?gebak

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/22/2024

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?gebak

Transforms eigenvectors of a balanced matrix to those of the original nonsymmetric matrix.

Syntax

call sgebak(job, side, n, ilo, ihi, scale, m, v, ldv, info)

call dgebak(job, side, n, ilo, ihi, scale, m, v, ldv, info)

call cgebak(job, side, n, ilo, ihi, scale, m, v, ldv, info)

call zgebak(job, side, n, ilo, ihi, scale, m, v, ldv, info)

call gebak(v, scale [,ilo] [,ihi] [,job] [,side] [,info])

Include Files

mkl.fi, lapack.f90

Description

The routine is intended to be used after a matrix A has been balanced by a call to ?gebal, and eigenvectors of the balanced matrix A''₂₂ have subsequently been computed. For a description of balancing, see gebal. The balanced matrix A'' is obtained as A''= D*P*A*P^T*inv(D), where P is a permutation matrix and D is a diagonal scaling matrix. This routine transforms the eigenvectors as follows:

if x is a right eigenvector of A'', then P^T*inv(D)*x is a right eigenvector of A; if y is a left eigenvector of A'', then P^T*D*y is a left eigenvector of A.

Input Parameters

job

CHARACTER*1. Must be 'N' or 'P' or 'S' or 'B'. The same parameter job as supplied to ?gebal.

side

CHARACTER*1. Must be 'L' or 'R'.

If side = 'L', then left eigenvectors are transformed.

If side = 'R', then right eigenvectors are transformed.

n

INTEGER. The number of rows of the matrix of eigenvectors (n≥ 0).

ilo, ihi

INTEGER. The values ilo and ihi, as returned by ?gebal. (If n > 0, then 1 ≤ilo≤ihi≤n;

if n = 0, then ilo = 1 and ihi = 0.)

scale

REAL for single-precision flavors

DOUBLE PRECISION for double-precision flavors

Array, size at least max(1, n).

Contains details of the permutations and/or the scaling factors used to balance the original general matrix, as returned by ?gebal.

m

INTEGER. The number of columns of the matrix of eigenvectors (m≥ 0).

v

REAL for sgebak

DOUBLE PRECISION for dgebak

COMPLEX for cgebak

DOUBLE COMPLEX for zgebak.

Arrays:

v(ldv,*) contains the matrix of left or right eigenvectors to be transformed.

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 i-th 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 gebak interface are the following:

v: Holds the matrix V of size (n,m).
scale: 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: Must be 'L' or 'R'. The default value is 'L'.

Application Notes

The errors in this routine are negligible.

The approximate number of floating-point operations is approximately proportional to m*n.

Parent topic: Nonsymmetric Eigenvalue Problems: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?gebak

Syntax

Include Files

Description

Input Parameters

Output Parameters

LAPACK 95 Interface Notes

Application Notes