EIGENVECTOR

EIGENVECTOR calculates eigenvalues/vectors of a symmetric matrix.

# Usage

eigenvector gdxin i a gdxout eval evec


where

gdxin

name of gdxfile with matrix

i

name of set used in matrix

a

name of 2 dimensional parameter inside gdxin

gdxout

name of gdxfile for results (eigenvalues)

eval

name of 1 dimensional parameter inside gdxout

evec

name of 2 dimensional parameter inside gdxout

Calculates eigenvalues/vectors of symmetric matrix a(i,j) where i and j are aliased sets. eval will contain the eigenvalues and evec will contain the eigenvectors.

# Example

$onText Eigenvector example. octave:1> a = [1 2 4 7 11; 2 3 5 8 12; 4 5 6 9 13; 7 8 9 10 14; 11 12 13 14 15] a = 1 2 4 7 11 2 3 5 8 12 4 5 6 9 13 7 8 9 10 14 11 12 13 14 15 octave:2> eig(a) ans = -8.464425 -1.116317 -0.512109 -0.027481 45.120332 octave:3> [e1,e2] = eig(a) e1 = 0.5550905 -0.2642556 0.2892854 0.6748602 0.2879604 0.4820641 -0.2581518 0.2196341 -0.7349311 0.3355726 0.2865066 0.2159261 -0.8437897 0.0411896 0.3970041 -0.0992784 0.7711236 0.3943678 0.0055409 0.4898525 -0.6062562 -0.4714561 -0.0238286 0.0520829 0.6378888 e2 = -8.46442 0.00000 0.00000 0.00000 0.00000 0.00000 -1.11632 0.00000 0.00000 0.00000 0.00000 0.00000 -0.51211 0.00000 0.00000 0.00000 0.00000 0.00000 -0.02748 0.00000 0.00000 0.00000 0.00000 0.00000 45.12033$offText

Set i / i1*i5 /;

Alias (i,j);

Table a(i,j)
i1   i2   i3   i4   i5
i1    1    2    4    7   11
i2    2    3    5    8   12
i3    4    5    6    9   13
i4    7    8    9   10   14
i5   11   12   13   14   15;

Parameter
eval(i)   'eigenvalues'
evec(i,j) 'eigenvectors';