Description

Eigenvector example.

Contributor: Erwin Kalvelagen, October 2008.

Small Model of Type : GAMS

Category : GAMS Test library

Main file : eigvec01.gms

$title Test eigenvector utility (EIGVEC01,SEQ=410)

$ontext

Eigenvector example.

Contributor: Erwin Kalvelagen, October 2008.


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

;

scalar rc;
parameter eval(i) 'eigenvalues';
parameter evec(i,j) 'eigenvectors';

$libInclude linalg eigenvector i a eval evec
abort$execerror 'Trouble with calculating Eigenvector';
display a, eval, evec;