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version 1.6, 2010/08/13 21:04:11 version 1.18, 2020/05/21 21:46:09
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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/
   *
   *> \htmlonly
   *> Download ZLASSQ + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlassq.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlassq.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlassq.f">
   *> [TXT]</a>
   *> \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 <= ssq <= ( 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 (1+(N-1)*INCX)
   *>          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 December 2016
   *
   *> \ingroup complex16OTHERauxiliary
   *
   *  =====================================================================
       SUBROUTINE ZLASSQ( N, X, INCX, SCALE, SUMSQ )        SUBROUTINE ZLASSQ( N, X, INCX, SCALE, SUMSQ )
 *  *
 *  -- LAPACK auxiliary routine (version 3.2) --  *  -- LAPACK auxiliary routine (version 3.7.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  *     December 2016
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            INCX, N        INTEGER            INCX, N
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       COMPLEX*16         X( * )        COMPLEX*16         X( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  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.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  N       (input) INTEGER  
 *          The number of elements to be used from the vector X.  
 *  
 *  X       (input) COMPLEX*16 array, dimension (N)  
 *          The vector x as described above.  
 *             x( i )  = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.  
 *  
 *  INCX    (input) INTEGER  
 *          The increment between successive values of the vector X.  
 *          INCX > 0.  
 *  
 *  SCALE   (input/output) DOUBLE PRECISION  
 *          On entry, the value  scale  in the equation above.  
 *          On exit, SCALE is overwritten with the value  scl .  
 *  
 *  SUMSQ   (input/output) DOUBLE PRECISION  
 *          On entry, the value  sumsq  in the equation above.  
 *          On exit, SUMSQ is overwritten with the value  ssq .  
 *  
 * =====================================================================  * =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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       INTEGER            IX        INTEGER            IX
       DOUBLE PRECISION   TEMP1        DOUBLE PRECISION   TEMP1
 *     ..  *     ..
   *     .. External Functions ..
         LOGICAL            DISNAN
         EXTERNAL           DISNAN
   *     ..
 *     .. Intrinsic Functions ..  *     .. Intrinsic Functions ..
       INTRINSIC          ABS, DBLE, DIMAG        INTRINSIC          ABS, DBLE, DIMAG
 *     ..  *     ..
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 *  *
       IF( N.GT.0 ) THEN        IF( N.GT.0 ) THEN
          DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX           DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX
             IF( DBLE( X( IX ) ).NE.ZERO ) THEN              TEMP1 = ABS( DBLE( X( IX ) ) )
                TEMP1 = ABS( DBLE( X( IX ) ) )              IF( TEMP1.GT.ZERO.OR.DISNAN( TEMP1 ) ) THEN
                IF( SCALE.LT.TEMP1 ) THEN                 IF( SCALE.LT.TEMP1 ) THEN
                   SUMSQ = 1 + SUMSQ*( SCALE / TEMP1 )**2                    SUMSQ = 1 + SUMSQ*( SCALE / TEMP1 )**2
                   SCALE = TEMP1                    SCALE = TEMP1
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                   SUMSQ = SUMSQ + ( TEMP1 / SCALE )**2                    SUMSQ = SUMSQ + ( TEMP1 / SCALE )**2
                END IF                 END IF
             END IF              END IF
             IF( DIMAG( X( IX ) ).NE.ZERO ) THEN              TEMP1 = ABS( DIMAG( X( IX ) ) )
                TEMP1 = ABS( DIMAG( X( IX ) ) )              IF( TEMP1.GT.ZERO.OR.DISNAN( TEMP1 ) ) THEN
                IF( SCALE.LT.TEMP1 ) THEN                 IF( SCALE.LT.TEMP1 ) THEN
                   SUMSQ = 1 + SUMSQ*( SCALE / TEMP1 )**2                    SUMSQ = 1 + SUMSQ*( SCALE / TEMP1 )**2
                   SCALE = TEMP1                    SCALE = TEMP1
Removed from v.1.6  
changed lines
  Added in v.1.18

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