table of contents
| ggbak(3) | LAPACK | 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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