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sggbal.f(3)                         LAPACK                         sggbal.f(3)

NAME
       sggbal.f -

SYNOPSIS
   Functions/Subroutines
       subroutine sggbal (JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE,
           WORK, INFO)
           SGGBAL

Function/Subroutine Documentation
   subroutine sggbal (characterJOB, integerN, real, dimension( lda, * )A,
       integerLDA, real, dimension( ldb, * )B, integerLDB, integerILO,
       integerIHI, real, dimension( * )LSCALE, real, dimension( * )RSCALE,
       real, dimension( * )WORK, integerINFO)
       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.

       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 sggbal.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2                   Sat Nov 16 2013                    sggbal.f(3)