dlassq.f

          SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. 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