*> \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 *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \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 December 2016 * *> \ingroup OTHERauxiliary * * ===================================================================== SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. 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