naginterfaces.library.lapackeig.zggbak

naginterfaces.library.lapackeig.zggbak(job, side, ilo, ihi, lscale, rscale, v)

zggbak forms the right or left eigenvectors of the real generalized eigenvalue problem $Ax=\lambda Bx$, by backward transformation on the computed eigenvectors given by ztgevc(). It is necessary to call this function only if the optional balancing function zggbal() was previously called to balance the matrix pair $(A,B)$.

For full information please refer to the NAG Library document for f08ww

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f08/f08wwf.html

Parameters

jobstr, length 1

Specifies the backtransformation step required.

$job=\text{'N'}$

No transformations are done.

$job=\text{'P'}$

Only do backward transformations based on permutations.

$job=\text{'S'}$

Only do backward transformations based on scaling.

$job=\text{'B'}$

Do backward transformations for both permutations and scaling.

Note: this must be identical to the argument $job$ as supplied to zggbal().

sidestr, length 1

Indicates whether left or right eigenvectors are to be transformed.

$side=\text{'L'}$

The left eigenvectors are transformed.

$side=\text{'R'}$

The right eigenvectors are transformed.

iloint

$i_{lo}$ and $i_{hi}$ as determined by a previous call to zggbal().

ihiint

$i_{lo}$ and $i_{hi}$ as determined by a previous call to zggbal().

lscalefloat, array-like, shape $\left(n\right)$

Details of the permutations and scaling factors applied to the left side of the matrices $A$ and $B$, as returned by a previous call to zggbal().

rscalefloat, array-like, shape $\left(n\right)$

Details of the permutations and scaling factors applied to the right side of the matrices $A$ and $B$, as returned by a previous call to zggbal().

vcomplex, array-like, shape $(n,m)$

The matrix of right or left eigenvectors, as returned by zggbal().

Returns

vcomplex, ndarray, shape $(n,m)$

The transformed right or left eigenvectors.

Raises

NagValueError

(errno $-1$)

On entry, error in parameter $job$.

Constraint: $job=\text{'N'}$, $\text{'P'}$, $\text{'S'}$ or $\text{'B'}$.

(errno $-2$)

On entry, error in parameter $side$.

Constraint: $side=\text{'L'}$ or $\text{'R'}$.

(errno $-3$)

On entry, error in parameter $\text{n}$.

Constraint: $n\ge 0$.

(errno $-4$)

On entry, error in parameter $ilo$.

(errno $-5$)

On entry, error in parameter $ihi$.

(errno $-8$)

On entry, error in parameter $\text{m}$.

Constraint: $0\le m\le n$.

Notes

If the matrix pair has been previously balanced using the function zggbal() then zggbak backtransforms the eigenvector solution given by ztgevc(). This is usually the sixth and last step in the solution of the generalized eigenvalue problem.

For a description of balancing, see the document for zggbal().

References

Ward, R C, 1981, Balancing the generalized eigenvalue problem, SIAM J. Sci. Stat. Comp. (2), 141–152