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## zlartg()

subroutine zlartg | ( | complex(wp) | f,
|  | complex(wp) | g,
|  | real(wp) | c,
|  | complex(wp) | s,
|  | complex(wp) | r )

ZLARTG generates a plane rotation with real cosine and complex sine.

Purpose:

      !>
      !> ZLARTG generates a plane rotation so that
      !>
      !>    [  C         S  ] . [ F ]  =  [ R ]
      !>    [ -conjg(S)  C  ]   [ G ]     [ 0 ]
      !>
      !> where C is real and C**2 + |S|**2 = 1.
      !>
      !> The mathematical formulas used for C and S are
      !>
      !>    sgn(x) = {  x / |x|,   x != 0
      !>             {  1,         x  = 0
      !>
      !>    R = sgn(F) * sqrt(|F|**2 + |G|**2)
      !>
      !>    C = |F| / sqrt(|F|**2 + |G|**2)
      !>
      !>    S = sgn(F) * conjg(G) / sqrt(|F|**2 + |G|**2)
      !>
      !> Special conditions:
      !>    If G=0, then C=1 and S=0.
      !>    If F=0, then C=0 and S is chosen so that R is real.
      !>
      !> When F and G are real, the formulas simplify to C = F/R and
      !> S = G/R, and the returned values of C, S, and R should be
      !> identical to those returned by DLARTG.
      !>
      !> The algorithm used to compute these quantities incorporates scaling
      !> to avoid overflow or underflow in computing the square root of the
      !> sum of squares.
      !>
      !> This is the same routine ZROTG fom BLAS1, except that
      !> F and G are unchanged on return.
      !>
      !> Below, wp=>dp stands for double precision from LA_CONSTANTS module.
      !>

Parameters

  [in]

  F

      !>          F is COMPLEX(wp)
      !>          The first component of vector to be rotated.
      !>

  [in]

  G

      !>          G is COMPLEX(wp)
      !>          The second component of vector to be rotated.
      !>

  [out]

  C

      !>          C is REAL(wp)
      !>          The cosine of the rotation.
      !>

  [out]

  S

      !>          S is COMPLEX(wp)
      !>          The sine of the rotation.
      !>

  [out]

  R

      !>          R is COMPLEX(wp)
      !>          The nonzero component of the rotated vector.
      !>

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
      !>
      !>