cheequb()

subroutine cheequb	(	character	uplo,
		integer	n,
		complex, dimension( lda, * )	a,
		integer	lda,
		real, dimension( * )	s,
		real	scond,
		real	amax,
		complex, dimension( * )	work,
		integer	info )

CHEEQUB

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Purpose:

!>
!> CHEEQUB computes row and column scalings intended to equilibrate a
!> Hermitian matrix A (with respect to the Euclidean norm) and reduce
!> its condition number. The scale factors S are computed by the BIN
!> algorithm (see references) so that the scaled matrix B with elements
!> B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of
!> the smallest possible condition number over all possible diagonal
!> scalings.
!> 

Parameters

[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	A	!> A is COMPLEX array, dimension (LDA,N) !> The N-by-N Hermitian matrix whose scaling factors are to be !> computed. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[out]	S	!> S is REAL array, dimension (N) !> If INFO = 0, S contains the scale factors for A. !>
[out]	SCOND	!> SCOND is REAL !> If INFO = 0, S contains the ratio of the smallest S(i) to !> the largest S(i). If SCOND >= 0.1 and AMAX is neither too !> large nor too small, it is not worth scaling by S. !>
[out]	AMAX	!> AMAX is REAL !> Largest absolute value of any matrix element. If AMAX is !> very close to overflow or very close to underflow, the !> matrix should be scaled. !>
[out]	WORK	!> WORK is COMPLEX array, dimension (2*N) !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, the i-th diagonal element is nonpositive. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

References:

Livne, O.E. and Golub, G.H., "Scaling by Binormalization",
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679