gebak(3)

NAME
gebak - gebak: back-transform eigvec

SYNOPSIS

  Functions

subroutine cgebak (job, side, n, ilo, ihi, scale, m, v, ldv, info)
CGEBAK
subroutine dgebak (job, side, n, ilo, ihi, scale, m, v, ldv, info)
DGEBAK
subroutine sgebak (job, side, n, ilo, ihi, scale, m, v, ldv, info)
SGEBAK
subroutine zgebak (job, side, n, ilo, ihi, scale, m, v, ldv, info)
ZGEBAK

Detailed Description

Function Documentation

  subroutine cgebak (character job, character side, integer n, integer ilo, integer ihi, real, dimension( * ) scale, integer m, complex, dimension( ldv, * ) v, integer ldv, integer info)

CGEBAK

Purpose:

    !>
    !> CGEBAK forms the right or left eigenvectors of a complex general
    !> matrix by backward transformation on the computed eigenvectors of the
    !> balanced matrix output by CGEBAL.
    !>

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 CGEBAL.
    !>

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

    SCALE

    !>          SCALE is REAL array, dimension (N)
    !>          Details of the permutation and scaling factors, as returned
    !>          by CGEBAL.
    !>

    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 CHSEIN or CTREVC.
    !>          On exit, V is overwritten by the transformed eigenvectors.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array 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.

  subroutine dgebak (character job, character side, integer n, integer ilo, integer ihi, double precision, dimension( * ) scale, integer m, double precision, dimension( ldv, * ) v, integer ldv, integer info)

DGEBAK

Purpose:

    !>
    !> DGEBAK forms the right or left eigenvectors of a real general matrix
    !> by backward transformation on the computed eigenvectors of the
    !> balanced matrix output by DGEBAL.
    !>

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 DGEBAL.
    !>

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

    SCALE

    !>          SCALE is DOUBLE PRECISION array, dimension (N)
    !>          Details of the permutation and scaling factors, as returned
    !>          by DGEBAL.
    !>

    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 DHSEIN or DTREVC.
    !>          On exit, V is overwritten by the transformed eigenvectors.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array 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.

  subroutine sgebak (character job, character side, integer n, integer ilo, integer ihi, real, dimension( * ) scale, integer m, real, dimension( ldv, * ) v, integer ldv, integer info)

SGEBAK

Purpose:

    !>
    !> SGEBAK forms the right or left eigenvectors of a real general matrix
    !> by backward transformation on the computed eigenvectors of the
    !> balanced matrix output by SGEBAL.
    !>

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 SGEBAL.
    !>

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

    SCALE

    !>          SCALE is REAL array, dimension (N)
    !>          Details of the permutation and scaling factors, as returned
    !>          by SGEBAL.
    !>

    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 SHSEIN or STREVC.
    !>          On exit, V is overwritten by the transformed eigenvectors.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array 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.

  subroutine zgebak (character job, character side, integer n, integer ilo, integer ihi, double precision, dimension( * ) scale, integer m, complex*16, dimension( ldv, * ) v, integer ldv, integer info)

ZGEBAK

Purpose:

    !>
    !> ZGEBAK forms the right or left eigenvectors of a complex general
    !> matrix by backward transformation on the computed eigenvectors of the
    !> balanced matrix output by ZGEBAL.
    !>

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 ZGEBAL.
    !>

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

    SCALE

    !>          SCALE is DOUBLE PRECISION array, dimension (N)
    !>          Details of the permutation and scaling factors, as returned
    !>          by ZGEBAL.
    !>

    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 ZHSEIN or ZTREVC.
    !>          On exit, V is overwritten by the transformed eigenvectors.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of the array 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.

Author

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