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!> \brief \b DROTG
!
! =========== DOCUMENTATION ===========
!
! Online html documentation available at
! http://www.netlib.org/lapack/explore-html/
!
!> \par Purpose:
! =============
!>
!> \verbatim
!>
!> DROTG constructs a plane rotation
!> [ c s ] [ a ] = [ r ]
!> [ -s c ] [ b ] [ 0 ]
!> satisfying c**2 + s**2 = 1.
!>
!> The computation uses the formulas
!> sigma = sgn(a) if |a| > |b|
!> = sgn(b) if |b| >= |a|
!> r = sigma*sqrt( a**2 + b**2 )
!> c = 1; s = 0 if r = 0
!> c = a/r; s = b/r if r != 0
!> The subroutine also computes
!> z = s if |a| > |b|,
!> = 1/c if |b| >= |a| and c != 0
!> = 1 if c = 0
!> This allows c and s to be reconstructed from z as follows:
!> If z = 1, set c = 0, s = 1.
!> If |z| < 1, set c = sqrt(1 - z**2) and s = z.
!> If |z| > 1, set c = 1/z and s = sqrt( 1 - c**2).
!>
!> \endverbatim
!>
!> @see lartg, @see lartgp
!
! Arguments:
! ==========
!
!> \param[in,out] A
!> \verbatim
!> A is DOUBLE PRECISION
!> On entry, the scalar a.
!> On exit, the scalar r.
!> \endverbatim
!>
!> \param[in,out] B
!> \verbatim
!> B is DOUBLE PRECISION
!> On entry, the scalar b.
!> On exit, the scalar z.
!> \endverbatim
!>
!> \param[out] C
!> \verbatim
!> C is DOUBLE PRECISION
!> The scalar c.
!> \endverbatim
!>
!> \param[out] S
!> \verbatim
!> S is DOUBLE PRECISION
!> The scalar s.
!> \endverbatim
!
! Authors:
! ========
!
!> \author Edward Anderson, Lockheed Martin
!
!> \par Contributors:
! ==================
!>
!> Weslley Pereira, University of Colorado Denver, USA
!
!> \ingroup rotg
!
!> \par Further Details:
! =====================
!>
!> \verbatim
!>
!> 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
!>
!> \endverbatim
!
! =====================================================================
subroutine DROTG( a, b, c, s )
integer, parameter :: wp = kind(1.d0)
!
! -- Reference BLAS level1 routine --
! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
!
! .. Constants ..
real(wp), parameter :: zero = 0.0_wp
real(wp), parameter :: one = 1.0_wp
! ..
! .. Scaling constants ..
real(wp), parameter :: safmin = real(radix(0._wp),wp)**max( &
minexponent(0._wp)-1, &
1-maxexponent(0._wp) &
)
real(wp), parameter :: safmax = real(radix(0._wp),wp)**max( &
1-minexponent(0._wp), &
maxexponent(0._wp)-1 &
)
! ..
! .. Scalar Arguments ..
real(wp) :: a, b, c, s
! ..
! .. Local Scalars ..
real(wp) :: anorm, bnorm, scl, sigma, r, z
! ..
anorm = abs(a)
bnorm = abs(b)
if( bnorm == zero ) then
c = one
s = zero
b = zero
else if( anorm == zero ) then
c = zero
s = one
a = b
b = one
else
scl = min( safmax, max( safmin, anorm, bnorm ) )
if( anorm > bnorm ) then
sigma = sign(one,a)
else
sigma = sign(one,b)
end if
r = sigma*( scl*sqrt((a/scl)**2 + (b/scl)**2) )
c = a/r
s = b/r
if( anorm > bnorm ) then
z = s
else if( c /= zero ) then
z = one/c
else
z = one
end if
a = r
b = z
end if
return
end subroutine
|
