SRC/dggbal.f(3)

NAME
SRC/dggbal.f

SYNOPSIS

  Functions/Subroutines
subroutine dggbal (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info)
DGGBAL

Function/Subroutine Documentation

  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.

Author

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