LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ clartg()

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

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

Purpose:
 CLARTG 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)

 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 CLARTG.

 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 a faster version of the BLAS1 routine CROTG, except for
 the following differences:
    F and G are unchanged on return.
    If G=0, then C=1 and S=0.
    If F=0, then C=0 and S is chosen so that R is real.

 Below, wp=>sp stands for single 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
Edward Anderson, Lockheed Martin
Date
August 2016
Contributors:
Weslley Pereira, University of Colorado Denver, USA
Further Details:
  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