```      SUBROUTINE ZLAQHP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
*
*  -- LAPACK auxiliary routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          EQUED, UPLO
INTEGER            N
DOUBLE PRECISION   AMAX, SCOND
*     ..
*     .. Array Arguments ..
DOUBLE PRECISION   S( * )
COMPLEX*16         AP( * )
*     ..
*
*  Purpose
*  =======
*
*  ZLAQHP 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.
*
*  AP      (input/output) 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.
*
*  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*          = 'Y':  Equilibration was done, i.e., A has been replaced by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, 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

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