zggbal()

subroutine zggbal	(	character	job,
		integer	n,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		integer	ilo,
		integer	ihi,
		double precision, dimension( * )	lscale,
		double precision, dimension( * )	rscale,
		double precision, dimension( * )	work,
		integer	info )

ZGGBAL

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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

[in]	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. !>
[in]	N	!> N is INTEGER !> The order of the matrices A and B. N >= 0. !>
[in,out]	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. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[in,out]	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. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>
[out]	ILO	!> ILO is INTEGER !>
[out]	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. !>
[out]	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. !>
[out]	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. !>
[out]	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'. !>
[out]	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.
!>