NAME

ggbak - ggbak: back-transform eigvec

SYNOPSIS

Functions

subroutine cggbak (job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)
CGGBAK subroutine dggbak (job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)
DGGBAK subroutine sggbak (job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)
SGGBAK subroutine zggbak (job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)
ZGGBAK

Detailed Description

Function Documentation

subroutine cggbak (character job, character side, integer n, integer ilo, integer ihi, real, dimension( * ) lscale, real, dimension( * ) rscale, integer m, complex, dimension( ldv, * ) v, integer ldv, integer info)

CGGBAK

Purpose:



 CGGBAK forms the right or left eigenvectors of a complex generalized


 eigenvalue problem A*x = lambda*B*x, by backward transformation on


 the computed eigenvectors of the balanced pair of matrices output by


 CGGBAL.

Parameters

JOB



          JOB is CHARACTER*1


          Specifies the type of backward transformation required:


          = 'N':  do nothing, return immediately;


          = 'P':  do backward transformation for permutation only;


          = 'S':  do backward transformation for scaling only;


          = 'B':  do backward transformations for both permutation and


                  scaling.


          JOB must be the same as the argument JOB supplied to CGGBAL.

SIDE



          SIDE is CHARACTER*1


          = 'R':  V contains right eigenvectors;


          = 'L':  V contains left eigenvectors.



          N is INTEGER


          The number of rows of the matrix V.  N >= 0.

ILO



          ILO is INTEGER

IHI



          IHI is INTEGER


          The integers ILO and IHI determined by CGGBAL.


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

LSCALE



          LSCALE is REAL array, dimension (N)


          Details of the permutations and/or scaling factors applied


          to the left side of A and B, as returned by CGGBAL.

RSCALE



          RSCALE is REAL array, dimension (N)


          Details of the permutations and/or scaling factors applied


          to the right side of A and B, as returned by CGGBAL.



          M is INTEGER


          The number of columns of the matrix V.  M >= 0.



          V is COMPLEX array, dimension (LDV,M)


          On entry, the matrix of right or left eigenvectors to be


          transformed, as returned by CTGEVC.


          On exit, V is overwritten by the transformed eigenvectors.

LDV



          LDV is INTEGER


          The leading dimension of the matrix V. LDV >= max(1,N).

INFO



          INFO is INTEGER


          = 0:  successful exit.


          < 0:  if INFO = -i, the i-th argument had an illegal value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:



  See R.C. Ward, Balancing the generalized eigenvalue problem,


                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.

Definition at line 146 of file cggbak.f.

subroutine dggbak (character job, character side, integer n, integer ilo, integer ihi, double precision, dimension( * ) lscale, double precision, dimension( * ) rscale, integer m, double precision, dimension( ldv, * ) v, integer ldv, integer info)

DGGBAK

Purpose:



 DGGBAK forms the right or left eigenvectors of a real generalized


 eigenvalue problem A*x = lambda*B*x, by backward transformation on


 the computed eigenvectors of the balanced pair of matrices output by


 DGGBAL.

Parameters

JOB



          JOB is CHARACTER*1


          Specifies the type of backward transformation required:


          = 'N':  do nothing, return immediately;


          = 'P':  do backward transformation for permutation only;


          = 'S':  do backward transformation for scaling only;


          = 'B':  do backward transformations for both permutation and


                  scaling.


          JOB must be the same as the argument JOB supplied to DGGBAL.

SIDE



          SIDE is CHARACTER*1


          = 'R':  V contains right eigenvectors;


          = 'L':  V contains left eigenvectors.



          N is INTEGER


          The number of rows of the matrix V.  N >= 0.

ILO



          ILO is INTEGER

IHI



          IHI is INTEGER


          The integers ILO and IHI determined by DGGBAL.


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

LSCALE



          LSCALE is DOUBLE PRECISION array, dimension (N)


          Details of the permutations and/or scaling factors applied


          to the left side of A and B, as returned by DGGBAL.

RSCALE



          RSCALE is DOUBLE PRECISION array, dimension (N)


          Details of the permutations and/or scaling factors applied


          to the right side of A and B, as returned by DGGBAL.



          M is INTEGER


          The number of columns of the matrix V.  M >= 0.



          V is DOUBLE PRECISION array, dimension (LDV,M)


          On entry, the matrix of right or left eigenvectors to be


          transformed, as returned by DTGEVC.


          On exit, V is overwritten by the transformed eigenvectors.

LDV



          LDV is INTEGER


          The leading dimension of the matrix V. LDV >= max(1,N).

INFO



          INFO is INTEGER


          = 0:  successful exit.


          < 0:  if INFO = -i, the i-th argument had an illegal value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:



  See R.C. Ward, Balancing the generalized eigenvalue problem,


                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.

Definition at line 145 of file dggbak.f.

subroutine sggbak (character job, character side, integer n, integer ilo, integer ihi, real, dimension( * ) lscale, real, dimension( * ) rscale, integer m, real, dimension( ldv, * ) v, integer ldv, integer info)

SGGBAK

Purpose:



 SGGBAK forms the right or left eigenvectors of a real generalized


 eigenvalue problem A*x = lambda*B*x, by backward transformation on


 the computed eigenvectors of the balanced pair of matrices output by


 SGGBAL.

Parameters

JOB



          JOB is CHARACTER*1


          Specifies the type of backward transformation required:


          = 'N':  do nothing, return immediately;


          = 'P':  do backward transformation for permutation only;


          = 'S':  do backward transformation for scaling only;


          = 'B':  do backward transformations for both permutation and


                  scaling.


          JOB must be the same as the argument JOB supplied to SGGBAL.

SIDE



          SIDE is CHARACTER*1


          = 'R':  V contains right eigenvectors;


          = 'L':  V contains left eigenvectors.



          N is INTEGER


          The number of rows of the matrix V.  N >= 0.

ILO



          ILO is INTEGER

IHI



          IHI is INTEGER


          The integers ILO and IHI determined by SGGBAL.


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

LSCALE



          LSCALE is REAL array, dimension (N)


          Details of the permutations and/or scaling factors applied


          to the left side of A and B, as returned by SGGBAL.

RSCALE



          RSCALE is REAL array, dimension (N)


          Details of the permutations and/or scaling factors applied


          to the right side of A and B, as returned by SGGBAL.



          M is INTEGER


          The number of columns of the matrix V.  M >= 0.



          V is REAL array, dimension (LDV,M)


          On entry, the matrix of right or left eigenvectors to be


          transformed, as returned by STGEVC.


          On exit, V is overwritten by the transformed eigenvectors.

LDV



          LDV is INTEGER


          The leading dimension of the matrix V. LDV >= max(1,N).

INFO



          INFO is INTEGER


          = 0:  successful exit.


          < 0:  if INFO = -i, the i-th argument had an illegal value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:



  See R.C. Ward, Balancing the generalized eigenvalue problem,


                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.

Definition at line 145 of file sggbak.f.

subroutine zggbak (character job, character side, integer n, integer ilo, integer ihi, double precision, dimension( * ) lscale, double precision, dimension( * ) rscale, integer m, complex16, dimension( ldv, ) v, integer ldv, integer info)

ZGGBAK

Purpose:



 ZGGBAK forms the right or left eigenvectors of a complex generalized


 eigenvalue problem A*x = lambda*B*x, by backward transformation on


 the computed eigenvectors of the balanced pair of matrices output by


 ZGGBAL.

Parameters

JOB



          JOB is CHARACTER*1


          Specifies the type of backward transformation required:


          = 'N':  do nothing, return immediately;


          = 'P':  do backward transformation for permutation only;


          = 'S':  do backward transformation for scaling only;


          = 'B':  do backward transformations for both permutation and


                  scaling.


          JOB must be the same as the argument JOB supplied to ZGGBAL.

SIDE



          SIDE is CHARACTER*1


          = 'R':  V contains right eigenvectors;


          = 'L':  V contains left eigenvectors.



          N is INTEGER


          The number of rows of the matrix V.  N >= 0.

ILO



          ILO is INTEGER

IHI



          IHI is INTEGER


          The integers ILO and IHI determined by ZGGBAL.


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

LSCALE



          LSCALE is DOUBLE PRECISION array, dimension (N)


          Details of the permutations and/or scaling factors applied


          to the left side of A and B, as returned by ZGGBAL.

RSCALE



          RSCALE is DOUBLE PRECISION array, dimension (N)


          Details of the permutations and/or scaling factors applied


          to the right side of A and B, as returned by ZGGBAL.



          M is INTEGER


          The number of columns of the matrix V.  M >= 0.



          V is COMPLEX*16 array, dimension (LDV,M)


          On entry, the matrix of right or left eigenvectors to be


          transformed, as returned by ZTGEVC.


          On exit, V is overwritten by the transformed eigenvectors.

LDV



          LDV is INTEGER


          The leading dimension of the matrix V. LDV >= max(1,N).

INFO



          INFO is INTEGER


          = 0:  successful exit.


          < 0:  if INFO = -i, the i-th argument had an illegal value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:



  See R.C. Ward, Balancing the generalized eigenvalue problem,


                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.

Definition at line 146 of file zggbak.f.

Author

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