zlarfg.f man page

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.

Date:

November 2017

Definition at line 108 of file zlarfg.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page zlarfg(3) is an alias of zlarfg.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK