zlaqhe()

subroutine zlaqhe	(	character	uplo,
		integer	n,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		double precision, dimension( * )	s,
		double precision	scond,
		double precision	amax,
		character	equed
	)

ZLAQHE scales a Hermitian matrix.

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Purpose:

 ZLAQHE equilibrates a Hermitian matrix A using the scaling factors
 in the vector S.

Parameters

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in,out]	A	A is COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A * diag(S).
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(N,1).
[in]	S	S is DOUBLE PRECISION array, dimension (N) The scale factors for A.
[in]	SCOND	SCOND is DOUBLE PRECISION Ratio of the smallest S(i) to the largest S(i).
[in]	AMAX	AMAX is DOUBLE PRECISION Absolute value of largest matrix entry.
[out]	EQUED	EQUED is CHARACTER*1 Specifies whether or not equilibration was done. = 'N': No equilibration. = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).

Internal Parameters:

  THRESH is a threshold value used to decide if scaling should be done
  based on the ratio of the scaling factors.  If SCOND < THRESH,
  scaling is done.

  LARGE and SMALL are threshold values used to decide if scaling should
  be done based on the absolute size of the largest matrix element.
  If AMAX > LARGE or AMAX < SMALL, scaling is done.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 133 of file zlaqhe.f.

*
*  -- LAPACK auxiliary routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          EQUED, UPLO
      INTEGER            LDA, N
      DOUBLE PRECISION   AMAX, SCOND
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   S( * )
      COMPLEX*16         A( LDA, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, THRESH
      parameter( one = 1.0d+0, thresh = 0.1d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, J
      DOUBLE PRECISION   CJ, LARGE, SMALL
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           lsame, dlamch
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible
*
      IF( n.LE.0 ) THEN
         equed = 'N'
         RETURN
      END IF
*
*     Initialize LARGE and SMALL.
*
      small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
      large = one / small
*
      IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
*
*        No equilibration
*
         equed = 'N'
      ELSE
*
*        Replace A by diag(S) * A * diag(S).
*
         IF( lsame( uplo, 'U' ) ) THEN
*
*           Upper triangle of A is stored.
*
            DO 20 j = 1, n
               cj = s( j )
               DO 10 i = 1, j - 1
                  a( i, j ) = cj*s( i )*a( i, j )
   10          CONTINUE
               a( j, j ) = cj*cj*dble( a( j, j ) )
   20       CONTINUE
         ELSE
*
*           Lower triangle of A is stored.
*
            DO 40 j = 1, n
               cj = s( j )
               a( j, j ) = cj*cj*dble( a( j, j ) )
               DO 30 i = j + 1, n
                  a( i, j ) = cj*s( i )*a( i, j )
   30          CONTINUE
   40       CONTINUE
         END IF
         equed = 'Y'
      END IF
*
      RETURN
*
*     End of ZLAQHE
*

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