CROTG(3)

💅 CROTG(3) — Library Functions Manual ✨

okay bestie, buckle up 🫶 this is the CROTG page straight outta the Library Functions Manual, and it's genuinely iconic. we're doing Givens rotations today and you're gonna slay it, no cap.

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📛 NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/BLAS/SRC/crotg.f90

like yes, that's the whole name, it's giving "full government name at the DMV" energy but that's literally what the page says 💀

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🌸 SYNOPSIS

Functions/Subroutines

• subroutine CROTG (a, b, c, s) — CROTG generates a Givens rotation with real cosine and complex sine. 💫

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🧚 Function/Subroutine Documentation

subroutine CROTG (complex(wp) a, complex(wp) b, real(wp) c, complex(wp) s)

CROTG generates a Givens rotation with real cosine and complex sine. that's the whole vibe, bestie 👑

✨ Purpose

okay so here's what it actually does — CROTG constructs a plane rotation, and the way it looks is:

!> CROTG constructs a plane rotation
!>    [  c         s ] [ a ] = [ r ]
!>    [ -conjg(s)  c ] [ b ]   [ 0 ]
!> where c is real, s is complex, and c**2 + conjg(s)*s = 1.
!>
!> The computation uses the formulas
!>    |x| = sqrt( Re(x)**2 + Im(x)**2 )
!>    sgn(x) = x / |x|  if x /= 0
!>           = 1        if x  = 0
!>    c = |a| / sqrt(|a|**2 + |b|**2)
!>    s = sgn(a) * conjg(b) / sqrt(|a|**2 + |b|**2)
!>    r = sgn(a)*sqrt(|a|**2 + |b|**2)
!> When a and b are real and r /= 0, the formulas simplify to
!>    c = a / r
!>    s = b / r
!> the same as in SROTG when |a| > |b|.  When |b| >= |a|, the
!> sign of c and s will be different from those computed by SROTG
!> if the signs of a and b are not the same.
!>
!>

like, the math is mathing 🧮✨ and the c is real, s is complex, and c**2 + conjg(s)*s = 1 — that's the whole personality of this rotation.

👀 See also

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

ngl if you need the more accurate one, the LARTG girlies have you covered 💅

🎀 Parameters

• A

!>          A is COMPLEX
!>          On entry, the scalar a.
!>          On exit, the scalar r.
!>

so A goes in as a and comes out as r — it's giving main character transformation arc, we love a glow-up 🦋

• B

!>          B is COMPLEX
!>          The scalar b.
!>

• C

!>          C is REAL
!>          The scalar c.
!>

• S

!>          S is COMPLEX
!>          The scalar s.
!>

👑 Author

Weslley Pereira, University of Colorado Denver, USA — periodt, thank you Weslley 🫶

📅 Date

December 2021

🔍 Further Details:

!>
!> Based on the algorithm from
!>
!>  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
!>
!>

so it's built on Anderson E. (2017), "Algorithm 978: Safe Scaling in the Level 1 BLAS", ACM Trans Math Softw 44:1--28, over at https://doi.org/10.1145/3061665 — cite your sources bestie, it's the law 📚💖

Definition at line 88 of file crotg.f90.

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🌈 Author

Generated automatically by Doxygen for LAPACK from the source code. not me being auto-generated 💀 the robots did this one, I'm just the messenger ✨

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and that's the whole page!! 💜 the footer says this is LAPACK, Version 3.12.0, dated /home/abui...C/crotg.f90(3) — so yeah, that's the source/version/date sign-off, mwah, go rotate some planes responsibly 🎀🌸🔥