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dlassq.f
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*> \brief \b DLASSQ updates a sum of squares represented in scaled form.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLASSQ + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlassq.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlassq.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlassq.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ )
*
* .. Scalar Arguments ..
* INTEGER INCX, N
* DOUBLE PRECISION SCALE, SUMSQ
* ..
* .. Array Arguments ..
* DOUBLE PRECISION X( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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.
*> \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 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.
*> \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 scl , the scaling factor
*> for the sum of squares.
*> \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 smsq , the basic sum of
*> squares from which scl has been factored out.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
* =====================================================================
SUBROUTINE DLASSQ( 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 ..
DOUBLE PRECISION X( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER IX
DOUBLE PRECISION ABSXI
* ..
* .. External Functions ..
LOGICAL DISNAN
EXTERNAL DISNAN
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS
* ..
* .. Executable Statements ..
*
IF( N.GT.0 ) THEN
DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX
ABSXI = ABS( X( IX ) )
IF( ABSXI.GT.ZERO.OR.DISNAN( ABSXI ) ) THEN
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

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