Coverage for pygeodesy/karney.py: 94%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''Wrapper around several C{geomath.Math} functions from I{Karney}'s Python package U{geographiclib 

5<https://PyPI.org/project/geographiclib>}, provided that package is installed. 

6 

7Methods of the I{wrapped} L{Geodesic<geodesicw.Geodesic>} and L{GeodesicLine<geodesicw.GeodesicLine>} 

8classes return a L{GDict} instance offering access to the C{dict} items either by C{key} or by 

9C{attribute} name. 

10 

11With env variable C{PYGEODESY_GEOGRAPHICLIB} left undefined or set to C{"2"}, modules L{geodesicw}, 

12L{geodesicx} and this module will use U{GeographicLib 2.0+<https://GeographicLib.SourceForge.io/C++/doc/>} 

13and newer transcoding, otherwise C{1.52} or older. 

14 

15Karney-based functionality 

16========================== 

17 

181. The following classes and functions in C{pygeodesy} 

19 

20 - L{AlbersEqualArea}, L{AlbersEqualArea2}, L{AlbersEqualArea4}, 

21 L{AlbersEqualAreaCylindrical}, L{AlbersEqualAreaNorth}, L{AlbersEqualAreaSouth} -- 

22 U{AlbersEqualArea<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AlbersEqualArea.html>} 

23 

24 - L{AuxAngle}, L{AuxDST}, L{AuxDLat}, L{AuxLat} -- U{AuxAngle 

25 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AuxAngle.html>}, 

26 U{DST<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1DST.html>}, 

27 U{DAuxLatitude<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1DAuxLatitude.html>}, 

28 U{AuxLatitude<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AuxLatitude.html>} in I{GeographicLib 2.2+} 

29 

30 - L{CassiniSoldner} -- U{CassiniSoldner<https://GeographicLib.SourceForge.io/C++/doc/ 

31 classGeographicLib_1_1CassiniSoldner.html>} 

32 

33 - L{EcefKarney} -- U{Geocentric<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Geocentric.html>} 

34 

35 - L{Elliptic} -- U{EllipticFunction<https://GeographicLib.SourceForge.io/C++/doc/ 

36 classGeographicLib_1_1EllipticFunction.html>} 

37 

38 - L{EquidistantExact}, L{EquidistantGeodSolve}, L{EquidistantKarney} -- U{AzimuthalEquidistant 

39 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AzimuthalEquidistant.html>} 

40 

41 - L{Etm}, L{ExactTransverseMercator} -- U{TransverseMercatorExact 

42 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercatorExact.html>} 

43 

44 - L{Geodesic}, L{GeodesicLine} -- I{wrapped} U{geodesic.Geodesic<https://PyPI.org/project/geographiclib>}, 

45 I{wrapped} U{geodesicline.GeodesicLine<https://PyPI.org/project/geographiclib>} 

46 

47 - L{GeodesicAreaExact}, L{PolygonArea} -- U{PolygonArea<https://GeographicLib.SourceForge.io/C++/doc/ 

48 classGeographicLib_1_1PolygonAreaT.html>} 

49 

50 - L{GeodesicExact}, L{GeodesicLineExact} -- U{GeodesicExact<https://GeographicLib.SourceForge.io/C++/doc/ 

51 classGeographicLib_1_1GeodesicExact.html>}, U{GeodesicLineExact<https://GeographicLib.SourceForge.io/C++/doc/ 

52 classGeographicLib_1_1GeodesicLineExact.html>} 

53 

54 - L{GeoidKarney} -- U{Geoid<https://GeographicLib.SourceForge.io/C++/doc/geoid.html>} 

55 

56 - L{Georef} -- U{Georef<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Georef.html>} 

57 

58 - L{GnomonicExact}, L{GnomonicGeodSolve}, L{GnomonicKarney} -- U{Gnomonic 

59 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Gnomonic.html>} 

60 

61 - L{Intersector} -- U{Intersect 

62 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Intersect.html>} from I{GeographicLib 2.3+} 

63 

64 - L{JacobiConformal} -- U{JacobiConformal 

65 <https://geographiclib.sourceforge.io/C++/doc/classGeographicLib_1_1experimental_1_1JacobiConformal.html>} 

66 

67 - L{KTransverseMercator} - U{TransverseMercator 

68 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>} 

69 

70 - L{LocalCartesian}, L{Ltp} -- U{LocalCartesian<https://GeographicLib.SourceForge.io/C++/doc/ 

71 classGeographicLib_1_1LocalCartesian.html>} 

72 

73 - L{Osgr} -- U{OSGB<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1OSGB.html>} 

74 

75 - L{rhumb.aux_}, L{RhumbAux}, L{RhumbLineAux} -- U{Rhumb 

76 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>} and U{RhumbLine 

77 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>} from I{GeographicLib 2.2+} 

78 

79 - L{rhumb.ekx}, L{Rhumb}, L{RhumbLine} -- U{Rhumb 

80 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>}, 

81 U{RhumbLine<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>}, 

82 U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>} 

83 from I{GeographicLib 2.0} 

84 

85 - L{Ups} -- U{PolarStereographic<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1PolarStereographic.html>} 

86 

87 - L{Utm} -- U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>} 

88 

89 - L{UtmUps}, L{Epsg} -- U{UTMUPS<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1UTMUPS.html>} 

90 

91 - L{atan1d}, L{atan2d}, L{sincos2}, L{sincos2d}, L{tand} -- U{geomath.Math 

92 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Math.html>} 

93 

94are I{transcoded} from C++ classes in I{Karney}'s U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>}. 

95 

962. These C{pygeodesy} modules and classes 

97 

98 - L{ellipsoidalGeodSolve}, L{ellipsoidalKarney}, L{geodesici}, L{geodsolve}, L{karney}, L{rhumb.solve} 

99 - L{EquidistantKarney}, L{FrechetKarney}, L{GeodesicSolve}, L{GeodesicLineSolve}, L{GnomonicGeodSolve}, 

100 L{GnomonicKarney}, L{HeightIDWkarney}, L{Intersectool} 

101 

102are or use I{wrappers} around I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>} or 

103C++ utility U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}, 

104U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>} or 

105U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}. 

106 

1073. All C{pygeodesy} functions and methods to compute I{ellipsoidal} intersections, nearest points and trilaterations 

108 

109 - L{ellipsoidalExact.intersection3}, L{ellipsoidalExact.intersections2}, L{ellipsoidalExact.nearestOn}, 

110 L{ellipsoidalExact.LatLon.intersection3}, L{ellipsoidalExact.LatLon.intersections2}, 

111 L{ellipsoidalExact.LatLon.nearestOn}, L{ellipsoidalExact.LatLon.trilaterate5} 

112 

113 - L{ellipsoidalKarney.intersection3}, L{ellipsoidalKarney.intersections2}, L{ellipsoidalKarney.nearestOn}, 

114 L{ellipsoidalKarney.LatLon.intersection3}, L{ellipsoidalKarney.LatLon.intersections2}, 

115 L{ellipsoidalKarney.LatLon.nearestOn}, L{ellipsoidalKarney.LatLon.trilaterate5} 

116 

117 - L{ellipsoidalVincenty.intersection3}, L{ellipsoidalVincenty.intersections2}, L{ellipsoidalVincenty.nearestOn}, 

118 L{ellipsoidalVincenty.LatLon.intersection3}, L{ellipsoidalVincenty.LatLon.intersections2}, 

119 L{ellipsoidalVincenty.LatLon.nearestOn}, L{ellipsoidalVincenty.LatLon.trilaterate5} 

120 

121 - L{RhumbLineAux.Intersection} and L{RhumbLine.Intersection} 

122 

123are implementations of I{Karney}'s iterative solution posted under U{The B{ellipsoidal} case 

124<https://GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>} and in paper U{Geodesics 

125on an ellipsoid of revolution<https://ArXiv.org/pdf/1102.1215.pdf>} (pp 20-21, section B{14. MARITIME BOUNDARIES}). 

126 

1274. The C{pygeodesy} methods to compute I{ellipsoidal} intersections and nearest points 

128 

129 - L{RhumbLineAux.Intersecant2}, L{RhumbLineAux.PlumbTo}, L{RhumbLine.Intersecant2} and L{RhumbLine.PlumbTo} 

130 

131are I{transcoded} of I{Karney}'s iterative C++ function U{rhumb-intercept 

132<https://SourceForge.net/p/geographiclib/discussion/1026620/thread/2ddc295e/>}. 

133 

1345. Spherical functions 

135 

136 - L{pygeodesy.excessKarney_}, L{sphericalTrigonometry.areaOf} 

137 

138in C{pygeodesy} are based on I{Karney}'s post U{Area of a spherical polygon 

139<https://MathOverflow.net/questions/97711/the-area-of-spherical-polygons>}, 3rd Answer. 

140''' 

141# make sure int/int division yields float quotient, see .basics 

142from __future__ import division as _; del _ # PYCHOK semicolon 

143 

144from pygeodesy.basics import _copysign, isint, neg, unsigned0, _xgeographiclib, \ 

145 _zip, _version_info 

146from pygeodesy.constants import NAN, _isfinite as _math_isfinite, _0_0, \ 

147 _1_16th, _1_0, _2_0, _180_0, _N_180_0, _360_0 

148from pygeodesy.errors import GeodesicError, _ValueError, _xkwds, _xkwds_get1 

149from pygeodesy.fmath import cbrt, fremainder, norm2 

150# from pygeodesy.internals import _version_info # from .basics 

151from pygeodesy.interns import NN, _2_, _a12_, _area_, _azi1_, _azi2_, _azi12_, \ 

152 _composite_, _lat1_, _lat2_, _lon1_, _lon2_, \ 

153 _m12_, _M12_, _M21_, _number_, _s12_, _S12_, \ 

154 _UNDER_, _X_, _BAR_ # PYCHOK used! 

155from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv 

156from pygeodesy.named import ADict, _NamedBase, _NamedTuple, notImplemented, _Pass 

157from pygeodesy.props import deprecated_method, Property_RO, property_ROnce 

158from pygeodesy.units import Azimuth as _Azi, Degrees as _Deg, Lat, Lon, \ 

159 Meter as _M, Meter2 as _M2, Number_ 

160from pygeodesy.utily import atan2d, sincos2d, tand, _unrollon, fabs 

161 

162# from math import fabs # from .utily 

163 

164__all__ = _ALL_LAZY.karney 

165__version__ = '24.07.25' 

166 

167_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_ 

168_perimeter_ = 'perimeter' 

169 

170 

171class _GTuple(_NamedTuple): # in .testNamedTuples 

172 '''(INTERNAL) Helper. 

173 ''' 

174 def toGDict(self, **updates): # NO name=NN 

175 '''Convert this C{*Tuple} to a L{GDict}. 

176 

177 @kwarg updates: Optional items to apply (C{name=value} pairs) 

178 ''' 

179 r = GDict(_zip(self._Names_, self)) # strict=True 

180 if updates: 

181 r.update(updates) 

182 if self._iteration is not None: 

183 r._iteration = self._iteration 

184 return r 

185 

186 

187class _Lat(Lat): 

188 '''(INTERNAL) Latitude B{C{lat}}. 

189 ''' 

190 def __init__(self, *lat, **Error_name): 

191 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError) 

192 Lat.__new__(_Lat, *lat, **kwds) 

193 

194 

195class _Lon(Lon): 

196 '''(INTERNAL) Longitude B{C{lon}}. 

197 ''' 

198 def __init__(self, *lon, **Error_name): 

199 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError) 

200 Lon.__new__(_Lon, *lon, **kwds) 

201 

202 

203class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea 

204 '''3-Tuple C{(number, perimeter, area)} with the C{number} 

205 of points of the polygon or polyline, the C{perimeter} in 

206 C{meter} and the C{area} in C{meter} I{squared}. 

207 ''' 

208 _Names_ = (_number_, _perimeter_, _area_) 

209 _Units_ = ( Number_, _M, _M2) 

210 

211 

212class Caps(object): 

213 '''(INTERNAL) Overriden by C{Caps} below. 

214 ''' 

215 EMPTY = 0 # formerly aka NONE 

216 _CAP_1 = 1 << 0 # for goedesici/-w 

217 _CAP_1p = 1 << 1 # for goedesici/-w 

218 _CAP_2 = 1 << 2 

219 _CAP_3 = 1 << 3 # for goedesici/-w 

220 _CAP_4 = 1 << 4 # for goedesicw 

221 _CAP_ALL = 0x1F 

222# _CAP_MASK = _CAP_ALL 

223 LATITUDE = 1 << 7 # compute latitude C{lat2} 

224 LONGITUDE = 1 << 8 | _CAP_3 # compute longitude C{lon2} 

225 AZIMUTH = 1 << 9 # azimuths C{azi1} and C{azi2} 

226 DISTANCE = 1 << 10 | _CAP_1 # compute distance C{s12} 

227 DISTANCE_IN = 1 << 11 | _CAP_1 | _CAP_1p # allow distance C{s12} in Direct 

228 REDUCEDLENGTH = 1 << 12 | _CAP_1 | _CAP_2 # compute reduced length C{m12} 

229 GEODESICSCALE = 1 << 13 | _CAP_1 | _CAP_2 # compute geodesic scales C{M12} and C{M21} 

230 AREA = 1 << 14 | _CAP_4 # compute area C{S12} 

231 

232 STANDARD = AZIMUTH | DISTANCE | LATITUDE | LONGITUDE 

233 

234 _DIRECT3 = AZIMUTH | LATITUDE | LONGITUDE # for goedesicw only 

235 _INVERSE3 = AZIMUTH | DISTANCE # for goedesicw only 

236 _STD = STANDARD # for goedesicw only 

237 _STD_LINE = _STD | DISTANCE_IN # for goedesici/-w 

238 

239 LINE_CAPS = _STD_LINE | REDUCEDLENGTH | GEODESICSCALE # .geodesici only 

240 LONG_UNROLL = 1 << 15 # unroll C{lon2} in .Direct and .Position 

241# = 1 << 16 # unused 

242 LINE_OFF = 1 << 17 # Line without updates from parent geodesic or rhumb 

243 REVERSE2 = 1 << 18 # reverse C{azi2} 

244 ALL = 0x7F80 | _CAP_ALL # without LONG_UNROLL, LINE_OFF, REVERSE2 and _DEBUG_* 

245 

246 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE 

247 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA 

248 

249 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE 

250 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA 

251 

252 _SALP_CALPs_ = 1 << 19 # (INTERNAL) GeodesicExact._GenInverse 

253 

254 _DEBUG_AREA = 1 << 20 # (INTERNAL) include Line details 

255 _DEBUG_DIRECT = 1 << 21 # (INTERNAL) include Direct details 

256 _DEBUG_INVERSE = 1 << 22 # (INTERNAL) include Inverse details 

257 _DEBUG_LINE = 1 << 23 # (INTERNAL) include Line details 

258 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \ 

259 _DEBUG_LINE | _SALP_CALPs_ 

260 

261 _OUT_ALL = ALL # see geographiclib.geodesiccapabilities.py 

262 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL 

263 

264 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE 

265 _AZIMUTH_LATITUDE_LONG_UNROLL = AZIMUTH | LATITUDE | LONG_UNROLL 

266 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE 

267# _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK # == DISTANCE_IN in .gx, .gxline 

268 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE 

269# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE 

270 

271 def items(self): 

272 '''Yield all I{public} C{Caps} as 2-tuple C{(NAME, mask)}. 

273 ''' 

274 for n, C in Caps.__class__.__dict__.items(): 

275 if isint(C) and not n.startswith(_UNDER_) \ 

276 and n.replace(_UNDER_, NN).isupper(): 

277 yield n, C 

278 

279 def toStr(self, Cask, sep=_BAR_): 

280 '''Return C{Caps} or an C{outmask} as C{str} or tuple of C{str}s. 

281 ''' 

282 s = (n for n, C in sorted(Caps.items()) 

283 if C and (Cask & C) == C) # and int1s(C) <= 3 

284 return sep.join(s) if sep else tuple(s) 

285 

286Caps = Caps() # PYCHOK singleton 

287'''I{Enum}-style masks to be bit-C{or}'ed to specify geodesic or 

288rhumb capabilities (C{caps}) and expected results (C{outmask}). 

289 

290C{AREA} - compute area C{S12}, 

291 

292C{AZIMUTH} - include azimuths C{azi1} and C{azi2}, 

293 

294C{DISTANCE} - compute distance C{s12} and angular distance C{a12}, 

295 

296C{DISTANCE_IN} - allow distance C{s12} in C{.Direct}, 

297 

298C{EMPTY} - nothing, formerly aka C{NONE}, 

299 

300C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21}, 

301 

302C{LATITUDE} - compute latitude C{lat2}, 

303 

304C{LINE_OFF} - Line without updates from parent geodesic or rhumb. 

305 

306C{LONGITUDE} - compute longitude C{lon2}, 

307 

308C{LONG_UNROLL} - unroll C{lon2} in C{.Direct}, 

309 

310C{REDUCEDLENGTH} - compute reduced length C{m12}, 

311 

312C{REVERSE2} - reverse C{azi2}, 

313 

314and C{ALL} - all of the above. 

315 

316C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}''' 

317 

318_key2Caps = dict(a12 =Caps.DISTANCE, # in GDict._unCaps 

319 azi2=Caps.AZIMUTH, 

320 lat2=Caps.LATITUDE, 

321 lon2=Caps.LONGITUDE, 

322 m12 =Caps.REDUCEDLENGTH, 

323 M12 =Caps.GEODESICSCALE, 

324 M21 =Caps.GEODESICSCALE, 

325 s12 =Caps.DISTANCE, 

326 S12 =Caps.AREA) 

327 

328 

329class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases 

330 '''(INTERNAL) Base class for C{Geodesic*}, C{Geodesic*Exact}, C{Intersectool} and C{Rhumb*Base}. 

331 ''' 

332 ALL = Caps.ALL 

333 AREA = Caps.AREA 

334 AZIMUTH = Caps.AZIMUTH 

335 DISTANCE = Caps.DISTANCE 

336 DISTANCE_IN = Caps.DISTANCE_IN 

337 EMPTY = Caps.EMPTY # aka NONE 

338 GEODESICSCALE = Caps.GEODESICSCALE 

339 LATITUDE = Caps.LATITUDE 

340 LINE_CAPS = Caps.LINE_CAPS 

341 LINE_OFF = Caps.LINE_OFF 

342 LONGITUDE = Caps.LONGITUDE 

343 LONG_UNROLL = Caps.LONG_UNROLL 

344 REDUCEDLENGTH = Caps.REDUCEDLENGTH 

345 STANDARD = Caps.STANDARD 

346 _STD_LINE = Caps._STD_LINE # for geodesici 

347 

348 _caps = 0 # None 

349 _debug = 0 # or Caps._DEBUG_... 

350 

351 @Property_RO 

352 def caps(self): 

353 '''Get the capabilities (bit-or'ed C{Caps}). 

354 ''' 

355 return self._caps 

356 

357 def caps_(self, caps): 

358 '''Check the available capabilities. 

359 

360 @arg caps: Bit-or'ed combination of L{Caps} values 

361 for all capabilities to be checked. 

362 

363 @return: C{True} if I{all} B{C{caps}} are available, 

364 C{False} otherwise (C{bool}). 

365 ''' 

366 caps &= Caps._OUT_ALL 

367 return (self.caps & caps) == caps 

368 

369 @property 

370 def debug(self): 

371 '''Get the C{debug} option (C{bool}). 

372 ''' 

373 return bool(self._debug) 

374 

375 @debug.setter # PYCHOK setter! 

376 def debug(self, debug): 

377 '''Set the C{debug} option (C{bool}) to include 

378 more details in L{GDict} results. 

379 ''' 

380 self._debug = Caps._DEBUG_ALL if debug else 0 

381 

382 def _iter2tion(self, r, iter=None, **unused): 

383 '''(INTERNAL) Copy C{C{s}.iter} into C{B{r}._iteration}. 

384 ''' 

385 if iter is not None: 

386 self._iteration = r._iteration = iter 

387 return r 

388 

389 

390class Direct9Tuple(_GTuple): 

391 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc 

392 length C{a12}, angles C{lat2}, C{lon2} and azimuth C{azi2} in C{degrees}, 

393 distance C{s12} and reduced length C{m12} in C{meter} and area C{S12} in 

394 C{meter} I{squared}. 

395 ''' 

396 _Names_ = (_a12_, _lat2_, _lon2_, _azi2_, _s12_, _m12_, _M12_, _M21_, _S12_) 

397 _Units_ = (_Azi, _Lat, _Lon, _Azi, _M, _Pass, _Pass, _Pass, _M2) 

398 

399 

400class GDict(ADict): # XXX _NamedDict 

401 '''A C{dict} with both C{key} I{and} C{attribute} access to the C{dict} items. 

402 

403 Results of all C{geodesic} and C{rhumb} methods (with capitalized named) are 

404 returned as L{GDict} instances, see for example L{GeodesicExact} and L{RhumbAux}. 

405 ''' 

406 def toDirect9Tuple(self, dflt=NAN): 

407 '''Convert this L{GDict} result to a 9-tuple, like I{Karney}'s method 

408 C{geographiclib.geodesic.Geodesic._GenDirect}. 

409 

410 @kwarg dflt: Default value for missing items (C{any}). 

411 

412 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, 

413 s12, m12, M12, M21, S12)} 

414 ''' 

415 return self._toTuple(Direct9Tuple, dflt) 

416 

417 def toGeodSolve12Tuple(self, dflt=NAN): # PYCHOK 12 args 

418 '''Convert this L{GDict} result to a 12-Tuple, compatible with I{Karney}'s 

419 U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>} 

420 result. 

421 

422 @kwarg dflt: Default value for missing items (C{any}). 

423 

424 @return: L{GeodSolve12Tuple}C{(lat1, lon1, azi1, lat2, lon2, azi2, 

425 s12, a12, m12, M12, M21, S12)}. 

426 ''' 

427 return self._toTuple(_MODS.geodsolve.GeodSolve12Tuple, dflt) 

428 

429 def toInverse10Tuple(self, dflt=NAN): 

430 '''Convert this L{GDict} result to a 10-tuple, like I{Karney}'s 

431 method C{geographiclib.geodesic.Geodesic._GenInverse}. 

432 

433 @kwarg dflt: Default value for missing items (C{any}). 

434 

435 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1, 

436 salp2, calp2, m12, M12, M21, S12)}. 

437 ''' 

438 return self._toTuple(Inverse10Tuple, dflt) 

439 

440 def _toNAN(self, outmask): # .GeodesicLineExact._GenPosition 

441 '''(INTERNAL) Convert this C{GDict} to all C{NAN}s. 

442 ''' 

443 d = dict((n, NAN) for n in GeodSolve12Tuple._Names_) 

444 return self.set_(**d)._unCaps(outmask) 

445 

446 @deprecated_method 

447 def toRhumb7Tuple(self, dflt=NAN): # PYCHOK no cover 

448 '''DEPRECATED on 23.12.07, use method C{toRhumb8Tuple}. 

449 

450 @return: A I{DEPRECATED} L{Rhumb7Tuple}. 

451 ''' 

452 return self._toTuple(_MODS.deprecated.classes.Rhumb7Tuple, dflt) 

453 

454 def toRhumb8Tuple(self, dflt=NAN): 

455 '''Convert this L{GDict} result to a 8-tuple. 

456 

457 @kwarg dflt: Default value for missing items (C{any}). 

458 

459 @return: L{Rhumb8Tuple}C{(lat1, lon1, lat2, lon2, 

460 azi12, s12, S12, a12)}. 

461 ''' 

462 return self._toTuple(Rhumb8Tuple, dflt) 

463 

464 def toRhumbSolve7Tuple(self, dflt=NAN): 

465 '''Convert this L{GDict} result to a 8-tuple. 

466 

467 @kwarg dflt: Default value for missing items (C{any}). 

468 

469 @return: L{RhumbSolve7Tuple}C{(lat1, lon1, lat2, lon2, 

470 azi12, s12, S12)}. 

471 ''' 

472 return self._toTuple(_MODS.rhumb.solve.RhumbSolve7Tuple, dflt) 

473 

474 def _toTuple(self, nTuple, dflt): 

475 '''(INTERNAL) Convert this C{GDict} to an B{C{nTuple}}. 

476 ''' 

477 _g = getattr 

478 t = tuple(_g(self, n, dflt) for n in nTuple._Names_) 

479 return nTuple(t, iteration=self._iteration) 

480 

481 def _2X(self, gl, _2X=_X_): # .Intersectool, .Intersector 

482 '''(INTERNAL) Rename C{-2} attr to C{-X} or C{-M}. 

483 ''' 

484 X = GDict(self) 

485 for n in (_lat2_, _lon2_, _azi2_, _s12_, _a12_): 

486 if n in X: # X._X = X._2 

487 X[n[:-1] + _2X] = X.pop(n) 

488 v = getattr(gl, n, X) 

489 if v is not X: # X._2 = gl._2 

490 X[n] = v 

491 return X 

492 

493 def _unCaps(self, outmask): # in .geodsolve 

494 '''(INTERNAL) Remove superfluous items. 

495 ''' 

496 for k, C in _key2Caps.items(): 

497 if k in self and (outmask & C) != C: 

498 self.pop(k) # delattr(self, k) 

499 return self 

500 

501 

502class GeodSolve12Tuple(_GTuple): 

503 '''12-Tuple C{(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12)} with 

504 angles C{lat1}, C{lon1}, C{azi1}, C{lat2}, C{lon2} and C{azi2} and arc C{a12} all in 

505 C{degrees}, initial C{azi1} and final C{azi2} forward azimuths, distance C{s12} and 

506 reduced length C{m12} in C{meter}, area C{S12} in C{meter} I{squared} and geodesic 

507 scale factors C{M12} and C{M21}, both C{scalar}, see U{GeodSolve 

508 <https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}. 

509 ''' 

510 # from GeodSolve --help option -f ... lat1 lon1 azi1 lat2 lon2 azi2 s12 a12 m12 M12 M21 S12 

511 _Names_ = (_lat1_, _lon1_, _azi1_, _lat2_, _lon2_, _azi2_, _s12_, _a12_, _m12_, _M12_, _M21_, _S12_) 

512 _Units_ = (_Lat, _Lon, _Azi, _Lat, _Lon, _Azi, _M, _Deg, _Pass, _Pass, _Pass, _M2) 

513 

514 

515class Inverse10Tuple(_GTuple): 

516 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length 

517 C{a12} in C{degrees}, distance C{s12} and reduced length C{m12} in C{meter}, area 

518 C{S12} in C{meter} I{squared} and the sines C{salp1}, C{salp2} and cosines C{calp1}, 

519 C{calp2} of the initial C{1} and final C{2} (forward) azimuths. 

520 ''' 

521 _Names_ = (_a12_, _s12_, 'salp1', 'calp1', 'salp2', 'calp2', _m12_, _M12_, _M21_, _S12_) 

522 _Units_ = (_Azi, _M, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _M2) 

523 

524 def toGDict(self, **updates): 

525 '''Convert this C{Inverse10Tuple} to a L{GDict}. 

526 

527 @kwarg updates: Optional items to apply (C{nam=value} pairs) 

528 ''' 

529 return _GTuple.toGDict(self, azi1=atan2d(self.salp1, self.calp1), # PYCHOK namedTuple 

530 azi2=atan2d(self.salp2, self.calp2), # PYCHOK namedTuple 

531 **updates) # PYCHOK indent 

532 

533 

534class _kWrapped(object): # in .geodesicw 

535 ''''(INTERNAL) Wrapper for some of I{Karney}'s U{geographiclib 

536 <https://PyPI.org/project/geographiclib>} classes. 

537 ''' 

538 

539 @property_ROnce 

540 def geographiclib(self): 

541 '''Lazily import C{geographiclib}, provided the U{geographiclib 

542 <https://PyPI.org/project/geographiclib>} package is installed, 

543 otherwise raise a C{LazyImportError}. 

544 ''' 

545 g = _xgeographiclib(self.__class__.__module__, 1, 49) 

546 from geographiclib.geodesic import Geodesic 

547 g.Geodesic = Geodesic 

548 from geographiclib.geodesicline import GeodesicLine 

549 g.GeodesicLine = GeodesicLine 

550 from geographiclib.geomath import Math 

551 g.Math = Math 

552 return g 

553 

554 @property_ROnce 

555 def Math(self): 

556 '''Wrap the C{geomath.Math} class, provided the U{geographiclib 

557 <https://PyPI.org/project/geographiclib>} package is installed, 

558 otherwise C{None}. 

559 ''' 

560 try: 

561 g = self.geographiclib 

562 M = g.Math 

563 if _version_info(g) < (2,): 

564 if _K_2_0: 

565 M = None 

566# elif not _K_2_0: # XXX set 2.0? 

567# _K_2_0 = True 

568 except (AttributeError, ImportError): 

569 M = None 

570 return M 

571 

572_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py 

573 

574 

575class Rhumb8Tuple(_GTuple): 

576 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1}, 

577 C{lat2} and longitudes C{lon1}, C{lon2} of both points, the azimuth of the 

578 rhumb line C{azi12}, the distance C{s12}, the area C{S12} under the rhumb 

579 line and the angular distance C{a12} between both points. 

580 ''' 

581 _Names_ = (_lat1_, _lon1_, _lat2_, _lon2_, _azi12_, _s12_, _S12_, _a12_) 

582 _Units_ = ( Lat, Lon, Lat, Lon, _Azi, _M, _M2, _Deg) 

583 

584 def toDirect9Tuple(self, dflt=NAN, **a12_azi1_azi2_m12_M12_M21): 

585 '''Convert this L{Rhumb8Tuple} result to a 9-tuple, like I{Karney}'s 

586 method C{geographiclib.geodesic.Geodesic._GenDirect}. 

587 

588 @kwarg dflt: Default value for missing items (C{any}). 

589 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments 

590 to specify or override L{Inverse10Tuple} items. 

591 

592 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, s12, 

593 m12, M12, M21, S12)} 

594 ''' 

595 d = dict(azi1=self.azi12, M12=_1_0, m12=self.s12, # PYCHOK attr 

596 azi2=self.azi12, M21=_1_0) # PYCHOK attr 

597 if a12_azi1_azi2_m12_M12_M21: 

598 d.update(a12_azi1_azi2_m12_M12_M21) 

599 return self._toTuple(Direct9Tuple, dflt, d) 

600 

601 def toInverse10Tuple(self, dflt=NAN, **a12_m12_M12_M21_salp1_calp1_salp2_calp2): 

602 '''Convert this L{Rhumb8Tuple} to a 10-tuple, like I{Karney}'s 

603 method C{geographiclib.geodesic.Geodesic._GenInverse}. 

604 

605 @kwarg dflt: Default value for missing items (C{any}). 

606 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword 

607 arguments to specify or override L{Inverse10Tuple} items. 

608 

609 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1, salp2, calp2, 

610 m12, M12, M21, S12)}. 

611 ''' 

612 s, c = sincos2d(self.azi12) # PYCHOK attr 

613 d = dict(salp1=s, calp1=c, M12=_1_0, m12=self.s12, # PYCHOK attr 

614 salp2=s, calp2=c, M21=_1_0) 

615 if a12_m12_M12_M21_salp1_calp1_salp2_calp2: 

616 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2) 

617 return self._toTuple(Inverse10Tuple, dflt, d) 

618 

619 def _toTuple(self, nTuple, dflt, updates={}): 

620 '''(INTERNAL) Convert this C{Rhumb8Tuple} to an B{C{nTuple}}. 

621 ''' 

622 _g = self.toGDict(**updates).get 

623 t = tuple(_g(n, dflt) for n in nTuple._Names_) 

624 return nTuple(t, name=self.name) 

625 

626 @deprecated_method 

627 def _to7Tuple(self): 

628 '''DEPRECATED, do not use!''' 

629 return _MODS.deprecated.classes.Rhumb7Tuple(self[:-1]) 

630 

631 

632def _around(x): # in .utily.sincos2d 

633 '''I{Coarsen} a scalar by rounding small values to underflow to C{0.0}. 

634 

635 @return: Coarsened value (C{float}). 

636 

637 @see: I{Karney}'s U{geomath.Math.AngRound<https://SourceForge.net/p/ 

638 geographiclib/code/ci/release/tree/python/geographiclib/geomath.py>} 

639 ''' 

640 try: 

641 return _wrapped.Math.AngRound(x) 

642 except AttributeError: 

643 if x: 

644 y = _1_16th - fabs(x) 

645 if y > 0: # fabs(x) < _1_16th 

646 x = _copysign(_1_16th - y, x) 

647 else: 

648 x = _0_0 # -0 to 0 

649 return x 

650 

651 

652def _atan2d(y, x): 

653 '''Return C{atan2(B{y}, B{x})} in C{degrees}. 

654 ''' 

655 try: 

656 return _wrapped.Math.atan2d(y, x) 

657 except AttributeError: 

658 return atan2d(y, x) 

659 

660 

661def _cbrt(x): 

662 '''Return C{cubic root(B{x})}. 

663 ''' 

664 try: 

665 return _wrapped.Math.cbrt(x) 

666 except AttributeError: 

667 return cbrt(x) 

668 

669 

670def _copyBit(x, y): 

671 '''Like C{copysign0(B{x}, B{y})}, with C{B{x} > 0}. 

672 ''' 

673 return (-x) if _signBit(y) else x 

674 

675 

676def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases 

677 '''Return M{2 * cos(2 * x)} from cos(x) and sin(x). 

678 ''' 

679 r = cx - sx 

680 if r: 

681 r *= (cx + sx) * _2_0 

682 return r 

683 

684 

685def _diff182(deg0, deg, K_2_0=False): 

686 '''Compute C{deg - deg0}, reduced to C{[-180,180]} accurately. 

687 

688 @return: 2-Tuple C{(delta_angle, residual)} in C{degrees}. 

689 ''' 

690 try: 

691 return _wrapped.Math.AngDiff(deg0, deg) 

692 except AttributeError: 

693 if K_2_0 or _K_2_0: # geographiclib 2.0 

694 _r, _360 = fremainder, _360_0 

695 d, t = _sum2(_r(-deg0, _360), 

696 _r( deg, _360)) 

697 d, t = _sum2(_r( d, _360), t) 

698 if d in (_0_0, _180_0, _N_180_0): 

699 d = _copysign(d, -t if t else (deg - deg0)) 

700 else: 

701 _n = _norm180 

702 d, t = _sum2(_n(-deg0), _n(deg)) 

703 d = _n(d) 

704 if t > 0 and d == _180_0: 

705 d = _N_180_0 

706 d, t = _sum2(d, t) 

707 return d, t 

708 

709 

710def _fix90(deg): # mimick Math.LatFix 

711 '''Replace angle in C{degrees} outside [-90,90] by NAN. 

712 

713 @return: Angle C{degrees} or NAN. 

714 ''' 

715 try: 

716 return _wrapped.Math.LatFix(deg) 

717 except AttributeError: 

718 return NAN if fabs(deg) > 90 else deg 

719 

720 

721def _isfinite(x): # mimick geomath.Math.isfinite 

722 '''Check finiteness of C{x}. 

723 

724 @return: C{True} if finite. 

725 ''' 

726 try: 

727 return _wrapped.Math.isfinite(x) 

728 except AttributeError: 

729 return _math_isfinite(x) # and fabs(x) <= _MAX 

730 

731 

732def _llz2gl(gl, **llz2): # see .geodesici._llz2G 

733 '''(INTERNAL) Set C{gl.lat2, .lon2, .azi2} from C{llz2}. 

734 ''' 

735 if llz2: 

736 for n in (_lat2_, _lon2_, _azi2_): # _lat1_, _lon1_, _azi1_ 

737 v = llz2.get(n, None) 

738 if v is not None: 

739 setattr(gl, n, v) 

740 return gl 

741 

742 

743def _norm2(x, y): # mimick geomath.Math.norm 

744 '''Normalize C{B{x}} and C{B{y}}. 

745 

746 @return: 2-Tuple of C{(B{x}, B{y})}, normalized. 

747 ''' 

748 try: 

749 return _wrapped.Math.norm(x, y) 

750 except AttributeError: 

751 return norm2(x, y) 

752 

753 

754def _norm180(deg): # mimick geomath.Math.AngNormalize 

755 '''Reduce angle in C{degrees} to (-180,180]. 

756 

757 @return: Reduced angle C{degrees}. 

758 ''' 

759 try: 

760 return _wrapped.Math.AngNormalize(deg) 

761 except AttributeError: 

762 d = fremainder(deg, _360_0) 

763 if d in (_180_0, _N_180_0): 

764 d = _copysign(_180_0, deg) if _K_2_0 else _180_0 

765 return d 

766 

767 

768def _polygon(geodesic, points, closed, line, wrap): 

769 '''(INTERNAL) Compute the area or perimeter of a polygon, 

770 using a L{GeodesicExact}, L{GeodesicSolve} or (if the 

771 C{geographiclib} package is installed) a C{Geodesic} 

772 or C{geodesicw.Geodesic} instance. 

773 ''' 

774 if not wrap: # capability LONG_UNROLL can't be off 

775 notImplemented(None, wrap=wrap, up=3) 

776 

777 if _MODS.booleans.isBoolean(points): 

778 # recursive call for each boolean clip 

779 

780 def _a_p(clip, *args, **unused): 

781 return _polygon(geodesic, clip, *args) 

782 

783 if not closed: # closed only 

784 raise _ValueError(closed=closed, points=_composite_) 

785 

786 return points._sum1(_a_p, closed, line, wrap) 

787 

788 gP = geodesic.Polygon(line) 

789 _A = gP.AddPoint 

790 

791 Ps = _MODS.iters.PointsIter(points, loop=1, wrap=wrap) # base=LatLonEllipsoidalBase(0, 0) 

792 p1 = p0 = Ps[0] 

793 

794 # note, lon deltas are unrolled, by default 

795 _A(p1.lat, p1.lon) 

796 for p2 in Ps.iterate(closed=closed): 

797 if wrap and not Ps.looped: 

798 p2 = _unrollon(p1, p2) 

799 _A(p2.lat, p2.lon) 

800 p1 = p2 

801 if closed and line and p1 != p0: 

802 _A(p0.lat, p0.lon) 

803 

804 # gP.Compute returns (number_of_points, perimeter, signed area) 

805 return gP.Compute(False, True)[1 if line else 2] 

806 

807 

808def _polynomial(x, cs, i, j): # PYCHOK shared 

809 '''(INTERNAL) Like C++ C{GeographicLib.Math.hpp.polyval} but with a 

810 different signature and cascaded summation as C{karney._sum2_}. 

811 

812 @return: M{sum(cs[k] * x**(j - k - 1) for k in range(i, j)} 

813 ''' 

814 # assert 0 <= i <= j <= len(cs) 

815# try: 

816# return _wrapped.Math.polyval(j - i - 1, cs, i, x) 

817# except AttributeError: 

818# s, t = cs[i], _0_0 

819# for c in cs[i+1:j]: 

820# s, t = _sum2_(s * x, t * x, c) 

821# return s # + t 

822 s = cs[i] 

823 i += 1 

824 if x and i < j: 

825 s, _ = _sum2_(s, _0_0, x=x, *cs[i:j]) 

826 return s # + t 

827 

828 

829def _remainder(x, y): 

830 '''Remainder of C{x / y}. 

831 

832 @return: Remainder in the range M{[-y / 2, y / 2]}, preserving signed 0.0. 

833 ''' 

834 try: 

835 return _wrapped.Math.remainder(x, y) 

836 except AttributeError: 

837 return fremainder(x, y) 

838 

839 

840if _K_2_0: 

841 from math import cos as _cos, sin as _sin 

842 

843 def _sincos2(rad): 

844 return _sin(rad), _cos(rad) 

845 

846 _signBit = _MODS.basics.signBit 

847else: 

848 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared 

849 

850 def _signBit(x): 

851 '''(INTERNAL) GeographicLib 1.52-. 

852 ''' 

853 return x < 0 

854 

855 

856def _sincos2d(deg): 

857 '''Return sine and cosine of an angle in C{degrees}. 

858 

859 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}. 

860 ''' 

861 try: 

862 return _wrapped.Math.sincosd(deg) 

863 except AttributeError: 

864 return sincos2d(deg) 

865 

866 

867def _sincos2de(deg, t): 

868 '''Return sine and cosine of a corrected angle in C{degrees}. 

869 

870 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}. 

871 ''' 

872 try: 

873 return _wrapped.Math.sincosde(deg, t) 

874 except AttributeError: 

875 return sincos2d(deg, adeg=t) 

876 

877 

878def _sum2(u, v): # mimick geomath.Math.sum, actually sum2 

879 '''Error-free summation like C{geomath.Math.sum}. 

880 

881 @return: 2-Tuple C{(B{u} + B{v}, residual)}. 

882 

883 @note: The C{residual} can be the same as B{C{u}} or B{C{v}}. 

884 

885 @see: U{Algorithm 3.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}. 

886 ''' 

887 try: 

888 return _wrapped.Math.sum(u, v) 

889 except AttributeError: 

890 s = u + v 

891 r = s - v 

892 t = s - r 

893 # if Algorithm_3_1: 

894 # t = (u - t) + (v + r) 

895 # elif C_CPP: # Math::sum C/C++ 

896 # r -= u 

897 # t -= v 

898 # t += r 

899 # t = -t 

900 # else: 

901 t = (u - r) + (v - t) 

902 return s, t 

903 

904 

905def _sum2_(s, t, *vs, **x): 

906 '''Accumulate any B{C{vs}} into a previous C{_sum2(s, t)}. 

907 

908 @kwarg x: Optional polynomial C{B{x}=1} (C{scalar}). 

909 

910 @return: 2-Tuple C{(B{s} + B{t} + sum(B{vs}), residual)}. 

911 

912 @see: I{Karney's} C++ U{Accumulator<https://GeographicLib.SourceForge.io/ 

913 C++/doc/Accumulator_8hpp_source.html>} comments for more details and 

914 function C{_sum2} above. 

915 

916 @note: NOT "error-free", see C{pygeodesy.test/testKarney.py}. 

917 ''' 

918 x = _xkwds_get1(x, x=_1_0) 

919 p = x != _1_0 

920 

921 _s2, _u0 = _sum2, unsigned0 

922 for v in vs: 

923 if p: 

924 s *= x 

925 t *= x 

926 if v: 

927 t, u = _s2(t, v) # start at the least- 

928 if s: 

929 s, t = _s2(s, t) # significant end 

930 if s: 

931 t += u # accumulate u into t 

932# elif t: # s == 0 implies t == 0 

933# raise _AssertionError(t=t, txt_not_=_0_) 

934 else: 

935 s = _u0(u) # result is u, t = 0 

936 else: 

937 s, t = _u0(t), u 

938 return s, t 

939 

940 

941def _tand(x): 

942 '''Return C{tan(B{x})} in C{degrees}. 

943 ''' 

944 try: 

945 return _wrapped.Math.tand(x) 

946 except AttributeError: 

947 return tand(x) 

948 

949 

950def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2 

951 '''Unroll B{C{lon2 - lon1}} like C{geodesic.Geodesic.Inverse}. 

952 

953 @return: 2-Tuple C{(B{lon2} - B{lon1}, B{lon2})} with B{C{lon2}} 

954 unrolled if C{B{wrap} is True}, normalized otherwise. 

955 ''' 

956 if wrap: 

957 d, t = _diff182(lon1, lon2) 

958 lon2, _ = _sum2_(d, t, lon1) # (lon1 + d) + t 

959 else: 

960 lon2 = _norm180(lon2) 

961 return (lon2 - lon1), lon2 

962 

963 

964def _unsigned2(x): 

965 '''(INTERNAL) Unsign B{C{x}}. 

966 ''' 

967 return (neg(x), True) if _signBit(x) else (x, False) 

968 

969 

970__all__ += _ALL_DOCS(_CapsBase) 

971 

972# **) MIT License 

973# 

974# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

975# 

976# Permission is hereby granted, free of charge, to any person obtaining a 

977# copy of this software and associated documentation files (the "Software"), 

978# to deal in the Software without restriction, including without limitation 

979# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

980# and/or sell copies of the Software, and to permit persons to whom the 

981# Software is furnished to do so, subject to the following conditions: 

982# 

983# The above copyright notice and this permission notice shall be included 

984# in all copies or substantial portions of the Software. 

985# 

986# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

987# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

988# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

989# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

990# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

991# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

992# OTHER DEALINGS IN THE SOFTWARE.