naginterfaces.library.lapackeig.dggbak

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

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

For full information please refer to the NAG Library document for f08wj

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f08/f08wjf.html

Parameters

jobstr, length 1

Specifies the backward transformation 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 the same argument $job$ as supplied to dggbal().

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 dggbal().

ihiint

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

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 dggbal().

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 dggbal().

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

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

Returns

vfloat, 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 dggbal() then dggbak backtransforms the eigenvector solution given by dtgevc(). 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 dggbal().

References

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