zlaqhp.f

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*> \brief \b ZLAQHP scales a Hermitian matrix stored in packed form.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE ZLAQHP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
*
*       .. Scalar Arguments ..
*       CHARACTER          EQUED, UPLO
*       INTEGER            N
*       DOUBLE PRECISION   AMAX, SCOND
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   S( * )
*       COMPLEX*16         AP( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZLAQHP equilibrates a Hermitian matrix A using the scaling factors
*> in the vector S.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          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
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] AP
*> \verbatim
*>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
*>          On entry, 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.
*>
*>          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
*>          the same storage format as A.
*> \endverbatim
*>
*> \param[in] S
*> \verbatim
*>          S is DOUBLE PRECISION array, dimension (N)
*>          The scale factors for A.
*> \endverbatim
*>
*> \param[in] SCOND
*> \verbatim
*>          SCOND is DOUBLE PRECISION
*>          Ratio of the smallest S(i) to the largest S(i).
*> \endverbatim
*>
*> \param[in] AMAX
*> \verbatim
*>          AMAX is DOUBLE PRECISION
*>          Absolute value of largest matrix entry.
*> \endverbatim
*>
*> \param[out] EQUED
*> \verbatim
*>          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          = 'Y':  Equilibration was done, i.e., A has been replaced by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).
*> \endverbatim
*
*> \par Internal Parameters:
*  =========================
*>
*> \verbatim
*>  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.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup laqhp
*
*  =====================================================================
      SUBROUTINE zlaqhp( UPLO, N, AP, S, SCOND, AMAX, EQUED )
*
*  -- 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            N
      DOUBLE PRECISION   AMAX, SCOND
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   S( * )
      COMPLEX*16         AP( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, THRESH
      parameter( one = 1.0d+0, thresh = 0.1d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, J, JC
      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.
*
            jc = 1
            DO 20 j = 1, n
               cj = s( j )
               DO 10 i = 1, j - 1
                  ap( jc+i-1 ) = cj*s( i )*ap( jc+i-1 )
   10          CONTINUE
               ap( jc+j-1 ) = cj*cj*dble( ap( jc+j-1 ) )
               jc = jc + j
   20       CONTINUE
         ELSE
*
*           Lower triangle of A is stored.
*
            jc = 1
            DO 40 j = 1, n
               cj = s( j )
               ap( jc ) = cj*cj*dble( ap( jc ) )
               DO 30 i = j + 1, n
                  ap( jc+i-j ) = cj*s( i )*ap( jc+i-j )
   30          CONTINUE
               jc = jc + n - j + 1
   40       CONTINUE
         END IF
         equed = 'Y'
      END IF
*
      RETURN
*
*     End of ZLAQHP
*
      END