SRC/clartg.f90(3)          Library Functions Manual          SRC/clartg.f90(3)

NAME
       SRC/clartg.f90

SYNOPSIS
   Functions/Subroutines
       subroutine clartg (f, g, c, s, r)
           CLARTG generates a plane rotation with real cosine and complex
           sine.

Function/Subroutine Documentation
   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)
           !>
           !> 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 SLARTG.
           !>
           !> 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 CROTG fom BLAS1, except that
           !> F and G are unchanged on return.
           !>
           !> Below, wp=>sp stands for single precision from LA_CONSTANTS module.
           !>

       Parameters
           F

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

           G

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

           C

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

           S

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

           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
           !>
           !>

       Definition at line 115 of file clartg.f90.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0               SRC/clartg.f90(3)