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## dlarfgp()

subroutine dlarfgp | ( | integer | n,
|  | double precision | alpha,
|  | double precision, dimension( * ) | x,
|  | integer | incx,
|  | double precision | tau )

DLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.

Download DLARFGP + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> 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.
      !>

Parameters

  [in]

  N

      !>          N is INTEGER
      !>          The order of the elementary reflector.
      !>

  [in,out]

  ALPHA

      !>          ALPHA is DOUBLE PRECISION
      !>          On entry, the value alpha.
      !>          On exit, it is overwritten with the value beta.
      !>

  [in,out]

  X

      !>          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.
      !>

  [in]

  INCX

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

  [out]

  TAU

      !>          TAU is DOUBLE PRECISION
      !>          The value tau.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.