spoequ()

subroutine spoequ	(	integer	n,
		real, dimension( lda, * )	a,
		integer	lda,
		real, dimension( * )	s,
		real	scond,
		real	amax,
		integer	info )

SPOEQU

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Purpose:

!>
!> SPOEQU computes row and column scalings intended to equilibrate a
!> symmetric 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.
!> 

Parameters

[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	A	!> A is REAL array, dimension (LDA,N) !> The N-by-N symmetric 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 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 !> 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.