zlarfg (3) - Linux Manuals

NAME

zlarfg.f -

SYNOPSIS

Functions/Subroutines

subroutine zlarfg (N, ALPHA, X, INCX, TAU)
ZLARFG generates an elementary reflector (Householder matrix).

Function/Subroutine Documentation

subroutine zlarfg (integerN, complex*16ALPHA, complex*16, dimension( * )X, integerINCX, complex*16TAU)

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:

September 2012

Definition at line 107 of file zlarfg.f.

Author

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