table of contents
| 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.
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.
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.
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.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |