zppequ()

subroutine zppequ	(	character	uplo,
		integer	n,
		complex*16, dimension( * )	ap,
		double precision, dimension( * )	s,
		double precision	scond,
		double precision	amax,
		integer	info )

ZPPEQU

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Purpose:

!>
!> ZPPEQU computes row and column scalings intended to equilibrate a
!> Hermitian positive definite matrix A in packed storage 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.
!> 

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]	AP	!> AP is COMPLEX*16 array, dimension (N*(N+1)/2) !> The upper or lower triangle of the Hermitian matrix A, packed !> columnwise in a linear array. The j-th column of A is stored !> in the array AP as follows: !> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; !> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=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.