ggbal(3)

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

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

    A

              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

              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

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

    A

              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

              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

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

    A

              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

              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, complex*16, dimension( lda, * ) a, integer lda, complex*16, 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

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

    A

              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

              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.