LAPACK  3.5.0
LAPACK: Linear Algebra PACKage
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dlarfg.f File Reference

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Functions/Subroutines

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

Function/Subroutine Documentation

subroutine dlarfg ( integer  N,
double precision  ALPHA,
double precision, dimension( * )  X,
integer  INCX,
double precision  TAU 
)

DLARFG generates an elementary reflector (Householder matrix).

Download DLARFG + dependencies [TGZ] [ZIP] [TXT]
Purpose:
 DLARFG generates a real elementary reflector H of order n, such
 that

       H * ( alpha ) = ( beta ),   H**T * H = I.
           (   x   )   (   0  )

 where alpha and beta are scalars, and x is an (n-1)-element real
 vector. H is represented in the form

       H = I - tau * ( 1 ) * ( 1 v**T ) ,
                     ( v )

 where tau is a real scalar and v is a real (n-1)-element
 vector.

 If the elements of x are all zero, then tau = 0 and H is taken to be
 the unit matrix.

 Otherwise  1 <= tau <= 2.
Parameters
[in]N
          N is INTEGER
          The order of the elementary reflector.
[in,out]ALPHA
          ALPHA is DOUBLE PRECISION
          On entry, the value alpha.
          On exit, it is overwritten with the value beta.
[in,out]X
          X is DOUBLE PRECISION 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 DOUBLE PRECISION
          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 dlarfg.f.

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