LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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zlarfg.f File Reference

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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).

Download ZLARFG + dependencies [TGZ] [ZIP] [TXT]
 ZLARFG generates a complex elementary reflector H of order n, such

       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 .
          N is INTEGER
          The order of the elementary reflector.
          ALPHA is COMPLEX*16
          On entry, the value alpha.
          On exit, it is overwritten with the value beta.
          X is COMPLEX*16 array, dimension
          On entry, the vector x.
          On exit, it is overwritten with the vector v.
          INCX is INTEGER
          The increment between elements of X. INCX > 0.
          TAU is COMPLEX*16
          The value tau.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
September 2012

Definition at line 107 of file zlarfg.f.

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