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larfgp(3) LAPACK 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

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Tue Jun 30 2026 04:57:07 Version 3.12.0