Metode Simulasi Monte Carlo(1)

7/23/2019 Metode Simulasi Monte Carlo(1)

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ARNITA IRIANTI/20914009COMPUTATIONAL SCIENCEITB

1

TUGAS 2

SIMULASI CARLO

Soal

Buatlah program utu!

m"ghamp#r# #la# m"ggua!a

#t"gralt"tu

(

utu!

)

"

ga

,10-.0-100-.00-1000-.000-10000-100000& Ru program $"*a+a! 10 !al#utu! $"t#ap )a

ratarata!a hamp#ra #t"gral t"tu +ag )#p"rol"h& Buat )o!um"ta$# +ag

*"r#$# algor#tma-%otoh output- ta*l" ha$#l ' p"r%o*aa )a ratarata

hamp#ra #t"gral- ormula ha$#l )ata #tt#g- )a !"$#mpula )ar# $#mula$#

##&

Penyelesaian:

f(x)= ∫ )dx3a$#l aal#t#! #t"gral +ag )#p"rol"h a)alah0&421.2.19

Gambar 1.Graf L!as In"e#ral sin $%

2

&



Algoritma yang digunakan sebagaiberikut :

1& Bag!#t!a *#laga ra)om u#ra)

2& I#$#al#$a$# Nma5)art +ag )#gua!a-%#la# ma!$#mum ug$#-am#-*ma5-)a 5

6& #put a )a *4& P"g$a!alaa 7 $,m# 8 ma5

m#ra) a& or#,0-#:N-#8

8

*& # a*$5;%- ma!a

%,a*$5

.& M""tu!a lua$ )# *a<ah atau

)#ata$ $um*u + # 5;0

a& lua$ )#ata$ $um*u57 +,%u#ra)-

ma!a7 #

+:,5- N88

*& lua$ )# *a<ah $um*u 57

+, %u#ra)- ma!a7

# +;,5- N=

& Output7

a& Lua$ ar"a )art r"$7

r"$,N/Nma5&%&*a

*& 5-+- )a Lua$ #t"gral 5 >ru $"*a+a! 10 utu! ma$#gma$#g Nma5?

Program menggunakan C++ dengan source code sebagai berikut :

//Soal 7 It"gral )ar# $#@2- )g *ata$ 702p#

#%lu)" :#o$tr"am;

#%lu)" :$t)#o&h;

#%lu)" :math&h;

#%lu)" :$tr"am;

#%lu)" :$t)l#*&h;

#%lu)" :t#m"&h;

u$#g am"$pa%" $t)

)ou*l" u#ra)

>

r"tur)ou*l" ra)/ )ou*l" RANDMA@



?

)ou*l" )ou*l" 5



>

)ou*l" +, $#55

r"tur +

?

#t ma#

>

)ou*l" r"$-5-+-a-*-%,0& // )"!lara$#

#t N,0- Ntot- #- p"r%o*aa

//##$#al#$a$# a,0& //*ata$ ata$

*,26&141//*ata$ *a<ah

$+$t"mFTITLE TEGNIG SIMULASI MONTE CARLOF

$+$t"mFColor 1HF

%out :: Ft TEGNIG SIMULASI MONTE CARLOF

%out :: Ftol"h 7Ar#ta Ir#at#F

%out::FM"gh#tug #la# #t"gral )"ga Mot"

CarloF

%out::FP"r%o*aa !" , F%#;;p"r%o*aa

%out::FHug$#7 5, $#52F

%out::F*ata$ #t"gra$#7

5,J0-2p#KF %out::FMa$u!!a

umlah )art , F%#;; Ntot

$ra)t#m"NULL//$

"")

// m"%ar# ma5#mum ug$# )"ga %ara

Mot"Carlo or #,0#:Ntot#88

>

5,a8*au#ra)

# a*$5;% >%,a*$5?

?




//M"%ar# #t"gral ug$# )"ga %ara

mot"%arlo o$tr"am out

out&op"F1Mot"Carlo)ata&t5tF//ha$#l utu! )# plot

) gu plot or#,0#:Ntot#88

>

5,a8*au#ra)

# 5;0&

>

+,%u#ra)

#+:,5>N88? //lua$ )ata$ $um*u 5

?

"l$"

>

+,%u#ra)

# +;,5>N? //lua$ )#*a<ah $um*u 5

?

out::5::F F::+::FF

?

out&%lo$"

r"$ ,)ou*l"N/)ou*l"Ntot%*a

pr#tF3a$#l It"gra$#+a,F-r"$

r"tur 0

?




Hasil running sebagai berikut :

Plo" #ra'i (i GNU )lo"N*1

+1

0&'

1Mot"CarloE)ata&t

5t$#55

0&

0&4

&2

0

/0&2

/0&4

/0&

/0&'

/1

0 1 2 6 4 . O

@

Gambar.2. Plo" L!as In"e#ral (en#an N*1+

0

H 0 5 1



N *1+++++

@

Gambar.,. Plo" L!as In"e#ral (en#an N*1+++++

3a$#l/output +ag )# ha$#l!a utu! ma$#g ma$#g )art N7

Tabel 1. -asil L!as In"e#ral !n"! masin#masin# (ar" $N&

N 3a$#l Rata/

10 0&O'0

.0 0&904

100 0&'4.

.00 0&.9'

1000 0&0

.000 0&1..

10000 0&.4

100000 0&.4

Tabel 2. -asil L!as Ra"a Ra"a !n"! se"ia) N

H 0 5 1



Graf /. Plo" L!as In"e#ral Ra"ara"a "er0a(a) N

Formulasi hasil data fitting

0&9

0&'

0&O

0&

0&.

0&4

0&6

0&2

0&1

0

Graf N "er0a(a) L!asIn"e#ral

0 20000 40000 0000 '0000100000 120000

N

+ , 2E05 80&O2

S"r#"$1L#"ar S"r#"$1

Gambar . Gra'i Mo(el Re#resi Linear

Data Lua$ #t"gral )"ga umlah )art N pa)a gra#! )"ga

m"gua!a r"gr"$# l#"ar m"gha$#l!a ormula$# )ata #tt#g $"*aga#

*"r#!ut7

* 2.1+3

% 4 +.532

N$6ar"& TREN6

10 0&199

.0 0&19

100 0&19

.00 0&1

1000 0&1

.000 0&

10000 0&

100000 0&.

Tabel ,. 6a"a C!r7e 8i""in#

L

! a s I n " e # r a l



0&O.

0&O

0&.

0&

0&..

0&.

0&4.

0&4

Gra'i C!r7e8i""in#

S"r#"$1

Gambar 5. Gra'i C!r7e 8i""in#

0&O.

Graf Re#resi linear L!asTer0a(a)banya

6ar"

0&

0&.

0& S"r#"$1

0&..

0&. 0 20000 40000 0000 '0000 100000 120000

N

Gambar 3. Gra'i 6a"a 'i""in# Men##!naan Re#resi

Qra#! )#ata$ m"ggam*ar!a tr") l#" +ag m"uu !" *a<ah )#

maa m"rupa!a ha$#l lua$ $"%ara um"r#! +ag m")"!at# ha$#l

aal#t#!+a- #!a )art N +ag )#gua!a $"ma!# *a+a!&

T R E N 6

L ! a s




Kesimpulan :

1& S#mula$# Mot" Carlo a)alah $uatu mo)"l pro*a*#l#$t#! +ag

m"l#*at!a u$ur !"mug!#a )"ga m"ggua!a *#laga a%a!ra)om um*"r )#la!u!a )"ga *atua !omput"r&

2& Pr#$#p !"ra )"ga m"m*ag!#t!a *#laga *#laga a%a! atau

$amp"l )ar# $uatu ar#a*l" a%a! +ag t"lah )#!"tahu# )#$tr#*u$#+a

$"h#gga $#mula$# Mot" Carlo m"#ru ha$#l aal#t#!+a $"%ara um"r#!

$"h#gga )"ga $"ma!# *a+a! ag!a ra)om +ag )#g""rat" ma!a

$"ma!# a!urat ha$#l+a& 3al ## t"rl#hat *ah<a $"ma!# *a+a! )art N

$"h#gga ha$#l $#mula$# lua$ #t"gral m")"!at# ha$#l aal#t#! +ag

)#p"rol"h&

Metode Simulasi Monte Carlo(1)

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