Man page - larfgp(3)

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Manual

larfgp

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine clarfgp (integer n, complex alpha, complex, dimension( * ) x,integer incx, complex tau)
subroutine dlarfgp (integer n, double precision alpha, double precision,dimension( * ) x, integer incx, double precision tau)
subroutine slarfgp (integer n, real alpha, real, dimension( * ) x, integerincx, real tau)
subroutine zlarfgp (integer n, complex*16 alpha, complex*16, dimension( * )x, integer incx, complex*16 tau)
Author

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

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 Tennessee

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

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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine slarfgp (integer n, real alpha, real, dimension( * ) x, integerincx, 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

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 Tennessee

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

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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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