| larfg(3) | LAPACK | larfg(3) |
larfg - larfg: generate Householder reflector
subroutine clarfg (n, alpha, x, incx, tau)
CLARFG generates an elementary reflector (Householder matrix).
subroutine dlarfg (n, alpha, x, incx, tau)
DLARFG generates an elementary reflector (Householder matrix).
subroutine slarfg (n, alpha, x, incx, tau)
SLARFG generates an elementary reflector (Householder matrix).
subroutine zlarfg (n, alpha, x, incx, tau)
ZLARFG generates an elementary reflector (Householder matrix).
CLARFG generates an elementary reflector (Householder matrix).
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
N is INTEGER
The order of the elementary reflector.
ALPHA
ALPHA is COMPLEX
On entry, the value alpha.
On exit, it is overwritten with the value beta.
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.
INCX
INCX is INTEGER
The increment between elements of X. INCX > 0.
TAU
TAU is COMPLEX
The value tau.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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.
SLARFG generates an elementary reflector (Householder matrix).
Purpose:
SLARFG 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 REAL
On entry, the value alpha.
On exit, it is overwritten with the value beta.
X
X is REAL 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 REAL
The value tau.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
ZLARFG generates an elementary reflector (Householder matrix).
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
N is INTEGER
The order of the elementary reflector.
ALPHA
ALPHA is COMPLEX*16
On entry, the value alpha.
On exit, it is overwritten with the value beta.
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.
INCX
INCX is INTEGER
The increment between elements of X. INCX > 0.
TAU
TAU is COMPLEX*16
The value tau.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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| Thu Aug 7 2025 17:26:25 | Version 3.12.0 |