Visible to Intel only — GUID: GUID-FFAF7A3C-A508-4402-B351-5851A691416F
Visible to Intel only — GUID: GUID-FFAF7A3C-A508-4402-B351-5851A691416F
?ggbak
Forms the right or left eigenvectors of a generalized eigenvalue problem.
Syntax
call sggbak(job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)
call dggbak(job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)
call cggbak(job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)
call zggbak(job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)
call ggbak(v [, ilo] [,ihi] [,lscale] [,rscale] [,job] [,info])
Include Files
- mkl.fi, lapack.f90
Description
The routine forms the right or left eigenvectors of a real/complex generalized eigenvalue problem
A*x = λ*B*x
by backward transformation on the computed eigenvectors of the balanced pair of matrices output by ggbal.
Input Parameters
- job
-
CHARACTER*1. Specifies the type of backward transformation required. Must be 'N', 'P', 'S', or 'B'.
If job = 'N', then no operations are done; return.
If job = 'P', then do backward transformation for permutation only.
If job = 'S', then do backward transformation for scaling only.
If job = 'B', then do backward transformation for both permutation and scaling. This argument must be the same as the argument job supplied to ?ggbal.
- side
-
CHARACTER*1. Must be 'L' or 'R'.
If side = 'L', then v contains left eigenvectors.
If side = 'R', then v contains right eigenvectors.
- n
-
INTEGER. The number of rows of the matrix V (n≥ 0).
- ilo, ihi
-
INTEGER. The integers ilo and ihi determined by ?gebal. Constraint:
If n > 0, then 1 ≤ilo≤ihi≤n;
if n = 0, then ilo = 1 and ihi = 0.
- lscale, rscale
-
REAL for single precision flavors
DOUBLE PRECISION for double precision flavors.
Arrays, size at least max(1, n).
The array lscale contains details of the permutations and/or scaling factors applied to the left side of A and B, as returned by ?ggbal.
The array rscale contains details of the permutations and/or scaling factors applied to the right side of A and B, as returned by ?ggbal.
- m
-
INTEGER. The number of columns of the matrix V
(m≥ 0).
- v
-
REAL for sggbak
DOUBLE PRECISION for dggbak
COMPLEX for cggbak
DOUBLE COMPLEX for zggbak.
Array v(ldv,*) . Contains the matrix of right or left eigenvectors to be transformed, as returned by tgevc.
The second dimension of v must be at least max(1, m).
- ldv
-
INTEGER. The leading dimension of v; at least max(1, n) .
Output Parameters
- v
-
Overwritten by the transformed eigenvectors
- info
-
INTEGER.
If info = 0, the execution is successful.
If info = -i, the ith parameter had an illegal value.
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine ggbak interface are the following:
- v
-
Holds the matrix V of size (n,m).
- lscale
-
Holds the vector of length n.
- rscale
-
Holds the vector of length n.
- ilo
-
Default value for this argument is ilo = 1.
- ihi
-
Default value for this argument is ihi = n.
- job
-
Must be 'B', 'S', 'P', or 'N'. The default value is 'B'.
- side
-
If omitted, this argument is restored based on the presence of arguments lscale and rscale as follows:
side = 'L', if lscale is present and rscale omitted,
side = 'R', if lscale is omitted and rscale present.
Note that there will be an error condition if both lscale and rscale are present or if they both are omitted.