larfg(3)

Library Functions Manual

larfg(3)

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 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 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.

Definition at line 105 of file clarfg.f.

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 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 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.

Definition at line 105 of file dlarfg.f.

subroutine slarfg (integer n, real alpha, real, dimension( * ) x, integer incx, 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 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 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.

Definition at line 105 of file slarfg.f.

subroutine zlarfg (integer n, complex16 alpha, complex16, 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 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 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.

Definition at line 105 of file zlarfg.f.

Author

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