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clarfg.f File Reference

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Functions/Subroutines

subroutine clarfg (N, ALPHA, X, INCX, TAU)
 CLARFG generates an elementary reflector (Householder matrix). More...
 

Function/Subroutine Documentation

subroutine clarfg ( integer  N,
complex  ALPHA,
complex, dimension( * )  X,
integer  INCX,
complex  TAU 
)

CLARFG generates an elementary reflector (Householder matrix).

Download CLARFG + dependencies [TGZ] [ZIP] [TXT]
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
[in]N
          N is INTEGER
          The order of the elementary reflector.
[in,out]ALPHA
          ALPHA is COMPLEX
          On entry, the value alpha.
          On exit, it is overwritten with the value beta.
[in,out]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.
[in]INCX
          INCX is INTEGER
          The increment between elements of X. INCX > 0.
[out]TAU
          TAU is COMPLEX
          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 clarfg.f.

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