larfgp(3)

Library Functions Manual

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 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 103 of file clarfgp.f.

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 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 103 of file dlarfgp.f.

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 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 103 of file slarfgp.f.

subroutine zlarfgp (integer n, complex16 alpha, complex16, 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 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 103 of file zlarfgp.f.

Author

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