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';

execute_unload 'mat.gdx', i, a;
execute '=eigenvector.exe mat.gdx i a ev.gdx eval evec';
execute_load 'ev.gdx', eval, evec;

display a, eval, evec;