LABORATORIUM PEMBELAJARAN ILMU KOMPUTER FAKULTAS ILMU KOMPUTER UNIVERSITAS BRAWIJAYA
BAB NAMA NIM TANGGAL GGAL JENIS ASISTEN
: KETIDAKPASTIAN : CINDY CUNDAY CUNDAY CICIMBY : 145150207111 145150207111130 130 : 03/1 3/12/2 2/2016 016 : LATIHAN : - DIVA KUNIANINGTYAS - ADITA N!E PATI"I
1. DEFI DEFINI NISI SI MASA MASALA LAH H 1# B$%&' $%&'() () *&)&* &)&*(+ (+ 2
,) ,). .
ACC
$%* $%*( ((+ (+( (() () ). ).' '
*(&) (&) -*( -*(&) &)
.$ .$%&
'$.&('(.&() () .$+( &$+('()# 2# D&'$.(& D&'$.(& (. ('.( .&)'(. .&)'(. $)('& $)('&.. .%'$ .%'$ 8$%&'. 8$%&'. : T$'()() (%( 130 140 140 130 140 110 190 210 160 190
K((% +(
K+$.%+
LDL
U*%
K$+(
326 101 64 109 199 155 421 204 110 247
139 26 13 197 15 115 277 22 14 15
99 15 122 123 127 0 165 162 109 127
56 59 44 63 60 52 56 4 60 55
T&)& S$() $)( $)( S$() $)( T&)& T&)& S$() S$()
H&.) $,(%( *()(+ () .$).'() (&+ '+(&&'(& *$))('() .$%$*( 8($ ).' ('.( 8(% 8$%&'. : (# T$'()() T$'()() (%( (%( ; 150< 150< K((% K((% +( ; 179< 179< K+$.%+ K+$.%+ ; 252< 252< LDL LDL ; 135< 135< U*% ; 72 8# T$'()() T$'()() (%( ; 150< K((% +( ; 115< K+$.%+ ; 122< LDL ; 70< U*% ; 62 ,# T$'()() T$'()() (%( (%( ; 100< 100< K((% K((% +( ; 100< 100< K+$.%+ K+$.%+ ; 15< 15< LDL LDL ; 127< 127< U*% ; 29 B. JAW JAWAB
1# J(=(8 : (# P%8 P%8(8 (8&+ &+&. &.( ( K+( K+(& &' ' - P$+$* P$+$*(%() (%() ( ( () () *$*&+&' *$*&+&'&& $)(* $)(* && () $)(* $)(* -
'$*)'&)() P$+$* P$+$*(%() (%() *(.( *(.( () () (.( '&) '&) () () *$*&+& *$*&+&'& '& ( ( &&
() ( '$*)'&)()# 8# P%8(8&+&.( B$%(%(.
-
A( 8$8$%(( 8+( $)() 8$%8((& =(%)( () *$*&+&'& .()( & $.&( 8+()(< *&(+ *$*&+&'& .()( >?@ () >-> # K$.&'( $$%() *$)(*8&+ (+( (. =(%)(< *('(
8$%(( %8(8&+&.( 8+( &(*8&+ $)() (+( (. .()(# - P$+$*(%() ( 8( ( $)() (%(. *+( (%& '$( ( ((+( $)(# ,# T$%$*( B($ - M$)'+(&&'(&'() (. '*$) 8$%((%'() && / '(.( '(.( () (( (+(* '*$) .$%$8.# K+(&&'(& +)() / $)$%&.( $)('&. & (. %*(
-
('&.# # ('.% K$(.&() C$%.(&). ('.% - J&'( $$%() *$*)(& $(+( .$%.$). () *$)&)&'(&'() 8$8$%(( '$*)'&)() $)('&.< *('( $)('&. $)() C .$%.&)& *$)(& %.() $%.(*( -
(+(* %.() $)&()# M$)$).'() (('( $%() '(%(=() &.$%&*( (.( .&(' &.$%&*( +$ 1 : &'( .&(' ++ &'.$ () .&(' ++ =(=(),(%( *('( &.+(' +$ 2 : &'( .&(' ++ &'.$ () ++ =(=(),(%( *('( ,(()() +$ 3 : &'( ++ &'.$ () ++ =(=(),(%( *('( &.$%&*(#
2# J(=(8 1. Labeling Data set Y mewakili kelas. 1 = rendah , 2 = sedang, 3 = tinggi
2. Memisahkan X berdasarkan grup/ kelas X1 untuk kelas rendah, X2 untuk kelas sedang, dan X3 untuk kelas tinggi
3. Hitung mean dari setiap kelas dan mean glbal
!. Hitung mean "rre"ted #mean setiap kelas $ mean glbal%
&. Hitung matrik k'arian grup
(umus )
*. Hitung likelihd dari setiap "ur'ature
(umus ) a. +ekanan darah = 1&, -adar gula = 1, -lestrl = 2&2, LDL = 13&,
0mur
= 1.&21211
e $1/2
=
2
b. +ekanan darah = 1&, -adar gula = 11&, -lestrl = 122, LDL = , 0mur = *2
=
1.&21211
e $1/2
". +ekanan darah = 1, -adar gula = 1, -lestrl = 1&, LDL = 12, 0mur = 2
=
1.&21211
e $1/2
A. DEFINISI MASALAH C(%&+( () $&)&&'() ,). $%*((+(() &)&( )(.( () ((.
&$+$(&'() *$))('() .$%$*( 8($ (.( () +(&)< '$*&() : (# T)''() +$.(' '$.&('(.&() (( $%*((+(() .$%$8. 8# T$).'() ('.()( 8+$ (.( ** ,# I*+$*$).(&'() .$%$*( .$%$8. '$(+(* '$ %%(* # B(.+( *&)&*(+ 2 '( & (%& $%*((+(() .$%$8. () &'() (( %%(* () .$+( ()( 8(. $# T)''() (&+)( B. JAWAB
1# (# 8# 130 326 139 99 56 .&)& 190 421 277 165 56 .&)& 210 204 22 162 4 .&)& 140 101 26 15 59 $() 140 199 15 127 60 $() 160 110 14 109 60 $() 190 247 15 127 55 $() 140 64 13 122 44 %$)( 130 109 197 123 63 %$)( 110 155 115 0 52 %$)( ,#
example.java import import import import import import
java.io.BufferedReader; java.io.FileReader; java.io.IOException; java.io.InputStreamReader; java.util.logging.Level; java.util.logging.Logger;
public class example public static void main!String"# args$ t%ro&s IOException String data"#"# ' ne& String"()#"*#; String tinggi"#"# ' ne& String"+#"*#; String sedang"#"# ' ne& String",#"*#; String renda%"#"# ' ne& String"+#"*#; --mean corrected double tinggimc"#"# ' ne& double"+#"/#; double sedangmc"#"# ' ne& double",#"/#; double renda%mc"#"# ' ne& double"+#"/#; --mean covarian double tinggicov"#"# ' ne& double"/#"/#; double sedangcov"#"# ' ne& double"/#"/#; double renda%cov"#"# ' ne& double"/#"/#; double globalcov"#"# ' ne& double"/#"/#; --global invers double globalinv"#"#; --prior double tinggiprior; double sedangprior; double renda%prior; --dis0riminan double tinggidis0; double sedangdis0; double renda%dis0; --inde0s untu0 pemeca%an arra1 2 tinggi3sedang3renda%3pus%ers int xc3 xs3 xt; xc ' xs ' xt ' ); double ug"# ' ne& double"/#;--mean global double uc"# ' ne& double"/#;--mean tinggi double us"# ' ne& double"/#;--mean sedang double ut"# ' ne& double"/#;--mean renda% --
--input double dicari"# ' (43 (53 (53 ,,3 +6 ; double dicari"# ' ne& double"/#; BufferedReader in'ne& BufferedReader!ne& InputStreamReader!S1stem.in$$; S1stem.out.println!7Input 8ata 7$; S1stem.out.println!77$; S1stem.out.print!79e0anan 8ara% 2 7$; dicari")#' Float.parseFloat!in.readLine!$$;
S1stem.out.print!7:adar ula 2 7$; dicari"(#' Float.parseFloat!in.readLine!$$; S1stem.out.print!7:olesterol 2 7$; dicari"<#' Float.parseFloat!in.readLine!$$; S1stem.out.print!7L8L 2 7$; dicari"+#' Float.parseFloat!in.readLine!$$; S1stem.out.print!7=mur 2 7$; dicari",#' Float.parseFloat!in.readLine!$$; tr1 data ' get8ata!7data.txt7$; 6 catc% !IOException ex$ Logger.getLogger!main.class.get>ame!$$.log!Level.SE?ERE3 null3 ex$; 6 --memisa% arra1 tinggi3sedang3renda% for !String"# data( 2 data$ --S1stem.out.println!data("/#$; for !int l ' ); l @ data")#.lengt%; lAA$ s&itc% !data("/#$ case 7tinggi72 tinggi"xc#"l# ' data("l#; --S1stem.out.println!77Atinggi"xc# "l#$; brea0; case 7sedang72 sedang"xs#"l# ' data("l#; brea0; case 7renda%72 renda%"xt#"l# ' data("l#; brea0; 6 6 s&itc% !data("/#$ case 7tinggi72 xcAA; brea0; case 7sedang72 xsAA; brea0; case 7renda%72 xtAA; brea0; 6 6 --mean ug ' mean!data$; -- S1stem.out.println!7panjang tinggi 2 7Atinggi")# "(#$; -for !int i ' ); i @ tinggi.lengt%; iAA$ -S1stem.out.println!tinggi"i#"(#$; -6 uc ' mean!tinggi$;
us ' mean!sedang$; ut ' mean!renda%$;
----
for !int 0 ' ); 0 @ug.lengt%; 0AA$ S1stem.out.print!up"0#A7 7$; 6 S1stem.out.println!77$; --meancorrected tinggimc ' meanCorrected!tinggi3 ug$; sedangmc ' meanCorrected!sedang3 ug$; renda%mc ' meanCorrected!renda%3 ug$;
-for !int 0 ' ); 0 @ pus%ermc.lengt%; 0AA$ -for !int l ' ); l @ pus%ermc")#.lengt%; lA A$ -S1stem.out.printf!7D.+f7A7 73 pus%ermc"0#"l#$; -6 -S1stem.out.println!77$; -6
--
S1stem.out.println!renda%mc")#")#$;
--matri0s covarian tinggicov ' covarian!tinggimc$; sedangcov ' covarian!sedangmc$; renda%cov ' covarian!renda%mc$; globalcov ' globalCovarioan!data.lengt%3 tinggicov3 tinggi.lengt%3 sedangcov3 sedang.lengt%3 renda%cov3 renda%.lengt%$; --invers cov global globalinv ' invert!globalcov$; -for !int 0 ' ); 0 @globalinv.lengt%; 0AA$ -for !int l ' ); l @ globalinv")#.lengt%; lA A$ -S1stem.out.printf!7D.+f7A7 73 globalinv"0#"l#$; -6 -S1stem.out.println!77$; -6 --prior tinggiprior ' !double$tinggi.lengt% !double$data.lengt%; sedangprior ' !double$sedang.lengt% !double$data.lengt%; renda%prior ' !double$renda%.lengt% !double$data.lengt%; --dis0riminan tinggidis0 ' dis0riminan!uc3 globalinv3 dicari3 tinggiprior$;
sedangdis0 ' dis0riminan!us3 globalinv3 dicari3 sedangprior$; renda%dis0 ' dis0riminan!ut3 globalinv3 dicari3 renda%prior$; -S1stem.out.printf!7D.+f7A7 73 tinggidis0$; -S1stem.out.printf!7D.+f7A7 73 sedangdis0$; -S1stem.out.printf!7D.+f7A7 73 renda%dis0$; -S1stem.out.printf!7D.+f7A7 73 pus%erdis0$; -S1stem.out.println!tinggidis0$; -S1stem.out.println!sedangdis0$; -S1stem.out.println!renda%dis0$; -S1stem.out.println!pus%erdis0$; -String :elasasil'79inggi7; double tmp'tinggidis0; if!tmp@ sedangdis0$ tmp'sedangdis0; :elasasil'7Sedang7; 6 if !tmp@ renda%dis0$ tmp'renda%dis0; :elasasil'7Renda%7; 6
S1stem.out.println!78ata 1ang anda masu0an adala% 0elas 2 7A:elasasil$; 6 public static String"#"# get8ata!String source$ t%ro&s IOException BufferedReader in ' ne& BufferedReader!ne& FileReader!source$$; String line; String result"#"# ' ne& String"()#"*#; int i ' )3 j; &%ile !!line ' in.readLine!$$ ' null$ j ' ); String"# arr ' line.split!7 7$; for !String tmp 2 arr$ result"i#"j# ' tmp; jAA; 6 iAA; 6 in.close!$; return result; 6 private static double"# mean!String"#"# arra1$ double result"# ' ne& double"/#; double fitur(3 fitur<3 fitur+3 fitur,3 fitur/3 n; fitur( ' fitur< ' fitur+ ' fitur, ' fitur/ ' n ' );
--S1stem.out.println!arra1.lengt%$; for !int 0 ' ); 0 @ arra1.lengt%; 0AA$ fitur( A' Float.parseFloat!arra1"0#")#$; fitur< A' Float.parseFloat!arra1"0#"(#$; fitur+ A' Float.parseFloat!arra1"0#"<#$; fitur, A' Float.parseFloat!arra1"0#"+#$; fitur/ A' Float.parseFloat!arra1"0#",#$; nAA; 6 result")# ' fitur( - n; result"(# ' fitur< - n; result"<# ' fitur+ - n; result"+# ' fitur, - n; result",# ' fitur/ - n; return result;
6 private static double"#"# meanCorrected!String"#"# arra13 double"# ug$ double result"#"# ' ne& double"arra1.lengt%# "ug.lengt%#; for !int 0 ' ); 0 @ arra1.lengt%; 0AA$ result"0#")# ' Float.parseFloat!arra1"0#")#$ ug")#; result"0#"(# ' Float.parseFloat!arra1"0#"(#$ ug"(#; result"0#"<# ' Float.parseFloat!arra1"0#"<#$ ug"<#; result"0#"+# ' Float.parseFloat!arra1"0#"+#$ ug"+#; result"0#",# ' Float.parseFloat!arra1"0#",#$ ug",#; 6 return result; 6
private static double"#"# covarian!double"#"# arra1$ double transposearra1"#"# ' ne& double"arra1")#.lengt%#"arra1.lengt%#; double n ' arra1.lengt%; transposearra1 ' transpose!arra1$; double result"#"# ' ne& double"transposearra1.lengt%#"arra1")#.lengt%#; result ' per0alian!transposearra13 arra1$; --pembagian dengan n for !int i ' ); i @ result.lengt%; iAA$ for !int j ' ); j @ result")#.lengt%; jAA$ result"i#"j# ' result"i#"j# - n; 6 6
return result; 6 private static double"#"# globalCovarioan!int lengt%3 double"#"# tinggicov3 int lengt%)3 double"#"# sedangcov3 int lengt%(3 double"#"# renda%cov3 int lengt%<$ double result"#"# ' ne& double"/#"/#; for !int i ' ); i @ tinggicov.lengt%; iAA$ for !int j ' ); j @ tinggicov")#.lengt%; jAA$ result"i#"j# ' !!tinggicov"i#"j# G lengt%)$ A !sedangcov"i#"j# G lengt%($ A !renda%cov"i#"j# G lengt%<$$ - lengt%; 6 6 return result; 6 --invers matri0s public static double"#"# invert!double a"#"#$ int n ' a.lengt%; double x"#"# ' ne& double"n#"n#; double b"#"# ' ne& double"n#"n#; int index"# ' ne& int"n#; for !int i ' ); i @ n; AAi$ b"i#"i# ' (; 6 -- 9ransform t%e matrix into an upper triangle gaussian!a3 index$;
-- =pdate t%e matrix b"i#"j# &it% t%e ratios stored for !int i ' ); i @ n (; AAi$ for !int j ' i A (; j @ n; AAj$ for !int 0 ' ); 0 @ n; AA0$ b"index"j##"0# ' a"index"j##"i# G b"index"i##
"0#; 6 6 6 -- Herform bac0&ard substitutions for !int i ' ); i @ n; AAi$ x"n (#"i# ' b"index"n (##"i# - a"index"n (##"n (#; for !int j ' n <; j ' ); j$ x"j#"i# ' b"index"j##"i#; for !int 0 ' j A (; 0 @ n; AA0$ x"j#"i# ' a"index"j##"0# G x"0#"i#; 6 x"j#"i# -' a"index"j##"j#; 6
6 return x; 6 -- Jet%od to tinggi out t%e partialpivoting aussian -- elimination. ere index"# stores pivoting order. public static void gaussian!double a"#"#3 int index"#$ int n ' index.lengt%; double c"# ' ne& double"n#; -- InitialiKe t%e index for !int i ' ); i @ n; AAi$ index"i# ' i; 6 -- Find t%e rescaling factors3 one from eac% ro& for !int i ' ); i @ n; AAi$ double c( ' ); for !int j ' ); j @ n; AAj$ double c) ' Jat%.abs!a"i#"j#$; if !c) c($ c( ' c); 6 6 c"i# ' c(; 6 -- Searc% t%e pivoting element from eac% column int 0 ' ); for !int j ' ); j @ n (; AAj$ double pi( ' ); for !int i ' j; i @ n; AAi$ double pi) ' Jat%.abs!a"index"i##"j#$; pi) -' c"index"i##; if !pi) pi($ pi( ' pi); 0 ' i; 6 6 -- Interc%ange ro&s according to t%e pivoting order int itmp ' index"j# ' index"0# ' for !int i double
index"j#; index"0#; itmp; ' j A (; i @ n; AAi$ pj ' a"index"i##"j# - a"index"j##
"j#; -- Record pivoting ratios belo& t%e diagonal a"index"i##"j# ' pj;
-- Jodif1 ot%er elements accordingl1 for !int l ' j A (; l @ n; AAl$ a"index"i##"l# ' pj G a"index"j##"l#; 6 6 6 6 private static double dis0riminan!double"# mean3 double"#"# globalinv3 double"# dicari3 double prior$ double result ' ); double meanfix"#"# ' ne& double"(#"mean.lengt%#; for !int i ' ); i @ mean.lengt%; iAA$ meanfix")#"i# ' mean"i#; 6 double meanfixtranspose"#"# ' ne& double"mean.lengt%#"(#; for !int i ' ); i @ mean.lengt%; iAA$ meanfixtranspose"i#")# ' mean"i#; 6 double dicaritranspose"#"# ' ne& double"dicari.lengt%#"(#; for !int i ' ); i @ dicari.lengt%; iAA$ dicaritranspose"i#")# ' dicari"i#; 6 ------------------------------------------------------------------------------Gleft side --mean x globalinvers double meanxglobalinv"#"# ' ne& double"meanfix.lengt%#"globalinv")#.lengt%#; meanxglobalinv ' per0alian!meanfix3 globalinv$; --result left side double tmpleftside "#"# ' ne& double"meanxglobalinv.lengt%# "dicaritranspose")#.lengt%#; tmpleftside ' per0alian!meanxglobalinv3 dicaritranspose$; double leftside ' tmpleftside ")#")#; --Gcenter --meanxglobal x meanfixtranspose double meanxglobalxmeanfixtranspose "#"# ' ne& double"meanxglobalinv.lengt%# "meanfixtranspose")#.lengt%#; meanxglobalxmeanfixtranspose ' per0alian!meanxglobalinv3 meanfixtranspose$; --result center side double centerside ' meanxglobalxmeanfixtranspose")#")#-<; --Grig%t side double ln ' Jat%.log!prior$; double rig%tside ' !double$ln; -------------------------------------------------------------------------------
--result result ' leftside centerside A rig%tside; return result; 6
private static double"#"# transpose!double"#"# arra1$ double result"#"# ' ne& double"arra1")#.lengt%# "arra1.lengt%#; for !int i ' ); i @ arra1.lengt%; iAA$ for !int j ' ); j @ arra1")#.lengt%; jAA$ result"j#"i# ' arra1"i#"j#; 6 6 return result; 6 private static double"#"# per0alian!double"#"# transposearra13 double"#"# arra1$ double result"#"# ' ne& double"transposearra1.lengt%#"arra1")#.lengt%#; for !int i ' ); i @ transposearra1.lengt%; iAA$ for !int j ' ); j @ arra1")#.lengt%; jAA$ for !int 0 ' ); 0 @ transposearra1")#.lengt%; 0AA$ result"i#"j# A' transposearra1"i#"0# G arra1"0#"j#; 6 6 6 return result; 6 6
P$)$+(() S%,$ C$ M$. *(&) &)('() ).' *$)(.% $%&.)() &).& (%& LDA • M$. (%%( $.D(.( &)('() ).' *$)(*8&+ (.( (%& ).$( • () *()( ).$( $8((& (.(8($ M$. *$() &)('() ).' *$)&.) *$() • M$. *$()C%%$,.$ &)('() ).' *$)&.) *$() ,%%$,.$ • ).' $%&.)() LDA M$. ,(%&() &)('() ).' *$)&.) ,(%&() ).' • $%&.)() LDA M$. +8(+,(%&() &)('() ).' *$)&.) +8(+ ,(%&() • ).' $%&.)() LDA M$. &)$%. &)('() ).' *$)&.) &)$%. ).' $%&.)() • LDA M$. (&() &)('() ).' *$)&.) (&() ).' • $%&.)() LDA M$. &'%&*&)() &)('() ).' *$)&.) &'%&*&)() ).' •
$%&.)() LDA M$. .%()$ &)('() ).' *$)&.) .%()$ ).' • $%&.)() LDA M$. $%'(+&() &)('() ).' *$)&.) $%'(+&() ).' • $%&.)() LDA # T$'()() (%( : 130 K((% +( : 326 K+$.%+ :139 LDL : 99 U*% : 56 T$'()() (%( : 125 K((% +( : 226 K+$.%+ :10 LDL : 120 U*% : 49
$#
C. KESIMPULAN 1# J$+('() ')$ '$.&('(.&() (+(* '$,$%(() 8(.()
K$.&('(.&()
*$%('()
(.
$%*((+(()
'(%$)(
*)'&)
*$)(+()& '&.( *$*8(. (. '$.() () .$%8(&'# A( 8()(' *((+( :
T&(' .( '$((() (+()< '$*(,$.()< ++# (%.&(++ 8$%(8+$# K$8$)(%() &)%*(& .&(' 8&( &(*&)->+(%() ()()() *(.(@
)& $)%# K$.&('(.&() (+(* .&)('()< *&# 8() '$*$ ))$.$%*&)&.&,#
K(+() $*( (+ & (.( 8&( &)(.('()< %$()&) ('() +(%
8&(( %$.A( 8()(' *((+( 2# S$8.'() () $+('() .$%& () 8$%8)() $)() '$.&('(.&() P%8(8&+&.( K+(&' ((+( P%8(8&+&.( *$%('() ,(%( ()
&)('()
(+(*
*$)&.)
'$.&('(.&()
$)()
(+()
'().&.(# D(+(* %8(8&+&.( '+(&' &$8. ( $)() ( %&%&
%8(8&+&. '(%$)( 8$%8)() $)() (*$ (.( &.$*# P%8(8&+&.( B($ ((+( $8( .$%$*( $)() ( $)(&%() 8$%8$(# D(+(* $)(&%() B($< .$%$*( &)& *$)(.('() $8$%(( ( $%((. '$$%,((() 8$'.& (% 8$%8( $,(%(
%(&)(+ '$.&'( (( $.)' 8(%# T$%& H(%.+$ () 8$%((%'() (( &*)() '+(&' ((+( $8( .$%$*( () *$))('() $)$'(.() '+(&' ).'
&&*+$*$).(&'() (( %()'(&() $)$%&*( %(& AM () M# T$%& S()) () &((%'() (( $+() ((+( .$%& '(&.())( ().(%( '((&.( (+%()< 8()=&. () )&$ (( %$
'*)&'( T$%& D$*.$%-S($% ((+( (. teori *(.$*(.&'( ).' $*8'.&() 8$%((%'() 8$+&$ ),.&) () +(&8+$ %$()&) )& '$$%,((() () $*&'&%() () *(' ('(+< () &)('() ).' *$)'*8&)(&'() .)() &)%*(& () .$%&( 8'.& ).' *$)'(+'+(& '$*)'&)() (%& (.
$%&.&=(# T$%& FF ($ ((+( $)&)'(.() (%& loi!" B+$() () 8$%((() $)() ')$ '$8$)(%() $8(&()# S((. loi!" '+(&' *$)(.('() 8(=( $(+( (+ ((. &$'%$&'() (+(* &.&+( 8&)$% 0 (.( 1< &.(* (.( .&< ( (.( .&('< loi!" #$%%& *$)().&'() '$8$)(%() 8+$() $)() .&)'(. '$8$)(%()#
3# J$+('()
()
8$%&'()
,).
8((&*()(
.$%$*(
8($
((.
*$)$+$(&'() '$.&('(.&() (+(* '$,$%(() 8(.() T$%$*( 8($ *$))('() %8(8+&+&.( %&% () .$%&% ).' &)('() (+(* '$.&('(.&()# C). $))(())( :