ggbak(3)

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

    !>          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.
    !>

  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

    !>          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.
    !>

  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

    !>          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.
    !>

  subroutine zggbak (character job, character side, integer n, integer ilo, integer ihi, double precision, dimension( * ) lscale, double precision, dimension( * ) rscale, integer m, complex*16, 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

    !>          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.
    !>

Author

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