F08NWF (ZGEBAK) (PDF version)
F08 Chapter Contents
F08 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F08NWF (ZGEBAK)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

+− Contents

    1  Purpose
    2  Specification
    3  Description
    4  References
    5  Parameters
    6  Error Indicators and Warnings
    7  Accuracy
    8  Further Comments
    9  Example

1  Purpose

F08NWF (ZGEBAK) transforms eigenvectors of a balanced matrix to those of the original complex general matrix.

2  Specification

SUBROUTINE F08NWF ( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, INFO)
INTEGER  N, ILO, IHI, M, LDV, INFO
REAL (KIND=nag_wp)  SCALE(*)
COMPLEX (KIND=nag_wp)  V(LDV,*)
CHARACTER(1)  JOB, SIDE
The routine may be called by its LAPACK name zgebak.

3  Description

F08NWF (ZGEBAK) is intended to be used after a complex general matrix A has been balanced by F08NVF (ZGEBAL), and eigenvectors of the balanced matrix A22′′ have subsequently been computed.
For a description of balancing, see the document for F08NVF (ZGEBAL). 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

None.

5  Parameters

1:     JOB – CHARACTER(1)Input
On entry: this must be the same parameter JOB as supplied to F08NVF (ZGEBAL).
Constraint: JOB='N', 'P', 'S' or 'B'.
2:     SIDE – CHARACTER(1)Input
On entry: indicates whether left or right eigenvectors are to be transformed.
SIDE='L'
The left eigenvectors are transformed.
SIDE='R'
The right eigenvectors are transformed.
Constraint: SIDE='L' or 'R'.
3:     N – INTEGERInput
On entry: n, the number of rows of the matrix of eigenvectors.
Constraint: N≥0.
4:     ILO – INTEGERInput
5:     IHI – INTEGERInput
On entry: the values ilo and ihi, as returned by F08NVF (ZGEBAL).
Constraints:
  • if N>0, 1≤ILO≤IHI≤N;
  • if N=0, ILO=1 and IHI=0.
6:     SCALE(*) – REAL (KIND=nag_wp) arrayInput
Note: the dimension of the array SCALE must be at least max1,N.
On entry: details of the permutations and/or the scaling factors used to balance the original complex general matrix, as returned by F08NVF (ZGEBAL).
7:     M – INTEGERInput
On entry: m, the number of columns of the matrix of eigenvectors.
Constraint: M≥0.
8:     V(LDV,*) – COMPLEX (KIND=nag_wp) arrayInput/Output
Note: the second dimension of the array V must be at least max1,M.
On entry: the matrix of left or right eigenvectors to be transformed.
On exit: the transformed eigenvectors.
9:     LDV – INTEGERInput
On entry: the first dimension of the array V as declared in the (sub)program from which F08NWF (ZGEBAK) is called.
Constraint: LDV≥max1,N.
10:   INFO – INTEGEROutput
On exit: INFO=0 unless the routine detects an error (see Section 6).

6  Error Indicators and Warnings

INFO<0
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  Further Comments

The total number of real floating point operations is approximately proportional to nm.
The real analogue of this routine is F08NJF (DGEBAK).

9  Example

See Section 9 in F08NVF (ZGEBAL).
F08NWF (ZGEBAK) (PDF version)
F08 Chapter Contents
F08 Chapter Introduction
NAG Library Manual
© The Numerical Algorithms Group Ltd, Oxford, UK. 2011