zlarfg.f File Reference

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Functions/Subroutines
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]

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:

[in]	N	N is INTEGER The order of the elementary reflector.
[in,out]	ALPHA	ALPHA is COMPLEX*16 On entry, the value alpha. On exit, it is overwritten with the value beta.
[in,out]	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.
[in]	INCX	INCX is INTEGER The increment between elements of X. INCX > 0.
[out]	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.

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