metode simulasi monte carlo(1)
TRANSCRIPT
7/23/2019 Metode Simulasi Monte Carlo(1)
http://slidepdf.com/reader/full/metode-simulasi-monte-carlo1 1/10
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 $%
2
&
7/23/2019 Metode Simulasi Monte Carlo(1)
http://slidepdf.com/reader/full/metode-simulasi-monte-carlo1 2/10
Algoritma yang digunakan sebagaiberikut :
1& Bag!#t!a *#laga ra)om u#ra)
2& I#$#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@
7/23/2019 Metode Simulasi Monte Carlo(1)
http://slidepdf.com/reader/full/metode-simulasi-monte-carlo1 3/10
?
)ou*l" )ou*l" 5
7/23/2019 Metode Simulasi Monte Carlo(1)
http://slidepdf.com/reader/full/metode-simulasi-monte-carlo1 4/10
>
)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*$5?
?
7/23/2019 Metode Simulasi Monte Carlo(1)
http://slidepdf.com/reader/full/metode-simulasi-monte-carlo1 5/10
ARNITA IRIANTI/20914009COMPUTATIONAL SCIENCEITB
//M"%ar# #t"gral ug$# )"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
?
7/23/2019 Metode Simulasi Monte Carlo(1)
http://slidepdf.com/reader/full/metode-simulasi-monte-carlo1 6/10
ARNITA IRIANTI/20914009COMPUTATIONAL SCIENCEITB
Hasil running sebagai berikut :
Plo" #ra'i (i GNU )lo"N*1
+1
0&'
1Mot"CarloE)ata&t
5t$#55
0&
0&4
&2
0
/0&2
/0&4
/0&
/0&'
/1
0 1 2 6 4 . O
@
Gambar.2. Plo" L!as In"e#ral (en#an N*1+
0
H 0 5 1
7/23/2019 Metode Simulasi Monte Carlo(1)
http://slidepdf.com/reader/full/metode-simulasi-monte-carlo1 7/10
N *1+++++
@
Gambar.,. Plo" L!as In"e#ral (en#an N*1+++++
3a$#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
7/23/2019 Metode Simulasi Monte Carlo(1)
http://slidepdf.com/reader/full/metode-simulasi-monte-carlo1 8/10
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
7/23/2019 Metode Simulasi Monte Carlo(1)
http://slidepdf.com/reader/full/metode-simulasi-monte-carlo1 9/10
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 $"ma!# *a+a!&
T R E N 6
L ! a s
7/23/2019 Metode Simulasi Monte Carlo(1)
http://slidepdf.com/reader/full/metode-simulasi-monte-carlo1 10/10
ARNITA IRIANTI/20914009COMPUTATIONAL SCIENCEITB
Kesimpulan :
1& S#mula$# 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&