zlarfg.f(3)

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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