DLARTG(3)

DLARTG(3) 💅✨

okay bestie, welcome to this Library Functions Manual page for DLARTG(3). It’s giving real cosine + real sine rotation, and the math is iconic. No cap, every detail is here.

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🌸 NAME 🌸

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

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✨ SYNOPSIS ✨

Functions/Subroutines

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

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💖 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.

Purpose:

okay so the whole point, bestie: 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.

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 (Doxygen edition)

Generated automatically by Doxygen for LAPACK from the source code.

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