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

    !>          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, 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

    !>          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

Generated automatically by Doxygen for LAPACK from the source code.