SRC/slartg.f90(3)

💅 SRC/slartg.f90(3) 💅

Library Functions Manual — okay bestie, this is the page for SRC/slartg.f90, and it is literally all about generating a plane rotation with real cosine and real sine. Slay. ✨

✨ NAME ✨

SRC/slartg.f90

🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine slartg (f, g, c, s, r) — SLARTG generates a plane rotation with real cosine and real sine.

🎀 Function/Subroutine Documentation 🎀

💖 subroutine slartg (real(wp) f, real(wp) g, real(wp) c, real(wp) s, real(wp) r) 💖

subroutine slartg (real(wp) f, real(wp) g, real(wp) c, real(wp) s, real(wp)
       r)

SLARTG generates a plane rotation with real cosine and real sine. Iconic behavior, no cap. 💅

🌟 Purpose 🌟

SLARTG generates a plane rotation so that

   [  C  S  ]  .  [ F ]  =  [ R ]
   [ -S  C  ]     [ G ]     [ 0 ]

where C**2 + S**2 = 1.

The mathematical formulas used for C and S are

R = sign(F) * sqrt(F**2 + G**2)
C = F / R
S = G / R

Hence C >= 0. The algorithm used to compute these quantities incorporates scaling to avoid overflow or underflow in computing the square root of the sum of squares. Very careful, very demure. 🎀

🚨 Caveat bestie: this version is discontinuous in R at F = 0, but it returns the same C and S as CLARTG for complex inputs (F,0) and (G,0).

This is a more accurate version of the BLAS1 routine SROTG, with the following other differences:

• F and G are unchanged on return.
• If G=0, then C=1 and S=0.
• If F=0 and (G .ne. 0), then C=0 and S=sign(1,G) without doing any floating point operations (saves work in SBDSQR when there are zeros on the diagonal).
• Below, wp=>sp stands for single precision from LA_CONSTANTS module.

🌸 Parameters 🌸

• F — F is REAL(wp). The first component of vector to be rotated.
• G — G is REAL(wp). The second component of vector to be rotated.
• C — C is REAL(wp). The cosine of the rotation.
• S — S is REAL(wp). The sine of the rotation.
• R — R is REAL(wp). The nonzero component of the rotated vector.

👑 Author 👑

Edward Anderson, Lockheed Martin

📅 Date 📅

July 2016

🫶 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 110 of file slartg.f90.

🌈 Author 🌈

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, source SRC/slartg.f90(3), date July 2016. Periodt. 💖