FDC NodeADD Example

lose all;home;clc;clear all;

for i=1:1:7

for j =1:1:7

M0(j,i)=i+7*(j-1);

end

end

for i=2:1:7

for j =1:1:i-1

M0(i,j)=M0(j,i);

end

end

for i=1:1:7

for j =1:1:7

C0(i,i)=1;

end

end

for i=1:1:7;

for j=1:1:7;

T(i,j)=0;

end

end

for i=1:1:7;

T(i,i)=1;

end

pivot_i=6;

pivot_j=1;

beta=-(M0(pivot_j,7)/M0(pivot_i,7));

T(pivot_j,pivot_i)=beta;

P1T=transpose(T);

M1=T*M0*P1T;

C1=T*C0*P1T;

M0

beta

T

M1

C0

C1

eig(M0)

eig(M1)

eig(C0)

eig(C1)

===============Results:=======================================

M0 =

1 2 3 4 5 6 7

2 9 10 11 12 13 14

3 10 17 18 19 20 21

4 11 18 25 26 27 28

5 12 19 26 33 34 35

6 13 20 27 34 41 42

7 14 21 28 35 42 49

beta =

-0.1667

T =

1.0000 0 0 0 0 -0.1667 0

0 1.0000 0 0 0 0 0

0 0 1.0000 0 0 0 0

0 0 0 1.0000 0 0 0

0 0 0 0 1.0000 0 0

0 0 0 0 0 1.0000 0

0 0 0 0 0 0 1.0000

M1 =

0.1389 -0.1667 -0.3333 -0.5000 -0.6667 -0.8333 0

-0.1667 9.0000 10.0000 11.0000 12.0000 13.0000 14.0000

-0.3333 10.0000 17.0000 18.0000 19.0000 20.0000 21.0000

-0.5000 11.0000 18.0000 25.0000 26.0000 27.0000 28.0000

-0.6667 12.0000 19.0000 26.0000 33.0000 34.0000 35.0000

-0.8333 13.0000 20.0000 27.0000 34.0000 41.0000 42.0000

0.0000 14.0000 21.0000 28.0000 35.0000 42.0000 49.0000

C0 =

1 0 0 0 0 0 0

0 1 0 0 0 0 0

0 0 1 0 0 0 0

0 0 0 1 0 0 0

0 0 0 0 1 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

C1 =

1.0278 0 0 0 0 -0.1667 0

0 1.0000 0 0 0 0 0

0 0 1.0000 0 0 0 0

0 0 0 1.0000 0 0 0

0 0 0 0 1.0000 0 0

-0.1667 0 0 0 0 1.0000 0

0 0 0 0 0 0 1.0000

ans =

0.0000

1.5872

1.9341

2.6120

4.9038

10.7566

153.2063

ans =

152.3052

10.7022

4.9255

0.0000

2.6489

1.9610

1.5961

ans =

1

1

1

1

1

1

1

ans =

0.8466

1.0000

1.0000

1.0000

1.0000

1.0000

1.1811

Remind:

1. Location of beta is (j,i) not (i,j)

Observation:

1. eigan values of M are close but not the same

2. eigan values of C are not the same