--- rpl/lapack/lapack/zlarfgp.f	2010/08/13 21:04:10	1.3
+++ rpl/lapack/lapack/zlarfgp.f	2018/05/29 07:18:28	1.17
@@ -1,9 +1,113 @@
+*> \brief \b ZLARFGP 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 ZLARFGP + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarfgp.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarfgp.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarfgp.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE ZLARFGP( N, ALPHA, X, INCX, TAU )
+*
+*       .. Scalar Arguments ..
+*       INTEGER            INCX, N
+*       COMPLEX*16         ALPHA, TAU
+*       ..
+*       .. Array Arguments ..
+*       COMPLEX*16         X( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> ZLARFGP generates a complex elementary reflector H of order n, such
+*> that
+*>
+*>       H**H * ( alpha ) = ( beta ),   H**H * H = I.
+*>              (   x   )   (   0  )
+*>
+*> where alpha and beta are scalars, beta is real and non-negative, and
+*> x is an (n-1)-element complex vector.  H is represented in the form
+*>
+*>       H = I - tau * ( 1 ) * ( 1 v**H ) ,
+*>                     ( v )
+*>
+*> where tau is a complex scalar and v is a complex (n-1)-element
+*> vector. Note that H is not hermitian.
+*>
+*> If the elements of x are all zero and alpha is real, 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 COMPLEX*16
+*>          On entry, the value alpha.
+*>          On exit, it is overwritten with the value beta.
+*> \endverbatim
+*>
+*> \param[in,out] X
+*> \verbatim
+*>          X is COMPLEX*16 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 COMPLEX*16
+*>          The value tau.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2017
+*
+*> \ingroup complex16OTHERauxiliary
+*
+*  =====================================================================
       SUBROUTINE ZLARFGP( N, ALPHA, X, INCX, TAU )
 *
-*  -- LAPACK auxiliary routine (version 3.2.2) --
+*  -- LAPACK auxiliary routine (version 3.8.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     June 2010
+*     November 2017
 *
 *     .. Scalar Arguments ..
       INTEGER            INCX, N
@@ -13,48 +117,6 @@
       COMPLEX*16         X( * )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  ZLARFGP generates a complex elementary reflector H of order n, such
-*  that
-*
-*        H' * ( alpha ) = ( beta ),   H' * H = I.
-*             (   x   )   (   0  )
-*
-*  where alpha and beta are scalars, beta is real and non-negative, and
-*  x is an (n-1)-element complex vector.  H is represented in the form
-*
-*        H = I - tau * ( 1 ) * ( 1 v' ) ,
-*                      ( v )
-*
-*  where tau is a complex scalar and v is a complex (n-1)-element
-*  vector. Note that H is not hermitian.
-*
-*  If the elements of x are all zero and alpha is real, 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) COMPLEX*16
-*          On entry, the value alpha.
-*          On exit, it is overwritten with the value beta.
-*
-*  X       (input/output) COMPLEX*16 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) COMPLEX*16
-*          The value tau.
-*
 *  =====================================================================
 *
 *     .. Parameters ..
@@ -135,7 +197,7 @@
             BETA = BETA*BIGNUM
             ALPHI = ALPHI*BIGNUM
             ALPHR = ALPHR*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
@@ -160,7 +222,7 @@
          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 
+*           it loses relative accuracy. This is a BIG problem. Solution: flush TAU
 *           to ZERO (or TWO or whatever makes a nonnegative real number for BETA).
 *
 *           (Bug report provided by Pat Quillen from MathWorks on Jul 29, 2009.)
@@ -187,7 +249,7 @@
                BETA = XNORM
             END IF
 *
-         ELSE 
+         ELSE
 *
 *           This is the general case.
 *