BLAS/SRC/drotg.f90(3)

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version 3.12.1 · 3 versions
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✨ BLAS/SRC/drotg.f90(3) ✨

Library Functions Manual? Bestie, we're deep in the manual-verse and the page name is BLAS/SRC/drotg.f90. It's giving BLAS rotation realness, and yes, DROTG is the main character. 💅

🌸 NAME 🌸

BLAS/SRC/drotg.f90 — that's the name, and that's the page. Periodt.

🦋 SYNOPSIS 🦋

Functions/Subroutines

  • subroutine drotg (a, b, c, s) — DROTG

🎀 Function/Subroutine Documentation 🎀

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

DROTG

✨ Purpose ✨

Okay so DROTG constructs a plane rotation, and the whole point is this matrix situation right here:

!> DROTG 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).
!>
!>

Yes, that's the exact formula block, no cap. The z stash is lowkey giving "save it for later" energy so c and s can be reconstructed — iconic. 👑

👀 See also 👀

  • lartg: generate plane rotation, more accurate than BLAS rot,
  • lartgp: generate plane rotation, more accurate than BLAS rot

💖 Parameters 💖

  • A — A is DOUBLE PRECISION. On entry, the scalar a. On exit, the scalar r.
  • B — B is DOUBLE PRECISION. On entry, the scalar b. On exit, the scalar z.
  • C — C is DOUBLE PRECISION. The scalar c.
  • S — S is DOUBLE PRECISION. The scalar s.

🌟 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
!>
!>

Definition at line 91 of file drotg.f90.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

✨ Okay bestie, that's the whole page! Cute footer sign-off: LAPACK Version 3.12.0 · BLAS/SRC/drotg.f90(3) — no extra date in this footer, just the version-and-source energy. 🎀

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