ZROTG(3)

Manual name: zrotg.f90(3) — Library Functions Manual. Bestie, we’re keeping every single fact, every formula, and every little LAPACK detail. 💅✨

💖 NAME

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

✨ SYNOPSIS

Functions/Subroutines

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

🦋 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.

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

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.

🌸 Author

Generated automatically by Doxygen for LAPACK from the source code.

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Source/version: LAPACK Version 3.12.0 · page path: /home/abui...C/zrotg.f90(3) · date: December 2021. Bye bestie, go slay those rotations! 🫶✨💖