Library Functions Manual

NAME¶

ggbal - ggbal: balance matrix

SYNOPSIS¶

Functions¶

subroutine CGGBAL (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info)
CGGBAL subroutine DGGBAL (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info)
DGGBAL subroutine SGGBAL (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info)
SGGBAL subroutine ZGGBAL (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info)
ZGGBAL

Detailed Description¶

Function Documentation¶

subroutine CGGBAL (character job, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, integer ilo, integer ihi, real, dimension( * ) lscale, real, dimension( * ) rscale, real, dimension( * ) work, integer info)¶

CGGBAL

Purpose:

!>
!> CGGBAL balances a pair of general complex matrices (A,B).  This
!> involves, first, permuting A and B by similarity transformations to
!> isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N
!> elements on the diagonal; and second, applying a diagonal similarity
!> transformation to rows and columns ILO to IHI to make the rows
!> and columns as close in norm as possible. Both steps are optional.
!>
!> Balancing may reduce the 1-norm of the matrices, and improve the
!> accuracy of the computed eigenvalues and/or eigenvectors in the
!> generalized eigenvalue problem A*x = lambda*B*x.
!>

Parameters

JOB

!>          JOB is CHARACTER*1
!>          Specifies the operations to be performed on A and B:
!>          = 'N':  none:  simply set ILO = 1, IHI = N, LSCALE(I) = 1.0
!>                  and RSCALE(I) = 1.0 for i=1,...,N;
!>          = 'P':  permute only;
!>          = 'S':  scale only;
!>          = 'B':  both permute and scale.
!>

!>          N is INTEGER
!>          The order of the matrices A and B.  N >= 0.
!>

!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, the input matrix A.
!>          On exit, A is overwritten by the balanced matrix.
!>          If JOB = 'N', A is not referenced.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A. LDA >= max(1,N).
!>

!>          B is COMPLEX array, dimension (LDB,N)
!>          On entry, the input matrix B.
!>          On exit, B is overwritten by the balanced matrix.
!>          If JOB = 'N', B is not referenced.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B. LDB >= max(1,N).
!>

ILO

!>          ILO is INTEGER
!>

IHI

!>          IHI is INTEGER
!>          ILO and IHI are set to integers such that on exit
!>          A(i,j) = 0 and B(i,j) = 0 if i > j and
!>          j = 1,...,ILO-1 or i = IHI+1,...,N.
!>          If JOB = 'N' or 'S', ILO = 1 and IHI = N.
!>

LSCALE

!>          LSCALE is REAL array, dimension (N)
!>          Details of the permutations and scaling factors applied
!>          to the left side of A and B.  If P(j) is the index of the
!>          row interchanged with row j, and D(j) is the scaling factor
!>          applied to row j, then
!>            LSCALE(j) = P(j)    for J = 1,...,ILO-1
!>                      = D(j)    for J = ILO,...,IHI
!>                      = P(j)    for J = IHI+1,...,N.
!>          The order in which the interchanges are made is N to IHI+1,
!>          then 1 to ILO-1.
!>

RSCALE

!>          RSCALE is REAL array, dimension (N)
!>          Details of the permutations and scaling factors applied
!>          to the right side of A and B.  If P(j) is the index of the
!>          column interchanged with column j, and D(j) is the scaling
!>          factor applied to column j, then
!>            RSCALE(j) = P(j)    for J = 1,...,ILO-1
!>                      = D(j)    for J = ILO,...,IHI
!>                      = P(j)    for J = IHI+1,...,N.
!>          The order in which the interchanges are made is N to IHI+1,
!>          then 1 to ILO-1.
!>

WORK

!>          WORK is REAL array, dimension (lwork)
!>          lwork must be at least max(1,6*N) when JOB = 'S' or 'B', and
!>          at least 1 when JOB = 'N' or 'P'.
!>

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.
!>

Definition at line 175 of file cggbal.f.

subroutine DGGBAL (character job, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, integer ilo, integer ihi, double precision, dimension( * ) lscale, double precision, dimension( * ) rscale, double precision, dimension( * ) work, integer info)¶

DGGBAL

Purpose:

!>
!> DGGBAL balances a pair of general real matrices (A,B).  This
!> involves, first, permuting A and B by similarity transformations to
!> isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N
!> elements on the diagonal; and second, applying a diagonal similarity
!> transformation to rows and columns ILO to IHI to make the rows
!> and columns as close in norm as possible. Both steps are optional.
!>
!> Balancing may reduce the 1-norm of the matrices, and improve the
!> accuracy of the computed eigenvalues and/or eigenvectors in the
!> generalized eigenvalue problem A*x = lambda*B*x.
!>

Parameters

JOB

!>          JOB is CHARACTER*1
!>          Specifies the operations to be performed on A and B:
!>          = 'N':  none:  simply set ILO = 1, IHI = N, LSCALE(I) = 1.0
!>                  and RSCALE(I) = 1.0 for i = 1,...,N.
!>          = 'P':  permute only;
!>          = 'S':  scale only;
!>          = 'B':  both permute and scale.
!>

!>          N is INTEGER
!>          The order of the matrices A and B.  N >= 0.
!>

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the input matrix A.
!>          On exit,  A is overwritten by the balanced matrix.
!>          If JOB = 'N', A is not referenced.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A. LDA >= max(1,N).
!>

!>          B is DOUBLE PRECISION array, dimension (LDB,N)
!>          On entry, the input matrix B.
!>          On exit,  B is overwritten by the balanced matrix.
!>          If JOB = 'N', B is not referenced.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B. LDB >= max(1,N).
!>

ILO

!>          ILO is INTEGER
!>

IHI

!>          IHI is INTEGER
!>          ILO and IHI are set to integers such that on exit
!>          A(i,j) = 0 and B(i,j) = 0 if i > j and
!>          j = 1,...,ILO-1 or i = IHI+1,...,N.
!>          If JOB = 'N' or 'S', ILO = 1 and IHI = N.
!>

LSCALE

!>          LSCALE is DOUBLE PRECISION array, dimension (N)
!>          Details of the permutations and scaling factors applied
!>          to the left side of A and B.  If P(j) is the index of the
!>          row interchanged with row j, and D(j)
!>          is the scaling factor applied to row j, then
!>            LSCALE(j) = P(j)    for J = 1,...,ILO-1
!>                      = D(j)    for J = ILO,...,IHI
!>                      = P(j)    for J = IHI+1,...,N.
!>          The order in which the interchanges are made is N to IHI+1,
!>          then 1 to ILO-1.
!>

RSCALE

!>          RSCALE is DOUBLE PRECISION array, dimension (N)
!>          Details of the permutations and scaling factors applied
!>          to the right side of A and B.  If P(j) is the index of the
!>          column interchanged with column j, and D(j)
!>          is the scaling factor applied to column j, then
!>            LSCALE(j) = P(j)    for J = 1,...,ILO-1
!>                      = D(j)    for J = ILO,...,IHI
!>                      = P(j)    for J = IHI+1,...,N.
!>          The order in which the interchanges are made is N to IHI+1,
!>          then 1 to ILO-1.
!>

WORK

!>          WORK is DOUBLE PRECISION array, dimension (lwork)
!>          lwork must be at least max(1,6*N) when JOB = 'S' or 'B', and
!>          at least 1 when JOB = 'N' or 'P'.
!>

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.
!>

Definition at line 175 of file dggbal.f.

subroutine SGGBAL (character job, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, integer ilo, integer ihi, real, dimension( * ) lscale, real, dimension( * ) rscale, real, dimension( * ) work, integer info)¶

SGGBAL

Purpose:

!>
!> SGGBAL balances a pair of general real matrices (A,B).  This
!> involves, first, permuting A and B by similarity transformations to
!> isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N
!> elements on the diagonal; and second, applying a diagonal similarity
!> transformation to rows and columns ILO to IHI to make the rows
!> and columns as close in norm as possible. Both steps are optional.
!>
!> Balancing may reduce the 1-norm of the matrices, and improve the
!> accuracy of the computed eigenvalues and/or eigenvectors in the
!> generalized eigenvalue problem A*x = lambda*B*x.
!>

Parameters

JOB

!>          JOB is CHARACTER*1
!>          Specifies the operations to be performed on A and B:
!>          = 'N':  none:  simply set ILO = 1, IHI = N, LSCALE(I) = 1.0
!>                  and RSCALE(I) = 1.0 for i = 1,...,N.
!>          = 'P':  permute only;
!>          = 'S':  scale only;
!>          = 'B':  both permute and scale.
!>

!>          N is INTEGER
!>          The order of the matrices A and B.  N >= 0.
!>

!>          A is REAL array, dimension (LDA,N)
!>          On entry, the input matrix A.
!>          On exit,  A is overwritten by the balanced matrix.
!>          If JOB = 'N', A is not referenced.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A. LDA >= max(1,N).
!>

!>          B is REAL array, dimension (LDB,N)
!>          On entry, the input matrix B.
!>          On exit,  B is overwritten by the balanced matrix.
!>          If JOB = 'N', B is not referenced.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B. LDB >= max(1,N).
!>

ILO

!>          ILO is INTEGER
!>

IHI

!>          IHI is INTEGER
!>          ILO and IHI are set to integers such that on exit
!>          A(i,j) = 0 and B(i,j) = 0 if i > j and
!>          j = 1,...,ILO-1 or i = IHI+1,...,N.
!>          If JOB = 'N' or 'S', ILO = 1 and IHI = N.
!>

LSCALE

!>          LSCALE is REAL array, dimension (N)
!>          Details of the permutations and scaling factors applied
!>          to the left side of A and B.  If P(j) is the index of the
!>          row interchanged with row j, and D(j)
!>          is the scaling factor applied to row j, then
!>            LSCALE(j) = P(j)    for J = 1,...,ILO-1
!>                      = D(j)    for J = ILO,...,IHI
!>                      = P(j)    for J = IHI+1,...,N.
!>          The order in which the interchanges are made is N to IHI+1,
!>          then 1 to ILO-1.
!>

RSCALE

!>          RSCALE is REAL array, dimension (N)
!>          Details of the permutations and scaling factors applied
!>          to the right side of A and B.  If P(j) is the index of the
!>          column interchanged with column j, and D(j)
!>          is the scaling factor applied to column j, then
!>            LSCALE(j) = P(j)    for J = 1,...,ILO-1
!>                      = D(j)    for J = ILO,...,IHI
!>                      = P(j)    for J = IHI+1,...,N.
!>          The order in which the interchanges are made is N to IHI+1,
!>          then 1 to ILO-1.
!>

WORK

!>          WORK is REAL array, dimension (lwork)
!>          lwork must be at least max(1,6*N) when JOB = 'S' or 'B', and
!>          at least 1 when JOB = 'N' or 'P'.
!>

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.
!>

Definition at line 175 of file sggbal.f.

subroutine ZGGBAL (character job, integer n, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ldb, ) b, integer ldb, integer ilo, integer ihi, double precision, dimension( * ) lscale, double precision, dimension( * ) rscale, double precision, dimension( * ) work, integer info)¶

ZGGBAL

Purpose:

!>
!> ZGGBAL balances a pair of general complex matrices (A,B).  This
!> involves, first, permuting A and B by similarity transformations to
!> isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N
!> elements on the diagonal; and second, applying a diagonal similarity
!> transformation to rows and columns ILO to IHI to make the rows
!> and columns as close in norm as possible. Both steps are optional.
!>
!> Balancing may reduce the 1-norm of the matrices, and improve the
!> accuracy of the computed eigenvalues and/or eigenvectors in the
!> generalized eigenvalue problem A*x = lambda*B*x.
!>

Parameters

JOB

!>          JOB is CHARACTER*1
!>          Specifies the operations to be performed on A and B:
!>          = 'N':  none:  simply set ILO = 1, IHI = N, LSCALE(I) = 1.0
!>                  and RSCALE(I) = 1.0 for i=1,...,N;
!>          = 'P':  permute only;
!>          = 'S':  scale only;
!>          = 'B':  both permute and scale.
!>

!>          N is INTEGER
!>          The order of the matrices A and B.  N >= 0.
!>

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the input matrix A.
!>          On exit, A is overwritten by the balanced matrix.
!>          If JOB = 'N', A is not referenced.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A. LDA >= max(1,N).
!>

!>          B is COMPLEX*16 array, dimension (LDB,N)
!>          On entry, the input matrix B.
!>          On exit, B is overwritten by the balanced matrix.
!>          If JOB = 'N', B is not referenced.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B. LDB >= max(1,N).
!>

ILO

!>          ILO is INTEGER
!>

IHI

!>          IHI is INTEGER
!>          ILO and IHI are set to integers such that on exit
!>          A(i,j) = 0 and B(i,j) = 0 if i > j and
!>          j = 1,...,ILO-1 or i = IHI+1,...,N.
!>          If JOB = 'N' or 'S', ILO = 1 and IHI = N.
!>

LSCALE

!>          LSCALE is DOUBLE PRECISION array, dimension (N)
!>          Details of the permutations and scaling factors applied
!>          to the left side of A and B.  If P(j) is the index of the
!>          row interchanged with row j, and D(j) is the scaling factor
!>          applied to row j, then
!>            LSCALE(j) = P(j)    for J = 1,...,ILO-1
!>                      = D(j)    for J = ILO,...,IHI
!>                      = P(j)    for J = IHI+1,...,N.
!>          The order in which the interchanges are made is N to IHI+1,
!>          then 1 to ILO-1.
!>

RSCALE

!>          RSCALE is DOUBLE PRECISION array, dimension (N)
!>          Details of the permutations and scaling factors applied
!>          to the right side of A and B.  If P(j) is the index of the
!>          column interchanged with column j, and D(j) is the scaling
!>          factor applied to column j, then
!>            RSCALE(j) = P(j)    for J = 1,...,ILO-1
!>                      = D(j)    for J = ILO,...,IHI
!>                      = P(j)    for J = IHI+1,...,N.
!>          The order in which the interchanges are made is N to IHI+1,
!>          then 1 to ILO-1.
!>

WORK

!>          WORK is DOUBLE PRECISION array, dimension (lwork)
!>          lwork must be at least max(1,6*N) when JOB = 'S' or 'B', and
!>          at least 1 when JOB = 'N' or 'P'.
!>

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.
!>

Definition at line 175 of file zggbal.f.

Author¶

Generated automatically by Doxygen for LAPACK from the source code.

Version 3.12.0

LAPACK

Source file:	ggbal.3.en.gz (from lapack-man 3.12.0-3.2)
Source last updated:	2024-11-04T16:48:44Z
Converted to HTML:	2025-01-18T04:09:46Z