ggbak - Man Page

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

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

          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

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

V

          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.

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

          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

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

V

          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.

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

          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

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

V

          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.

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

          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

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

V

          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.