carta
clarfgp(3)

clarfgp3

Part of clarfgp.f(3).

Function/Subroutine 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.

Definition at line 103 of file clarfgp.f.

History

  • Arch Linux 2026-11-01: the text shown here
  • Debian 12 (Bookworm)
  • Debian 11 (Bullseye)
  • Debian 10 (Buster)
  • Debian 9 (Stretch)
  • Debian 8 (Jessie)
  • Debian 7 (Wheezy)

Author

Generated automatically by Doxygen for LAPACK from the source code.

From lapack-doc 3.12.1-2 in Arch Linux 2026-11-01. Parsed by carta from the page's man source.