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

NAME
       SRC/dlartg.f90

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

Function/Subroutine Documentation
   subroutine dlartg (real(wp) f, real(wp) g, real(wp) c, real(wp) s, real(wp)
       r)
       DLARTG generates a plane rotation with real cosine and real sine.

       Purpose:


           !>
           !> DLARTG generates a plane rotation so that
           !>
           !>    [  C  S  ]  .  [ F ]  =  [ R ]
           !>    [ -S  C  ]     [ G ]     [ 0 ]
           !>
           !> where C**2 + S**2 = 1.
           !>
           !> The mathematical formulas used for C and S are
           !>    R = sign(F) * sqrt(F**2 + G**2)
           !>    C = F / R
           !>    S = G / R
           !> Hence C >= 0. 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 version is discontinuous in R at F = 0 but it returns the same
           !> C and S as ZLARTG for complex inputs (F,0) and (G,0).
           !>
           !> This is a more accurate version of the BLAS1 routine DROTG,
           !> with the following other differences:
           !>    F and G are unchanged on return.
           !>    If G=0, then C=1 and S=0.
           !>    If F=0 and (G .ne. 0), then C=0 and S=sign(1,G) without doing any
           !>       floating point operations (saves work in DBDSQR when
           !>       there are zeros on the diagonal).
           !>
           !> Below, wp=>dp stands for double precision from LA_CONSTANTS module.
           !>

       Parameters
           F

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

           G

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

           C

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

           S

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

           R

           !>          R is REAL(wp)
           !>          The nonzero component of the rotated vector.
           !>

       Author
           Edward Anderson, Lockheed Martin

       Date
           July 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
           !>
           !>

       Definition at line 110 of file dlartg.f90.

Author
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LAPACK                          Version 3.12.0               SRC/dlartg.f90(3)