dlarfg.f - Man Page

subroutine dlarfg (n, alpha, x, incx, tau)
DLARFG generates an elementary reflector (Householder matrix).

DLARFG generates an elementary reflector (Householder matrix).  

Purpose:

 DLARFG 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, 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.

 Otherwise  1 <= tau <= 2.

Parameters

N

          N is INTEGER
          The order of the elementary reflector.

ALPHA

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

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.

INCX

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

TAU

          TAU is DOUBLE PRECISION
          The value tau.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 105 of file dlarfg.f.