BLAS/SRC/zrotg.f90(3) | Library Functions Manual | BLAS/SRC/zrotg.f90(3) |
NAME
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
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