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    1: *> \brief \b ZLASSQ updates a sum of squares represented in scaled form.
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download ZLASSQ + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlassq.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlassq.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlassq.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZLASSQ( N, X, INCX, SCALE, SUMSQ )
   22: *
   23: *       .. Scalar Arguments ..
   24: *       INTEGER            INCX, N
   25: *       DOUBLE PRECISION   SCALE, SUMSQ
   26: *       ..
   27: *       .. Array Arguments ..
   28: *       COMPLEX*16         X( * )
   29: *       ..
   30: *
   31: *
   32: *> \par Purpose:
   33: *  =============
   34: *>
   35: *> \verbatim
   36: *>
   37: *> ZLASSQ returns the values scl and ssq such that
   38: *>
   39: *>    ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
   40: *>
   41: *> where x( i ) = abs( X( 1 + ( i - 1 )*INCX ) ). The value of sumsq is
   42: *> assumed to be at least unity and the value of ssq will then satisfy
   43: *>
   44: *>    1.0 <= ssq <= ( sumsq + 2*n ).
   45: *>
   46: *> scale is assumed to be non-negative and scl returns the value
   47: *>
   48: *>    scl = max( scale, abs( real( x( i ) ) ), abs( aimag( x( i ) ) ) ),
   49: *>           i
   50: *>
   51: *> scale and sumsq must be supplied in SCALE and SUMSQ respectively.
   52: *> SCALE and SUMSQ are overwritten by scl and ssq respectively.
   53: *>
   54: *> The routine makes only one pass through the vector X.
   55: *> \endverbatim
   56: *
   57: *  Arguments:
   58: *  ==========
   59: *
   60: *> \param[in] N
   61: *> \verbatim
   62: *>          N is INTEGER
   63: *>          The number of elements to be used from the vector X.
   64: *> \endverbatim
   65: *>
   66: *> \param[in] X
   67: *> \verbatim
   68: *>          X is COMPLEX*16 array, dimension (1+(N-1)*INCX)
   69: *>          The vector x as described above.
   70: *>             x( i )  = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
   71: *> \endverbatim
   72: *>
   73: *> \param[in] INCX
   74: *> \verbatim
   75: *>          INCX is INTEGER
   76: *>          The increment between successive values of the vector X.
   77: *>          INCX > 0.
   78: *> \endverbatim
   79: *>
   80: *> \param[in,out] SCALE
   81: *> \verbatim
   82: *>          SCALE is DOUBLE PRECISION
   83: *>          On entry, the value  scale  in the equation above.
   84: *>          On exit, SCALE is overwritten with the value  scl .
   85: *> \endverbatim
   86: *>
   87: *> \param[in,out] SUMSQ
   88: *> \verbatim
   89: *>          SUMSQ is DOUBLE PRECISION
   90: *>          On entry, the value  sumsq  in the equation above.
   91: *>          On exit, SUMSQ is overwritten with the value  ssq .
   92: *> \endverbatim
   93: *
   94: *  Authors:
   95: *  ========
   96: *
   97: *> \author Univ. of Tennessee
   98: *> \author Univ. of California Berkeley
   99: *> \author Univ. of Colorado Denver
  100: *> \author NAG Ltd.
  101: *
  102: *> \date December 2016
  103: *
  104: *> \ingroup complex16OTHERauxiliary
  105: *
  106: *  =====================================================================
  107:       SUBROUTINE ZLASSQ( N, X, INCX, SCALE, SUMSQ )
  108: *
  109: *  -- LAPACK auxiliary routine (version 3.7.0) --
  110: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  111: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  112: *     December 2016
  113: *
  114: *     .. Scalar Arguments ..
  115:       INTEGER            INCX, N
  116:       DOUBLE PRECISION   SCALE, SUMSQ
  117: *     ..
  118: *     .. Array Arguments ..
  119:       COMPLEX*16         X( * )
  120: *     ..
  121: *
  122: * =====================================================================
  123: *
  124: *     .. Parameters ..
  125:       DOUBLE PRECISION   ZERO
  126:       PARAMETER          ( ZERO = 0.0D+0 )
  127: *     ..
  128: *     .. Local Scalars ..
  129:       INTEGER            IX
  130:       DOUBLE PRECISION   TEMP1
  131: *     ..
  132: *     .. External Functions ..
  133:       LOGICAL            DISNAN
  134:       EXTERNAL           DISNAN
  135: *     ..
  136: *     .. Intrinsic Functions ..
  137:       INTRINSIC          ABS, DBLE, DIMAG
  138: *     ..
  139: *     .. Executable Statements ..
  140: *
  141:       IF( N.GT.0 ) THEN
  142:          DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX
  143:             TEMP1 = ABS( DBLE( X( IX ) ) )
  144:             IF( TEMP1.GT.ZERO.OR.DISNAN( TEMP1 ) ) THEN
  145:                IF( SCALE.LT.TEMP1 ) THEN
  146:                   SUMSQ = 1 + SUMSQ*( SCALE / TEMP1 )**2
  147:                   SCALE = TEMP1
  148:                ELSE
  149:                   SUMSQ = SUMSQ + ( TEMP1 / SCALE )**2
  150:                END IF
  151:             END IF
  152:             TEMP1 = ABS( DIMAG( X( IX ) ) )
  153:             IF( TEMP1.GT.ZERO.OR.DISNAN( TEMP1 ) ) THEN
  154:                IF( SCALE.LT.TEMP1 ) THEN
  155:                   SUMSQ = 1 + SUMSQ*( SCALE / TEMP1 )**2
  156:                   SCALE = TEMP1
  157:                ELSE
  158:                   SUMSQ = SUMSQ + ( TEMP1 / SCALE )**2
  159:                END IF
  160:             END IF
  161:    10    CONTINUE
  162:       END IF
  163: *
  164:       RETURN
  165: *
  166: *     End of ZLASSQ
  167: *
  168:       END