?ggbak

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?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.

Parent topic: Generalized Nonsymmetric Eigenvalue Problems: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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