eigvec02.gms : Test eigenvector/eigenvalue utilities
Eigenvalue/vector test.
Construct A to have known eigenvalues/vectors: A X = X lam
A = 2 1 X = 1 1 lam = 1
1 2 -1 1 3
Contributor: Steve Dirkse, October 2008
Small Model of Type: GAMS
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$title Test eigenvector/eigenvalue utilities (EIGVEC02,SEQ=413)
$ontext
Eigenvalue/vector test.
Construct A to have known eigenvalues/vectors: A X = X lam
A = 2 1 X = 1 1 lam = 1
1 2 -1 1 3
Contributor: Steve Dirkse, October 2008
$offtext
set I / i1 * i2 /;
alias (I,J,K);
parameters
A(I,J) 'constructed to have known eigenvectors/values'
X0(I,J) 'known eigenvectors'
X(I,J)
lam0(I) 'known eigenvalues' /
i1 1
i2 3
/,
lam(I)
s(J) 'scales for the eigenvector comparison'
;
table A(I,J)
i1 i2
i1 2 1
i2 1 2 ;
table X0(I,J)
i1 i2
i1 1 1
i2 -1 1 ;
scalar rc;
execute_unload 'A.gdx', I, A;
execute 'eigenvalue A.gdx I A tmp1.gdx lam > tmp1.log';
rc=errorlevel;
abort$(rc > 0) 'Nonzero return code from eigenvalue', rc;
execute_load 'tmp1.gdx', lam;
rc=errorlevel;
abort$(rc > 0) 'Error loading eigenvalue from tmp1.gdx', rc;
abort$[smax{I, abs(lam(I)-lam0(I))} > 1e-8] 'Bad eigenvalues in tmp1.gdx';
execute 'eigenvector A.gdx I A tmp2.gdx lam X > tmp2.log';
rc=errorlevel;
abort$(rc > 0) 'Nonzero return code from eigenvector', rc;
execute_load 'tmp2.gdx', lam, X;
rc=errorlevel;
abort$(rc > 0) 'Error loading eigenvalues/vectors from tmp2.gdx', rc;
execute_unload 'all.gdx';
abort$[smax{I, abs(lam(I)-lam0(I))} > 1e-8] 'Bad eigenvalues in tmp2.gdx';
s(J) = X0('i1',J) / X('i1',J);
X(I,J) = X(I,J) * s(J);
abort$[smax{(I,J), abs(X(I,J)-X0(I,J))} > 1e-8] 'Bad eigenvectors in tmp2.gdx';
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