*> \brief \b DNRM2 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX) * * .. Scalar Arguments .. * INTEGER INCX,N * .. * .. Array Arguments .. * DOUBLE PRECISION X(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DNRM2 returns the euclidean norm of a vector via the function *> name, so that *> *> DNRM2 := sqrt( x'*x ) *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in] X *> \verbatim *> X is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of DX *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup double_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> -- This version written on 25-October-1982. *> Modified on 14-October-1993 to inline the call to DLASSQ. *> Sven Hammarling, Nag Ltd. *> \endverbatim *> * ===================================================================== DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INCX,N * .. * .. Array Arguments .. DOUBLE PRECISION X(*) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE,ZERO PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) * .. * .. Local Scalars .. DOUBLE PRECISION ABSXI,NORM,SCALE,SSQ INTEGER IX * .. * .. Intrinsic Functions .. INTRINSIC ABS,SQRT * .. IF (N.LT.1 .OR. INCX.LT.1) THEN NORM = ZERO ELSE IF (N.EQ.1) THEN NORM = ABS(X(1)) ELSE SCALE = ZERO SSQ = ONE * The following loop is equivalent to this call to the LAPACK * auxiliary routine: * CALL DLASSQ( N, X, INCX, SCALE, SSQ ) * DO 10 IX = 1,1 + (N-1)*INCX,INCX IF (X(IX).NE.ZERO) THEN ABSXI = ABS(X(IX)) IF (SCALE.LT.ABSXI) THEN SSQ = ONE + SSQ* (SCALE/ABSXI)**2 SCALE = ABSXI ELSE SSQ = SSQ + (ABSXI/SCALE)**2 END IF END IF 10 CONTINUE NORM = SCALE*SQRT(SSQ) END IF * DNRM2 = NORM RETURN * * End of DNRM2. * END