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163 lines
3.8 KiB
163 lines
3.8 KiB
2 years ago
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!> \brief \b DLARTG generates a plane rotation with real cosine and real sine.
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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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! SUBROUTINE DLARTG( F, G, C, S, R )
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!
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! .. Scalar Arguments ..
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! REAL(wp) C, F, G, R, S
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! ..
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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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!> DLARTG generates a plane rotation so that
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!>
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!> [ C S ] . [ F ] = [ R ]
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!> [ -S C ] [ G ] [ 0 ]
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!>
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!> where C**2 + S**2 = 1.
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!>
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!> The mathematical formulas used for C and S are
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!> R = sign(F) * sqrt(F**2 + G**2)
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!> C = F / R
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!> S = G / R
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!> Hence C >= 0. The algorithm used to compute these quantities
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!> incorporates scaling to avoid overflow or underflow in computing the
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!> square root of the sum of squares.
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!>
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!> This version is discontinuous in R at F = 0 but it returns the same
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!> C and S as ZLARTG for complex inputs (F,0) and (G,0).
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!>
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!> This is a more accurate version of the BLAS1 routine DROTG,
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!> with the following other differences:
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!> F and G are unchanged on return.
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!> If G=0, then C=1 and S=0.
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!> If F=0 and (G .ne. 0), then C=0 and S=sign(1,G) without doing any
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!> floating point operations (saves work in DBDSQR when
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!> there are zeros on the diagonal).
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!>
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!> Below, wp=>dp stands for double precision from LA_CONSTANTS module.
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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] F
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!> \verbatim
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!> F is REAL(wp)
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!> The first component of vector to be rotated.
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!> \endverbatim
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!>
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!> \param[in] G
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!> \verbatim
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!> G is REAL(wp)
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!> The second component of vector to be rotated.
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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 REAL(wp)
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!> The cosine of the rotation.
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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 REAL(wp)
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!> The sine of the rotation.
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!> \endverbatim
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!>
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!> \param[out] R
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!> \verbatim
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!> R is REAL(wp)
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!> The nonzero component of the rotated vector.
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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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!> \date July 2016
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!
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!> \ingroup OTHERauxiliary
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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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!> \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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subroutine DLARTG( f, g, c, s, r )
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use LA_CONSTANTS, &
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only: wp=>dp, zero=>dzero, half=>dhalf, one=>done, &
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safmin=>dsafmin, safmax=>dsafmax
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!
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! -- LAPACK auxiliary routine --
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! -- LAPACK 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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! February 2021
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!
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! .. Scalar Arguments ..
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real(wp) :: c, f, g, r, s
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! ..
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! .. Local Scalars ..
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real(wp) :: d, f1, fs, g1, gs, u, rtmin, rtmax
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! ..
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! .. Intrinsic Functions ..
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intrinsic :: abs, sign, sqrt
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! ..
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! .. Constants ..
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rtmin = sqrt( safmin )
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rtmax = sqrt( safmax/2 )
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! ..
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! .. Executable Statements ..
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!
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f1 = abs( f )
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g1 = abs( g )
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if( g == zero ) then
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c = one
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s = zero
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r = f
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else if( f == zero ) then
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c = zero
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s = sign( one, g )
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r = g1
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else if( f1 > rtmin .and. f1 < rtmax .and. &
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g1 > rtmin .and. g1 < rtmax ) then
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d = sqrt( f*f + g*g )
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c = f1 / d
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r = sign( d, f )
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s = g / r
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else
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u = min( safmax, max( safmin, f1, g1 ) )
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fs = f / u
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gs = g / u
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d = sqrt( fs*fs + gs*gs )
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c = abs( fs ) / d
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r = sign( d, f )
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s = gs / r
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r = r*u
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end if
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return
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end subroutine
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