naginterfaces.library.lapackeig.zggbak¶

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

zggbak forms the right or left eigenvectors of the real generalized eigenvalue problem , 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 .

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

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f08/f08wwf.html

Parameters
jobstr, length 1

Specifies the backtransformation step required.

No transformations are done.

Only do backward transformations based on permutations.

Only do backward transformations based on scaling.

Do backward transformations for both permutations and scaling.

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

sidestr, length 1

Indicates whether left or right eigenvectors are to be transformed.

The left eigenvectors are transformed.

The right eigenvectors are transformed.

iloint

and as determined by a previous call to zggbal().

ihiint

and as determined by a previous call to zggbal().

lscalefloat, array-like, shape

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

rscalefloat, array-like, shape

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

vcomplex, array-like, shape

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

Returns
vcomplex, ndarray, shape

The transformed right or left eigenvectors.

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: , , or .

(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

(errno )

On entry, error in parameter .

(errno )

On entry, error in parameter .

Constraint: .

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