ZLARTG(3)

💅 ZLARTG(3) 💅

okay bestie, welcome to the Library Functions Manual page for ZLARTG. We're gonna make this rotation routine make sense, no cap. ✨

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✨ NAME ✨

The NAME tea is literally this path, character for character:

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

✨ SYNOPSIS ✨

Functions/Subroutines

   Functions/Subroutines
       subroutine ZLARTG (f, g, c, s, r)
           ZLARTG generates a plane rotation with real cosine and complex sine.

🦋 Function/Subroutine Documentation 🦋

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

ZLARTG generates a plane rotation with real cosine and complex sine. That's the whole vibe. 💫

✨ Purpose ✨

okay so the main character moment: ZLARTG 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, bestie:

• 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 DLARTG.

The algorithm used to compute these quantities incorporates scaling to avoid overflow or underflow in computing the square root of the sum of squares. Safety first, always. 💅

This is the same routine ZROTG fom BLAS1, except that F and G are unchanged on return.

Below, wp=>dp stands for double precision from LA_CONSTANTS module.

🎀 Parameters 🎀

• F — F is COMPLEX(wp). The first component of vector to be rotated.
• G — G is COMPLEX(wp). The second component of vector to be rotated.
• C — C is REAL(wp). The cosine of the rotation.
• S — S is COMPLEX(wp). The sine of the rotation.
• R — 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 zlartg.f90.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

mwah 💋 this page is sourced from LAPACK Version 3.12.0, dated December 2021, and the file is /home/abui.../zlartg.f90(3). Byeee 🫶