02a Matlab Intro

8/10/2019 02a Matlab Intro

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2014-02-24ETH Zrich

Modeling and Simulating Social Systems

with MATLAB

Lecture 2 Introduction to MATLAB

Chair of Sociology, in articular of

Modeling and Si!ulation

"li#ia $oolley, To%ia& 'uhn, (ario Bia&ini, (ir) *el%ing


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2014-02-24 Modeling and Simulating Social Systems with MATLAB 22

Schedule of the course

1+0224!2

00

100

1+0

240

10

0+04

1404

0.0.

120.

1/0.

20.

Introduction to

MATLAB

Introduction to

&ocial-&cience

!odeling and

&i!ulation&

$or)ing on

roect&

&e!inarthe&i&3

*anding in &e!inar the&i&

and gi#ing a re&entation

canceled


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2014-02-24 Modeling and Simulating Social Systems with MATLAB

"eadlines

(eadline for roect roo&al&

Monday #$ March 2!#4at !idnight

(eadline for roect reort&

Tue&day #% May 2!#4 at !idnight

"ral roect re&entation&

$edne&day #4 Mayto 5riday#& May 2!#4


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MATLAB

$hy MATLAB6

Language i& 7uic) to learn, ea&y to u&e, rich in

functionality, good lotting a%ilitie&

MATLAB i& co!!ercial &oft8are fro!

Math$or)&, %ut there are free MATLAB clone&

8ith li!ited functionality "cta#e and Scila%3

MATLAB can %e do8nloaded fro! ide&eth9ch


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MATLAB en'ironment


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(hat is MATLAB)

MATLAB deri#e& it& na!e fro! matri: la*oratory

Interreted language ;o co!ilation li)e in Crocedural?i!erati#e rogra!!ing

Matri:?array?#ector rogra!!ing

"%ect-oriented rogra!!ing3


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+'er'iew , (hat is MATLAB)

MATLAB deri#e& it& na!e fro! !atri: la%oratory Scalars

@ector&

Matrice&

x11


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MATLAB deri#e& it& na!e fro! !atri: la%oratory Scalar&

-ectors

Matrice&

x11 x12 x13

x11

x12

x13


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@ector&

Matrices

x11 x12 x13

x21 x22 x23


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@ector&

Matrice& Multi,dimensional

x111 x121 x131x211 x221 x231



.oc/et calculator

MATLAB can %e u&ed a& a oc)et calculator

>> 1+2+3

ans=

6

>> (1+2)/3

ans=

1



-aria*les and o0erators

@aria%le a&&ign!ent i& !ade 8ith D

@aria%le na!e& are ca&e &en&iti#eNum, num, NUM are all different #aria%le&

>> num=10

num =

10

The &e!icolon ED cancel& the #alidation di&lay

>> B=5;

>> C=10*B

C =

50



-aria*les and o0erators

Ba&ic oerator& < - F ? addition &u%traction !ultilication di#i&ion

G H:onentiation

&7rt3 S7uare root co!!ent

>> a=2; % First trm

>> !=5; % "#$n trm

>> #=&; % 'ir trm

>> =a*(srt(#) + !2);>>

=

56



"ata structures1 -ectors

@ector& are u&ed to &tore a &et of &calar& @ector& are defined %y u&ing &7uare %rac)et J K

>> =-0 2 . 10

=

0 2 . 10


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"ata structures1 "efining 'ectors

>> =026

=

0 2 . 6

@ector& can %e u&ed to generate a regular li&t of

&calar& %y !ean& of colon D n1kn2generate a #ector of #alue& going fro! n1to n2

8ith &te k

The default #alue ofk i& 1

>> =25

=

2 3 . 5



"ata structures1 Accessing 'ectors

>> =1053;

>> (2)ans =

15

Acce&& to the #alue& contained in a #ector x(i) return the ithele!ent of #ectorx

x(i)i& a &calar and can %e a&&igned a ne8 #alue

>> =15;

>> (3)=10;

>>

=

1 2 10 . 5


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"ata structures1 Sie of 'ectors

>> =1053;

>> s=nt()

s =

5

@ector& oeration& The co!!and length(x)return the &i9e of the #ectorx

x(i)return an error if i>length(x)>> =1053;

>> (6)

444 n #s matri imnsi$ns



"ata structures1 3ncrease sie of 'ectors

>> =15;

>> (6)=10;

>>

=

1 2 3 . 5 10

@ector& oeration& @ector &i9e& can %e dyna!ically increa&ed %y

a&&igning a ne8 #alue, out&ide the #ector


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"ata structures1 3ncrease sie of 'ectors

>> =15;

>> (6)=10;

>>

=

1 2 3 . 5 10

@ector& oeration& @ector &i9e& can %e dyna!ically increa&ed %y

a&&igning a ne8 #alue, out&ide the #ector

Important: the first element of

a vector has index 1



"ata structures1 Su*,'ectors

@ector& oeration& Su%#ector& can %e addre&&ed %y u&ing a colon

x(i:j)return the &u% #ector ofx&tarting fro! the ith

ele!ent to the th

one>> =1022;

>> =(2.);

>>

=

12 1. 16



"ata structures1 Matrices

Matrice& are t8o di!en&ional #ector&

Can %e defined %y u&ing &e!icolon into &7uare

%rac)et& J K

>> =-0 2 . ; 1 3 5 ; 7 7 7

=0 2 .1 3 57 7 7

>> =-1. ; 57 ; 128

=1 2 3 .5 6 8 71 3 5 8




>> =-0 2 . ; 1 3 5 ; 7 7 7

=0 2 .1 3 5

7 7 7

>> =(2,3)

=

5

Acce&&ing the ele!ent& of a !atri: x(i,j) return the #alue located atithline andjthcolu!n

iandjcan %e relaced %y a colon D to acce&& the

entire line or colu!n




>> =-0 2 . ; 1 3 5 ; 7 7 7

=0 2 .1 3 5

7 7 7

>> =(2,)

=

1 3 5

Acce&& to the #alue& contained in a !atri: x(i,j) return the #alue located atithline andjthcolu!n




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>> =-0 2 . ; 1 3 5 ; 7 7 7

=0 2 .1 3 57 7 7

>> =(,3)

=

.

5

7

Acce&& to the #alue& contained in a !atri: x(i,j) return the #alue located atithline andjthcolu!n




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Matrices o0erations1 Trans0ose

Tran&o&e !atri: S8itche& line& and colu!n&

transpose(x) or &i!ly x

>> =-13 ; .6 =1 2 3. 5 6

>> trans9$s() =

1 .2 53 6

>> : =1 .2 5

3 6


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Matrices o0erations

Inter-!atrice& oeration& CA> =-1 2;3 . ; B=-2 2;1 1;

>> C=+B

C =3 .

. 5

>> C=


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Matrices o0erations1 Multi0lication

Inter-!atrice& oeration& CAFB i& a !atri: roduct eturn& C 8ith

C(i,j) = (k=1 to N)A(i,k)*B(k,j)

; i& the nu!%er of colu!n& of A 8hich !u&t e7ual the

nu!%er of ro8& of B


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Matrices o0erations

Inter-!atrice& oeration& CA> =-1 2;3 . ; B=-2 2;1 1;

>> C=+B

C =3 .

. 5

>> C=


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Element,wise multi0lication

Inter-!atrice& oeration& CAFB return& C 8ith C(i,j) = A(i,j)*B(i,j)

A and B !u&t ha#e the &a!e &i9e, unle&& one of the! i& a &calar

>> =-2 2 2;. . .;

>> B=-2 2 2;1 1 1;

>> C=*BC =. . .. . .


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Element,wise di'ision

Inter-!atrice& oeration& CA?B return& C 8ith C(i,j) = A(i,j)/B(i,j)

A and B !u&t ha#e the &a!e &i9e, unle&& one of the! i& a &calar

>> =-2 2 2;. . .;

>> B=-2 2 2;1 1 1;

>> C=/B

C =

1 1 1. . .


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Matrices o0erations1 "i'ision

Inter-!atrice& oeration& :A% return& the &olution of the linear e7uation AF:%

A i& a n-%y-n !atri: and % i& a colu!n #ector of &i9e n

>> =-3 2


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Matrices1 reating

Matrice& can al&o created %y the&e co!!and&

ran(n, m)

a !atri: of &i9e n: m, containing rando!

nu!%er& J0,1K

r$s(n, m), $ns(n, m)a !atri: containing 0 or 1 for all ele!ent&


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Matrices "imensions

>> = r$s(3,.);

>> si()

ans =

3 .

>> si(,1)

ans =

3

>> si(,2)

ans =

.

si() return& info a%out a !atri:D& di!en&ion&


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The forloo0

@ector& are often roce&&ed 8ith loo& in order

to acce&& and roce&& each #alue, one after the

other

Synta:

?$r i=

@

n

$ith- ithe na!e of the running #aria%le

- xa #ector containing the &e7uence of #alue& a&&igned to i


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The forloo0

>> ?$r i=13

i2n

i =

1

i =

.

i =

&

MATLAB 8ait& for the )ey8ord n%efore co!uting

the re&ult


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The forloo0

>> ?$r i=13

(i)=i2;n

>>

=

1 . &

MATLAB 8ait& for the )ey8ord n%efore co!uting

the re&ult


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onditional statements1 if

The )ey8ord ifi& u&ed to te&t a condition Synta:

i? (#$niti$n)

sun# $? #$mmansn

The condition i& a Boolean oeration

The &e7uence of co!!and& i& e:ecuted if the te&ted

condition i& true


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Logical o0erators

Logical oerator& N , O le&& than, greater than

e7ual to

PP and QQ or

R not Rtrue i& !l"e3

1 &tand& for true, 0 &tand& for fal&e3


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2014-02-24 Modeling and Simulating Social Systems with MATLAB //

onditional statements1 E5am0le

>> trs$=5;

>> =.5;

>> i? (Atrs$)

i?? = trs$ < ;

n

>> i??

i?? =

05

An e:a!le


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onditional statements1 else

The )ey8ord elsei& otional Synta:

i? (#$niti$n)

sun# $? #$mmans n1

s

sun# $? #$mmans n2

n

>> i? (Atrs$)

i?? = trs$ < ;

s

i?? = trs$;

n


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Scri0ts and functions

H:ternal file& u&ed to &tore and &a#e &e7uence&

of co!!and&

Scrit& Si!le &e7uence of co!!and&

lo%al #aria%le&

5unction&

(edicated to a articular ta&) Inut& and outut&

Local #aria%le&


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Should %e &a#ed a& mfile&

5ro! the

(irectory $indo8


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Scrit& Create ! file, eg sumD#t$rm

Tye co!!and& in the file

Tye the file na!e, eg sumD#t$r, in the co!!and8indo8

%sum of 4 values in x

=-1 3 5 8;

=(1)+(2)+(3)+(.);

sum-ectorm

>> sumD#t$r

=16


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Ma)e &ure that the file i& in your 8or)ing

directory


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5unction& Create ! file, eg a!s$utDam

(eclare inut& and outut& in the fir&t line of the file,

function [out1, out2, ] = functionName (in1, in2, )

eg ?un#ti$n - = a!s$utDa()

U&e the function in the co!!and 8indo8

functionName(in1, in2, )

eg a!s$utDa()


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?un#ti$n - = a!s$utDa()

% Compute the absolute value of x

i? (A0)

= > =a!s$utDa(>

=

5


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?un#ti$n - = a!s$utDa()

% Compute the absolute value of x

i? (A0)

= > =a!s$utDa(>

=

5


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E5ercise #

om0ute1

a) b)

c)

Slide&?e:erci&e& 888&o!&eth9ch?!atla%

255

10718

+

=

100

0i

i

=

10

5

2 )(i

ii


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E5ercise 2

Sol#e for 51

4522

32

223321432

4321

4321

4321

4321

=++

=

=++=+

xxxx

xxxx

xxxx

xxxx


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E5ercise %

6i*onacci se7uence1 8rite a function 8hich

co!ute& the 5i%onacci &e7uence of a gi#en

nu!%er nand return& the re&ult in a #ector

The 5i%onacci &e7uence F(n) i& gi#en %y


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8eferences

htt??888!ath8or)&ch?roduct&?!atla%?inde:

ht!l

htt??888!ath8or)&ch?!atla%central?inde:ht!

l htt&??ide&eth9ch?
http://www.mathworks.ch/products/matlab/index.htmlhttp://www.mathworks.ch/products/matlab/index.htmlhttp://www.mathworks.ch/matlabcentral/index.htmlhttp://www.mathworks.ch/matlabcentral/index.htmlhttps://ides.ethz.ch/https://ides.ethz.ch/http://www.mathworks.ch/matlabcentral/index.htmlhttp://www.mathworks.ch/matlabcentral/index.htmlhttp://www.mathworks.ch/products/matlab/index.htmlhttp://www.mathworks.ch/products/matlab/index.html

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02a Matlab Intro