dlassq.f

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      SUBROUTINE dlassq( N, X, INCX, SCALE, SUMSQ )
*
*  -- LAPACK auxiliary routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      INTEGER            INCX, N
      DOUBLE PRECISION   SCALE, SUMSQ
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   X( * )
*     ..
*
*  Purpose
*  =======
*
*  DLASSQ  returns the values  scl  and  smsq  such that
*
*     ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
*
*  where  x( i ) = X( 1 + ( i - 1 )*INCX ). The value of  sumsq  is
*  assumed to be non-negative and  scl  returns the value
*
*     scl = max( scale, abs( x( i ) ) ).
*
*  scale and sumsq must be supplied in SCALE and SUMSQ and
*  scl and smsq are overwritten on SCALE and SUMSQ 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) DOUBLE PRECISION array, dimension (N)
*          The vector for which a scaled sum of squares is computed.
*             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  scl , the scaling factor
*          for the sum of squares.
*
*  SUMSQ   (input/output) DOUBLE PRECISION
*          On entry, the value  sumsq  in the equation above.
*          On exit, SUMSQ is overwritten with  smsq , the basic sum of
*          squares from which  scl  has been factored out.
*
* =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      parameter( zero = 0.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            IX
      DOUBLE PRECISION   ABSXI
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs
*     ..
*     .. Executable Statements ..
*
      IF( n.GT.0 ) THEN
         DO 10 ix = 1, 1 + ( n-1 )*incx, incx
            IF( x( ix ).NE.zero ) THEN
               absxi = abs( x( ix ) )
               IF( scale.LT.absxi ) THEN
                  sumsq = 1 + sumsq*( scale / absxi )**2
                  scale = absxi
               ELSE
                  sumsq = sumsq + ( absxi / scale )**2
               END IF
            END IF
   10    CONTINUE
      END IF
      RETURN
*
*     End of DLASSQ
*
      END