zlassq.f

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*> \brief \b ZLASSQ updates a sum of squares represented in scaled form.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
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*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZLASSQ( N, X, INCX, SCALE, SUMSQ )
* 
*       .. Scalar Arguments ..
*       INTEGER            INCX, N
*       DOUBLE PRECISION   SCALE, SUMSQ
*       ..
*       .. Array Arguments ..
*       COMPLEX*16         X( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZLASSQ returns the values scl and ssq such that
*>
*>    ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
*>
*> where x( i ) = abs( X( 1 + ( i - 1 )*INCX ) ). The value of sumsq is
*> assumed to be at least unity and the value of ssq will then satisfy
*>
*>    1.0 .le. ssq .le. ( sumsq + 2*n ).
*>
*> scale is assumed to be non-negative and scl returns the value
*>
*>    scl = max( scale, abs( real( x( i ) ) ), abs( aimag( x( i ) ) ) ),
*>           i
*>
*> scale and sumsq must be supplied in SCALE and SUMSQ respectively.
*> SCALE and SUMSQ are overwritten by scl and ssq respectively.
*>
*> The routine makes only one pass through the vector X.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of elements to be used from the vector X.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*>          X is COMPLEX*16 array, dimension (N)
*>          The vector x as described above.
*>             x( i )  = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*>          INCX is INTEGER
*>          The increment between successive values of the vector X.
*>          INCX > 0.
*> \endverbatim
*>
*> \param[in,out] SCALE
*> \verbatim
*>          SCALE is DOUBLE PRECISION
*>          On entry, the value  scale  in the equation above.
*>          On exit, SCALE is overwritten with the value  scl .
*> \endverbatim
*>
*> \param[in,out] SUMSQ
*> \verbatim
*>          SUMSQ is DOUBLE PRECISION
*>          On entry, the value  sumsq  in the equation above.
*>          On exit, SUMSQ is overwritten with the value  ssq .
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup complex16OTHERauxiliary
*
*  =====================================================================
      SUBROUTINE zlassq( N, X, INCX, SCALE, SUMSQ )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            incx, n
      DOUBLE PRECISION   scale, sumsq
*     ..
*     .. Array Arguments ..
      COMPLEX*16         x( * )
*     ..
*
* =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   zero
      parameter( zero = 0.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            ix
      DOUBLE PRECISION   temp1
*     ..
*     .. External Functions ..
      LOGICAL            disnan
      EXTERNAL           disnan
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, dble, dimag
*     ..
*     .. Executable Statements ..
*
      IF( n.GT.0 ) THEN
         DO 10 ix = 1, 1 + ( n-1 )*incx, incx
            temp1 = abs( dble( x( ix ) ) )
            IF( temp1.GT.zero.OR.disnan( temp1 ) ) THEN
               IF( scale.LT.temp1 ) THEN
                  sumsq = 1 + sumsq*( scale / temp1 )**2
                  scale = temp1
               ELSE
                  sumsq = sumsq + ( temp1 / scale )**2
               END IF
            END IF
            temp1 = abs( dimag( x( ix ) ) )
            IF( temp1.GT.zero.OR.disnan( temp1 ) ) THEN
               IF( scale.LT.temp1 ) THEN
                  sumsq = 1 + sumsq*( scale / temp1 )**2
                  scale = temp1
               ELSE
                  sumsq = sumsq + ( temp1 / scale )**2
               END IF
            END IF
   10    continue
      END IF
*
      return
*
*     End of ZLASSQ
*
      END