NAME

       zggbal.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zggbal (JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE, WORK, INFO)
           ZGGBAL

Function/Subroutine Documentation

   subroutine zggbal (characterJOB, integerN, complex*16, dimension( lda, * )A, integerLDA,
       complex*16, dimension( ldb, * )B, integerLDB, integerILO, integerIHI, double precision,
       dimension( * )LSCALE, double precision, dimension( * )RSCALE, double precision, dimension(
       * )WORK, integerINFO)
       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 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.

       Date:
           November 2011

       Further Details:

             See R.C. WARD, Balancing the generalized eigenvalue problem,
                            SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.

       Definition at line 177 of file zggbal.f.

Author

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