!>
!> 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.
!> 

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.
!> 

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