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

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