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 byztgevc()
. It is necessary to call this function only if the optional balancing functionzggbal()
was previously called to balance the matrix pair .For full information please refer to the NAG Library document for f08ww
https://support.nag.com/numeric/nl/nagdoc_30.1/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()
thenzggbak
backtransforms the eigenvector solution given byztgevc()
. 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