zrotg.f90 - Man Page
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.
Referenced By
The man page zrotg(3) is an alias of zrotg.f90(3).
Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK