zggbak(3P) Sun Performance Library zggbak(3P)NAMEzggbak - form 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
SYNOPSIS
SUBROUTINE ZGGBAK(JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, LDV,
INFO)
CHARACTER * 1 JOB, SIDE
DOUBLE COMPLEX V(LDV,*)
INTEGER N, ILO, IHI, M, LDV, INFO
DOUBLE PRECISION LSCALE(*), RSCALE(*)
SUBROUTINE ZGGBAK_64(JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
LDV, INFO)
CHARACTER * 1 JOB, SIDE
DOUBLE COMPLEX V(LDV,*)
INTEGER*8 N, ILO, IHI, M, LDV, INFO
DOUBLE PRECISION LSCALE(*), RSCALE(*)
F95 INTERFACE
SUBROUTINE GGBAK(JOB, SIDE, [N], ILO, IHI, LSCALE, RSCALE, [M], V,
[LDV], [INFO])
CHARACTER(LEN=1) :: JOB, SIDE
COMPLEX(8), DIMENSION(:,:) :: V
INTEGER :: N, ILO, IHI, M, LDV, INFO
REAL(8), DIMENSION(:) :: LSCALE, RSCALE
SUBROUTINE GGBAK_64(JOB, SIDE, [N], ILO, IHI, LSCALE, RSCALE, [M], V,
[LDV], [INFO])
CHARACTER(LEN=1) :: JOB, SIDE
COMPLEX(8), DIMENSION(:,:) :: V
INTEGER(8) :: N, ILO, IHI, M, LDV, INFO
REAL(8), DIMENSION(:) :: LSCALE, RSCALE
C INTERFACE
#include <sunperf.h>
void zggbak(char job, char side, int n, int ilo, int ihi, double
*lscale, double *rscale, int m, doublecomplex *v, int ldv,
int *info);
void zggbak_64(char job, char side, long n, long ilo, long ihi, double
*lscale, double *rscale, long m, doublecomplex *v, long ldv,
long *info);
PURPOSEzggbak 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 ZGG‐
BAL.
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 ZGGBAL.
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 ZGGBAL. 1 <= ILO <=
IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
IHI (input)
The integers ILO and IHI determined by ZGGBAL. 1 <= ILO <=
IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
LSCALE (input)
Details of the permutations and/or scaling factors applied to
the left side of A and B, as returned by ZGGBAL.
RSCALE (input)
Details of the permutations and/or scaling factors applied to
the right side of A and B, as returned by ZGGBAL.
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 ZTGEVC. On exit, V is overwrit‐
ten 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.
6 Mar 2009 zggbak(3P)
