ZLARFG(3)

📦 version 3.12.0, in opensuse-leap 16.0

🌸 NAME 🌸

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

okay so this page lives in the Library Functions Manual, and the header path is shown as /home/abui...RC/zlarfg.f(3) — twice, because apparently it needed main character energy. The NAME is literally that build path up there. 💅

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine ZLARFG (n, alpha, x, incx, tau)
    ZLARFG generates an elementary reflector (Householder matrix).

💖 Function/Subroutine Documentation 💖

subroutine ZLARFG (integer n, complex*16 alpha, complex*16, dimension( * )
       x, integer incx, complex*16 tau)

ZLARFG generates an elementary reflector (Householder matrix). No cap. 👑

✨ Purpose ✨

So, bestie, ZLARFG generates a complex elementary reflector H of order n, such that:

H**H * ( alpha ) = ( beta ),   H**H * H = I.
       (   x   )   (   0  )

Here alpha and beta are scalars, beta is real, 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. Important vibe check: H is not hermitian. Periodt.

If all the elements of x are zero and alpha is real, then tau = 0 and H is taken to be the unit matrix.

Otherwise, 1 <= real(tau) <= 2 and abs(tau-1) <= 1.

🎀 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.

Definition at line 105 of file zlarfg.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

source/version: LAPACK, Version 3.12.0; path: /home/abui...RC/zlarfg.f(3); date: not printed on this page — mwah, bye bestie 💜

📦 where this page comes from