dgebak(3S)

NAME
     DGEBAK - form the right or left eigenvectors of a real general matrix by
     backward transformation on the computed eigenvectors of the balanced
     matrix output by DGEBAL

SYNOPSIS
     SUBROUTINE DGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, INFO )

         CHARACTER      JOB, SIDE

         INTEGER        IHI, ILO, INFO, LDV, M, N

         DOUBLE         PRECISION SCALE( * ), V( LDV, * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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.

ARGUMENTS
     JOB     (input) 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    (input) CHARACTER*1
             = 'R':  V contains right eigenvectors;
             = 'L':  V contains left eigenvectors.

     N       (input) INTEGER
             The number of rows of the matrix V.  N >= 0.

     ILO     (input) INTEGER
             IHI     (input) 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   (input) DOUBLE PRECISION array, dimension (N)
             Details of the permutation and scaling factors, as returned by
             DGEBAL.

     M       (input) INTEGER
             The number of columns of the matrix V.  M >= 0.

     V       (input/output) 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     (input) INTEGER
             The leading dimension of the array V. LDV >= max(1,N).

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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