NAG Library Routine Document

F08WJF (DGGBAK)

+− 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

F08WJF (DGGBAK) forms the right or left eigenvectors of the real generalized eigenvalue problem Ax=λBx, by backward transformation on the computed eigenvectors given by F08YKF (DTGEVC). It is necessary to call this routine only if the optional balancing routine F08WHF (DGGBAL) was previously called to balance the matrix pair A,B.

2 Specification

SUBROUTINE F08WJF (

JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, LDV, INFO)

INTEGER	N, ILO, IHI, M, LDV, INFO
REAL (KIND=nag_wp)	LSCALE(), RSCALE(), V(LDV,*)
CHARACTER(1)	JOB, SIDE

The routine may be called by its LAPACK name dggbak.

3 Description

If the matrix pair has been previously balanced using the routine F08WHF (DGGBAL) then F08WJF (DGGBAK) backtransforms the eigenvector solution given by F08YKF (DTGEVC). This is usually the sixth and last step in the solution of the generalized eigenvalue problem.

For a description of balancing, see the document for F08WHF (DGGBAL).

4 References

Ward R C (1981) Balancing the generalized eigenvalue problem SIAM J. Sci. Stat. Comp. 2 141–152

5 Parameters

1: JOB – CHARACTER(1)Input

On entry: specifies the backward transformation step required.

JOB='N': No transformations are done.
JOB='P': Only do backward transformations based on permutations.
JOB='S': Only do backward transformations based on scaling.
JOB='B': Do backward transformations for both permutations and scaling.

Note: this must be the same parameter JOB as supplied to F08WHF (DGGBAL).

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 order of the matrices A and B of the generalized eigenvalue problem.

Constraint: N≥0.

4: ILO – INTEGERInput

5: IHI – INTEGERInput

On entry: ilo and ihi as determined by a previous call to F08WHF (DGGBAL).

Constraints:

if N>0, 1≤ILO≤IHI≤N;
if N=0, ILO=1 and IHI=0.

6: LSCALE(*) – REAL (KIND=nag_wp) arrayInput

Note: the dimension of the array LSCALE must be at least max1,N.

On entry: details of the permutations and scaling factors applied to the left side of the matrices A and B, as returned by a previous call to F08WHF (DGGBAL).

7: RSCALE(*) – REAL (KIND=nag_wp) arrayInput

Note: the dimension of the array RSCALE must be at least max1,N.

On entry: details of the permutations and scaling factors applied to the right side of the matrices A and B, as returned by a previous call to F08WHF (DGGBAL).

8: M – INTEGERInput