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[bytom/vapor.git] / vendor / gonum.org / v1 / gonum / lapack / internal / testdata / netlib / dlarfg.f

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-*> \brief \b DLARFG generates an elementary reflector (Householder matrix).
-*
-*  =========== 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 September 2012
-*
-*> \ingroup doubleOTHERauxiliary
-*
-*  =====================================================================
-      SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )
-*
-*  -- 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   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