NAG FL Interface
f08njf (dgebak)

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1 Purpose

f08njf transforms eigenvectors of a balanced matrix to those of the original real nonsymmetric matrix.

2 Specification

Fortran Interface
Subroutine f08njf ( job, side, n, ilo, ihi, scale, m, v, ldv, info)
Integer, Intent (In) :: n, ilo, ihi, m, ldv
Integer, Intent (Out) :: info
Real (Kind=nag_wp), Intent (In) :: scale(*)
Real (Kind=nag_wp), Intent (Inout) :: v(ldv,*)
Character (1), Intent (In) :: job, side
C Header Interface
#include <nag.h>
void  f08njf_ (const char *job, const char *side, const Integer *n, const Integer *ilo, const Integer *ihi, const double scal[], const Integer *m, double v[], const Integer *ldv, Integer *info, const Charlen length_job, const Charlen length_side)
The routine may be called by the names f08njf, nagf_lapackeig_dgebak or its LAPACK name dgebak.

3 Description

f08njf is intended to be used after a real nonsymmetric matrix A has been balanced by f08nhf, and eigenvectors of the balanced matrix A22 have subsequently been computed.
For a description of balancing, see the document for f08nhf. The balanced matrix A is obtained as A=DPAPTD-1, where P is a permutation matrix and D is a diagonal scaling matrix. This routine transforms left or right eigenvectors as follows:

4 References


5 Arguments

1: job Character(1) Input
On entry: this must be the same argument job as supplied to f08nhf.
Constraint: job='N', 'P', 'S' or 'B'.
2: side Character(1) Input
On entry: indicates whether left or right eigenvectors are to be transformed.
The left eigenvectors are transformed.
The right eigenvectors are transformed.
Constraint: side='L' or 'R'.
3: n Integer Input
On entry: n, the number of rows of the matrix of eigenvectors.
Constraint: n0.
4: ilo Integer Input
5: ihi Integer Input
On entry: the values ilo and ihi, as returned by f08nhf.
  • if n>0, 1 ilo ihi n ;
  • if n=0, ilo=1 and ihi=0.
6: scale(*) Real (Kind=nag_wp) array Input
Note: the dimension of the array scale must be at least max(1,n).
On entry: details of the permutations and/or the scaling factors used to balance the original real nonsymmetric matrix, as returned by f08nhf.
7: m Integer Input
On entry: m, the number of columns of the matrix of eigenvectors.
Constraint: m0.
8: v(ldv,*) Real (Kind=nag_wp) array Input/Output
Note: the second dimension of the array v must be at least max(1,m).
On entry: the matrix of left or right eigenvectors to be transformed.
On exit: the transformed eigenvectors.
9: ldv Integer Input
On entry: the first dimension of the array v as declared in the (sub)program from which f08njf is called.
Constraint: ldv max(1,n) .
10: info Integer Output
On exit: info=0 unless the routine detects an error (see Section 6).

6 Error Indicators and Warnings

If info=-i, argument i had an illegal value. An explanatory message is output, and execution of the program is terminated.

7 Accuracy

The errors are negligible.

8 Parallelism and Performance

f08njf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments

The total number of floating-point operations is approximately proportional to nm.
The complex analogue of this routine is f08nwf.

10 Example

See f08nhf.