BLAS/SRC/crotg.f90(3)

💖 NAME

Okay bestie, this is the BLAS/SRC/crotg.f90 page from the Library Functions Manual, and it’s all about crotg — the BLAS subroutine that builds a Givens rotation with a real cosine and a complex sine. ✨

🎀 SYNOPSIS

Functions/Subroutines

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

Here’s the full signature, exactly as promised:

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

CROTG generates a Givens rotation with real cosine and complex sine. 🫶

💅 Function/Subroutine Documentation

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

CROTG generates a Givens rotation with real cosine and complex sine.

✨ Purpose

Okay so CROTG constructs a plane rotation, and the matrix situation is literally this:

[  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 SROTG when |a| > |b|. When |b| >= |a|, the sign of c and s will be different from those computed by SROTG 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 COMPLEX. On entry, the scalar a. On exit, the scalar r.
• B — B is COMPLEX. The scalar b.
• C — C is REAL. The scalar c.
• S — S is 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 crotg.f90.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole page, bestie — final source/version vibe: LAPACK, Version 3.12.0, page BLAS/SRC/crotg.f90(3), with the function dated December 2021. Mwah 💋✨