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)