BLAS/SRC/srotg.f90(3)

📦
version 3.12.1 · 3 versions
, in arch rolling

💅 BLAS/SRC/srotg.f90 ✨

okay bestie, buckle up — this is the manual page for BLAS/SRC/srotg.f90, which is a very specific little gem in the LAPACK/BLAS universe. it's the home of srotg, a Fortran subroutine that builds plane rotations, and honestly? it's giving main character energy for something so small. 🎀

✨ SYNOPSIS ✨

Functions/Subroutines

  • subroutine srotg (a, b, c, s) — the one, the only, SROTG 🌟

🦋 Function/Subroutine Documentation 🦋

subroutine srotg (real(wp) a, real(wp) b, real(wp) c, real(wp) s)

SROTG, periodt. that's the name, that's the vibe. 💜

🎀 Purpose 🎀

okay so picture this — per the original docs, and i'm quoting the vibe here:

!>
!> SROTG constructs a plane rotation
!>    [  c  s ] [ a ] = [ r ]
!>    [ -s  c ] [ b ]   [ 0 ]
!> satisfying c**2 + s**2 = 1.
!>
!> The computation uses the formulas
!>    sigma = sgn(a)    if |a| >  |b|
!>          = sgn(b)    if |b| >= |a|
!>    r = sigma*sqrt( a**2 + b**2 )
!>    c = 1; s = 0      if r = 0
!>    c = a/r; s = b/r  if r != 0
!> The subroutine also computes
!>    z = s    if |a| > |b|,
!>      = 1/c  if |b| >= |a| and c != 0
!>      = 1    if c = 0
!> This allows c and s to be reconstructed from z as follows:
!>    If z = 1, set c = 0, s = 1.
!>    If |z| < 1, set c = sqrt(1 - z**2) and s = z.
!>    If |z| > 1, set c = 1/z and s = sqrt( 1 - c**2).
!>
!>

like, it literally constructs a plane rotation and it does not apologize for it. the way that c**2 + s**2 = 1 just... holds. iconic. 😭💖

🌈 See also 🌈

  • lartg — generate plane rotation, more accurate than BLAS rot, 🌸
  • lartgp — generate plane rotation, more accurate than BLAS rot ✨

(iykyk — if you want the more accurate one, those are your girls.)

👑 Parameters 👑

  • A — A is REAL. On entry, the scalar a. On exit, the scalar r. 🔄 it literally becomes a different thing, no cap.
  • B — B is REAL. On entry, the scalar b. On exit, the scalar z. bestie it transforms too 😭
  • C — C is REAL. The scalar c. 💅
  • S — S is REAL. The scalar s. 🫶
fr fr, watch out — A and B are not the same on the way out. on entry they're a and b, on exit they're r and z. that's the whole plot twist of this subroutine. 🍓

⭐ Author ⭐

Edward Anderson, Lockheed Martin 👑

💜 Contributors: 💜

Weslley Pereira, University of Colorado Denver, USA 🌸

🔥 Further Details: 🔥

!>
!>  Anderson E. (2017)
!>  Algorithm 978: Safe Scaling in the Level 1 BLAS
!>  ACM Trans Math Softw 44:1--28
!>  https://doi.org/10.1145/3061665
!>
!>

like, read the paper, it ate. 📚✨

🧚 Definition 🧚

Definition at line 91 of file srotg.f90. — yes, line 91, we counted. 💀

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code. — Doxygen did the typing, we just did the vibes. 🙈

okay that's the whole page, bestie! and a cute sign-off as promised: this lil masterpiece is from LAPACK, Version 3.12.0, dated BLAS/SRC/srotg.f90(3) — slay, go build your plane rotations. 🎀💅✨

📦 where this page comes from