CLARFG(3)

💅 CLARFG (3) — from the Library Functions Manual 🎀

So bestie, the file we're talking about is literally this one:

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

That's the NAME section, yeah — it's a Fortran source file, iykyk. ✨

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines

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

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🌸 Function/Subroutine Documentation 🌸

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

CLARFG generates an elementary reflector (Householder matrix). periodt. 👑

💖 Purpose:

!>
!> CLARFG 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, with beta 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. 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.
!>
!> Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1 .
!>

Okay so like, translation bestie: you hand it a scalar alpha and a vector x, and it builds you a complex elementary reflector H of order n that zeroes out x and leaves you with a real beta. Math slay. 🔥

Big mood notes though, fr fr:

• H is NOT hermitian — the page says it right there, don't come for me. 🙈
• If every element of x is zero and alpha is real → tau = 0 and H is just the unit matrix. Chill. 💅
• Otherwise you get 1 <= real(tau) <= 2 and abs(tau-1) <= 1. Those are the bounds, no cap. ⭐

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🎀 Parameters

• N

!>          N is INTEGER
!>          The order of the elementary reflector.

It's an INTEGER, and it's literally the order of the elementary reflector. Main character parameter. ✨

• ALPHA

!>          ALPHA is COMPLEX
!>          On entry, the value alpha.
!>          On exit, it is overwritten with the value beta.

COMPLEX. Comes in as alpha, leaves as beta — she gets a whole glow-up on the way out. 💖 overwritten, bestie, so don't go looking for alpha afterwards.

• 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.

COMPLEX array, dimension (1+(N-2)*abs(INCX)) — copy that exactly, it's giving "you will need this many elements" energy. Goes in as x, comes out as v. 🦋

• INCX

!>          INCX is INTEGER
!>          The increment between elements of X. INCX > 0.

INTEGER, the stride between elements of X, and INCX > 0 — that's a requirement, not a suggestion, okay? 😭

• TAU

!>          TAU is COMPLEX
!>          The value tau.

COMPLEX, and it's the value tau. Short king, does its job. 🫶

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🌈 Author

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

The whole squad, icons only. 👑

⭐ Definition at line 105 of file clarfg.f.

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💜 Author (again, but the meta one)

Generated automatically by Doxygen for LAPACK from the source code. Not me writing it by hand, the robots did that part. 🧚

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Quick vibe check before you go: TAU is an output, ALPHA and X get overwritten, and H is not hermitian. That's the whole tea. 🍓

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~ and that's the page, bestie ~ 💅✨ This little number comes from LAPACK, Version 3.12.0, and the source file lives at /home/abui...RC/clarfg.f(3) — go off, Householder icon. 🎀🦋💖