SRC/dlartg.f90(3)

SRC/dlartg.f90(3) 💅✨

okay bestie, welcome to the Library Functions Manual — this page is SRC/dlartg.f90, and it's all about DLARTG doing plane-rotation math with real cosine and real sine. it's giving linear algebra main character energy. 🫶

🌸 NAME 🌸

SRC/dlartg.f90 💖

✨ SYNOPSIS ✨

Functions/Subroutines

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

       subroutine dlartg (f, g, c, s, r)
           DLARTG generates a plane rotation with real cosine and real sine.

🧚 Function/Subroutine Documentation 🧚

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

DLARTG generates a plane rotation with real cosine and real sine. periodt. 👑

Purpose

okay so DLARTG 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. no cap, that's the safety bit. 💅

This version is discontinuous in R at F = 0 but it returns the same C and S as ZLARTG for complex inputs (F,0) and (G,0). 🌀

This is a more accurate version of the BLAS1 routine DROTG, 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 DBDSQR when there are zeros on the diagonal). 💀

Below, wp=>dp stands for double 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 dlartg.f90. 📍

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code. 🤖

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that's the whole page, bestie — mwah 💋 this is LAPACK, Version 3.12.0, page SRC/dlartg.f90(3), and the doc date is July 2016. go rotate something cute. 🎀🦋