zlaqhe.f

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      SUBROUTINE zlaqhe( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
*
*  -- LAPACK auxiliary routine (version 3.2) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      CHARACTER          equed, uplo
      INTEGER            lda, n
      DOUBLE PRECISION   amax, scond
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   s( * )
      COMPLEX*16         a( lda, * )
*     ..
*
*  Purpose
*  =======
*
*  ZLAQHE equilibrates a Hermitian matrix A using the scaling factors
*  in the vector S.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the upper or lower triangular part of the
*          Hermitian matrix A is stored.
*          = 'U':  Upper triangular
*          = 'L':  Lower triangular
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  A       (input/output) 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).
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(N,1).
*
*  S       (input) DOUBLE PRECISION array, dimension (N)
*          The scale factors for A.
*
*  SCOND   (input) DOUBLE PRECISION
*          Ratio of the smallest S(i) to the largest S(i).
*
*  AMAX    (input) DOUBLE PRECISION
*          Absolute value of largest matrix entry.
*
*  EQUED   (output) 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*          = 'Y':  Equilibration was done, i.e., A has been replaced by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.
*
*  =====================================================================
*
*     .. 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
*
      END