Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - balances a pair of general real matrices (A,B)

SYNOPSIS

       SUBROUTINE SGGBAL( JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE, WORK, INFO )

           CHARACTER      JOB

           INTEGER        IHI, ILO, INFO, LDA, LDB, N

           REAL           A( LDA, * ), B( LDB, * ), LSCALE( * ), RSCALE( * ), WORK( * )

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.

ARGUMENTS

        JOB     (input) 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       (input) INTEGER
                The order of the matrices A and B.  N >= 0.

        A       (input/output) 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     (input) INTEGER
                The leading dimension of the array A. LDA >= max(1,N).

        B       (input/output) 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     (input) INTEGER
                The leading dimension of the array B. LDB >= max(1,N).

        ILO     (output) INTEGER
                IHI     (output) 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  (output) 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  (output) 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    (workspace) 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    (output) INTEGER
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th argument had an illegal value.

FURTHER DETAILS

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

 LAPACK routine (version 3.2)               April 2011                            SGGBAL(3lapack)