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
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0               SRC/dlartg.f90(3)