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| larfgp(3) | LAPACK | larfgp(3) |
NAME
larfgp - larfgp: generate Householder reflector, beta ≥ 0
SYNOPSIS
Functions
subroutine clarfgp (n, alpha, x, incx, tau)
CLARFGP generates an elementary reflector (Householder matrix) with
non-negative beta. subroutine dlarfgp (n, alpha, x, incx, tau)
DLARFGP generates an elementary reflector (Householder matrix) with
non-negative beta. subroutine slarfgp (n, alpha, x, incx, tau)
SLARFGP generates an elementary reflector (Householder matrix) with
non-negative beta. subroutine zlarfgp (n, alpha, x, incx, tau)
ZLARFGP generates an elementary reflector (Householder matrix) with
non-negative beta.
Detailed Description
Function Documentation
subroutine clarfgp (integer n, complex alpha, complex, dimension( * ) x, integer incx, complex tau)
CLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.
Purpose:
CLARFGP 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, beta is real and non-negative, 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.
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.
Definition at line 103 of file clarfgp.f.
subroutine dlarfgp (integer n, double precision alpha, double precision, dimension( * ) x, integer incx, double precision tau)
DLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.
Purpose:
DLARFGP 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, beta is non-negative, 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.
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.
Definition at line 103 of file dlarfgp.f.
subroutine slarfgp (integer n, real alpha, real, dimension( * ) x, integer incx, real tau)
SLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.
Purpose:
SLARFGP 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, beta is non-negative, 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.
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.
Definition at line 103 of file slarfgp.f.
subroutine zlarfgp (integer n, complex*16 alpha, complex*16, dimension( * ) x, integer incx, complex*16 tau)
ZLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.
Purpose:
ZLARFGP 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, beta is real and non-negative, 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.
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.
Definition at line 103 of file zlarfgp.f.
Author
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