naginterfaces.library.lapackeig.dggbak¶
- naginterfaces.library.lapackeig.dggbak(job, side, ilo, ihi, lscale, rscale, v)[source]¶
dggbak
forms the right or left eigenvectors of the real generalized eigenvalue problem , by backward transformation on the computed eigenvectors given bydtgevc()
. It is necessary to call this function only if the optional balancing functiondggbal()
was previously called to balance the matrix pair .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.
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 the same argument as supplied to
dggbal()
.- 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
dggbal()
.- ihiint
and as determined by a previous call to
dggbal()
.- 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
dggbal()
.- 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
dggbal()
.- vfloat, array-like, shape
The matrix of right or left eigenvectors, as returned by
dggbal()
.
- Returns
- vfloat, 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
dggbal()
thendggbak
backtransforms the eigenvector solution given bydtgevc()
. 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