9/12/2011

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Pengolahan Data - Scilab

Setia Budi Sasongko

Pengolahan Data

� Interpolasi� Pencocokan Kurva (Curve Fitting)

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Interpolasi Linear

D

E

C

BA

f (x2)

f (x1)

f (x)

x2x1 x

AD

DE

AB

BC =

12

12

1

1 )()()()(

xx

xfxf

xx

xfxf

−−

=−−

( ) ( )112

121

)()()( xx

xx

xfxfxfxf −

−−

+=

Regresi Linear, y=a0 + a1x

)(1

101

∑ −−∑ ===

n

iii

n

ii xaaye

∑ −−=∑==

n

iii

n

ii xaaye

110

1)(

∑ −−=∑===

n

iii

n

iir xaayeS

1

210

1

2 )(

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Persamaan Linear: y=a0 + a1x

0)(21

100

=∑ −−−=∂∂

=

n

iii

r xaaya

S

( )[ ] 021

101

=∑ −−−=∂∂

=

n

iiii

r xxaaya

S

∑ ∑ ∑ =−− 010 ii xaay

∑ ∑ ∑ =−− 0210 iiii xaxaxy

∑

∑=

∑∑

∑

ii

i

ii

i

yx

y

a

a

xx

xn

1

02

( )∑ ∑−∑ ∑ ∑−=

221ii

iiii

xxn

yxyxna

xaya 10 −=

∑ −−=∑===

n

iii

n

iir xaayeS

1

210

1

2 )(

Least square:

Contoh:

x 1 3 5 7 10 12 13 16 18 20

y 4 2 6 5 8 7 10 9 12 11

n ( i ) x y x2 xy

1 1 4 1 4

2 3 2 9 6

3 5 6 25 30

4 7 5 49 35

5 10 8 100 80

6 12 7 144 84

7 13 10 169 130

8 16 9 256 144

9 18 12 324 216

10 20 11 400 220

Jumlah

105 74 1477 949

a1= {(10 x 949) – (105 x 74)}/{(10 x 1477) – (105)2}= 0,4593.

a0 = 7,4 - (0,4593) x 10,5=2.577

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Perintah Scilab: reglin

[a,b,sigma]= reglin( x,y )

Fungsi: penyelesaian problem regresi linear dengan least square untuk model persamaan: y = a*x + b .

Keterangan: Data x dan y berupa vektor baris.

1 x=[1,3,5,7,10,12,13,16,18,20];

2 y=[4,2,6,5,8,7,10,9,12,11];

3 [a,b]= reglin(x,y)

Regresi polinomial

mmxaxaxaay ++++= ⋯

2210

∑

∑

∑

=

∑∑∑

∑∑∑

∑∑

ii

ii

i

iii

iii

ii

yx

yx

y

a

a

a

xxx

xxx

xxn

22

1

0

432

32

2

A = inv(SGX) . SGXY

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1 function [A]=repolisbs(x,y,pk)

2 [m,n]=size(x);

3 for i=1:(pk+1)

4 for j=1:i

5 k=i+j-2;

6 jml=0;

7 for l=1:n

8 jml=jml+x(1,l)^k;

9 end

10 sgx(i,j)=jml;

11 sgx(j,i)=jml;

12 end

13 jmlxy=0;

14 for l=1:n

15 jmlxy=jmlxy+y(1,l)*x(1,l)^(i-1);

16 end

17 sgxy(i,1)=jmlxy;

18 end

19 A=inv(sgx)*sgxy

20 endfunction

Perintah Scilab: polyPerintah Scilab: poly

poly (a ,’x’, [‘ket’])

Fungsi: Pendefinisian persamaan polinomialDimana:

a = matrik atau bilangan riilx = simbol variabel

‘ket’= berupa opsional dari string dari ‘roots’ atau ‘coeff’defaultnya adalah roots

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Contoh: aplikasi polyContoh: aplikasi poly

-->A=[3 -1 6]A =

3. - 1. 6.-->akr=poly(A,'x','roots')akr =

2 318 + 9x - 8x + x

-->prs=poly(A,'x','coeff')prs =

23 - x + 6x

-->

Perintah Scilab: hornerPerintah Scilab: hornerhorner (P ,x )

Fungsi: Mengevaluasi polinomial/rasionalDimana: P matrik polinomial atau rasional,

x= bilangan riil .

-->A=[3 1 -2]A =

3. 1. - 2.-->p=poly(A,'x','coeff')p =

23 + x - 2x

-->b=horner(p,0)b =

3.-->b=horner(p,1)b =

2.

-->