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-version 1.2, 2010/08/07 13:22:19
+version 1.18, 2023/08/07 08:38:57
  Line 1
+ *> \brief \b DLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.
+ *
+ *  =========== DOCUMENTATION ===========
+ *
+ * Online html documentation available at
+ *            http://www.netlib.org/lapack/explore-html/
+ *
+ *> \htmlonly
+ *> Download DLARFGP + dependencies
+ *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfgp.f">
+ *> [TGZ]</a>
+ *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarfgp.f">
+ *> [ZIP]</a>
+ *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarfgp.f">
+ *> [TXT]</a>
+ *> \endhtmlonly
+ *
+ *  Definition:
+ *  ===========
+ *
+ *       SUBROUTINE DLARFGP( N, ALPHA, X, INCX, TAU )
+ *
+ *       .. Scalar Arguments ..
+ *       INTEGER            INCX, N
+ *       DOUBLE PRECISION   ALPHA, TAU
+ *       ..
+ *       .. Array Arguments ..
+ *       DOUBLE PRECISION   X( * )
+ *       ..
+ *
+ *
+ *> \par Purpose:
+ *  =============
+ *>
+ *> \verbatim
+ *>
+ *> DLARFGP 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, beta is non-negative, 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.
+ *> \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.
+ *
+ *> \ingroup doubleOTHERauxiliary
+ *
+ *  =====================================================================
        SUBROUTINE DLARFGP( N, ALPHA, X, INCX, TAU )
  *
- *  -- LAPACK auxiliary routine (version 3.2.2) --
+ *  -- LAPACK auxiliary routine --
  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
- *     June 2010
  *
  *     .. Scalar Arguments ..
        INTEGER            INCX, N
- Line 13
+ Line 114
        DOUBLE PRECISION   X( * )
  *     ..
  *
- *  Purpose
- *  =======
- *
- *  DLARFGP generates a real elementary reflector H of order n, such
- *  that
- *
- *        H * ( alpha ) = ( beta ),   H' * H = I.
- *            (   x   )   (   0  )
- *
- *  where alpha and beta are scalars, beta is non-negative, and x is
- *  an (n-1)-element real vector.  H is represented in the form
- *
- *        H = I - tau * ( 1 ) * ( 1 v' ) ,
- *                      ( 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.
- *
- *  Arguments
- *  =========
- *
- *  N       (input) INTEGER
- *          The order of the elementary reflector.
- *
- *  ALPHA   (input/output) DOUBLE PRECISION
- *          On entry, the value alpha.
- *          On exit, it is overwritten with the value beta.
- *
- *  X       (input/output) DOUBLE PRECISION array, dimension
- *                         (1+(N-2)*abs(INCX))
- *          On entry, the vector x.
- *          On exit, it is overwritten with the vector v.
- *
- *  INCX    (input) INTEGER
- *          The increment between elements of X. INCX > 0.
- *
- *  TAU     (output) DOUBLE PRECISION
- *          The value tau.
- *
  *  =====================================================================
  *
  *     .. Parameters ..
- Line 119
+ Line 178
              CALL DSCAL( N-1, BIGNUM, X, INCX )
              BETA = BETA*BIGNUM
              ALPHA = ALPHA*BIGNUM
-             IF( ABS( BETA ).LT.SMLNUM )
+             IF( (ABS( BETA ).LT.SMLNUM) .AND. (KNT .LT. 20) )
       $         GO TO 10
  *
  *           New BETA is at most 1, at least SMLNUM
- Line 141
+ Line 200
           IF ( ABS(TAU).LE.SMLNUM ) THEN
  *
  *           In the case where the computed TAU ends up being a denormalized number,
  *           it loses relative accuracy. This is a BIG problem. Solution: flush TAU
  *           to ZERO. This explains the next IF statement.
  *
  *           (Bug report provided by Pat Quillen from MathWorks on Jul 29, 2009.)
- Line 157
+ Line 216
                 BETA = -SAVEALPHA
              END IF
  *
           ELSE
  *
  *           This is the general case.
  *

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