Man page - larfg(3)

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Manual

larfg

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine clarfg (integer n, complex alpha, complex, dimension( * ) x,integer incx, complex tau)
subroutine dlarfg (integer n, double precision alpha, double precision,dimension( * ) x, integer incx, double precision tau)
subroutine slarfg (integer n, real alpha, real, dimension( * ) x, integerincx, real tau)
subroutine zlarfg (integer n, complex*16 alpha, complex*16, dimension( * )x, integer incx, complex*16 tau)
Author

NAME

larfg - larfg: generate Householder reflector

SYNOPSIS

Functions

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).

Detailed Description

Function Documentation

subroutine clarfg (integer n, complex alpha, complex, dimension( * ) x,integer incx, complex tau)

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

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 dlarfg (integer n, double precision alpha, double precision,dimension( * ) x, integer incx, double precision tau)

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

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 slarfg (integer n, real alpha, real, dimension( * ) x, integerincx, real tau)

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

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 zlarfg (integer n, complex*16 alpha, complex*16, dimension( * )x, integer incx, complex*16 tau)

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

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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