BLAS/SRC/zrotg.f90(3)

🦋 NAME 🦋

Okay bestie, this is the page for BLAS/SRC/zrotg.f90(3) — and yes, it’s giving Library Functions Manual energy. The main character is the zrotg subroutine, and it’s here to construct a Givens rotation with a real cosine and a complex sine. Slay. 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine zrotg (a, b, c, s)
    ZROTG generates a Givens rotation with real cosine and complex sine.

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💅 Function/Subroutine Documentation 💅

subroutine zrotg (complex(wp) a, complex(wp) b, real(wp) c, complex(wp) s)

ZROTG generates a Givens rotation with real cosine and complex sine. No cap, that’s the whole vibe check for this subroutine.

Purpose:

!>
!> ZROTG constructs a plane rotation
!>    [  c         s ] [ a ] = [ r ]
!>    [ -conjg(s)  c ] [ b ]   [ 0 ]
!> where c is real, s is complex, and c**2 + conjg(s)*s = 1.
!>
!> The computation uses the formulas
!>    |x| = sqrt( Re(x)**2 + Im(x)**2 )
!>    sgn(x) = x / |x|  if x /= 0
!>           = 1        if x  = 0
!>    c = |a| / sqrt(|a|**2 + |b|**2)
!>    s = sgn(a) * conjg(b) / sqrt(|a|**2 + |b|**2)
!>    r = sgn(a)*sqrt(|a|**2 + |b|**2)
!> When a and b are real and r /= 0, the formulas simplify to
!>    c = a / r
!>    s = b / r
!> the same as in DROTG when |a| > |b|.  When |b| >= |a|, the
!> sign of c and s will be different from those computed by DROTG
!> if the signs of a and b are not the same.
!>
!>

See also

• lartg: generate plane rotation, more accurate than BLAS rot,
• lartgp: generate plane rotation, more accurate than BLAS rot

Parameters

• A — A is DOUBLE COMPLEX. On entry, the scalar a. On exit, the scalar r. 🫶
• B — B is DOUBLE COMPLEX. The scalar b.
• C — C is DOUBLE PRECISION. The scalar c.
• S — S is DOUBLE COMPLEX. The scalar s.

Author

Weslley Pereira, University of Colorado Denver, USA. Iconic. 👑

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 88 of file zrotg.f90.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. Automation ate, honestly. ✨

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Okay that’s the whole page, bestie! This tea was served by LAPACK Version 3.12.0 for BLAS/SRC/zrotg.f90(3), with December 2021 date energy. 🫶💖🎀