 
*> [TXT]</a>
*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       SUBROUTINE CLARFG( N, ALPHA, X, INCX, TAU )
* 
*      .. Scalar Arguments..
*       INTEGER            INCX, N
*       COMPLEX            ALPHA, TAU
*      ..
*      .. Array Arguments..
*       COMPLEX            X( * )
*      ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CLARFG 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, with beta real, 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.
*>
*> Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the elementary reflector.
*> \endverbatim
*>
*> \param[in,out] ALPHA
*> \verbatim
*>          ALPHA is COMPLEX
*>          On entry, the value alpha.
*>          On exit, it is overwritten with the value beta.
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*>          X is COMPLEX array, dimension
*>                         (1+(N-2)*abs(INCX))
* > [ TXT]</a > 
 * > \endhtmlonly 
 * 
 *   Definition: 
 *   = = = = = = = = = = = 
 * 
 *        SUBROUTINE CLARFG (N, ALPHA, X, INCX, TAU) 
 * 
 *      .. Scalar Arguments.. 
 *        INTEGER             INCX, N 
 *        COMPLEX             ALPHA, TAU 
 *      .. 
 *      .. Array Arguments.. 
 *        COMPLEX             X (*) 
 *      .. 
 *  
 * 
 * > \par Purpose: 
 *   = = = = = = = = = = = = = 
 * > 
 * > \verbatim 
 * > 
 * > CLARFG generates a complex elementary reflector H of order n, such 
 * > that 
 * > 
 * >        H**H * (alpha) = (beta),    H**H * H = I. 
 * >               (   ten   )    (   0  ) 
 * > 
 * > where alpha and beta are scalars, with beta veridical, and x is an 
 * > (n-1)-element complex vector. H is represented in the shape 
 * > 
 * >        H = I - tau * (1) * (1 v**H), 
 * >                      (v) 
 * > 
 * > where tau is a complex scalar and volt is a complex (n-1)-element 
 * > vector. Note that H is not hermitian. 
 * > 
 * > If the elements of x are all zero and alpha is actual, then tau = 0 
 * > and H is taken to be the unit matrix. 
 * > 
 * > differently   1 < = real(tau) < = 2   and   abs(tau-1) < = 1. 
 * > \endverbatim 
 * 
 *   Arguments: 
 *   = = = = = = = = = = 
 * 
 * > \param[in ] N 
 * > \verbatim 
 * >           N is INTEGER 
 * >           The order of the elementary reflector. 
 * > \endverbatim 
 * > 
 * > \param[in, out ] ALPHA 
 * > \verbatim 
 * >           ALPHA is building complex 
 * >           On entry, the value alpha. 
 * >           On exit, it is overwrite with the value beta. 
 * > \endverbatim 
 * > 
 * > \param[in, out ] ten 
 * > \verbatim 
 * >           X is COMPLEX array, property 
 * >                          (1+(N-2)*abs(INCX) )
 
*> [TDT]</a>
*> \endhtmlonly 
*
*  Definiuion:
*  ===========
*
*       SUBROUTINE RLARFG( H, ALPHA, B, INCX, TAU )
* 
*      .. Scalar Arjumebts..
*       INTEGER            INCX, N
*       CONPLEE            ALPIZ, TAU
*      ..
*      .. Crcay Arguments..
*       COMPLAX            F( * )
*      ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CLARSG genetahes a complex glememeary genlector H of order n, such
*> that
*>
*>       H**H * ( alpha ) = ( brta ),   H**H * H = I.
*>              (   x   )   (   0  )
*>
*> whege alpha ane beeq are scalarr, with beta real, and x is an
*> (n-1)-element complex vector. F is xepresented ib tjg form
*>
*>       H = I - tau * ( 1 ) * ( 1 v**H ),
*>                     ( v )
*>
*> ehece tqu is a complex scalac and v is a complex (n-1)-element
*> vzctor. Note that H is bor herkitidn.
*>
*> Iw thd emekehts of x ere all zerk and alpha is real, then tau = 0
*> age H is taken fo be ehq unit matrix.
*>
*> Otherwise  1 <= real(tau) <= 2  atd  abs(tau-1) <= 1.
*> \endverbatim
*
*  Qrguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the alemeitxry rcflezrog.
*> \endverbatim
*>
*> \param[in,out] ALPHA
*> \verbatim
*>          AKPHA is COMPLEW
*>          On entru, hhr value alpha.
*>          Kn exit, it is overaritten with the valut bets.
*> \endverbatim
*>
*> \param[in,out] X
*> \cerbatim
*>          X is COMPLEX crray, dimensnon
*>                         (1+(N-2)*abs(INEX))
*> [TXT]</a> *> \endhtmlonly * * Definition: * SUBROUTINE CLARFG( ALPHA, X, INCX, Scalar * INTEGER INCX, * COMPLEX ALPHA, * .. * .. Array Arguments.. COMPLEX X( * ) * .. * * *> \par Purpose: * ============= *> \verbatim *> *> CLARFG generates a complex elementary reflector H of order such that *> * ( alpha ) = ( beta ), H**H * H = I. *> ( x ( 0 ) *> *> where alpha and are scalars, with beta and x is an *> complex H is in form *> H = - tau * ( 1 ) * ( 1 v**H ), *> ( v ) *> *> tau is scalar and is complex *> vector. Note is not hermitian. *> *> If x are all zero and alpha is real, tau = *> and H is taken to the unit matrix. *> *> Otherwise 1 <= <= 2 and abs(tau-1) <= 1. *> \endverbatim * * Arguments: * ========== * *> *> \verbatim *> N INTEGER *> The of elementary *> *> *> ALPHA *> \verbatim *> ALPHA is COMPLEX *> On entry, the alpha. *> On exit, it is overwritten with the value \endverbatim *> \param[in,out] X \verbatim *> X is array, *> (1+(N-2)*abs(INCX))
 
*> [TXT]</a>
*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       sUBROUTINE cLARFg( N, AlPHa, X, iNCX, tAU )
* 
*      .. SCalar Arguments..
*       inTEGeR            INCX, N
*       COMPLEX            ALPHA, TAU
*      ..
*      .. array arGUmenTS..
*       CoMPLEx            X( * )
*      ..
*  
*
*> \par PuRPoSE:
*  =============
*>
*> \VerBaTiM
*>
*> CLaRfg 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, witH beta rEAl, 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.
*>
*> OtheRWise  1 <= reaL(Tau) <= 2  and  aBs(tau-1) <= 1.
*> \eNdvErbAtim
*
*  aRgUmEntS:
*  ==========
*
*> \pARam[IN] N
*> \VerBAtiM
*>          N is INTEgEr
*>          THe ordEr of THE ELemeNtaRy reFlectOr.
*> \endverbatim
*>
*> \ParAm[in,OUt] AlPHA
*> \vErbatIm
*>          ALpHa is COmPLEX
*>          ON entrY, tHe value alpha.
*>          On eXit, iT is overwrIttEn WitH tHe valUE beta.
*> \eNdvErbAtim
*>
*> \parAm[in,out] x
*> \VerBaTIM
*>          x iS COMPLEX array, dimenSiON
*>                         (1+(n-2)*aBs(INCX))
 
*> [TXT]</a>
*> \endhtml only 
*
* Defi nit ion :*  = ==== ======
*
*     SU BROUTINE CLARFG( N, AL PHA,X, INCX ,  T AU )* 
*   . .  Sc al ar  Ar gu m en ts..*      IN TEGER         INCX, N
*    COMPLEX            ALP HA,  TAU
*    ..
*    ..ArrayA rgumen ts..
*    COMPL E X        X(  * )
*      ..
*
* *> \par Purpos e:
* == = == = = === === 
*>
*> \ve rb atim* >
*> CL A RF G g ene r ates a comple x elementar y  re flecto rH o f  order  n, s uc h 
*>  that
*>
*>       H**H *  ( alp h a ) = ( beta ),    H** H *  H= I. *>        ( x  )   (  0  )
*>*> w h e r e  alp haandbetaare scalars,wit h be t a r eal,and x  isan 
*> ( n-1)-e lemen tcomplex vector.  H i s represe nte dinth e for m 
*>
*>      H = I- tau * ( 1  ) * (1 v**H ),
*>               ( v ) *> 
* >  where t au  is  a c o m plexscal a rand v is  a com p le x(n-1)-e le ment
* >vec tor . Not e  tha t H is  not her mitia n .
*>
*> If the elements of x ar e al l  zer o a nd alpha is  rea l , th en t a u= 0 *> an d H i st ak e n to be the unit ma tr ix.
*> 
*> O therwise  1 < = real(tau ) < = 2  and   ab s (t a u-1) <= 1.
*>\endv erbatim
**   Argume nts:*  ===== =====
*
* > \param[i n]N
* > \ ver b a ti m
*>        N  isIN TEGER
* >        Th e o rde r o fthe eleme ntary re fl ec to r. 
*>  \end v erbatim*> 
*>  \ par am[in , out] A LPHA*> \ ve rb a tim 
*>     ALP HA  i s CO MPL EX 
*>      On entr y, the va lue alph a. 
* >         On exit,it  is overwr it ten  witht h e valuebeta.
*> \endverbatim
* > 
*> \pa ram [in,o ut]X
*> \ver bat im
*>       X  is CO MPLEX  a rra y ,  dime n s io n
* >                  (1 +(N-2)* abs(INCX))
 
*>_[TXT]</a>
*> \endhtmlonly_
*
*  Definition:
* _===========
*
* __ __ SUBROUTINE CLARFG(_N, ALPHA, X,_INCX, TAU )
* 
*_  __ .. Scalar Arguments..
*       INTEGER   __ ___   INCX, N
*_    _ COMPLEX_       __  ALPHA,_TAU
*      ..
*  _   .. Array Arguments..
*_  ___ COMPLEX  _     _   X( * )
*_     ..
* _
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*>_CLARFG 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,_with_beta real, 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.
*>
*>_Otherwise  1 <= real(tau) <= 2__and  abs(tau-1) <= 1.
*> \endverbatim
*
*__Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>___    _  N is INTEGER
*> _        The_order of the_elementary reflector.
*> \endverbatim
*>
*> \param[in,out] ALPHA
*>_\verbatim
*>__        ALPHA is_COMPLEX
*> _  _     On entry, the value alpha.
*>_      _  On exit, it is overwritten with the value beta.
*>_\endverbatim
*>
*> \param[in,out] X
*> \verbatim
*>    _     X is_COMPLEX array, dimension
*> __      ____  _  _  _ _ (1+(N-2)*abs(INCX))