r"!#(1,3x =

0.9501 0.2311 0.6068



Matrix Index

+he matrix indices begin #rom / (not 0 (as in !)) +he matrix indices m%st be positi&e integer

1i&en2

A($3), A(0)

-rror2 ??? S%bscript indices m%st either be real positi&e integers or logicals*

A(4,3)

-rror2 ??? 5ndex exceeds matrix dimensions*



"oncatenation o Matrices

x = [1 2], y = [4 5], z=[ 0 0]

$ = [ x y]

1 2 4 5

B = [x ; y]

1 2

4 5

! 6 7x y 8'9

-rror2

??? -rror %sing 66: &ertcat !A+ arg%ments dimensions are not consistent*



O#erators $arith!etic%

; addition$ s%btraction

< m%ltiplication

= di&ision> poer

complex con@%gate transpose



Matrices O#erations

1i&en A and 2

Addition S%btraction Brod%ct +ranspose



O#erators $&le!ent by&le!ent%

*< element$by$element m%ltiplication

*= element$by$element di&ision*> element$by$element poer



'he use o ()* + (&le!ent*O#eration

C6 x>3

-rorr2 ??? -rror %sing 66: mpoer Matrix m%st be s%are*

6x<y

-rorr2

??? -rror %sing 66: mtimes 5nner matrix dimensions m%st agree*

A 6 7/ 3 8 E / 48 3 /9

A 6 / 3

E / 4

3 $/

y 6 A( ,2)

y6

4 $/

b 6 x *< y

b6

$

c 6 x * = y

c6

0* 0*E $

d 6 x *>3

d6

/ 4 G

x 6 A(/,2)

x6

/ 3



asic 'as-: .lot the unctionsin$x% between /≤x≤4π !reate an x$array o# /00 samples beteen 0 an

4π*

!alc%late sin(*) o# the x$array

Blot the y$array

xlins&ace12,34&i,/225(

ysin1x5(

&lot1y50 10 20 30 40 50 60 70 80 90 100-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1



.lot the unction e0x12sin$x%between /≤x≤4π !reate an x$array o# /00 samples beteen 0

and 4π*

!alc%late sin(*) o# the x$array

!alc%late e$x=D o# the x$array

M%ltiply the arrays y and y/

xlins&ace12,34&i,/225(

ysin1x5(

y/ex&1-x'65(

y0y4y/(



.lot the unction e0x12sin$x%between /≤x≤4π M%ltiply the arrays y and y/ correctly

Blot the y3$array

y0y.4y/(

&lot1y05

0 10 20 30 40 50 60 70 80 90 100-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7



3is#lay 4acilities

plot(*)

stem(*)

*xam&le+xlins&ace12,34&i,/225(ysin1x5(&lot1y5&lot1x,y5

*xam&le+stem1y5stem1x,y5

0 10 20 30 40 50 60 70 80 90 100-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 10 20 30 40 50 60 70 80 90 100-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7



3is#lay 4acilities

title(*)

xlabel(*)

ylabel(*)

title178his is the sinus unction95

xlabel17x 1secs595

ylabel17sin1x5950 10 20 30 40 50 60 70 80 90 100-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1This is the sinus function

x (secs)

s i n ( x )



O#erators $relational,logical% 66 -%al to

H6 .ot e%al to

I Strictly smaller

: Strictly greater

I6 Smaller than or e%al to

:6 1reater than e%al to J And operator

K Or operator



4low "ontrol

i#

#or

hile

brea

L*



"ontrol Structures

5# Statement Syntax

i# (!ondition/)

Matlab !ommandselsei# (!ondition3)

Matlab !ommands

elsei# (!ondition)

Matlab !ommandselse

Matlab !ommands

end

"ome ummy *xam&les

i 11a65 : 1b55 "ome Matlab Commands(end

i 1a;65 "ome Matlab Commands(elsei 1b<5

"ome Matlab Commands(end

i 1a;65 "ome Matlab Commands(else

"ome Matlab Commands(end



"ontrol Structures

For loop syntax

#or i65ndexArrayMatlab !ommands

end

"ome ummy *xam&les

o$ i/+/22 "ome Matlab Commands(end

o$ =/+6+022 "ome Matlab Commands(end

o$ m/6+-2.0+-0/ "ome Matlab Commands(

end

o$ k>2./ 2.6 -/6 /0 ? [email protected] "ome Matlab Commands(end



"ontrol Structures

While Noop Syntax

hile (condition)

Matlab !ommands

end

ummy *xam&le

#hile 11a65 : 1b55 "ome Matlab Commands(end



5se o M04ile

!lic to createa ne M$File

-xtension P*mQ A text #ile containing script or #%nction or program to r%n



5se o M04ile

5# yo% incl%de P8Q at the

end o# each statement,

res%lt ill not be shon

immediately

Sa&e #ile as Denem430 *m



Writing 5ser 3e6ned 4unctions

F%nctions are m$#iles hich can be exec%ted byspeci#ying some inp%ts and s%pply some desired o%tp%ts*

+he code telling the Matlab that an m$#ile is act%ally a

#%nction is

Ro% sho%ld rite this command at the beginning o# the m$

#ile and yo% sho%ld sa&e the m$#ile ith a #ile name same

as the #%nction name

unction out/unctionname1in/5unction out/unctionname1in/,in0,in65unction >out/,out0unctionname1in/,in05



Writing 5ser 3e6ned 4unctions

-xamples

Write a #%nction 2 o%t6s%arer (A, ind)

Which taes the s%are o# the inp%t matrix i# the inp%t

indicator is e%al to /

And taes the element by element s%are o# the inp%t

matrix i# the inp%t indicator is e%al to 3

"ame Bame



Writing 5ser 3e6ned 4unctions Another #%nction hich taes an inp%t array and ret%rns the s%m and prod%ct

o# its elements as o%tp%ts

+he #%nction s%mprod(*) can be called #rom command indo or an m$#ile as



7otes: PQ is the neglect sign #or Matlab (e%ai&alent

o# P==Q in !)* Anything a#ter it on the same line

is neglected by Matlab compiler*

Sometimes sloing don the exec%tion is

done deliberately #or obser&ation p%rposes*Ro% can %se the command Ppa%seQ #or this

p%rpose

&ause #ait until any key&ause165 #ait 6 seconds



5seul "o!!ands

+he to commands %sed most by Matlab

%sers are

hel& unctionname

looko$ key#o$d



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fisika komputasi matlab

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