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.

lartg: generate plane rotation, more accurate than BLAS rot,

lartgp: generate plane rotation, more accurate than BLAS rot

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.

Weslley Pereira, University of Colorado Denver, USA

December 2021

 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