SRC/clartg.f90(3)

✨ NAME ✨

SRC/clartg.f90 — okay bestie, welcome to the SRC/clartg.f90 page from the Library Functions Manual. This is the file that’s giving “plane rotation with real cosine and complex sine” energy, and we’re gonna get into all of it. 💅

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🎀 SYNOPSIS 🎀

Functions/Subroutines

subroutine clartg (f, g, c, s, r)
    CLARTG generates a plane rotation with real cosine and complex sine.

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🌸 Function/Subroutine Documentation 🌸

subroutine clartg (complex(wp) f, complex(wp) g, real(wp) c, complex(wp) s, complex(wp) r)

CLARTG generates a plane rotation with real cosine and complex sine. Slay. ✨

Purpose

Okay so here’s the whole mathematical vibe, copied exactly because the formulas are literally the main character:

!>
!> CLARTG generates a plane rotation so that
!>
!>    [  C         S  ] . [ F ]  =  [ R ]
!>    [ -conjg(S)  C  ]   [ G ]     [ 0 ]
!>
!> where C is real and C**2 + |S|**2 = 1.
!>
!> The mathematical formulas used for C and S are
!>
!>    sgn(x) = {  x / |x|,   x != 0
!>             {  1,         x  = 0
!>
!>    R = sgn(F) * sqrt(|F|**2 + |G|**2)
!>
!>    C = |F| / sqrt(|F|**2 + |G|**2)
!>
!>    S = sgn(F) * conjg(G) / sqrt(|F|**2 + |G|**2)
!>
!> Special conditions:
!>    If G=0, then C=1 and S=0.
!>    If F=0, then C=0 and S is chosen so that R is real.
!>
!> When F and G are real, the formulas simplify to C = F/R and
!> S = G/R, and the returned values of C, S, and R should be
!> identical to those returned by SLARTG.
!>
!> 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 is the same routine CROTG fom BLAS1, except that
!> F and G are unchanged on return.
!>
!> Below, wp=>sp stands for single precision from LA_CONSTANTS module.
!>

Bestie, note the exact warning-ish lore: this is the same routine CROTG fom BLAS1, except that F and G are unchanged on return. Also yes, “fom” is literally in the original, so we’re keeping it. 😭

Parameters

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

Author

Weslley Pereira, University of Colorado Denver, USA. 🫶

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
!>
!>

Definition at line 115 of file clartg.f90.

That’s the exact line, bestie: 115 of clartg.f90. 📍

Author

Generated automatically by Doxygen for LAPACK from the source code. So not a human bestie, a whole documentation machine. 💀

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byeee bestie 🫶 this whole lil page is from LAPACK Version 3.12.0, date December 2021, and the footer tag is SRC/clartg.f90(3) — mwah 💋✨