zpoequb()

subroutine zpoequb	(	integer	N,
		complex*16, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( * )	S,
		double precision	SCOND,
		double precision	AMAX,
		integer	INFO
	)

ZPOEQUB

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Purpose:

 ZPOEQUB computes row and column scalings intended to equilibrate a
 Hermitian positive definite matrix A and reduce its condition number
 (with respect to the two-norm).  S contains the scale factors,
 S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
 elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
 choice of S puts the condition number of B within a factor N of the
 smallest possible condition number over all possible diagonal
 scalings.

 This routine differs from ZPOEQU by restricting the scaling factors
 to a power of the radix.  Barring over- and underflow, scaling by
 these factors introduces no additional rounding errors.  However, the
 scaled diagonal entries are no longer approximately 1 but lie
 between sqrt(radix) and 1/sqrt(radix).

Parameters

[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	A	A is COMPLEX*16 array, dimension (LDA,N) The N-by-N Hermitian positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]	S	S is DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A.
[out]	SCOND	SCOND is DOUBLE PRECISION 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 DOUBLE PRECISION Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.
[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.