zlaqhe.f.html

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      SUBROUTINE <a name="ZLAQHE.1"></a><a href="zlaqhe.f.html#ZLAQHE.1">ZLAQHE</a>( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          EQUED, UPLO
      INTEGER            LDA, N
      DOUBLE PRECISION   AMAX, SCOND
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   S( * )
      COMPLEX*16         A( LDA, * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="ZLAQHE.20"></a><a href="zlaqhe.f.html#ZLAQHE.1">ZLAQHE</a> equilibrates a Hermitian matrix A using the scaling factors
</span><span class="comment">*</span><span class="comment">  in the vector S.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  UPLO    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies whether the upper or lower triangular part of the
</span><span class="comment">*</span><span class="comment">          Hermitian matrix A is stored.
</span><span class="comment">*</span><span class="comment">          = 'U':  Upper triangular
</span><span class="comment">*</span><span class="comment">          = 'L':  Lower triangular
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
</span><span class="comment">*</span><span class="comment">          n by n upper triangular part of A contains the upper
</span><span class="comment">*</span><span class="comment">          triangular part of the matrix A, and the strictly lower
</span><span class="comment">*</span><span class="comment">          triangular part of A is not referenced.  If UPLO = 'L', the
</span><span class="comment">*</span><span class="comment">          leading n by n lower triangular part of A contains the lower
</span><span class="comment">*</span><span class="comment">          triangular part of the matrix A, and the strictly upper
</span><span class="comment">*</span><span class="comment">          triangular part of A is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          On exit, if EQUED = 'Y', the equilibrated matrix:
</span><span class="comment">*</span><span class="comment">          diag(S) * A * diag(S).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A.  LDA &gt;= max(N,1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  S       (input) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The scale factors for A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SCOND   (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">          Ratio of the smallest S(i) to the largest S(i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AMAX    (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">          Absolute value of largest matrix entry.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  EQUED   (output) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies whether or not equilibration was done.
</span><span class="comment">*</span><span class="comment">          = 'N':  No equilibration.
</span><span class="comment">*</span><span class="comment">          = 'Y':  Equilibration was done, i.e., A has been replaced by
</span><span class="comment">*</span><span class="comment">                  diag(S) * A * diag(S).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Internal Parameters
</span><span class="comment">*</span><span class="comment">  ===================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  THRESH is a threshold value used to decide if scaling should be done
</span><span class="comment">*</span><span class="comment">  based on the ratio of the scaling factors.  If SCOND &lt; THRESH,
</span><span class="comment">*</span><span class="comment">  scaling is done.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LARGE and SMALL are threshold values used to decide if scaling should
</span><span class="comment">*</span><span class="comment">  be done based on the absolute size of the largest matrix element.
</span><span class="comment">*</span><span class="comment">  If AMAX &gt; LARGE or AMAX &lt; SMALL, scaling is done.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      DOUBLE PRECISION   ONE, THRESH
      PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, J
      DOUBLE PRECISION   CJ, LARGE, SMALL
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.87"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      DOUBLE PRECISION   <a name="DLAMCH.88"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
      EXTERNAL           <a name="LSAME.89"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="DLAMCH.89"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          DBLE
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.LE.0 ) THEN
         EQUED = <span class="string">'N'</span>
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Initialize LARGE and SMALL.
</span><span class="comment">*</span><span class="comment">
</span>      SMALL = <a name="DLAMCH.105"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'Safe minimum'</span> ) / <a name="DLAMCH.105"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'Precision'</span> )
      LARGE = ONE / SMALL
<span class="comment">*</span><span class="comment">
</span>      IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        No equilibration
</span><span class="comment">*</span><span class="comment">
</span>         EQUED = <span class="string">'N'</span>
      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Replace A by diag(S) * A * diag(S).
</span><span class="comment">*</span><span class="comment">
</span>         IF( <a name="LSAME.117"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Upper triangle of A is stored.
</span><span class="comment">*</span><span class="comment">
</span>            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
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Lower triangle of A is stored.
</span><span class="comment">*</span><span class="comment">
</span>            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 = <span class="string">'Y'</span>
      END IF
<span class="comment">*</span><span class="comment">
</span>      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="ZLAQHE.145"></a><a href="zlaqhe.f.html#ZLAQHE.1">ZLAQHE</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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