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
!>
!>