dlartg()

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

[in]	F	F is REAL(wp) The first component of vector to be rotated.
[in]	G	G is REAL(wp) The second component of vector to be rotated.
[out]	C	C is REAL(wp) The cosine of the rotation.
[out]	S	S is REAL(wp) The sine of the rotation.
[out]	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.

   use la_constants, &
   only: wp=>dp, zero=>dzero, half=>dhalf, one=>done, &
         safmin=>dsafmin, safmax=>dsafmax
!
!  -- LAPACK auxiliary routine --
!  -- LAPACK is a software package provided by Univ. of Tennessee,    --
!  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
!     February 2021
!
!  .. Scalar Arguments ..
   real(wp) :: c, f, g, r, s
!  ..
!  .. Local Scalars ..
   real(wp) :: d, f1, fs, g1, gs, u, rtmin, rtmax
!  ..
!  .. Intrinsic Functions ..
   intrinsic :: abs, sign, sqrt
!  ..
!  .. Constants ..
   rtmin = sqrt( safmin )
   rtmax = sqrt( safmax/2 )
!  ..
!  .. Executable Statements ..
!
   f1 = abs( f )
   g1 = abs( g )
   if( g == zero ) then
      c = one
      s = zero
      r = f
   else if( f == zero ) then
      c = zero
      s = sign( one, g )
      r = g1
   else if( f1 > rtmin .and. f1 < rtmax .and. &
            g1 > rtmin .and. g1 < rtmax ) then
      d = sqrt( f*f + g*g )
      c = f1 / d
      r = sign( d, f )
      s = g / r
   else
      u = min( safmax, max( safmin, f1, g1 ) )
      fs = f / u
      gs = g / u
      d = sqrt( fs*fs + gs*gs )
      c = abs( fs ) / d
      r = sign( d, f )
      s = gs / r
      r = r*u
   end if
   return

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