SRC/zlarfg.f(3)

NAME
SRC/zlarfg.f

SYNOPSIS

  Functions/Subroutines
subroutine zlarfg (n, alpha, x, incx, tau)
ZLARFG generates an elementary reflector (Householder matrix).

Function/Subroutine Documentation

  subroutine zlarfg (integer n, complex*16 alpha, complex*16, dimension( * ) x, integer incx, complex*16 tau)

ZLARFG generates an elementary reflector (Householder matrix).

Purpose:

    !>
    !> ZLARFG 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*16
    !>          On entry, the value alpha.
    !>          On exit, it is overwritten with the value beta.
    !>

    X

    !>          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.
    !>

    INCX

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

    TAU

    !>          TAU is COMPLEX*16
    !>          The value tau.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 105 of file zlarfg.f.

Author

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