• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS
• FURTHER DETAILS

NAME

dggbak - form 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

SYNOPSIS

  SUBROUTINE DGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, 
 *      LDV, INFO)
  CHARACTER * 1 JOB, SIDE
  INTEGER N, ILO, IHI, M, LDV, INFO
  DOUBLE PRECISION LSCALE(*), RSCALE(*), V(LDV,*)

  SUBROUTINE DGGBAK_64( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, 
 *      LDV, INFO)
  CHARACTER * 1 JOB, SIDE
  INTEGER*8 N, ILO, IHI, M, LDV, INFO
  DOUBLE PRECISION LSCALE(*), RSCALE(*), V(LDV,*)

F95 INTERFACE

  SUBROUTINE GGBAK( JOB, SIDE, [N], ILO, IHI, LSCALE, RSCALE, [M], V, 
 *       [LDV], [INFO])
  CHARACTER(LEN=1) :: JOB, SIDE
  INTEGER :: N, ILO, IHI, M, LDV, INFO
  REAL(8), DIMENSION(:) :: LSCALE, RSCALE
  REAL(8), DIMENSION(:,:) :: V

  SUBROUTINE GGBAK_64( JOB, SIDE, [N], ILO, IHI, LSCALE, RSCALE, [M], 
 *       V, [LDV], [INFO])
  CHARACTER(LEN=1) :: JOB, SIDE
  INTEGER(8) :: N, ILO, IHI, M, LDV, INFO
  REAL(8), DIMENSION(:) :: LSCALE, RSCALE
  REAL(8), DIMENSION(:,:) :: V

C INTERFACE

#include <sunperf.h>

void dggbak(char job, char side, int n, int ilo, int ihi, double *lscale, double *rscale, int m, double *v, int ldv, int *info);

void dggbak_64(char job, char side, long n, long ilo, long ihi, double *lscale, double *rscale, long m, double *v, long ldv, long *info);

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 SGGBAL.

ARGUMENTS

• JOB (input)
  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 (input)
  

   = 'R':  V contains right eigenvectors;

   = 'L':  V contains left eigenvectors.

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

• ILO (input)
  The integers ILO and IHI determined by SGGBAL. 1 < = ILO < = IHI < = N, if N > 0; ILO =1 and IHI =0, if N =0.

• IHI (input)
  See the description for ILO.

• LSCALE (input)
  Details of the permutations and/or scaling factors applied to the left side of A and B, as returned by SGGBAL.

• RSCALE (input)
  Details of the permutations and/or scaling factors applied to the right side of A and B, as returned by SGGBAL.

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

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

• INFO (output)
  

   = 0:  successful exit.

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

FURTHER DETAILS

See R.C. Ward, Balancing the generalized eigenvalue problem, SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.