DLARFG(3)

💅 DLARFG(3) — Library Functions Manual ✨

okay bestie, welcome to the DLARFG(3) page from the Library Functions Manual — it’s giving linear algebra main character energy and we’re gonna read it together, no cap. 🫶

📛 NAME

This page is literally about this file path:

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

🛠️ SYNOPSIS

Functions/Subroutines

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

📘 Function/Subroutine Documentation

Here’s the exact signature, slay:

subroutine DLARFG (integer n, double precision alpha, double precision,
    dimension( * ) x, integer incx, double precision tau)

DLARFG generates an elementary reflector (Householder matrix).

🎯 Purpose

The purpose is giving real elementary reflector realness. Here’s the exact math tea ☕:

!>
!> DLARFG 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, 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.
!>
!> Otherwise  1 <= tau <= 2.
!>

🌸 Parameters

N 💫

N is INTEGER. It’s the order of the elementary reflector. iconic.

ALPHA 🍓

ALPHA is DOUBLE PRECISION. On entry, it’s the value alpha. On exit, it is overwritten with the value beta. glow-up moment, honestly.

X 🦋

X is a DOUBLE PRECISION array, dimension (1+(N-2)*abs(INCX)). On entry, it’s the vector x. On exit, it is overwritten with the vector v. she transformed 💅.

INCX ⚡

INCX is INTEGER. It’s the increment between elements of X. And bestie, INCX > 0 — periodt.

TAU 🎀

TAU is DOUBLE PRECISION. It’s the value tau.

Author 🫶

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 105 of file dlarfg.f.

🌈 Author

Generated automatically by Doxygen for LAPACK from the source code.

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