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

    !>          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, 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

    !>          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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