SRC/clarfg.f(3)            Library Functions Manual            SRC/clarfg.f(3)

NAME
       SRC/clarfg.f

SYNOPSIS
   Functions/Subroutines
       subroutine clarfg (n, alpha, x, incx, tau)
           CLARFG generates an elementary reflector (Householder matrix).

Function/Subroutine Documentation
   subroutine clarfg (integer n, complex alpha, complex, dimension( * ) x,
       integer incx, complex tau)
       CLARFG generates an elementary reflector (Householder matrix).

       Purpose:


            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 .

       Parameters
           N

                     N is INTEGER
                     The order of the elementary reflector.

           ALPHA

                     ALPHA is COMPLEX
                     On entry, the value alpha.
                     On exit, it is overwritten with the value beta.

           X

                     X is COMPLEX array, dimension
                                    (1+(N-2)*abs(INCX))
                     On entry, the vector x.
                     On exit, it is overwritten with the vector v.

           INCX

                     INCX is INTEGER
                     The increment between elements of X. INCX > 0.

           TAU

                     TAU is COMPLEX
                     The value tau.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 105 of file clarfg.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/clarfg.f(3)