clarfg.f - Man Page

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

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.