crotg()

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:

 CROTG 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 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

[in,out]	A	A is COMPLEX On entry, the scalar a. On exit, the scalar r.
[in]	B	B is COMPLEX The scalar b.
[out]	C	C is REAL The scalar c.
[out]	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