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*> \brief \b DLARFG** =========== DOCUMENTATION ===========** Online html documentation available at * http://www.netlib.org/lapack/explore-html/ **> \htmlonly*> Download DLARFG + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfg.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarfg.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarfg.f"> *> [TXT]</a>*> \endhtmlonly ** Definition:* ===========** SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )* * .. Scalar Arguments ..* INTEGER INCX, N* DOUBLE PRECISION ALPHA, TAU* ..* .. Array Arguments ..* DOUBLE PRECISION X( * )* ..* **> \par Purpose:* =============*>*> \verbatim*>*> DLARFG generates a real elementary reflector H of order n, such*> that*>*> H * ( alpha ) = ( beta ), H**T * H = I.*> ( x ) ( 0 )*>*> where alpha and beta are scalars, and x is an (n-1)-element real*> vector. H is represented in the form*>*> H = I - tau * ( 1 ) * ( 1 v**T ) ,*> ( v )*>*> where tau is a real scalar and v is a real (n-1)-element*> vector.*>*> If the elements of x are all zero, then tau = 0 and H is taken to be*> the unit matrix.*>*> Otherwise 1 <= tau <= 2.*> \endverbatim** Arguments:* ==========**> \param[in] N*> \verbatim*> N is INTEGER*> The order of the elementary reflector.*> \endverbatim*>*> \param[in,out] ALPHA*> \verbatim*> ALPHA is DOUBLE PRECISION*> On entry, the value alpha.*> On exit, it is overwritten with the value beta.*> \endverbatim*>*> \param[in,out] X*> \verbatim*> X is DOUBLE PRECISION array, dimension*> (1+(N-2)*abs(INCX))*> On entry, the vector x.*> On exit, it is overwritten with the vector v.*> \endverbatim*>*> \param[in] INCX*> \verbatim*> INCX is INTEGER*> The increment between elements of X. INCX > 0.*> \endverbatim*>*> \param[out] TAU*> \verbatim*> TAU is DOUBLE PRECISION*> The value tau.*> \endverbatim** Authors:* ========**> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. **> \date November 2011**> \ingroup doubleOTHERauxiliary** ===================================================================== SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )** -- LAPACK auxiliary routine (version 3.4.0) --* -- LAPACK is a software package provided by Univ. of Tennessee, --* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--* November 2011** .. Scalar Arguments .. INTEGER INCX, N DOUBLE PRECISION ALPHA, TAU* ..* .. Array Arguments .. DOUBLE PRECISION X( * )* ..** =====================================================================** .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )* ..* .. Local Scalars .. INTEGER J, KNT DOUBLE PRECISION BETA, RSAFMN, SAFMIN, XNORM* ..* .. External Functions .. DOUBLE PRECISION DLAMCH, DLAPY2, DNRM2 EXTERNAL DLAMCH, DLAPY2, DNRM2* ..* .. Intrinsic Functions .. INTRINSIC ABS, SIGN* ..* .. External Subroutines .. EXTERNAL DSCAL* ..* .. Executable Statements ..* IF( N.LE.1 ) THEN TAU = ZERO RETURN END IF* XNORM = DNRM2( N-1, X, INCX )* IF( XNORM.EQ.ZERO ) THEN** H = I* TAU = ZERO ELSE** general case* BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA ) SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' ) KNT = 0 IF( ABS( BETA ).LT.SAFMIN ) THEN** XNORM, BETA may be inaccurate; scale X and recompute them* RSAFMN = ONE / SAFMIN 10 CONTINUE KNT = KNT + 1 CALL DSCAL( N-1, RSAFMN, X, INCX ) BETA = BETA*RSAFMN ALPHA = ALPHA*RSAFMN IF( ABS( BETA ).LT.SAFMIN ) $ GO TO 10** New BETA is at most 1, at least SAFMIN* XNORM = DNRM2( N-1, X, INCX ) BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA ) END IF TAU = ( BETA-ALPHA ) / BETA CALL DSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX )** If ALPHA is subnormal, it may lose relative accuracy* DO 20 J = 1, KNT BETA = BETA*SAFMIN 20 CONTINUE ALPHA = BETA END IF* RETURN** End of DLARFG* END
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