/home/abui.../slarfgp.f(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 slarfgp.f(3) — bestie edition 💅

okay so this is the slarfgp.f(3) page from the Library Functions Manual, and it's all about making a real elementary reflector (Householder matrix) with non-negative beta. the vibes? linear algebra but make it iconic. 🦋

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slarfgp.f

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

  • subroutine SLARFGP (n, alpha, x, incx, tau) — SLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.

🌸 Function/Subroutine Documentation 🌸

🧚 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 💖

okay so here's the actual math tea, bestie — SLARFGP generates a real elementary reflector H of order n, such that:

!>
!> 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.
!>

highkey the whole personality is in that block: H is a real elementary reflector of order n, alpha and beta are scalars, beta is non-negative, and x is an (n-1)-element real vector. H is represented in the form above, 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. periodt. ✨

🌈 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.

Definition at line 103 of file slarfgp.f.

🌟 Author 🌟

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okay bye bestie! this page is from LAPACK Version 3.12.0, and the path on the page is /home/abui.../slarfgp.f(3). mwah 💋✨

📦 where this page comes from