zlaqhe.f

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      SUBROUTINE ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
*
*  -- LAPACK auxiliary routine (version 3.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver 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*          = 'Y':  Equilibration was done, i.e., A has been replaced by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