kopia lustrzana https://github.com/Dsplib/libdspl-2.0
152 wiersze
3.4 KiB
Fortran
152 wiersze
3.4 KiB
Fortran
!> \brief \b DROTG
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!
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! =========== DOCUMENTATION ===========
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!
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! Online html documentation available at
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! http://www.netlib.org/lapack/explore-html/
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!
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! Definition:
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! ===========
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!
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! DROTG constructs a plane rotation
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! [ c s ] [ a ] = [ r ]
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! [ -s c ] [ b ] [ 0 ]
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! satisfying c**2 + s**2 = 1.
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!
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!> \par Purpose:
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! =============
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!>
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!> \verbatim
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!>
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!> The computation uses the formulas
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!> sigma = sgn(a) if |a| > |b|
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!> = sgn(b) if |b| >= |a|
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!> r = sigma*sqrt( a**2 + b**2 )
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!> c = 1; s = 0 if r = 0
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!> c = a/r; s = b/r if r != 0
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!> The subroutine also computes
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!> z = s if |a| > |b|,
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!> = 1/c if |b| >= |a| and c != 0
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!> = 1 if c = 0
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!> This allows c and s to be reconstructed from z as follows:
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!> If z = 1, set c = 0, s = 1.
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!> If |z| < 1, set c = sqrt(1 - z**2) and s = z.
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!> If |z| > 1, set c = 1/z and s = sqrt( 1 - c**2).
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!>
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!> \endverbatim
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!
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! Arguments:
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! ==========
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!
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!> \param[in,out] A
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!> \verbatim
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!> A is DOUBLE PRECISION
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!> On entry, the scalar a.
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!> On exit, the scalar r.
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!> \endverbatim
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!>
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!> \param[in,out] B
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!> \verbatim
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!> B is DOUBLE PRECISION
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!> On entry, the scalar b.
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!> On exit, the scalar z.
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!> \endverbatim
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!>
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!> \param[out] C
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!> \verbatim
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!> C is DOUBLE PRECISION
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!> The scalar c.
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!> \endverbatim
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!>
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!> \param[out] S
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!> \verbatim
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!> S is DOUBLE PRECISION
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!> The scalar s.
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!> \endverbatim
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!
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! Authors:
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! ========
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!
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!> \author Edward Anderson, Lockheed Martin
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!
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!> \par Contributors:
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! ==================
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!>
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!> Weslley Pereira, University of Colorado Denver, USA
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!
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!> \ingroup single_blas_level1
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!
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!> \par Further Details:
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! =====================
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!>
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!> \verbatim
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!>
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!> Anderson E. (2017)
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!> Algorithm 978: Safe Scaling in the Level 1 BLAS
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!> ACM Trans Math Softw 44:1--28
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!> https://doi.org/10.1145/3061665
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!>
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!> \endverbatim
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!
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! =====================================================================
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subroutine DROTG( a, b, c, s )
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integer, parameter :: wp = kind(1.d0)
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!
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! -- Reference BLAS level1 routine --
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! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
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! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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!
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! .. Constants ..
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real(wp), parameter :: zero = 0.0_wp
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real(wp), parameter :: one = 1.0_wp
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! ..
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! .. Scaling constants ..
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real(wp), parameter :: safmin = real(radix(0._wp),wp)**max( &
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minexponent(0._wp)-1, &
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1-maxexponent(0._wp) &
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)
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real(wp), parameter :: safmax = real(radix(0._wp),wp)**max( &
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1-minexponent(0._wp), &
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maxexponent(0._wp)-1 &
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)
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! ..
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! .. Scalar Arguments ..
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real(wp) :: a, b, c, s
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! ..
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! .. Local Scalars ..
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real(wp) :: anorm, bnorm, scl, sigma, r, z
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! ..
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anorm = abs(a)
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bnorm = abs(b)
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if( bnorm == zero ) then
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c = one
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s = zero
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b = zero
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else if( anorm == zero ) then
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c = zero
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s = one
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a = b
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b = one
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else
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scl = min( safmax, max( safmin, anorm, bnorm ) )
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if( anorm > bnorm ) then
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sigma = sign(one,a)
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else
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sigma = sign(one,b)
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end if
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r = sigma*( scl*sqrt((a/scl)**2 + (b/scl)**2) )
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c = a/r
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s = b/r
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if( anorm > bnorm ) then
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z = s
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else if( c /= zero ) then
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z = one/c
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else
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z = one
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end if
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a = r
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b = z
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end if
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return
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end subroutine
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