subroutine dlarfg (N, ALPHA, X, INCX, TAU)
DLARFG generates an elementary reflector (Householder matrix).
DLARFG generates an elementary reflector (Householder matrix).
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:
N is INTEGER
The order of the elementary reflector.
ALPHA
ALPHA is DOUBLE PRECISION
On entry, the value alpha.
On exit, it is overwritten with the value beta.
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.
INCX
INCX is INTEGER
The increment between elements of X. INCX > 0.
TAU
TAU is DOUBLE PRECISION
The value tau.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Definition at line 108 of file dlarfg.f.
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