BLAS/SRC/zrotg.f90(3)      Library Functions Manual      BLAS/SRC/zrotg.f90(3)

NAME
       BLAS/SRC/zrotg.f90

SYNOPSIS
   Functions/Subroutines
       subroutine zrotg (a, b, c, s)
           ZROTG generates a Givens rotation with real cosine and complex
           sine.

Function/Subroutine Documentation
   subroutine zrotg (complex(wp) a, complex(wp) b, real(wp) c, complex(wp) s)
       ZROTG generates a Givens rotation with real cosine and complex sine.

       Purpose:


            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.

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

           lartgp:         generate plane rotation, more accurate than BLAS
           rot

       Parameters
           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.

       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 88 of file zrotg.f90.

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

LAPACK                          Version 3.12.0           BLAS/SRC/zrotg.f90(3)