SROTG(3)

Hey bestie! Welcome to SROTG(3), a page from the Library Functions Manual ✨. Buckle up, because this is a whole LAPACK BLAS subroutine doc and we are keeping every crumb.

🎀 NAME 🎀

Okay so the NAME section is literally just this path, no cap:

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

Yep. That's the name vibe. 💅

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✨ SYNOPSIS ✨

📚 Functions/Subroutines 📚

Lowkey tiny synopsis, highkey important:

subroutine SROTG (a, b, c, s)
    SROTG

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🦋 Function/Subroutine Documentation 🦋

💅 subroutine SROTG (real(wp) a, real(wp) b, real(wp) c, real(wp) s) 💅

SROTG — that's the line, bestie. Iconic.

💖 Purpose 💖

Here's the actual purpose block, verbatim because we do not mess with math:

!>
!> 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).
!>
!>

👀 See also 👀

The see-also energy is real. Here's the block exactly, including the line break and the rot, bestie:

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

lartgp:         generate plane rotation, more accurate than BLAS rot

🌸 Parameters 🌸

Four scalars, all REAL, all doing their thing:

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

🖋️ Author 🖋️

Edward Anderson, Lockheed Martin. Periodt.

🫶 Contributors 🫶

Weslley Pereira, University of Colorado Denver, USA.

🔥 Further Details 🔥

The citation block, preserving all the academic sparkle:

!>
!>  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 srotg.f90.

🖋️ Author 🖋️

Yep, another Author section. It says: Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie 💖 — LAPACK Version 3.12.0, footer path /home/abui...C/srotg.f90(3), and that's the cute sign-off. Bye 🫶