Coverage for pygeodesy/trf.py: 89%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''I{Veness}' Terrestrial Reference Frames (TRF). 

5 

6Classes L{RefFrame}, registry L{RefFrames} and L{TRFError}. 

7 

8Transcoded from I{Chris Veness'} (C) 2006-2022 JavaScript originals 

9U{latlon-ellipsoidal-referenceframe.js<https://GitHub.com/ChrisVeness/geodesy/blob/master/ 

10latlon-ellipsoidal-referenceframe.js>} and U{latlon-ellipsoidal-referenceframe-txparams.js 

11<https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe-txparams.js>}. 

12 

13Following is a copy of the comments in I{Veness}' U{latlon-ellipsoidal-referenceframe.js 

14<https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe.js>}. 

15 

16Modern geodetic reference frames: a latitude/longitude point defines a geographic location on, 

17above or below the earth’s surface, measured in degrees from the equator and the U{International 

18Reference Meridian<https://WikiPedia.org/wiki/IERS_Reference_Meridian>} (IRM) and metres above 

19the ellipsoid within a given I{Terrestrial Reference Frame} at a given I{epoch}. 

20 

21This is scratching the surface of complexities involved in high precision geodesy, but may 

22be of interest and/or value to those with less demanding requirements. More information U{here 

23<https://www.Movable-Type.co.UK/scripts/geodesy-library.html>} and U{here 

24<https://www.Movable-Type.co.UK/scripts/geodesy-library.html#latlon-ellipsoidal-referenceframe>}. 

25 

26Note that I{ITRF solutions} do not directly use an ellipsoid, but are specified by Cartesian 

27coordinates. The GRS80 ellipsoid is recommended for transformations to geographical coordinates. 

28 

29Note WGS84(G730/G873/G1150) are coincident with ITRF at 10-centimetre level, see also U{here 

30<ftp://ITRF.ENSG.IGN.Fr/pub/itrf/WGS84.TXT>}. WGS84(G1674) and ITRF20014 / ITRF2008 I{"are likely 

31to agree at the centimeter level"}, see also U{QPS/Qinsy<https://Confluence.QPS.NL/qinsy/ 

32en/how-to-deal-with-etrs89-datum-and-time-dependent-transformation-parameters-45353274.html>}. 

33 

34@var RefFrames.ETRF2000: RefFrame(name='ETRF2000', epoch=2005, datum=Datums.GRS80) .Xforms=(0, -14) 

35@var RefFrames.ETRF2005: RefFrame(name='ETRF2005', epoch=2005, datum=Datums.GRS80) .Xforms=(0, -1) 

36@var RefFrames.ETRF2008: RefFrame(name='ETRF2008', epoch=2008, datum=Datums.GRS80) .Xforms=(0, 0) 

37@var RefFrames.ETRF2014: RefFrame(name='ETRF2014', epoch=2014, datum=Datums.GRS80) .Xforms=(0, -14) 

38@var RefFrames.ETRF2020: RefFrame(name='ETRF2020', epoch=2020, datum=Datums.GRS80) .Xforms=(0, -14) 

39@var RefFrames.ETRF88: RefFrame(name='ETRF88', epoch=1988, datum=Datums.GRS80) .Xforms=(0, 0) 

40@var RefFrames.ETRF89: RefFrame(name='ETRF89', epoch=1989, datum=Datums.GRS80) .Xforms=(0, -1) 

41@var RefFrames.ETRF90: RefFrame(name='ETRF90', epoch=1990, datum=Datums.GRS80) .Xforms=(0, -1) 

42@var RefFrames.ETRF91: RefFrame(name='ETRF91', epoch=1991, datum=Datums.GRS80) .Xforms=(0, -1) 

43@var RefFrames.ETRF92: RefFrame(name='ETRF92', epoch=1992, datum=Datums.GRS80) .Xforms=(0, -1) 

44@var RefFrames.ETRF93: RefFrame(name='ETRF93', epoch=1993, datum=Datums.GRS80) .Xforms=(0, -1) 

45@var RefFrames.ETRF94: RefFrame(name='ETRF94', epoch=1994, datum=Datums.GRS80) .Xforms=(0, -1) 

46@var RefFrames.ETRF96: RefFrame(name='ETRF96', epoch=1996, datum=Datums.GRS80) .Xforms=(0, -1) 

47@var RefFrames.ETRF97: RefFrame(name='ETRF97', epoch=1997, datum=Datums.GRS80) .Xforms=(0, -1) 

48@var RefFrames.GDA2020: RefFrame(name='GDA2020', epoch=2020, datum=Datums.GRS80) .Xforms=(0, -4) 

49@var RefFrames.GDA94: RefFrame(name='GDA94', epoch=1994, datum=Datums.GRS80) .Xforms=(0, -3) 

50@var RefFrames.ITRF2000: RefFrame(name='ITRF2000', epoch=1997, datum=Datums.GRS80) .Xforms=(15, -5) 

51@var RefFrames.ITRF2005: RefFrame(name='ITRF2005', epoch=2000, datum=Datums.GRS80) .Xforms=(8, -3) 

52@var RefFrames.ITRF2008: RefFrame(name='ITRF2008', epoch=2005, datum=Datums.GRS80) .Xforms=(17, -2) 

53@var RefFrames.ITRF2014: RefFrame(name='ITRF2014', epoch=2010, datum=Datums.GRS80) .Xforms=(16, -1) 

54@var RefFrames.ITRF2020: RefFrame(name='ITRF2020', epoch=2015, datum=Datums.GRS80) .Xforms=(16, 0) 

55@var RefFrames.ITRF88: RefFrame(name='ITRF88', epoch=1988, datum=Datums.GRS80) .Xforms=(3, -4) 

56@var RefFrames.ITRF89: RefFrame(name='ITRF89', epoch=1989, datum=Datums.GRS80) .Xforms=(4, -4) 

57@var RefFrames.ITRF90: RefFrame(name='ITRF90', epoch=1988, datum=Datums.GRS80) .Xforms=(6, -4) 

58@var RefFrames.ITRF91: RefFrame(name='ITRF91', epoch=1988, datum=Datums.GRS80) .Xforms=(4, -4) 

59@var RefFrames.ITRF92: RefFrame(name='ITRF92', epoch=1988, datum=Datums.GRS80) .Xforms=(4, -4) 

60@var RefFrames.ITRF93: RefFrame(name='ITRF93', epoch=1988, datum=Datums.GRS80) .Xforms=(4, -4) 

61@var RefFrames.ITRF94: RefFrame(name='ITRF94', epoch=1993, datum=Datums.GRS80) .Xforms=(4, -4) 

62@var RefFrames.ITRF96: RefFrame(name='ITRF96', epoch=1997, datum=Datums.GRS80) .Xforms=(5, -5) 

63@var RefFrames.ITRF97: RefFrame(name='ITRF97', epoch=1997, datum=Datums.GRS80) .Xforms=(5, -4) 

64@var RefFrames.NAD83: RefFrame(name='NAD83', epoch=1997, datum=Datums.GRS80) .Xforms=(0, -6) 

65@var RefFrames.NAD83cors96: RefFrame(name='NAD83cors96', epoch=1997, datum=Datums.GRS80) .Xforms=(1, 0) 

66@var RefFrames.WGS84: RefFrame(name='WGS84', epoch=1984, datum=Datums.GRS80) .Xforms=(0, -1) 

67@var RefFrames.WGS84g1150: RefFrame(name='WGS84g1150', epoch=2001, datum=Datums.GRS80) .Xforms=(1, 0) 

68@var RefFrames.WGS84g1674: RefFrame(name='WGS84g1674', epoch=2005, datum=Datums.GRS80) .Xforms=(0, 0) 

69@var RefFrames.WGS84g1762: RefFrame(name='WGS84g1762', epoch=2005, datum=Datums.GRS80) .Xforms=(0, 0) 

70''' 

71 

72from pygeodesy.basics import map1, neg, isstr, _xinstanceof, _xisscalar, _zip 

73from pygeodesy.constants import _float as _F, _0_0s, _0_0, _0_001, _0_5, _1_0, _N_1_0 

74from pygeodesy.datums import Datums, _earth_datum, _GDA2020_, _minus, _Names7, \ 

75 Transform, _S1_S, _WGS84 

76from pygeodesy.errors import TRFError, _xattr, _xellipsoidall, _xkwds 

77from pygeodesy.interns import MISSING, NN, _AT_, _COMMASPACE_, _conversion_, \ 

78 _datum_, _DOT_, _exists_, _invalid_, _MINUS_, \ 

79 _NAD83_, _no_, _PLUS_, _reframe_, _s_, _SPACE_, \ 

80 _STAR_, _to_, _WGS84_, _x_, _intern as _i 

81from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS 

82from pygeodesy.named import ADict, classname, _lazyNamedEnumItem as _lazy, _Named, \ 

83 _NamedEnum, _NamedEnumItem, _NamedTuple, Fmt, unstr 

84from pygeodesy.props import deprecated_method, property_doc_, Property_RO, property_RO 

85# from pygeodesy.streprs import Fmt, unstr # from .named 

86from pygeodesy.units import Epoch, Float 

87 

88from math import ceil as _ceil 

89 

90__all__ = _ALL_LAZY.trf 

91__version__ = '24.02.24' 

92 

93_EP0CH = Epoch(0, low=0) 

94_Es = {_EP0CH: _EP0CH} # L{Epoch}s, deleted below 

95_GRS80 = Datums.GRS80 

96_inverse_ = 'inverse' 

97_MAS = _MM = _PPB = Float # Units 

98_MM2M = _0_001 # scale mm2m, ppb2ppM, mas2as 

99_mDays = (0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 0) 

100_366_0 = _F(sum(_mDays)) 

101_rates_ = 'rates' # PYCHOK used! 

102_Rs = {} # L{TRFXform7Tuple}s de-dup, deleted below 

103_S_S1 = _N_1_0 / _S1_S # Transform.s for .s1 == 0 

104_v_ = 'v' 

105_xform_ = 'xform' # PYCHOK used! 

106_Xs = {} # L{TRFXform7Tuple}s de-dup, deleted below 

107 

108_ETRF88_ = _i('ETRF88') 

109_ETRF89_ = _i('ETRF89') 

110_ETRF90_ = _i('ETRF90') 

111_ETRF91_ = _i('ETRF91') 

112_ETRF92_ = _i('ETRF92') 

113_ETRF93_ = _i('ETRF93') 

114_ETRF94_ = _i('ETRF94') 

115_ETRF96_ = _i('ETRF96') 

116_ETRF97_ = _i('ETRF97') 

117_ETRF2000_ = _i('ETRF2000') 

118_ETRF2005_ = _i('ETRF2005') 

119_ETRF2008_ = _i('ETRF2008') 

120_ETRF2014_ = _i('ETRF2014') 

121_ETRF2020_ = _i('ETRF2020') 

122_GDA94_ = _i('GDA94') 

123_ITRF_ = _i('ITRF') 

124_ITRF88_ = _i('ITRF88') 

125_ITRF89_ = _i('ITRF89') 

126_ITRF90_ = _i('ITRF90') 

127_ITRF91_ = _i('ITRF91') 

128_ITRF92_ = _i('ITRF92') 

129_ITRF93_ = _i('ITRF93') 

130_ITRF94_ = _i('ITRF94') 

131_ITRF96_ = _i('ITRF96') 

132_ITRF97_ = _i('ITRF97') 

133_ITRF2000_ = _i('ITRF2000') 

134_ITRF2005_ = _i('ITRF2005') 

135_ITRF2008_ = _i('ITRF2008') 

136_ITRF2014_ = _i('ITRF2014') 

137_ITRF2020_ = _i('ITRF2020') 

138_NAD83cors96_ = _i('NAD83cors96') 

139_WGS84g1150_ = _i('WGS84g1150') 

140_WGS84g1674_ = _i('WGS84g1674') 

141_WGS84g1762_ = _i('WGS84g1762') 

142 

143 

144def _E(epoch): # deleted below 

145 '''(INTERNAL) De-dup L{Epochs}s. 

146 ''' 

147 e = Epoch(_F(epoch)) 

148 return _Es.setdefault(e, e) # PYCHOK del 

149 

150 

151def _P(ps, name, _Ps): # deleted below 

152 '''(INTERNAL) De-dup L{TRFXform7Tuple}s. 

153 ''' 

154 t = TRFXform7Tuple(map(_F, ps), name=name) 

155 return _Ps.setdefault(t, t) 

156 

157 

158class RefFrame(_NamedEnumItem): 

159 '''Terrestrial Reference Frame (TRF) parameters. 

160 ''' 

161 _datum = _GRS80 # Datums.GRS80 or .WGS84 (L{Datum}) 

162 _epoch = _EP0CH # epoch, fractional year (L{Epoch}) 

163 

164 def __init__(self, epoch, datum, name=NN): 

165 '''New L{RefFrame}. 

166 

167 @arg epoch: Epoch, a fractional calendar year (C{scalar} or C{str}). 

168 @arg datum: Datum or ellipsoid (L{Datum}, {Ellipsoid}, L{Ellipsoid2} 

169 or L{a_f2Tuple}). 

170 @kwarg name: Unique, non-empty name (C{str}). 

171 

172 @raise NameError: A L{RefFrame} with that B{C{name}} already exists. 

173 

174 @raise TRFError: Invalid B{C{epoch}}. 

175 

176 @raise TypeError: Invalid B{C{datum}}. 

177 ''' 

178 if datum is not _GRS80: 

179 _earth_datum(self, datum, raiser=_datum_) 

180 self._epoch = _Epoch(epoch) 

181 self._Xto = {} # dict of Xforms 

182 if name: 

183 self._register(RefFrames, name) 

184 

185 def __eq__(self, other): 

186 return isinstance(other, RefFrame) and other.epoch == self.epoch \ 

187 and other.datum == self.datum 

188 

189 def __lt__(self, other): # for sorting 

190 return isinstance(other, RefFrame) and (self.name < other.name 

191 or self.epoch < other.epoch) 

192 

193 @deprecated_method # PYCHOK Python 3.5+ 

194 def __matmul__(self, point): 

195 '''DEPRECATED on 2024.02.16, use method C{B{point}.toRefFrame}.''' 

196 return _toRefFrame(point, self) 

197 

198 @property_RO 

199 def datum(self): 

200 '''Get this reference frame's datum (L{Datum}). 

201 ''' 

202 return self._datum 

203 

204 @property_RO 

205 def ellipsoid(self): 

206 '''Get this reference frame's ellipsoid (L{Ellipsoid} or L{Ellipsoid2}). 

207 ''' 

208 return self._datum.ellipsoid 

209 

210 @Property_RO 

211 def epoch(self): 

212 '''Get this reference frame's epoch (C{Epoch}). 

213 ''' 

214 return self._epoch 

215 

216 def toRefFrame(self, point, reframe2, **epoch2_epoch_name): 

217 '''Convert an ellipsoidal point from this reframe and from C{epoch} to 

218 an other C{reframe2} and C{epoch2 or epoch}. 

219 

220 @arg point: The point to convert (C{Cartesian} or C{LatLon}). 

221 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}). 

222 @kwarg epoch2_epoch_name: Optional keyword arguments C{B{epoch2}=None}, 

223 C{B{epoch}=None} and C{B{name}=NN}. 

224 

225 @return: A copy of the B{C{point}}, converted or renamed. 

226 

227 @raise TypeError: Invalid B{C{point}}. 

228 

229 @note: The B{C{point}}'s C{reframe} and C{epoch} are overridden by 

230 this reframe respectively B{C{epoch}} or this reframe's epoch. 

231 

232 @see: Ellipsoidal methods L{toRefFrame<ellipsoidalBase.LatLonEllipsoidalBase.toRefFrame>} 

233 and L{toRefFrame<ellipsoidalBase.CartesianEllipsoidalBase.toRefFrame>} 

234 for more details. 

235 ''' 

236 return _toRefFrame(point, reframe2, reframe=self, 

237 **_xkwds(epoch2_epoch_name, name=self.name)) 

238 

239 def toStr(self, epoch=None, name=NN, **unused): # PYCHOK expected 

240 '''Return this reference frame as a string. 

241 

242 @kwarg epoch: Override this reframe's epoch (C{scalar} or C{str}). 

243 @kwarg name: Override name (C{str}) or C{None} to exclude the 

244 reframe's name. 

245 

246 @return: This L{RefFrame}'s attributes (C{str}). 

247 ''' 

248 D = self.datum 

249 e = self.epoch if epoch is None else _Epoch(epoch) 

250 t = (Fmt.EQUAL(name=repr(name or self.name)), 

251 Fmt.EQUAL(epoch=e), 

252 Fmt.EQUAL(datum=_DOT_(classname(D) + _s_, D.name))) 

253 return _COMMASPACE_.join(t[int(name is None):]) 

254 

255 def Xform(self, reframe2): 

256 '''Get the converter Xform I{from} this reference frame I{to} C{reframe2}. 

257 

258 @arg reframe2: Destination frame to convert I{to} (L{RefFrame} or C{str}). 

259 

260 @return: The L{TRFXform} instance or C{None} if not available. 

261 

262 @raise TypeError: Invalid B{C{reframe2}}. 

263 ''' 

264 _xinstanceof(RefFrame, str, reframe2=reframe2) 

265 n2 = reframe2 if isstr(reframe2) else reframe2.name 

266 return self._Xto.get(n2, None) 

267 

268 def Xforms(self, inverse=False): 

269 '''Return all Xforms converting I{from} or I{to} this reference frame or both. 

270 

271 @kwarg inverse: If C{True}, get all I{inverse, to} Xforms (C{bool}) or if 

272 C{B{inverse}=2} (C{int}) get all I{to} Xforms I{inverted} 

273 plus all I{from} Xforms. 

274 

275 @return: An L{ADict} of C{name=}L{TRFXform}s I{from} this reframe or if 

276 C{B{inverse}=True} I{to} this reframe or if C{B{inverse}=2} both. 

277 ''' 

278 def _Xi(n2, i): 

279 for n1, r in RefFrames.items(): 

280 X = r._Xto.get(n2, None) 

281 if X: 

282 yield n1, (X.inverse() if i else X) 

283 

284 i = inverse == 2 

285 d = ADict(_Xi(self.name, i) if inverse else self._Xto) 

286 if i: 

287 d.update(self._Xto) # from overrides inverted to 

288 return d 

289 

290 

291class RefFrames(_NamedEnum): 

292 '''(INTERNAL) L{RefFrame} registry, I{must} be a sub-class 

293 to accommodate the L{_LazyNamedEnumItem} properties. 

294 ''' 

295 def _Lazy(self, epoch, datum=_GRS80, name=NN): 

296 '''(INTERNAL) Instantiate the L{RefFrame}. 

297 ''' 

298 return RefFrame(epoch, datum, name=name) 

299 

300RefFrames = RefFrames(RefFrame) # PYCHOK singleton 

301'''Some pre-defined L{RefFrame}s, all I{lazily} instantiated.''' 

302# <https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe.js> 

303RefFrames._assert( 

304 ETRF88 = _lazy(_ETRF88_, _E(1988)), # epoch, datum? 

305 ETRF89 = _lazy(_ETRF89_, _E(1989)), # epoch, datum? 

306 ETRF90 = _lazy(_ETRF90_, _E(1990)), # epoch, datum? 

307 ETRF91 = _lazy(_ETRF91_, _E(1991)), # epoch, datum? 

308 ETRF92 = _lazy(_ETRF92_, _E(1992)), # epoch, datum? 

309 ETRF93 = _lazy(_ETRF93_, _E(1993)), # epoch, datum? 

310 ETRF94 = _lazy(_ETRF94_, _E(1994)), # epoch, datum? 

311 ETRF96 = _lazy(_ETRF96_, _E(1996)), # epoch, datum? 

312 ETRF97 = _lazy(_ETRF97_, _E(1997)), # epoch, datum? 

313 ETRF2000 = _lazy(_ETRF2000_, _E(2005)), 

314 ETRF2005 = _lazy(_ETRF2005_, _E(2005)), # epoch, datum? 

315 ETRF2008 = _lazy(_ETRF2008_, _E(2008)), # epoch, datum? 

316 ETRF2014 = _lazy(_ETRF2014_, _E(2014)), # epoch, datum? 

317 ETRF2020 = _lazy(_ETRF2020_, _E(2020)), # epoch, datum? 

318 GDA94 = _lazy(_GDA94_, _E(1994)), # Australia 

319 GDA2020 = _lazy(_GDA2020_, _E(2020)), # Australia 

320 ITRF88 = _lazy(_ITRF88_, _E(1988)), 

321 ITRF89 = _lazy(_ITRF89_, _E(1989)), 

322 ITRF90 = _lazy(_ITRF90_, _E(1988)), 

323 ITRF91 = _lazy(_ITRF91_, _E(1988)), 

324 ITRF92 = _lazy(_ITRF92_, _E(1988)), 

325 ITRF93 = _lazy(_ITRF93_, _E(1988)), 

326 ITRF94 = _lazy(_ITRF94_, _E(1993)), 

327 ITRF96 = _lazy(_ITRF96_, _E(1997)), 

328 ITRF97 = _lazy(_ITRF97_, _E(1997)), 

329 ITRF2000 = _lazy(_ITRF2000_, _E(1997)), # aka ITRF00 

330 ITRF2005 = _lazy(_ITRF2005_, _E(2000)), 

331 ITRF2008 = _lazy(_ITRF2008_, _E(2005)), # aka ITRF08 

332 ITRF2014 = _lazy(_ITRF2014_, _E(2010)), 

333 ITRF2020 = _lazy(_ITRF2020_, _E(2015)), 

334 NAD83 = _lazy(_NAD83_, _E(1997)), 

335 NAD83cors96 = _lazy(_NAD83cors96_, _E(1997)), 

336 WGS84 = _lazy(_WGS84_, _E(1984), _WGS84), 

337 WGS84g1150 = _lazy(_WGS84g1150_, _E(2001), _WGS84), 

338 WGS84g1674 = _lazy(_WGS84g1674_, _E(2005), _WGS84), 

339 WGS84g1762 = _lazy(_WGS84g1762_, _E(2005), _WGS84)) # same epoch 

340 

341 

342class TransformXform(Transform): 

343 '''Helmert transformation, extended with an C{Xform} converter. 

344 

345 @see: L{Transform<datums.Transform>} and L{Xform<TRFXform>}. 

346 ''' 

347 _Xform = None 

348 

349 def __init__(self, name=NN, **tx_ty_tz_s_sx_sy_sz): # PYCHOK signature 

350 '''New L{TransformXform}. 

351 

352 @kwarg name: Optional name (C{str}), I{not registered}. 

353 

354 @see: L{Transform<datums.Transform>} for details. 

355 

356 @note: This L{TransformXform}'s name starts with C{"-"} iff 

357 I{inversed}. 

358 ''' 

359 Transform.__init__(self, **tx_ty_tz_s_sx_sy_sz) 

360 if name: 

361 self.name = name 

362 

363 def __eq__(self, other): 

364 return isinstance(other, TransformXform) and Transform.__eq__(self, other) 

365 

366 def __hash__(self): 

367 return Transform.__hash__(self) 

368 

369 def rename(self, name=NN): 

370 '''Change this transform's name. 

371 

372 @arg name: New name (C{str}), overriding this transform's Xform's name. 

373 

374 @return: The previous name (C{str}). 

375 ''' 

376 X = self.Xform 

377 n = name or (X.toStr() if X else NN) 

378 return Transform.rename(self, n) 

379 

380 def toRefFrame(self, point, name=NN): # PYCHOK signature 

381 '''Convert an ellipsoidal point using this transform and Xform. 

382 

383 @arg point: The point to convert (C{Cartesian} or C{LatLon}). 

384 

385 @return: A copy of the B{C{point}}, converted I{directly} to 

386 this transform's Xform's C{refName2} and C{epoch}. 

387 

388 @note: The B{C{point}}'s original C{reframe} and C{epoch} are 

389 I{ignored}, its C{datum} and C{height} are preserved 

390 but I{not} taken into account. 

391 ''' 

392 _ = _xellipsoidall(point) 

393 p = point.dup() if self.isunity else point.toTransform(self) 

394 X = self.Xform 

395 if X: # see _toRefFrame below 

396 p._reframe = X.reframe2 

397 p._epoch = X.epoch 

398 p.rename(name or self.name) 

399 return p 

400 

401 def toTransform(self, epoch1, **epoch2_inverse): 

402 '''Return this transform observed at B{C{epoch1}} as a Helmert 

403 L{TransformXform}, optionally at B{C{epoch2 or epoch1}}. 

404 

405 @arg epoch1: Epoch to observe I{from} (C{scalar}). 

406 @kwarg epoch2_inverse: Optional C{B{epoch2}=None} to observe 

407 I{to} and C{B{inverse}=False}, see method 

408 L{toTransform<TRFXform.toTransform>} from 

409 L{TRFXform}. 

410 

411 @return: The Helmert transform (L{TransformXform}). 

412 

413 @raise TRFError: Invalid B{C{epoch1}}, B{C{epoch2}} or 

414 missing Xform. 

415 ''' 

416 X = self.Xform 

417 if X is None: 

418 raise TRFError(Xform=X, txt=MISSING) 

419 return X.toTransform(epoch1, **epoch2_inverse) 

420 

421 def velocities(self, factor=_MM2M, **Vector_and_kwds): 

422 '''Compute the X, Y and Z I{velocities} of this transform. 

423 

424 @kwarg factor: Factor to scale this Xform's C{rates} (C{scalar}), 

425 default from C{milli-meter-} to C{meter-per-year}. 

426 @kwarg Vector_and_kwds: An optional, (3-D) C{B{Vector}=None} or 

427 cartesian class and additional C{B{Vector}} 

428 keyword arguments to return the I{velocities}. 

429 

430 @return: A L{Vector3Tuple}C{(x, y, z)} unless some B{C{Vector_and_kwds}} 

431 is specified or C{None} if this transform's Xform is missing. 

432 

433 @raise TypeError: Non-scalar B{C{factor}}. 

434 

435 @see: Altamimi, Z. "EUREF-TN-1-Jan-31-2024", U{Appendix A, equation (3) 

436 <http://ETRS89.ENSG.IGN.FR/pub/EUREF-TN-1-Jan-31-2024.pdf>}. 

437 ''' 

438 v = X = self.Xform 

439 if X is not None: 

440 r = X.rates * factor # eq (3) ... 

441 H = Transform(tx=r.sx, ty=r.sy, tz=r.sz, # Xyy-dot 

442 s=_S_S1, name=NN(self.name, _v_)) 

443 H.s1, H.rx, H.ry, H.rz = 0, self.rx, self.ry, self.rz 

444 v = H.transform(r.tx, r.ty, r.tz, inverse=False, # Xyy 

445 **Vector_and_kwds) 

446 return v 

447 

448 @property_doc_(''' the Xform (L{TRFXform}).''') 

449 def Xform(self): 

450 '''Get this Helmert transform's Xform (L{TRFXform} or C{None}). 

451 ''' 

452 return self._Xform 

453 

454 @Xform.setter # PYCHOK setter! 

455 def Xform(self, Xform): 

456 '''Set this Helmert transform's Xform (L{TRFXform}). 

457 

458 @raise TypeError: Invalid B{C{Xform}}. 

459 ''' 

460 _xinstanceof(TRFXform, Xform=Xform) 

461 self._Xform = Xform 

462 

463 

464class TRFXform7Tuple(_NamedTuple): 

465 '''7-Tuple C{(tx, ty, tz, s, sx, sy, sz)} of conversion parameters with 

466 translations C{tx}, C{ty} and C{tz} in C{milli-meter}, scale C{s} in 

467 C{ppb} and rates C{sx}, C{sy} and C{sz} in C{milli-arc-seconds-per-year}. 

468 

469 @note: The parameters are also named as C{(Tx, Ty, Tz, D, Rx, Ry, Rz)} 

470 or C{(T1, T2, T3, D, R1, R2, R3)}. 

471 

472 @see: Class L{TransformXform}'s matching keyword argument names. 

473 ''' 

474 _Names_ = _Names7 # ('tx', 'ty', 'tz', _s_, 'sx', 'sy', 'sz') == Transform.__init__ 

475 _Units_ = (_MM, _MM, _MM, _PPB, _MAS, _MAS, _MAS) 

476 

477 def __add__(self, other): 

478 _xinstanceof(TRFXform7Tuple, other=other) 

479 return type(self)(((a + b) for a, b in _zip(self, other)), name=_PLUS_) # .fsums._add_op 

480 

481 def __eq__(self, other): 

482 return isinstance(other, TRFXform7Tuple) and all(a == b for a, b in _zip(self, other)) 

483 # PYCHOK and self.name == other.name 

484 

485 def __hash__(self): 

486 return self._hash # memoized 

487 

488 def __mul__(self, factor): 

489 _xisscalar(factor=factor) 

490 return type(self)((s * factor for s in self), name=_STAR_) # .fsums._mul_op 

491 

492 def __neg__(self): 

493 return self.inverse() 

494 

495 def __sub__(self, other): 

496 _xinstanceof(TRFXform7Tuple, other=other) 

497 return type(self)(((a - b) for a, b in _zip(self, other)), name=_MINUS_) # .fsums._sub_op 

498 

499 @Property_RO 

500 def _hash(self): 

501 return hash(s for s in self) 

502 

503 def inverse(self, name=NN): 

504 '''Return the inverse of this transform. 

505 

506 @kwarg name: Optional name (C{str}). 

507 

508 @return: Inverse (L{TransformXform}). 

509 ''' 

510 n = name or _minus(self.name) 

511 return type(self)(map(neg, self), name=n) 

512 

513 @Property_RO 

514 def isunity(self): 

515 '''Is this a C{unity, identidy} transform (C{bool}). 

516 ''' 

517 return not any(self) 

518 

519 

520class TRFXform(_Named): 

521 '''A Terrestrial Reference Frame (TRF) converter between two 

522 reference frames observed at an C{epoch}. 

523 ''' 

524 _epoch = _EP0CH 

525 _epoch_d = _0_0 

526 _indir_d = NN # refName 

527 _inver_d = False 

528 refName1 = \ 

529 refName2 = NN 

530 rates = \ 

531 xform = None 

532 

533 def __init__(self, refName1, refName2, epoch=None, xform=None, 

534 rates=None, name=NN): 

535 '''New L{trfXform}. 

536 

537 @arg refName1: Source reframe (C{str}), converting I{from}. 

538 @arg refName2: Destination reframe (C{str}), converting I{to}. 

539 @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str}). 

540 @kwarg xform: I{Transform} parameters (L{TRFXform7Tuple}). 

541 @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), like B{C{xform}}, 

542 but in C{units-per-year}. 

543 @kwarg name: Optional name (C{str}), overriding the default from 

544 method L{toStr<TRFXform.toStr>}. 

545 

546 @return: The TRF converter (L{TRFXform}). 

547 

548 @raise TRFError: Invalid B{C{epoch}}, B{C{xform}} or B{C{rates}}. 

549 ''' 

550 self.refName1 = str(refName1) 

551 self.refName2 = str(refName2) 

552 _xinstanceof(TRFXform7Tuple, xform=xform, rates=rates) 

553 self.epoch = epoch 

554 self.xform = xform 

555 self.rates = rates 

556 self.rename(name or self.toStr()) 

557 

558 def __add__(self, other): 

559 _xinstanceof(TRFXform, other=other) 

560 assert self.epoch == other.epoch 

561 n = other.name 

562 n = NN(self.name, (NN if n.startswith(_MINUS_) else _PLUS_), n) 

563 return type(self)(self.refName1, other.refName2, epoch=self.epoch, 

564 xform=self.xform + other.xform, 

565 rates=self.rates + other.rates, 

566 name=n) 

567 

568 def __eq__(self, other): 

569 return isinstance(other, TRFXform) and self.epoch == other.epoch and \ 

570 self.xform == other.xform and self.rates == other.rates 

571 

572# def __hash__(self): 

573# return hash((self.xform._hash * 1e18 + self.rates._hash) * 1e5 + self.epoch) 

574 

575 def __lt__(self, other): # for sorting 

576 return isinstance(other, TRFXform) and (self.refName1 < other.refName1 

577 or self.refName2 < other.refName2 

578 or self.epoch < other.epoch) 

579 

580 def __neg__(self): 

581 return self.inverse() 

582 

583 def __repr__(self): 

584 return self.toRepr() 

585 

586 def __str__(self): 

587 return self.toStr() 

588 

589 def _at(self, epoch): 

590 '''(INTERNAL) Return C{"self.nameB{@}epoch"}. 

591 ''' 

592 n = self.name 

593 if epoch != self.epoch: 

594 _e = _AT_(NN, epoch) 

595 if not n.endswith(_e): 

596 n = NN(n, _e) 

597 return n 

598 

599 @property_doc_(''' the epoch, fractional year (L{Epoch}).''') 

600 def epoch(self): 

601 '''Get the epoch (L{Epoch}). 

602 ''' 

603 return self._epoch 

604 

605 @epoch.setter # PYCHOK setter! 

606 def epoch(self, epoch): 

607 '''Set the epoch (L{Epoch}, C{scalar} or C{str}). 

608 

609 @raise TRFError: Invalid B{C{epoch}}. 

610 ''' 

611 e = _Epoch(epoch) 

612 if self._epoch != e: 

613 self.rename(self._at(e)) 

614 self._epoch = e 

615 

616 @property_RO 

617 def epoched(self): 

618 '''Get this Xform's I{epoch} deltas (C{float}). 

619 ''' 

620 return self._epoch_d 

621 

622 @property_RO 

623 def indirected(self): 

624 '''Is this an I{indirected} Xform? (C{str}) or C{NN}. 

625 ''' 

626 return self._indir_d 

627 

628 def inverse(self, name=NN): 

629 '''Get an I{inverse} of this Xform, C{refName1} and C{-2} swapped. 

630 

631 @return: Inverse (L{TRFXform}). 

632 ''' 

633 return self.dup(refName1=self.refName2, xform=-self.xform, 

634 refName2=self.refName1, rates=-self.rates, 

635 name=name or _minus(self.name), 

636 _inver_d=not self.inversed) 

637 

638 @property_RO 

639 def inversed(self): 

640 '''Is this an I{inversed} Xform? (C{bool}). 

641 ''' 

642 return self._inver_d 

643 

644 def _reframe(self, name, datum=_GRS80): 

645 '''(INTERNAL) Get an un-/registered frame. 

646 ''' 

647 r = RefFrames.get(name) 

648 if r is None or r.datum != datum: 

649 r = RefFrame(self.epoch, datum) 

650 r.name = name # unregistered 

651 return r 

652 

653 @property_RO 

654 def reframe1(self): 

655 '''Get the un-/registered I{from} frame (C{RefFrame}). 

656 ''' 

657 return self._reframe(self.refName1) 

658 

659 @property_RO 

660 def reframe2(self): 

661 '''Get the un-/registered I{to} frame (C{RefFrame}). 

662 ''' 

663 return self._reframe(self.refName2) 

664 

665 def rename(self, name=NN): 

666 '''Change this Xform's name. 

667 

668 @arg name: New name (C{str}), overriding the base 

669 name C{"refName1B{@}epochB{x}refName2"}. 

670 

671 @return: The old name (C{str}). 

672 ''' 

673 return _Named.rename(self, name or self.toStr()) 

674 

675 def toEpoch(self, epoch): 

676 '''Convert this Xform to B{C{epoch}}, if needed. 

677 

678 @arg epoch: Epoch, fractional year (C{Epoch}, C{scalar} 

679 or C{str}). 

680 

681 @return: This Xform or a copy converted to B{C{epoch}}. 

682 

683 @raise TRFError: Invalid B{C{epoch}}. 

684 ''' 

685 e = _Epoch(epoch) 

686 X, d = self, e - self.epoch 

687 if d: 

688 t = X.xform + X.rates * d 

689 X = X.dup(epoch=e, xform=t, name=X._at(e)) 

690 X._epoch_d += d # abs(d)? 

691 return X 

692 

693 def toHelmert(self, factor=_MM2M): 

694 '''Return the Helmert transform from this Xform scaled accordingly. 

695 

696 @kwarg factor: Scale to convert C{milli-meter} (C{scalar}). 

697 

698 @return: The Helmert transform (L{TransformXform}). 

699 

700 @note: By defaut, Translations are converted from C{milli-meter} to 

701 C{meter}, rates from C{milli-arc-seconds} to C{arc-seconds} 

702 and scale from C{ppb} to C{ppM}. 

703 ''' 

704 h = self.xform * factor 

705 H = TransformXform(name=self.name, **dict(h.items())) 

706 H.Xform = self 

707 return H 

708 

709 def toRefFrame(self, point, epoch=None, datum=_GRS80, **epoch2_name): 

710 '''Convert an ellipsoidal point from this Xform's C{refName1} and 

711 C{epoch} to this Xform's C{refName2} and C{epoch2 or epoch}. 

712 

713 @arg point: The point to convert (C{Cartesian} or C{LatLon}). 

714 @kwarg epoch: Optional epoch ((L{Epoch}, C{scalar} or C{str})), 

715 overriding this Xform's C{epoch}. 

716 @kwarg datum: Optional datum to define a temporary L{RefFrame} from 

717 this Xform's C{refName1} or C{refName2} (C{datum}). 

718 @kwarg epoch2_name: Optional keyword arguments B{C{epoch2}=None} 

719 and C{B{name}=refName1}. 

720 

721 @return: A copy of the B{C{point}}, converted or renamed. 

722 

723 @see: Method L{RefFrame.toRefFrame} for more details. 

724 ''' 

725 def _r(name): 

726 r = RefFrames.get(name) 

727 if r is None or r.datum != datum: 

728 r = RefFrame(epoch or self.epoch, datum) 

729 r.name = name # unregistered 

730 return r 

731 

732 return _r(self.refName1).toRefFrame(point, 

733 _r(self.refName2), epoch=epoch, **epoch2_name) 

734 

735 def toRepr(self, **unused): # PYCHOK signature 

736 '''Return the represention of this Xform (C{str}). 

737 ''' 

738 return unstr(self.classname, name=self.name, epoch=self.epoch) 

739 

740 def toStr(self, epoch=None, **unused): # PYCHOK signature 

741 '''Return this Xform as C{"refName1B{@}epochB{x}refName2"} (C{str}). 

742 

743 @kwarg epoch: Epoch (C{Epoch}, C{scalar} or C{str}), overriding 

744 this Xform's epoch. 

745 ''' 

746 e = self.epoch if epoch is None else _Epoch(epoch) 

747 return NN(_AT_(self.refName1, e), _x_, self.refName2) 

748 

749 def toTransform(self, epoch, epoch2=None, inverse=False): 

750 '''Combine this Xform observed at B{C{epoch}} into a Helmert 

751 L{TransformXform}, optionally at B{C{epoch2 or epoch}}. 

752 

753 @arg epoch: Epoch to observe I{from} (C{scalar}). 

754 @kwarg epoch2: Optional epoch to observe I{to} (C{scalar}). 

755 @kwarg inverse: Use the Xform's inverse (C{bool}). 

756 

757 @return: The Helmert transform (L{TransformXform}). 

758 

759 @raise TRFError: Invalid B{C{epoch}} or B{C{epoch2}}. 

760 

761 @see: Method L{toHelmert}. 

762 ''' 

763 # X=self.toEpoch(epoch); if epoch2: X=X.toEpoch(epoch2) 

764 e = epoch if epoch2 is None else Epoch(epoch2=epoch2) 

765 X = self.toEpoch(e) 

766 if inverse: 

767 X = X.inverse() 

768 return X.toHelmert() 

769 

770 

771def date2epoch(year, month, day): 

772 '''Return the C{epoch} for a calendar day. 

773 

774 @arg year: Year of the date (C{scalar}). 

775 @arg month: Month in the B{C{year}} (C{scalar}, 1..12). 

776 @arg day: Day in the B{C{month}} (C{scalar}, 1..31). 

777 

778 @return: Epoch, the fractional year (C{float}). 

779 

780 @raise TRFError: Invalid B{C{year}}, B{C{month}} or B{C{day}}. 

781 

782 @note: Any B{C{year}} is considered a leap year, i.e. having 

783 29 days in February. 

784 ''' 

785 try: 

786 y, m, d = map1(int, year, month, day) 

787 if y > 0 and 1 <= m <= 12 and 1 <= d <= _mDays[m]: 

788 e = y + float(sum(_mDays[:m]) + d) / _366_0 

789 return Epoch(e, low=0) 

790 

791 raise ValueError # _invalid_ 

792 except (TRFError, TypeError, ValueError) as x: 

793 raise TRFError(year=year, month=month, day=day, cause=x) 

794 

795 

796def _direct(n1, n2): 

797 '''(INTERNAL) Get the C{n1} to C{n2} Xform or C{None}. 

798 ''' 

799 r = RefFrames.get(n1) 

800 return r._Xto.get(n2, None) if r else None 

801 

802 

803def _Epoch(e, **kwds): 

804 '''(INTERNAL) Get the C{Epoch(B{e})}. 

805 ''' 

806 return e if isinstance(e, Epoch) and not kwds else Epoch(e, **kwds) 

807 

808 

809def epoch2date(epoch): 

810 '''Return the date for a reference frame C{epoch}. 

811 

812 @arg epoch: Fractional year (C{scalar}). 

813 

814 @return: 3-Tuple C{(year, month, day)}. 

815 

816 @raise TRFError: Invalid B{C{epoch}}. 

817 

818 @note: Any B{C{year}} is considered a leap year, i.e. having 

819 29 days in February. 

820 ''' 

821 e = Epoch(epoch, low=0) 

822 y = int(e) 

823 d = int(_ceil((e - y) * _366_0)) 

824 for m, n in enumerate(_mDays[1:]): 

825 if d > n: 

826 d -= n 

827 else: 

828 break 

829 return y, (m + 1), max(1, d) 

830 

831 

832def _eXhaust(n1, n2): 

833 '''(INTERNAL) Yield all possible Xforms C{n1} to {n2} via 

834 any number of intermediate reframes. 

835 ''' 

836 R = dict(RefFrames) 

837 r = R.pop(n1, None) 

838 if r: 

839 Xs = list(r.Xforms(inverse=2).items()) 

840 while Xs: 

841 n, X = Xs.pop(0) 

842 if n == n2: 

843 yield X 

844 else: 

845 r = R.pop(n, None) 

846 if r: 

847 for n, x in r.Xforms(inverse=2).items(): 

848 x = x.toEpoch(X.epoch) 

849 Xs.append((n, X + x)) 

850 

851 

852def _indirects(n1, n2): 

853 '''(INTERNAL) Yield all Xforms between C{n1} and C{n2} via 

854 I{one} intermediate reframe C{n}. 

855 ''' 

856 def _X4(_Xto, n2): 

857 _d = _direct 

858 for n, X1 in _Xto.items(): 

859 X2 = _d(n, n2) 

860 if X2: 

861 yield X1, X2, n, True # + 

862 X2 = _d(n2, n) 

863 if X2: 

864 yield X1, X2, n, False # - 

865 

866 r1 = RefFrames.get(n1) 

867 if r1: 

868 for X1, X2, n, f in _X4(r1._Xto, n2): 

869 e1, e2 = X1.epoch, X2.epoch 

870 if e1 < e2: # X1 to e2 

871 X1 = X1.toEpoch(e2) 

872 e1 = e2 

873 elif e1 > e2: # X2 to e1 

874 X2 = X2.toEpoch(e1) 

875 # U{Appendix, Table 7, last column "Sum of the previous ..." 

876 # <https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf">} 

877 X = TRFXform(n1, n2, epoch=e1, 

878 xform=X1.xform + (X2.xform if f else -X2.xform), 

879 rates=X1.rates + (X2.rates if f else -X2.rates), 

880 name=NN(X1._at(e1), _PLUS_ if f else _MINUS_, 

881 X2._at(e1))) 

882 X._epoch_d = X1.epoched + X2.epoched # max, abs? 

883 X._indir_d = n # reframe? 

884 yield X 

885 

886 

887def _reframe(**name_reframe): 

888 '''(INTERNAL) Get a C{reframe}. 

889 ''' 

890 if len(name_reframe) == 1: 

891 for r in name_reframe.values(): 

892 break 

893 if isstr(r) and r: # not NN 

894 r = RefFrames.get(r) 

895 if r and isinstance(r, RefFrame): 

896 return r 

897 raise TRFError(**name_reframe) # _invalid_ 

898 

899 

900def _toRefFrame(point, reframe2, reframe=None, epoch=None, 

901 epoch2=None, name=NN, **LatLon_kwds): 

902 '''(INTERNAL) Convert an ellipsoidal point to C{reframe2} 

903 and C{epoch2 or epoch or pont.epoch or reframe.epoch}. 

904 ''' 

905 ll = _xellipsoidall(point) 

906 r1 = reframe or point.reframe 

907 if not r1: 

908 t = _SPACE_(_DOT_(repr(point), _reframe_), MISSING) 

909 raise TRFError(_no_(_conversion_), txt=t) 

910 

911 _xinstanceof(RefFrame, reframe2=reframe2, reframe=r1) 

912 

913 e1 = _Epoch(epoch or point.epoch or r1.epoch) 

914 e2 = e1 if epoch2 is None else Epoch(epoch2=epoch2) 

915 t0 = _toTransform0(r1.name, e1, reframe2.name, e2) 

916 if t0 is None: 

917 t = _SPACE_(RefFrame.__name__, _AT_(r1.name, e1), 

918 _to_, _AT_(reframe2.name, e2)) 

919 raise TRFError(_no_(_conversion_), txt=t) 

920 

921 if t0: # is not () 

922 if t0.isunity: 

923 p = point.dup() 

924 elif point.datum: 

925 p = point.toCartesian() if ll else point 

926 p = p.toDatum( r1.datum).toTransform(t0) \ 

927 .toDatum(reframe2.datum).toDatum(point.datum) 

928 if ll: 

929 p = p.toLatLon(LatLon=point.classof, **LatLon_kwds) 

930 elif ll: # and LatLon_kwds 

931 p = point.toTransform(t0, **LatLon_kwds) 

932 else: 

933 p = point.toTransform(t0) 

934 p._reframe = reframe2 # see TRFXform.toRefFrame above 

935 p._epoch = _xattr(t0.Xform, epoch=e2) 

936 p.rename(name or reframe2.name) 

937 else: 

938 p = point.dup(name=name) if name else point 

939 return p 

940 

941 

942def _toTransform0(n1, e1, n2, e2, **indirect_inverse): 

943 '''(INTERNAL) Return a L{TransformXform}, 0-tuple or C{None}. 

944 ''' 

945 if n1 == n2 and e1 == e2: 

946 return () # unity? 

947 

948 for X in _toTransforms(n1, e1, n2, e2, **indirect_inverse): 

949 return X # first OK? 

950 

951 if (n1.startswith(_ITRF_) and n2.startswith(_WGS84_)) or \ 

952 (n2.startswith(_ITRF_) and n1.startswith(_WGS84_)): 

953 return () # unity? 

954 

955 return None 

956 

957 

958def _toTransforms(n1, e1, n2, e2, indirect=True, inverse=True, exhaust=False): # MCCABE 16 

959 '''(INTERNAL) Yield all possible Helmert transforms, if any. 

960 ''' 

961 class Ts(list): # L{TransformXform}s de-dup 

962 def __call__(self, Xs, e1=e1, e2=e2, inverse=False): 

963 for X in Xs: 

964 if X: 

965 T = X.toTransform(e1, epoch2=e2, inverse=inverse) 

966 if T not in self: 

967 self.append(T) 

968 yield T 

969 

970 def _k(X): 

971 return -X.epoch 

972 

973 _Ts = Ts() 

974 

975 for T in _Ts((_direct(n1, n2),)): 

976 yield T 

977 if inverse: 

978 for T in _Ts((_direct(n2, n1),), inverse=True): 

979 yield T 

980 

981 if indirect: 

982 for T in _Ts(sorted(_indirects(n1, n2), key=_k)): 

983 yield T 

984 if inverse: 

985 for T in _Ts(sorted(_indirects(n2, n1), key=_k), inverse=True): 

986 yield T 

987 

988 if exhaust: 

989 for T in _Ts(sorted(_eXhaust(n1, n2), key=_k)): 

990 yield T 

991 for T in _Ts(sorted(_eXhaust(n2, n1), key=_k), inverse=True): 

992 yield T 

993 

994 

995def trfTransform0(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True, exhaust=False): 

996 '''Get a Helmert transform to convert one C{reframe} observed at C{epoch} 

997 to an other C{reframe2} at observed at C{epoch2 or epoch}. 

998 

999 @return: A L{TransformXform} instance, a C{0-tuple} for I{unity, identity} or 

1000 C{None} if no conversion exists. 

1001 

1002 @see: Function L{trfTransforms} for futher details. 

1003 ''' 

1004 return _trfT0s(_toTransform0, reframe, reframe2, epoch, epoch2, 

1005 indirect=indirect, inverse=inverse, exhaust=exhaust) 

1006 

1007 

1008def trfTransforms(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True, exhaust=False): 

1009 '''Yield all Helmert transform to convert one C{reframe} observed at C{epoch} 

1010 to an other C{reframe2} at observed at C{epoch2 or epoch}. 

1011 

1012 @arg reframe: The frame to convert I{from} (L{RefFrame} or C{str}). 

1013 @arg reframe2: The frame to convert I{to} (L{RefFrame} or C{str}). 

1014 @arg epoch: Epoch to observe I{from} (L{Epoch}, C{scalar} or C{str}), 

1015 otherwise C{B{reframe}}'s C{epoch}. 

1016 @kwarg epoch2: Optional epoch to observe to observe I{to} (L{Epoch}, C{scalar} 

1017 or C{str}), otherwise B{C{epoch}} or C{B{reframe}}'s C{epoch}. 

1018 @kwarg indirect: If C{True}, include transforms via I{one} intermediate reframe, 

1019 otherwise only I{direct} B{C{reframe}} to B{C{reframe2}} 

1020 transforms (C{bool}). 

1021 @kwarg inverse: If C{True}, include inverse, otherwise only forward transforms 

1022 (C{bool}). 

1023 @kwarg exhaust: If C{True}, exhaustively search for all aggregate, concatenated 

1024 transforms, forward and inverse (C{bool}). 

1025 

1026 @return: A L{TransformXform} instance for each available conversion. 

1027 

1028 @raise TRFError: Invalid B{C{reframe}}, B{C{epoch}}, B{C{reframe2}} or 

1029 B{C{epoch2}}. 

1030 

1031 @raise TypeError: Invalid B{C{reframe}} or B{C{reframe2}}. 

1032 ''' 

1033 return _trfT0s(_toTransforms, reframe, reframe2, epoch, epoch2, 

1034 indirect=indirect, inverse=inverse, exhaust=exhaust) 

1035 

1036 

1037def _trfT0s(_toT0s, reframe, reframe2, epoch, epoch2, **indirect_inverse_exhaust): 

1038 '''(INTERNAL) Handle C{trfTransforms0} and C{trfTransforms} calls. 

1039 ''' 

1040 r1 = _reframe(reframe=reframe) 

1041 e1 = r1.epoch if epoch is None else _Epoch(epoch) 

1042 r2 = _reframe(reframe2=reframe2) 

1043 e2 = e1 if epoch2 is None else Epoch(epoch2=epoch2) 

1044 return _toT0s(r1.name, e1, r2.name, e2, **indirect_inverse_exhaust) 

1045 

1046 

1047def trfXform(reframe1, reframe2, epoch=None, xform=None, rates=None, raiser=True): 

1048 '''Define a new Terrestrial Reference Frame (TRF) converter or get an 

1049 existing one. 

1050 

1051 @arg reframe1: Source frame (L{RefFrame} or C{str}), converting I{from}. 

1052 @arg reframe2: Destination frame (L{RefFrame} or C{str}), converting I{to}. 

1053 @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str}) 

1054 or C{None} for C{B{reframe2}}'s epoch. 

1055 @kwarg xform: I{Transform} parameters (L{TRFXform7Tuple}). 

1056 @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), as B{C{xform}}, 

1057 but in C{units-per-year}. 

1058 @kwarg raiser: If C{False}, do not raise an error if the converter 

1059 exists, replace it (C{bool}). 

1060 

1061 @return: The new TRF converter (L{TRFXform}) or if no B{C{epoch}}, 

1062 B{C{xform}} and B{C{rates}} are given, return the existing 

1063 one (L{TRFXform}) or C{None} if not available. 

1064 

1065 @raise TRFError: Invalid B{C{reframe1}}, B{C{reframe2}}, B{C{epoch}}, 

1066 B{C{xform}} or B{C{rates}} or the TRF converter 

1067 already exists. 

1068 ''' 

1069 try: 

1070 r1 = _reframe(reframe1=reframe1) 

1071 r2 = _reframe(reframe2=reframe2) 

1072 if epoch is None: 

1073 if xform is rates is None: 

1074 return r1._Xto.get(r2.name, None) 

1075 e = r2.epoch 

1076 else: 

1077 e = _Epoch(epoch) 

1078 return _trfX(r1.name, r2.name, raiser=raiser, epoch=e, 

1079 xform=xform, rates=rates) 

1080 except (TypeError, ValueError) as x: 

1081 t = unstr(trfXform, reframe1, reframe2, epoch=epoch) 

1082 raise TRFError(t, cause=x) 

1083 

1084 

1085def _trfX(n1, n2, raiser=True, **epoch_xform_rates): 

1086 '''(INTERNAL) New, I{unique} L{TRFXform} converter. 

1087 ''' 

1088 r1 = RefFrames.get(n1) 

1089 if r1 is None: 

1090 raise ValueError(_invalid_) 

1091 r2 = RefFrames.get(n2) 

1092 if r2 is None: 

1093 raise ValueError(_invalid_) 

1094 if raiser: 

1095 if n2 in r1._Xto: 

1096 raise ValueError(_exists_) 

1097 if n1 in r2._Xto: 

1098 raise ValueError(_SPACE_(_inverse_, _exists_)) 

1099 r1._Xto[n2] = X = TRFXform(n1, n2, **epoch_xform_rates) 

1100 return X 

1101 

1102 

1103def _X(*ps): # deleted below 

1104 return _P(ps, _xform_, _Xs) # PYCHOK del 

1105 

1106 

1107def _R(*ps): # deleted below 

1108 return _P(ps, _rates_, _Rs) # PYCHOK del 

1109 

1110 

1111_P_0_0s = TRFXform7Tuple(_0_0s(len(_Names7)), name='unity') 

1112 

1113# TRF conversions specified as an epoch and 2 sets of 7 parameters. Most from Altamimi, Z. U{"EUREF Technical 

1114# Note 1: Relationship and Transformation between the International and the European Terrestrial Reference 

1115# Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Appendix A, more at U{Quinsy QPS <https:// 

1116# confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ITRF_Transformation_Parameters.xlsx>}. 

1117# See also U{Quinsy International Terrestrial Reference Frame 2014 (ITRF2014)<https://confluence.QPS.NL/qinsy/latest/ 

1118# en/international-terrestrial-reference-frame-2014-itrf2014-182618383.html>}. 

1119_trfX(_ITRF2020_, _ITRF2014_, epoch=_E(2015), # <https://ITRF.IGN.Fr/docs/solutions/itrf2020/Transfo-ITRF2020_TRFs.txt> 

1120 xform=_X( -1.4, -0.9, 1.4, -0.42, _0_0, _0_0, _0_0), 

1121 rates=_R( _0_0, -0.1, 0.2, _0_0, _0_0, _0_0, _0_0)) 

1122_trfX(_ITRF2020_, _ITRF2008_, epoch=_E(2015), 

1123 xform=_X( 0.2, 1.0, 3.3, -0.29, _0_0, _0_0, _0_0), 

1124 rates=_R( _0_0, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0)) 

1125_trfX(_ITRF2020_, _ITRF2005_, epoch=_E(2015), 

1126 xform=_X( 2.7, 0.1, -1.4, 0.65, _0_0, _0_0, _0_0), 

1127 rates=_R( 0.3, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0)) 

1128_trfX(_ITRF2020_, _ITRF2000_, epoch=_E(2015), 

1129 xform=_X( -0.2, 0.8, -34.2, 2.25, _0_0, _0_0, _0_0), 

1130 rates=_R( 0.1, _0_0, -1.7, 0.11, _0_0, _0_0, _0_0)) 

1131_trfX(_ITRF2020_, _ITRF97_, epoch=_E(2015), 

1132 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36), 

1133 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1134_trfX(_ITRF2020_, _ITRF96_, epoch=_E(2015), 

1135 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36), 

1136 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1137_trfX(_ITRF2020_, _ITRF94_, epoch=_E(2015), 

1138 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36), 

1139 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1140_trfX(_ITRF2020_, _ITRF93_, epoch=_E(2015), 

1141 xform=_X( -65.8, 1.9, -71.3, 4.47, -3.36, -4.33, 0.75), 

1142 rates=_R( -2.8, -0.2, -2.3, 0.12, -0.11, -0.19, 0.07)) 

1143_trfX(_ITRF2020_, _ITRF92_, epoch=_E(2015), 

1144 xform=_X( 14.5, -1.9, -85.9, 3.27, _0_0, _0_0, 0.36), 

1145 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1146_trfX(_ITRF2020_, _ITRF91_, epoch=_E(2015), 

1147 xform=_X( 26.5, 12.1, -91.9, 4.67, _0_0, _0_0, 0.36), 

1148 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1149_trfX(_ITRF2020_, _ITRF90_, epoch=_E(2015), 

1150 xform=_X( 24.5, 8.1, -107.9, 4.97, _0_0, _0_0, 0.36), 

1151 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1152_trfX(_ITRF2020_, _ITRF89_, epoch=_E(2015), 

1153 xform=_X( 29.5, 32.1, -145.9, 8.37, _0_0, _0_0, 0.36), 

1154 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1155_trfX(_ITRF2020_, _ITRF88_, epoch=_E(2015), 

1156 xform=_X( 24.5, -3.9, -169.9, 11.47, 0.1, _0_0, 0.36), 

1157 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1158 

1159# see U{Transformation Parameters ITRF2014<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2014_ITRFs.txt>} and 

1160# Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and 

1161# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1.pdf>} Appendix A. 

1162_trfX(_ITRF2014_, _ITRF2008_, epoch=(2010), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2014/tp_14-08.php> 

1163 xform=_X( 1.6, 1.9, 2.4, -0.02, _0_0, _0_0, _0_0), 

1164 rates=_R( _0_0, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0)) 

1165_trfX(_ITRF2014_, _ITRF2005_, epoch=_E(2010), 

1166 xform=_X( 2.6, _1_0, -2.3, 0.92, _0_0, _0_0, _0_0), 

1167 rates=_R( 0.3, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0)) 

1168_trfX(_ITRF2014_, _ITRF2000_, epoch=_E(2010), 

1169 xform=_X( 0.7, 1.2, -26.1, 2.12, _0_0, _0_0, _0_0), 

1170 rates=_R( 0.1, 0.1, -1.9, 0.11, _0_0, _0_0, _0_0)) 

1171_trfX(_ITRF2014_, _ITRF97_, epoch=_E(2010), 

1172 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26), 

1173 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1174_trfX(_ITRF2014_, _ITRF96_, epoch=_E(2010), 

1175 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26), 

1176 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1177_trfX(_ITRF2014_, _ITRF94_, epoch=_E(2010), 

1178 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26), 

1179 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1180_trfX(_ITRF2014_, _ITRF93_, epoch=_E(2010), 

1181 xform=_X( -50.4, 3.3, -60.2, 4.29, -2.81, -3.38, 0.4), 

1182 rates=_R( -2.8, -0.1, -2.5, 0.12, -0.11, -0.19, 0.07)) 

1183_trfX(_ITRF2014_, _ITRF92_, epoch=_E(2010), 

1184 xform=_X( 15.4, 1.5, -70.8, 3.09, _0_0, _0_0, 0.26), 

1185 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1186_trfX(_ITRF2014_, _ITRF91_, epoch=_E(2010), 

1187 xform=_X( 27.4, 15.5, -76.8, 4.49, _0_0, _0_0, 0.26), 

1188 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1189_trfX(_ITRF2014_, _ITRF90_, epoch=_E(2010), 

1190 xform=_X( 25.4, 11.5, -92.8, 4.79, _0_0, _0_0, 0.26), 

1191 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1192_trfX(_ITRF2014_, _ITRF89_, epoch=_E(2010), 

1193 xform=_X( 30.4, 35.5, -130.8, 8.19, _0_0, _0_0, 0.26), 

1194 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1195_trfX(_ITRF2014_, _ITRF88_, epoch=_E(2010), 

1196 xform=_X( 25.4, -0.5, -154.8, 11.29, 0.1, _0_0, 0.26), 

1197 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1198 

1199# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference 

1200# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 1st and 2nd column 

1201_trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2005), 

1202 xform=_X( -0.5, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0), 

1203 rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0)) 

1204# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(1997), 

1205# xform=_X( -2.9, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0), 

1206# rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0)) 

1207# see U{Transformation Parameters ITRF2008<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2008_ITRFs.txt>} 

1208# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2008/tp_08-05.php> 

1209# xform=_X( -2.0, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0), 

1210# rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0)) 

1211_trfX(_ITRF2008_, _ITRF2000_, epoch=_E(2000), 

1212 xform=_X( -1.9, -1.7, -10.5, 1.34, _0_0, _0_0, _0_0), 

1213 rates=_R( 0.1, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0)) 

1214_trfX(_ITRF2008_, _ITRF97_, epoch=_E(2000), 

1215 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06), 

1216 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1217_trfX(_ITRF2008_, _ITRF96_, epoch=_E(2000), 

1218 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06), 

1219 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1220_trfX(_ITRF2008_, _ITRF94_, epoch=_E(2000), 

1221 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06), 

1222 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1223_trfX(_ITRF2008_, _ITRF93_, epoch=_E(2000), 

1224 xform=_X( -24.0, 2.4, -38.6, 3.41, -1.71, -1.48, -0.3), 

1225 rates=_R( -2.8, -0.1, -2.4, 0.09, -0.11, -0.19, 0.07)) 

1226_trfX(_ITRF2008_, _ITRF92_, epoch=_E(2000), 

1227 xform=_X( 12.8, 4.6, -41.2, 2.21, _0_0, _0_0, 0.06), 

1228 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1229_trfX(_ITRF2008_, _ITRF91_, epoch=_E(2000), 

1230 xform=_X( 24.8, 18.6, -47.2, 3.61, _0_0, _0_0, 0.06), 

1231 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1232_trfX(_ITRF2008_, _ITRF90_, epoch=_E(2000), 

1233 xform=_X( 22.8, 14.6, -63.2, 3.91, _0_0, _0_0, 0.06), 

1234 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1235_trfX(_ITRF2008_, _ITRF89_, epoch=_E(2000), 

1236 xform=_X( 27.8, 38.6, -101.2, 7.31, _0_0, _0_0, 0.06), 

1237 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1238_trfX(_ITRF2008_, _ITRF88_, epoch=_E(2000), 

1239 xform=_X( 22.8, 2.6, -125.2, 10.41, 0.1, _0_0, 0.06), 

1240 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1241 

1242# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference 

1243# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 3rd column 

1244# _trfX(_ITRF2005_, _ITRF2000_, epoch=_E(1997), 

1245# xform=_X( 0.7, -1.1, -0.4, 0.16, -0.2, 0.1 -1.8), 

1246# rates=_R( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0)) 

1247_trfX(_ITRF2005_, _ITRF2000_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2005/tp_05-00.php> 

1248 xform=_X( 0.1, -0.8, -5.8, 0.4, _0_0, _0_0, _0_0), 

1249 rates=_R( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0)) 

1250 

1251_trfX(_ITRF2000_, _ITRF97_, epoch=_E(1997), 

1252 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0), 

1253 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, -0.02)) # 0.02? 

1254_trfX(_ITRF2000_, _ITRF96_, epoch=_E(1997), 

1255 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0), 

1256 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1257_trfX(_ITRF2000_, _ITRF94_, epoch=_E(1997), 

1258 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0), 

1259 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1260_trfX(_ITRF2000_, _ITRF93_, epoch=_E(1988), 

1261 xform=_X( 12.7, 6.5, -20.9, 1.95, -0.39, 0.8, -1.14), 

1262 rates=_R( -2.9, -0.2, -0.6, 0.01, -0.11, -0.19, 0.07)) 

1263_trfX(_ITRF2000_, _ITRF92_, epoch=_E(1988), 

1264 xform=_X( 1.47, 1.35, -1.39, 0.75, _0_0, _0_0, -0.18), 

1265 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1266_trfX(_ITRF2000_, _ITRF91_, epoch=_E(1988), 

1267 xform=_X( 26.7, 27.5, -19.9, 2.15, _0_0, _0_0, -0.18), 

1268 rates=_R( _0_0, -0.6, -1.4, 0.01, _0_0, _0_0, 0.02)) 

1269_trfX(_ITRF2000_, _ITRF90_, epoch=_E(1988), 

1270 xform=_X( 2.47, 2.35, -3.59, 2.45, _0_0, _0_0, -0.18), 

1271 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1272_trfX(_ITRF2000_, _ITRF89_, epoch=_E(1988), 

1273 xform=_X( 2.97, 4.75, -7.39, 5.85, _0_0, _0_0, -0.18), 

1274 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1275_trfX(_ITRF2000_, _ITRF88_, epoch=_E(1988), 

1276 xform=_X( 2.47, 1.15, -9.79, 8.95, 0.1, _0_0, -0.18), 

1277 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1278 

1279# Soler, T .& Snay R.A. U{"Transforming Positions and Velocities between the International Terrestrial 

1280# Reference Frame of 2000 and North American Datum of 1983"<https://www.ResearchGate.net/publication/245291390>}, 

1281# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference 

1282# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 5th and 6th column 

1283_trfX(_ITRF97_, _ITRF96_, epoch=_E(1997), 

1284 xform=_X( -2.07, -0.21, 9.95, -0.93496, 0.1267, -0.22355, -0.06065,), 

1285 rates=_R( 0.69, -0.1, 1.86, -0.19201, 0.01347, -0.01514, 0.00027)) 

1286_trfX(_ITRF96_, _NAD83_, epoch=_E(1997), 

1287 xform=_X( 991.0, -190.72, -512.9, _0_0, 25.79, 9.65, 11.66,), 

1288 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.0532, -0.7423, -0.0316,)) 

1289 

1290# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and 

1291# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 1. 

1292# _trfX(_ITRF2020_, _ETRF2020_, epoch=_E(1989), # see Table 2 below 

1293# xform=_P_0_0s, 

1294# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753)) 

1295# _trfX(_ITRF2014_, _ETRF2014_, epoch=_E(1989), # see Table 3 below 

1296# xform=_P_0_0s, 

1297# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77)) 

1298_trfX(_ITRF2005_, _ETRF2005_, epoch=_E(1989), 

1299 xform=_X( 56.0, 48.0, -37.0, _0_0, _0_0, _0_0, _0_0), 

1300 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.054, 0.518, -0.781)) 

1301# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(1989), # see Table 4 below 

1302# xform=_X( 54.0, 51.0, -48.0, _0_0, _0_0, _0_0, _0_0), 

1303# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792)) 

1304_trfX(_ITRF97_, _ETRF97_, epoch=_E(1989), 

1305 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0), 

1306 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65)) 

1307_trfX(_ITRF96_, _ETRF96_, epoch=_E(1989), 

1308 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0), 

1309 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65)) 

1310_trfX(_ITRF94_, _ETRF94_, epoch=_E(1989), 

1311 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0), 

1312 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65)) 

1313_trfX(_ITRF93_, _ETRF93_, epoch=_E(1989), 

1314 xform=_X( 19.0, 53.0, -21.0, _0_0, _0_0, _0_0, _0_0), 

1315 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.32, 0.78, -0.67)) 

1316_trfX(_ITRF92_, _ETRF92_, epoch=_E(1989), 

1317 xform=_X( 38.0, 40.0, -37.0, 0.0, 0.0, 0.0, 0.0), 

1318 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68)) 

1319_trfX(_ITRF91_, _ETRF91_, epoch=_E(1989), 

1320 xform=_X( 21.0, 25.0, -37.0, _0_0, _0_0, _0_0, _0_0), 

1321 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68)) 

1322_trfX(_ITRF90_, _ETRF90_, epoch=_E(1989), 

1323 xform=_X( 19.0, 28.0, -23.0, _0_0, _0_0, _0_0, _0_0), 

1324 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71)) 

1325_trfX(_ITRF89_, _ETRF89_, epoch=_E(1989), 

1326 xform=_P_0_0s, 

1327 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71)) 

1328 

1329# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and 

1330# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 2. 

1331_trfX(_ITRF2020_, _ETRF2020_, epoch=_E(2015), 

1332 xform=_X( _0_0, _0_0, _0_0, _0_0, 2.236, 13.494, -19.578), 

1333 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753)) 

1334_trfX(_ITRF2014_, _ETRF2020_, epoch=_E(2015), 

1335 xform=_X( 1.4, 0.9, -1.4, 0.42, 2.236, 13.494, -19.578), 

1336 rates=_R( _0_0, 0.1, -0.2, _0_0, 0.086, 0.519, -0.753)) 

1337_trfX(_ITRF2008_, _ETRF2020_, epoch=_E(2015), 

1338 xform=_X( 3.0, 2.8, 0.5, 0.55, 2.236, 13.494, -19.578), 

1339 rates=_R( _0_0, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753)) 

1340_trfX(_ITRF2005_, _ETRF2020_, epoch=_E(2015), 

1341 xform=_X( 5.5, 1.9, -4.2, 1.49, 2.236, 13.494, -19.578), 

1342 rates=_R( 0.3, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753)) 

1343_trfX(_ITRF2000_, _ETRF2020_, epoch=_E(2015), 

1344 xform=_X( 2.6, 2.6, -37.0, 3.09, 2.236, 13.494, -19.578), 

1345 rates=_R( 0.1, 0.2, -2.1, 0.11, 0.086, 0.519, -0.753)) 

1346_trfX(_ITRF97_, _ETRF2020_, epoch=_E(2015), 

1347 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218), 

1348 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1349_trfX(_ITRF96_, _ETRF2020_, epoch=_E(2015), 

1350 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218), 

1351 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1352_trfX(_ITRF94_, _ETRF2020_, epoch=_E(2015), 

1353 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218), 

1354 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1355_trfX(_ITRF93_, _ETRF2020_, epoch=_E(2015), 

1356 xform=_X( -63.0, 3.7, -74.1, 5.31, -1.124, 9.164, -18.828), 

1357 rates=_R( -2.8, _0_0, -2.7, 0.12, -0.024, 0.329, -0.683)) 

1358_trfX(_ITRF92_, _ETRF2020_, epoch=_E(2015), 

1359 xform=_X( 17.3, -0.1, -88.7, 4.11, 2.236, 13.494, -19.218), 

1360 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1361_trfX(_ITRF91_, _ETRF2020_, epoch=_E(2015), 

1362 xform=_X( 29.3, 13.9, -94.7, 5.51, 2.236, 13.494, -19.218), 

1363 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1364_trfX(_ITRF90_, _ETRF2020_, epoch=_E(2015), 

1365 xform=_X( 27.3, 9.9, -110.7, 5.81, 2.236, 13.494, -19.218), 

1366 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1367_trfX(_ITRF89_, _ETRF2020_, epoch=_E(2015), 

1368 xform=_X( 32.3, 33.9, -148.7, 9.21, 2.236, 13.494, -19.218), 

1369 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1370_trfX(_ITRF88_, _ETRF2020_, epoch=_E(2015), 

1371 xform=_X( 27.3, -2.1, -172.7, 12.31, 2.336, 13.494, -19.218), 

1372 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1373 

1374# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and 

1375# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 3. 

1376_trfX(_ITRF2020_, _ETRF2014_, epoch=_E(2015), 

1377 xform=_X( -1.4, -0.9, 1.4, 0.42, 2.21, 13.806, -20.02), 

1378 rates=_R( _0_0, -0.1, 0.2, _0_0, 0.085, 0.531, -0.77)) 

1379_trfX(_ITRF2014_, _ETRF2014_, epoch=_E(2015), 

1380 xform=_X( _0_0, _0_0, _0_0, _0_0, 2.21, 13.806, -20.02), 

1381 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77)) 

1382_trfX(_ITRF2008_, _ETRF2014_, epoch=_E(2015), 

1383 xform=_X( -1.6, -1.9, -1.9, -0.13, 2.21, 13.806, -20.02), 

1384 rates=_R( _0_0, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77)) 

1385_trfX(_ITRF2005_, _ETRF2014_, epoch=_E(2015), 

1386 xform=_X( -4.1, -1.0, 2.8, -1.07, 2.21, 13.806, -20.02), 

1387 rates=_R( -0.3, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77)) 

1388_trfX(_ITRF2000_, _ETRF2014_, epoch=_E(2015), 

1389 xform=_X( -1.2, -1.7, 35.6, -2.67, 2.21, 13.806, -20.02), 

1390 rates=_R( -0.1, -0.1, 1.9, -0.11, 0.085, 0.531, -0.77)) 

1391_trfX(_ITRF97_, _ETRF2014_, epoch=_E(2015), 

1392 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38), 

1393 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1394_trfX(_ITRF96_, _ETRF2014_, epoch=_E(2015), 

1395 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38), 

1396 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1397_trfX(_ITRF94_, _ETRF2014_, epoch=_E(2015), 

1398 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38), 

1399 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1400_trfX(_ITRF93_, _ETRF2014_, epoch=_E(2015), 

1401 xform=_X( 64.4, -2.8, 72.7, -4.89, 5.570, 18.136, -20.77), 

1402 rates=_R( 2.8, 0.1, 2.5, -0.12, 0.195, 0.721, -0.84)) 

1403_trfX(_ITRF92_, _ETRF2014_, epoch=_E(2015), 

1404 xform=_X( -15.9, 1.0, 87.3, -3.69, 2.21, 13.806, -20.38), 

1405 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1406_trfX(_ITRF91_, _ETRF2014_, epoch=_E(2015), 

1407 xform=_X( -27.9, -13.0, 93.3, -5.09, 2.21, 13.806, -20.38), 

1408 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1409_trfX(_ITRF90_, _ETRF2014_, epoch=_E(2015), 

1410 xform=_X( -25.9, -9.0, 109.3, -5.39, 2.21, 13.806, -20.38), 

1411 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1412_trfX(_ITRF89_, _ETRF2014_, epoch=_E(2015), 

1413 xform=_X( -30.9, -33.0, 147.3, -8.79, 2.21, 13.806, -20.38), 

1414 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1415_trfX(_ITRF88_, _ETRF2014_, epoch=_E(2015), 

1416 xform=_X( -25.9, 3.0, 171.3, -11.89, 2.11, 13.806, -20.38), 

1417 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1418 

1419# see U{Altamimi, Z. "EUREF Technical Note 1: Relationship and Transformation between the International and 

1420# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 4, 

1421# U{Boucher, C. & Altamimi, Z. "Memo: Specifications for reference frame fixing in the analysis of a EUREF GPS 

1422# campaign" (2011) <https://ETRS89.ENSG.IGN.Fr/memo-V8.pdf>} and U{Altamimi, Z. "Key results of ITRF2014 and 

1423# implication to ETRS89 realization", EUREF2016<https://www.EUREF.EU/symposia/2016SanSebastian/01-02-Altamimi.pdf>}. 

1424_trfX(_ITRF2020_, _ETRF2000_, epoch=_E(2015), 

1425 xform=_X( 53.8, 51.8, -82.2, 2.25, 2.106, 12.74, -20.592), 

1426 rates=_R( 0.1, _0_0, -1.7, 0.11, 0.081, 0.49, -0.792)) 

1427# _trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2000), 

1428# xform=_X( 53.7, 51.2, -55.1, 1.02, 0.891, 5.39, -8.712), 

1429# rates=_R( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792)) 

1430_trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2015), 

1431 xform=_X( 55.2, 52.7, -83.6, 2.67, 2.106, 12.74, -20.592), 

1432 rates=_R( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792)) 

1433# _trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2000), 

1434# xform=_X( 52.1, 49.3, -58.5, 1.34, 0.891, 5.39, -8.712), 

1435# rates=_R( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)) 

1436_trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2015), 

1437 xform=_X( 53.6, 50.8, -85.5, 2.54, 2.106, 12.74, -20.592), 

1438 rates=_R( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)) 

1439# _trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2000), 

1440# xform=_X( 54.1, 50.2, -53.8, 0.4, 0.891, 5.39, -8.712), 

1441# rates=_R( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)) 

1442_trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2015), 

1443 xform=_X( 51.1, 51.7, -80.8, 1.6, 2.106, 12.74, -20.592), 

1444 rates=_R( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)) 

1445# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2000), 

1446# xform=_X( 54.0, 51.0, -48.0, _0_0, 0.891, 5.39, -8.712), 

1447# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792)) 

1448_trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2015), 

1449 xform=_X( 54.0, 51.0, -48.0, _0_0, 2.106, 12.74, -20.592), 

1450 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792)) 

1451_trfX(_ITRF97_, _ETRF2000_, epoch=_E(2015), 

1452 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952), 

1453 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1454_trfX(_ITRF96_, _ETRF2000_, epoch=_E(2015), 

1455 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952), 

1456 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1457_trfX(_ITRF94_, _ETRF2000_, epoch=_E(2015), 

1458 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952), 

1459 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1460_trfX(_ITRF93_, _ETRF2000_, epoch=_E(2015), 

1461 xform=_X( 119.6, 49.9, -10.9, -2.22, 5.466, 17.07, -21.342), 

1462 rates=_R( 2.9, 0.2, 0.6, -0.01, 0.191, 0.68, -0.862)) 

1463_trfX(_ITRF92_, _ETRF2000_, epoch=_E(2015), 

1464 xform=_X( 39.3, 53.7, 3.7, -1.02, 2.106, 12.74, -20.952), 

1465 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1466_trfX(_ITRF91_, _ETRF2000_, epoch=_E(2015), 

1467 xform=_X( 27.3, 39.7, 9.7, -2.42, 2.106, 12.74, -20.952), 

1468 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1469_trfX(_ITRF90_, _ETRF2000_, epoch=_E(2015), 

1470 xform=_X( 29.3, 43.7, 25.7, -2.72, 2.106, 12.74, -20.952), 

1471 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1472_trfX(_ITRF89_, _ETRF2000_, epoch=_E(2015), 

1473 xform=_X( 24.3, 19.7, 63.7, -6.12, 2.106, 12.74, -20.952), 

1474 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1475_trfX(_ITRF88_, _ETRF2000_, epoch=_E(2015), 

1476 xform=_X( 29.3, 55.7, 87.7, -9.22, 2.006, 12.74, -20.952), 

1477 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1478 

1479# GDA2020 "Geocentric Datum of Australia 2020 Technical Manual", v1.5, 2020-12-09, Table 3.3 and 3.4 

1480# <https://www.ICSM.gov.AU/sites/default/files/2020-12/GDA2020%20Technical%20Manual%20V1.5_4.pdf> 

1481# (the GDA2020 xforms are different but the rates are the same as GDA94, further below) 

1482_trfX(_ITRF2014_, _GDA2020_, epoch=_E(2020), 

1483 xform=_P_0_0s, 

1484 rates=_R( _0_0, _0_0, _0_0, _0_0, 1.50379, 1.18346, 1.20716)) 

1485_trfX(_ITRF2008_, _GDA2020_, epoch=_E(2020), 

1486 xform=_X( 13.79, 4.55, 15.22, 2.5, 0.2808, 0.2677, -0.4638), 

1487 rates=_R( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551)) 

1488_trfX(_ITRF2005_, _GDA2020_, epoch=_E(2020), 

1489 xform=_X( 40.32, -33.85, -16.72, 4.286, -1.2893, -0.8492, -0.3342), 

1490 rates=_R( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701)) 

1491_trfX(_ITRF2000_, _GDA2020_, epoch=_E(2020), 

1492 xform=_X(-105.52, 51.58, 231.68, 3.55, 4.2175, 6.3941, 0.8617), 

1493 rates=_R( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224)) 

1494 

1495# see Table 2 in U{Dawson, J. & Woods, A. "ITRF to GDA94 coordinate transformations", Journal of Applied 

1496# Geodesy 4 (2010), 189-199<https://www.ResearchGate.net/publication/258401581_ITRF_to_GDA94_coordinate_transformations>} 

1497# (note, sign of rotations for GDA94 reversed as "Australia assumes rotation to be of coordinate axes", 

1498# rather than the more conventional "position around the coordinate axes") 

1499_trfX(_ITRF2008_, _GDA94_, epoch=_E(1994), 

1500 xform=_X( -84.68, -19.42, 32.01, 9.71, -0.4254, 2.2578, 2.4015), 

1501 rates=_R( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551)) 

1502_trfX(_ITRF2005_, _GDA94_, epoch=_E(1994), 

1503 xform=_X( -79.73, -6.86, 38.03, 6.636, 0.0351, -2.1211, -2.1411), 

1504 rates=_R( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701)) 

1505_trfX(_ITRF2000_, _GDA94_, epoch=_E(1994), 

1506 xform=_X( -45.91, -29.85, -20.37, 7.07, -1.6705, 0.4594, 1.9356), 

1507 rates=_R( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224)) 

1508 

1509# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ 

1510# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83 and Pearson, C. & Snay, R. U{"Introducing 

1511# HTDP 3.1 to transform coordinates across time and spatial reference frames"<https://Geodesy.NOAA.gov/ 

1512# TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 7th column 

1513_trfX(_ITRF2008_, _NAD83_, epoch=_E(1997), 

1514 xform=_X( 993.43, -1903.31, -526.55, 1.71504, -25.91467, -9.42645, -11.59935), 

1515 rates=_R( 0.79, -0.6, -1.34, -0.10201, -0.06667, 0.75744, 0.05133)) 

1516# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ 

1517# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83 

1518_trfX(_ITRF2005_, _NAD83_, epoch=_E(1997), 

1519 xform=_X( 996.3, -1902.4, -521.9, 0.775, -25.915, -9.426, -11.599), 

1520 rates=_R( 0.5, -0.6, -1.3, -0.10201, -0.06667, 0.75744, 0.05133)) 

1521# see U{Solar, T. & Snay, R.A. "Transforming Positions and Velocities between the International Terrestrial Reference 

1522# Frame of 2000 and North American Datum of 1983" (2004)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>} 

1523_trfX(_ITRF2000_, _NAD83_, epoch=_E(1997), # note NAD83(CORS96) 

1524 xform=_X( 995.6, -1901.3, -521.5, 0.615, -25.915, -9.426, -11.599), 

1525 rates=_R( 0.7, -0.7, _0_5, -0.182, -0.06667, 0.75744, 0.05133)) 

1526_trfX(_ITRF90_, _NAD83_, epoch=_E(1997), 

1527 xform=_X( 973.0, -1919.2, -482.9, -0.9, -25.79, -9.65, -11.66), 

1528 rates=_R( _0_0, _0_0, _0_0, _0_0, -0.053, 0.742, 0.032)) 

1529_trfX(_ITRF90_, _WGS84_, epoch=_E(1984), # coverage 

1530 xform=_X( 60.0, -517.0, -223.0, -11.0, 18.3, -0.3, 7.0), 

1531 rates=_P_0_0s) 

1532 

1533# equivalents U{"Transformations Between NAD83 and WGS84"<https://www.NGS.NOAA.gov/CORS/Articles/WGS84NAD83.pdf>} 

1534trfXform(_NAD83cors96_, _NAD83_, epoch=_E(1997), xform=_P_0_0s, rates=_P_0_0s) 

1535trfXform(_WGS84g1150_, _ITRF2000_, epoch=_E(2004), xform=_P_0_0s, rates=_P_0_0s) 

1536 

1537del _E, _Es, _i, _P, _P_0_0s, _R, _Rs, _X, _Xs 

1538 

1539if __name__ == '__main__': 

1540 

1541 def _main(): 

1542 from pygeodesy.interns import _COLONSPACE_,_COMMA_, _NL_, _NLATvar_, _vs_ 

1543 from pygeodesy.lazily import printf 

1544 from time import localtime 

1545 

1546 D = date2epoch.__name__ 

1547 E = epoch2date.__name__ 

1548 y = localtime()[0] 

1549 for m in range(1, 13): 

1550 for d in (1, 15, _mDays[m] - 1, _mDays[m]): 

1551 f = '%s(%d,%3d,%3d)' % (D, y, m, d) 

1552 e = date2epoch(y, m, d) 

1553 t = epoch2date(e) 

1554 x = NN if t == (y, m, d) else _STAR_ 

1555 e = '%.3f' % (e,) 

1556 e = '%s, %s(%s)' % (e, E, e) 

1557 t = '%d,%3d,%3d' % t 

1558 printf('# %s = %s = %s %s', f, e, t, x) 

1559 

1560 # __doc__ of this file, force all into registery 

1561 def _RFs(): 

1562 yield NN 

1563 for t in RefFrames.toRepr(all=True).split(_NL_): 

1564 t = t.strip(_COMMA_) 

1565 n = t.split(_COLONSPACE_)[0].split(_DOT_)[1] 

1566 r = RefFrames.get(n) 

1567 x = len(r.Xforms()), -len(r.Xforms(inverse=True)) 

1568 yield '%s .Xforms=%s' % (t, x) 

1569 

1570 printf(_NLATvar_.join(sorted(_RFs())), nt=1) 

1571 

1572 X, t = (), 0 # all form 

1573 for r in RefFrames.values(): 

1574 X += tuple(r._Xto.values()) 

1575 for X in sorted(X): 

1576 t += 1 

1577 printf('#%4d %-24s xform=%r', t, X.name, X.xform) 

1578 printf('#%29s rates=%r', _SPACE_, X.rates) 

1579 

1580 t = _MODS.basics._args_kwds_names(Transform.__init__) 

1581 for n in TRFXform7Tuple._Names_: 

1582 if n not in t: 

1583 raise AssertionError(_SPACE_(n, _vs_, t)) 

1584 

1585 _main() 

1586 del _main 

1587 

1588# **) MIT License 

1589# 

1590# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1591# 

1592# Permission is hereby granted, free of charge, to any person obtaining a 

1593# copy of this software and associated documentation files (the "Software"), 

1594# to deal in the Software without restriction, including without limitation 

1595# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1596# and/or sell copies of the Software, and to permit persons to whom the 

1597# Software is furnished to do so, subject to the following conditions: 

1598# 

1599# The above copyright notice and this permission notice shall be included 

1600# in all copies or substantial portions of the Software. 

1601# 

1602# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1603# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1604# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1605# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1606# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1607# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1608# OTHER DEALINGS IN THE SOFTWARE. 

1609 

1610# % python -m pygeodesy.trf 

1611# 

1612# date2epoch(2024, 1, 1) = 2024.003, epoch2date(2024.003) = 2024, 1, 1 

1613# date2epoch(2024, 1, 15) = 2024.041, epoch2date(2024.041) = 2024, 1, 15 

1614# date2epoch(2024, 1, 30) = 2024.082, epoch2date(2024.082) = 2024, 1, 30 

1615# date2epoch(2024, 1, 31) = 2024.085, epoch2date(2024.085) = 2024, 1, 31 

1616# date2epoch(2024, 2, 1) = 2024.087, epoch2date(2024.087) = 2024, 2, 2 * 

1617# date2epoch(2024, 2, 15) = 2024.126, epoch2date(2024.126) = 2024, 2, 16 * 

1618# date2epoch(2024, 2, 28) = 2024.161, epoch2date(2024.161) = 2024, 2, 28 

1619# date2epoch(2024, 2, 29) = 2024.164, epoch2date(2024.164) = 2024, 3, 1 * 

1620# date2epoch(2024, 3, 1) = 2024.167, epoch2date(2024.167) = 2024, 3, 2 * 

1621# date2epoch(2024, 3, 15) = 2024.205, epoch2date(2024.205) = 2024, 3, 16 * 

1622# date2epoch(2024, 3, 30) = 2024.246, epoch2date(2024.246) = 2024, 3, 31 * 

1623# date2epoch(2024, 3, 31) = 2024.249, epoch2date(2024.249) = 2024, 4, 1 * 

1624# date2epoch(2024, 4, 1) = 2024.251, epoch2date(2024.251) = 2024, 4, 1 

1625# date2epoch(2024, 4, 15) = 2024.290, epoch2date(2024.290) = 2024, 4, 15 

1626# date2epoch(2024, 4, 29) = 2024.328, epoch2date(2024.328) = 2024, 4, 29 

1627# date2epoch(2024, 4, 30) = 2024.331, epoch2date(2024.331) = 2024, 4, 30 

1628# date2epoch(2024, 5, 1) = 2024.333, epoch2date(2024.333) = 2024, 5, 1 

1629# date2epoch(2024, 5, 15) = 2024.372, epoch2date(2024.372) = 2024, 5, 15 

1630# date2epoch(2024, 5, 30) = 2024.413, epoch2date(2024.413) = 2024, 5, 30 

1631# date2epoch(2024, 5, 31) = 2024.415, epoch2date(2024.415) = 2024, 6, 1 * 

1632# date2epoch(2024, 6, 1) = 2024.418, epoch2date(2024.418) = 2024, 6, 2 * 

1633# date2epoch(2024, 6, 15) = 2024.456, epoch2date(2024.456) = 2024, 6, 16 * 

1634# date2epoch(2024, 6, 29) = 2024.495, epoch2date(2024.495) = 2024, 6, 30 * 

1635# date2epoch(2024, 6, 30) = 2024.497, epoch2date(2024.497) = 2024, 7, 1 * 

1636# date2epoch(2024, 7, 1) = 2024.500, epoch2date(2024.500) = 2024, 7, 1 

1637# date2epoch(2024, 7, 15) = 2024.538, epoch2date(2024.538) = 2024, 7, 16 * 

1638# date2epoch(2024, 7, 30) = 2024.579, epoch2date(2024.579) = 2024, 7, 30 

1639# date2epoch(2024, 7, 31) = 2024.582, epoch2date(2024.582) = 2024, 7, 31 

1640# date2epoch(2024, 8, 1) = 2024.585, epoch2date(2024.585) = 2024, 8, 1 

1641# date2epoch(2024, 8, 15) = 2024.623, epoch2date(2024.623) = 2024, 8, 15 

1642# date2epoch(2024, 8, 30) = 2024.664, epoch2date(2024.664) = 2024, 8, 31 * 

1643# date2epoch(2024, 8, 31) = 2024.667, epoch2date(2024.667) = 2024, 9, 1 * 

1644# date2epoch(2024, 9, 1) = 2024.669, epoch2date(2024.669) = 2024, 9, 2 * 

1645# date2epoch(2024, 9, 15) = 2024.708, epoch2date(2024.708) = 2024, 9, 16 * 

1646# date2epoch(2024, 9, 29) = 2024.746, epoch2date(2024.746) = 2024, 9, 30 * 

1647# date2epoch(2024, 9, 30) = 2024.749, epoch2date(2024.749) = 2024, 10, 1 * 

1648# date2epoch(2024, 10, 1) = 2024.751, epoch2date(2024.751) = 2024, 10, 1 

1649# date2epoch(2024, 10, 15) = 2024.790, epoch2date(2024.790) = 2024, 10, 15 

1650# date2epoch(2024, 10, 30) = 2024.831, epoch2date(2024.831) = 2024, 10, 30 

1651# date2epoch(2024, 10, 31) = 2024.833, epoch2date(2024.833) = 2024, 10, 31 

1652# date2epoch(2024, 11, 1) = 2024.836, epoch2date(2024.836) = 2024, 11, 1 

1653# date2epoch(2024, 11, 15) = 2024.874, epoch2date(2024.874) = 2024, 11, 15 

1654# date2epoch(2024, 11, 29) = 2024.913, epoch2date(2024.913) = 2024, 11, 29 

1655# date2epoch(2024, 11, 30) = 2024.915, epoch2date(2024.915) = 2024, 12, 1 * 

1656# date2epoch(2024, 12, 1) = 2024.918, epoch2date(2024.918) = 2024, 12, 2 * 

1657# date2epoch(2024, 12, 15) = 2024.956, epoch2date(2024.956) = 2024, 12, 16 * 

1658# date2epoch(2024, 12, 30) = 2024.997, epoch2date(2024.997) = 2024, 12, 31 * 

1659# date2epoch(2024, 12, 31) = 2025.000, epoch2date(2025.000) = 2025, 1, 1 * 

1660 

1661# 1 WGS84g1150@2004xITRF2000 xform=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1662# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1663# 2 NAD83cors96@1997xNAD83 xform=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1664# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1665# 3 ITRF88@2015xETRF2014 xform=xform(tx=-25.9, ty=3.0, tz=171.3, s=-11.89, sx=2.11, sy=13.806, sz=-20.38) 

1666# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1667# 4 ITRF89@2015xETRF2000 xform=xform(tx=24.3, ty=19.7, tz=63.7, s=-6.12, sx=2.106, sy=12.74, sz=-20.952) 

1668# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1669# 5 ITRF89@2015xETRF2014 xform=xform(tx=-30.9, ty=-33.0, tz=147.3, s=-8.79, sx=2.21, sy=13.806, sz=-20.38) 

1670# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1671# 6 ITRF89@2015xETRF2020 xform=xform(tx=32.3, ty=33.9, tz=-148.7, s=9.21, sx=2.236, sy=13.494, sz=-19.218) 

1672# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1673# 7 ITRF89@1989xETRF89 xform=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1674# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71) 

1675# 8 ITRF90@1984xWGS84 xform=xform(tx=60.0, ty=-517.0, tz=-223.0, s=-11.0, sx=18.3, sy=-0.3, sz=7.0) 

1676# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1677# 9 ITRF90@2015xETRF2000 xform=xform(tx=29.3, ty=43.7, tz=25.7, s=-2.72, sx=2.106, sy=12.74, sz=-20.952) 

1678# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1679# 10 ITRF90@1989xETRF90 xform=xform(tx=19.0, ty=28.0, tz=-23.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1680# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71) 

1681# 11 ITRF90@1997xNAD83 xform=xform(tx=973.0, ty=-1919.2, tz=-482.9, s=-0.9, sx=-25.79, sy=-9.65, sz=-11.66) 

1682# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=-0.053, sy=0.742, sz=0.032) 

1683# 12 ITRF91@2015xETRF2000 xform=xform(tx=27.3, ty=39.7, tz=9.7, s=-2.42, sx=2.106, sy=12.74, sz=-20.952) 

1684# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1685# 13 ITRF91@1989xETRF91 xform=xform(tx=21.0, ty=25.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1686# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68) 

1687# 14 ITRF92@2015xETRF2000 xform=xform(tx=39.3, ty=53.7, tz=3.7, s=-1.02, sx=2.106, sy=12.74, sz=-20.952) 

1688# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1689# 15 ITRF92@2015xETRF2014 xform=xform(tx=-15.9, ty=1.0, tz=87.3, s=-3.69, sx=2.21, sy=13.806, sz=-20.38) 

1690# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1691# 16 ITRF92@2015xETRF2020 xform=xform(tx=17.3, ty=-0.1, tz=-88.7, s=4.11, sx=2.236, sy=13.494, sz=-19.218) 

1692# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1693# 17 ITRF92@1989xETRF92 xform=xform(tx=38.0, ty=40.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1694# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68) 

1695# 18 ITRF93@2015xETRF2000 xform=xform(tx=119.6, ty=49.9, tz=-10.9, s=-2.22, sx=5.466, sy=17.07, sz=-21.342) 

1696# rates=rates(tx=2.9, ty=0.2, tz=0.6, s=-0.01, sx=0.191, sy=0.68, sz=-0.862) 

1697# 19 ITRF93@2015xETRF2014 xform=xform(tx=64.4, ty=-2.8, tz=72.7, s=-4.89, sx=5.57, sy=18.136, sz=-20.77) 

1698# rates=rates(tx=2.8, ty=0.1, tz=2.5, s=-0.12, sx=0.195, sy=0.721, sz=-0.84) 

1699# 20 ITRF93@2015xETRF2020 xform=xform(tx=-63.0, ty=3.7, tz=-74.1, s=5.31, sx=-1.124, sy=9.164, sz=-18.828) 

1700# rates=rates(tx=-2.8, ty=0.0, tz=-2.7, s=0.12, sx=-0.024, sy=0.329, sz=-0.683) 

1701# 21 ITRF93@1989xETRF93 xform=xform(tx=19.0, ty=53.0, tz=-21.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1702# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.32, sy=0.78, sz=-0.67) 

1703# 22 ITRF94@2015xETRF2000 xform=xform(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952) 

1704# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1705# 23 ITRF94@2015xETRF2014 xform=xform(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38) 

1706# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1707# 24 ITRF94@2015xETRF2020 xform=xform(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218) 

1708# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1709# 25 ITRF94@1989xETRF94 xform=xform(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1710# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65) 

1711# 26 ITRF96@1989xETRF96 xform=xform(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1712# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65) 

1713# 27 ITRF97@1989xETRF97 xform=xform(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1714# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65) 

1715# 28 ITRF2000@1994xGDA94 xform=xform(tx=-45.91, ty=-29.85, tz=-20.37, s=7.07, sx=-1.6705, sy=0.4594, sz=1.9356) 

1716# rates=rates(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224) 

1717# 29 ITRF2000@2015xETRF2000 xform=xform(tx=54.0, ty=51.0, tz=-48.0, s=0.0, sx=2.106, sy=12.74, sz=-20.592) 

1718# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.081, sy=0.49, sz=-0.792) 

1719# 30 ITRF88@2015xETRF2000 xform=xform(tx=29.3, ty=55.7, tz=87.7, s=-9.22, sx=2.006, sy=12.74, sz=-20.952) 

1720# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1721# 31 ITRF88@2015xETRF2020 xform=xform(tx=27.3, ty=-2.1, tz=-172.7, s=12.31, sx=2.336, sy=13.494, sz=-19.218) 

1722# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1723# 32 ITRF96@2015xETRF2000 xform=xform(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952) 

1724# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1725# 33 ITRF97@2015xETRF2000 xform=xform(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952) 

1726# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1727# 34 ITRF2000@2015xETRF2014 xform=xform(tx=-1.2, ty=-1.7, tz=35.6, s=-2.67, sx=2.21, sy=13.806, sz=-20.02) 

1728# rates=rates(tx=-0.1, ty=-0.1, tz=1.9, s=-0.11, sx=0.085, sy=0.531, sz=-0.77) 

1729# 35 ITRF90@2015xETRF2014 xform=xform(tx=-25.9, ty=-9.0, tz=109.3, s=-5.39, sx=2.21, sy=13.806, sz=-20.38) 

1730# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1731# 36 ITRF90@2015xETRF2020 xform=xform(tx=27.3, ty=9.9, tz=-110.7, s=5.81, sx=2.236, sy=13.494, sz=-19.218) 

1732# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1733# 37 ITRF91@2015xETRF2014 xform=xform(tx=-27.9, ty=-13.0, tz=93.3, s=-5.09, sx=2.21, sy=13.806, sz=-20.38) 

1734# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1735# 38 ITRF96@2015xETRF2014 xform=xform(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38) 

1736# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1737# 39 ITRF97@2015xETRF2014 xform=xform(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38) 

1738# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1739# 40 ITRF2000@2015xETRF2020 xform=xform(tx=2.6, ty=2.6, tz=-37.0, s=3.09, sx=2.236, sy=13.494, sz=-19.578) 

1740# rates=rates(tx=0.1, ty=0.2, tz=-2.1, s=0.11, sx=0.086, sy=0.519, sz=-0.753) 

1741# 41 ITRF91@2015xETRF2020 xform=xform(tx=29.3, ty=13.9, tz=-94.7, s=5.51, sx=2.236, sy=13.494, sz=-19.218) 

1742# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1743# 42 ITRF96@2015xETRF2020 xform=xform(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218) 

1744# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1745# 43 ITRF97@2015xETRF2020 xform=xform(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218) 

1746# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1747# 44 ITRF2000@2020xGDA2020 xform=xform(tx=-105.52, ty=51.58, tz=231.68, s=3.55, sx=4.2175, sy=6.3941, sz=0.8617) 

1748# rates=rates(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224) 

1749# 45 ITRF2000@1988xITRF88 xform=xform(tx=2.47, ty=1.15, tz=-9.79, s=8.95, sx=0.1, sy=0.0, sz=-0.18) 

1750# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1751# 46 ITRF2000@1988xITRF89 xform=xform(tx=2.97, ty=4.75, tz=-7.39, s=5.85, sx=0.0, sy=0.0, sz=-0.18) 

1752# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1753# 47 ITRF2000@1988xITRF90 xform=xform(tx=2.47, ty=2.35, tz=-3.59, s=2.45, sx=0.0, sy=0.0, sz=-0.18) 

1754# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1755# 48 ITRF2000@1988xITRF91 xform=xform(tx=26.7, ty=27.5, tz=-19.9, s=2.15, sx=0.0, sy=0.0, sz=-0.18) 

1756# rates=rates(tx=0.0, ty=-0.6, tz=-1.4, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1757# 49 ITRF2000@1988xITRF92 xform=xform(tx=1.47, ty=1.35, tz=-1.39, s=0.75, sx=0.0, sy=0.0, sz=-0.18) 

1758# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1759# 50 ITRF2000@1988xITRF93 xform=xform(tx=12.7, ty=6.5, tz=-20.9, s=1.95, sx=-0.39, sy=0.8, sz=-1.14) 

1760# rates=rates(tx=-2.9, ty=-0.2, tz=-0.6, s=0.01, sx=-0.11, sy=-0.19, sz=0.07) 

1761# 51 ITRF2000@1997xITRF94 xform=xform(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0) 

1762# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1763# 52 ITRF2000@1997xITRF96 xform=xform(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0) 

1764# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1765# 53 ITRF97@1997xITRF96 xform=xform(tx=-2.07, ty=-0.21, tz=9.95, s=-0.93496, sx=0.1267, sy=-0.22355, sz=-0.06065) 

1766# rates=rates(tx=0.69, ty=-0.1, tz=1.86, s=-0.19201, sx=0.01347, sy=-0.01514, sz=0.00027) 

1767# 54 ITRF2000@1997xITRF97 xform=xform(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0) 

1768# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=-0.02) 

1769# 55 ITRF2000@1997xNAD83 xform=xform(tx=995.6, ty=-1901.3, tz=-521.5, s=0.615, sx=-25.915, sy=-9.426, sz=-11.599) 

1770# rates=rates(tx=0.7, ty=-0.7, tz=0.5, s=-0.182, sx=-0.06667, sy=0.75744, sz=0.05133) 

1771# 56 ITRF2005@2015xETRF2000 xform=xform(tx=51.1, ty=51.7, tz=-80.8, s=1.6, sx=2.106, sy=12.74, sz=-20.592) 

1772# rates=rates(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792) 

1773# 57 ITRF2005@1989xETRF2005 xform=xform(tx=56.0, ty=48.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1774# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.054, sy=0.518, sz=-0.781) 

1775# 58 ITRF2005@1994xGDA94 xform=xform(tx=-79.73, ty=-6.86, tz=38.03, s=6.636, sx=0.0351, sy=-2.1211, sz=-2.1411) 

1776# rates=rates(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701) 

1777# 59 ITRF2005@1997xNAD83 xform=xform(tx=996.3, ty=-1902.4, tz=-521.9, s=0.775, sx=-25.915, sy=-9.426, sz=-11.599) 

1778# rates=rates(tx=0.5, ty=-0.6, tz=-1.3, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133) 

1779# 60 ITRF2005@2015xETRF2014 xform=xform(tx=-4.1, ty=-1.0, tz=2.8, s=-1.07, sx=2.21, sy=13.806, sz=-20.02) 

1780# rates=rates(tx=-0.3, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77) 

1781# 61 ITRF2005@2015xETRF2020 xform=xform(tx=5.5, ty=1.9, tz=-4.2, s=1.49, sx=2.236, sy=13.494, sz=-19.578) 

1782# rates=rates(tx=0.3, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753) 

1783# 62 ITRF2005@2020xGDA2020 xform=xform(tx=40.32, ty=-33.85, tz=-16.72, s=4.286, sx=-1.2893, sy=-0.8492, sz=-0.3342) 

1784# rates=rates(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701) 

1785# 63 ITRF2005@2000xITRF2000 xform=xform(tx=0.1, ty=-0.8, tz=-5.8, s=0.4, sx=0.0, sy=0.0, sz=0.0) 

1786# rates=rates(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0) 

1787# 64 ITRF2008@1994xGDA94 xform=xform(tx=-84.68, ty=-19.42, tz=32.01, s=9.71, sx=-0.4254, sy=2.2578, sz=2.4015) 

1788# rates=rates(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551) 

1789# 65 ITRF2008@1997xNAD83 xform=xform(tx=993.43, ty=-1903.31, tz=-526.55, s=1.71504, sx=-25.91467, sy=-9.42645, sz=-11.59935) 

1790# rates=rates(tx=0.79, ty=-0.6, tz=-1.34, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133) 

1791# 66 ITRF96@1997xNAD83 xform=xform(tx=991.0, ty=-190.72, tz=-512.9, s=0.0, sx=25.79, sy=9.65, sz=11.66) 

1792# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0532, sy=-0.7423, sz=-0.0316) 

1793# 67 ITRF2008@2015xETRF2000 xform=xform(tx=53.6, ty=50.8, tz=-85.5, s=2.54, sx=2.106, sy=12.74, sz=-20.592) 

1794# rates=rates(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792) 

1795# 68 ITRF2008@2015xETRF2014 xform=xform(tx=-1.6, ty=-1.9, tz=-1.9, s=-0.13, sx=2.21, sy=13.806, sz=-20.02) 

1796# rates=rates(tx=0.0, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77) 

1797# 69 ITRF2008@2015xETRF2020 xform=xform(tx=3.0, ty=2.8, tz=0.5, s=0.55, sx=2.236, sy=13.494, sz=-19.578) 

1798# rates=rates(tx=0.0, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753) 

1799# 70 ITRF2008@2020xGDA2020 xform=xform(tx=13.79, ty=4.55, tz=15.22, s=2.5, sx=0.2808, sy=0.2677, sz=-0.4638) 

1800# rates=rates(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551) 

1801# 71 ITRF2008@2000xITRF2000 xform=xform(tx=-1.9, ty=-1.7, tz=-10.5, s=1.34, sx=0.0, sy=0.0, sz=0.0) 

1802# rates=rates(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0) 

1803# 72 ITRF2008@2000xITRF88 xform=xform(tx=22.8, ty=2.6, tz=-125.2, s=10.41, sx=0.1, sy=0.0, sz=0.06) 

1804# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1805# 73 ITRF2008@2000xITRF89 xform=xform(tx=27.8, ty=38.6, tz=-101.2, s=7.31, sx=0.0, sy=0.0, sz=0.06) 

1806# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1807# 74 ITRF2008@2000xITRF90 xform=xform(tx=22.8, ty=14.6, tz=-63.2, s=3.91, sx=0.0, sy=0.0, sz=0.06) 

1808# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1809# 75 ITRF2008@2000xITRF91 xform=xform(tx=24.8, ty=18.6, tz=-47.2, s=3.61, sx=0.0, sy=0.0, sz=0.06) 

1810# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1811# 76 ITRF2008@2000xITRF92 xform=xform(tx=12.8, ty=4.6, tz=-41.2, s=2.21, sx=0.0, sy=0.0, sz=0.06) 

1812# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1813# 77 ITRF2008@2000xITRF93 xform=xform(tx=-24.0, ty=2.4, tz=-38.6, s=3.41, sx=-1.71, sy=-1.48, sz=-0.3) 

1814# rates=rates(tx=-2.8, ty=-0.1, tz=-2.4, s=0.09, sx=-0.11, sy=-0.19, sz=0.07) 

1815# 78 ITRF2008@2000xITRF94 xform=xform(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06) 

1816# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1817# 79 ITRF2008@2000xITRF96 xform=xform(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06) 

1818# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1819# 80 ITRF2008@2000xITRF97 xform=xform(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06) 

1820# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1821# 81 ITRF2008@2005xITRF2005 xform=xform(tx=-0.5, ty=-0.9, tz=-4.7, s=0.94, sx=0.0, sy=0.0, sz=0.0) 

1822# rates=rates(tx=0.3, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1823# 82 ITRF2014@2015xETRF2000 xform=xform(tx=55.2, ty=52.7, tz=-83.6, s=2.67, sx=2.106, sy=12.74, sz=-20.592) 

1824# rates=rates(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.081, sy=0.49, sz=-0.792) 

1825# 83 ITRF2014@2015xETRF2014 xform=xform(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=2.21, sy=13.806, sz=-20.02) 

1826# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.085, sy=0.531, sz=-0.77) 

1827# 84 ITRF2014@2015xETRF2020 xform=xform(tx=1.4, ty=0.9, tz=-1.4, s=0.42, sx=2.236, sy=13.494, sz=-19.578) 

1828# rates=rates(tx=0.0, ty=0.1, tz=-0.2, s=0.0, sx=0.086, sy=0.519, sz=-0.753) 

1829# 85 ITRF2014@2020xGDA2020 xform=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1830# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=1.50379, sy=1.18346, sz=1.20716) 

1831# 86 ITRF2014@2010xITRF2000 xform=xform(tx=0.7, ty=1.2, tz=-26.1, s=2.12, sx=0.0, sy=0.0, sz=0.0) 

1832# rates=rates(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.0, sy=0.0, sz=0.0) 

1833# 87 ITRF2014@2010xITRF2005 xform=xform(tx=2.6, ty=1.0, tz=-2.3, s=0.92, sx=0.0, sy=0.0, sz=0.0) 

1834# rates=rates(tx=0.3, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0) 

1835# 88 ITRF2014@2010xITRF2008 xform=xform(tx=1.6, ty=1.9, tz=2.4, s=-0.02, sx=0.0, sy=0.0, sz=0.0) 

1836# rates=rates(tx=0.0, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0) 

1837# 89 ITRF2014@2010xITRF88 xform=xform(tx=25.4, ty=-0.5, tz=-154.8, s=11.29, sx=0.1, sy=0.0, sz=0.26) 

1838# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1839# 90 ITRF2014@2010xITRF89 xform=xform(tx=30.4, ty=35.5, tz=-130.8, s=8.19, sx=0.0, sy=0.0, sz=0.26) 

1840# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1841# 91 ITRF2014@2010xITRF90 xform=xform(tx=25.4, ty=11.5, tz=-92.8, s=4.79, sx=0.0, sy=0.0, sz=0.26) 

1842# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1843# 92 ITRF2014@2010xITRF91 xform=xform(tx=27.4, ty=15.5, tz=-76.8, s=4.49, sx=0.0, sy=0.0, sz=0.26) 

1844# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1845# 93 ITRF2014@2010xITRF92 xform=xform(tx=15.4, ty=1.5, tz=-70.8, s=3.09, sx=0.0, sy=0.0, sz=0.26) 

1846# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1847# 94 ITRF2014@2010xITRF93 xform=xform(tx=-50.4, ty=3.3, tz=-60.2, s=4.29, sx=-2.81, sy=-3.38, sz=0.4) 

1848# rates=rates(tx=-2.8, ty=-0.1, tz=-2.5, s=0.12, sx=-0.11, sy=-0.19, sz=0.07) 

1849# 95 ITRF2014@2010xITRF94 xform=xform(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26) 

1850# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1851# 96 ITRF2014@2010xITRF96 xform=xform(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26) 

1852# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1853# 97 ITRF2014@2010xITRF97 xform=xform(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26) 

1854# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1855# 98 ITRF2020@2015xETRF2000 xform=xform(tx=53.8, ty=51.8, tz=-82.2, s=2.25, sx=2.106, sy=12.74, sz=-20.592) 

1856# rates=rates(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.081, sy=0.49, sz=-0.792) 

1857# 99 ITRF2020@2015xETRF2014 xform=xform(tx=-1.4, ty=-0.9, tz=1.4, s=0.42, sx=2.21, sy=13.806, sz=-20.02) 

1858# rates=rates(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.085, sy=0.531, sz=-0.77) 

1859# 100 ITRF2020@2015xETRF2020 xform=xform(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=2.236, sy=13.494, sz=-19.578) 

1860# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.086, sy=0.519, sz=-0.753) 

1861# 101 ITRF2020@2015xITRF2000 xform=xform(tx=-0.2, ty=0.8, tz=-34.2, s=2.25, sx=0.0, sy=0.0, sz=0.0) 

1862# rates=rates(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.0, sy=0.0, sz=0.0) 

1863# 102 ITRF2020@2015xITRF2005 xform=xform(tx=2.7, ty=0.1, tz=-1.4, s=0.65, sx=0.0, sy=0.0, sz=0.0) 

1864# rates=rates(tx=0.3, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0) 

1865# 103 ITRF2020@2015xITRF2008 xform=xform(tx=0.2, ty=1.0, tz=3.3, s=-0.29, sx=0.0, sy=0.0, sz=0.0) 

1866# rates=rates(tx=0.0, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0) 

1867# 104 ITRF2020@2015xITRF2014 xform=xform(tx=-1.4, ty=-0.9, tz=1.4, s=-0.42, sx=0.0, sy=0.0, sz=0.0) 

1868# rates=rates(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1869# 105 ITRF2020@2015xITRF88 xform=xform(tx=24.5, ty=-3.9, tz=-169.9, s=11.47, sx=0.1, sy=0.0, sz=0.36) 

1870# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1871# 106 ITRF2020@2015xITRF89 xform=xform(tx=29.5, ty=32.1, tz=-145.9, s=8.37, sx=0.0, sy=0.0, sz=0.36) 

1872# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1873# 107 ITRF2020@2015xITRF90 xform=xform(tx=24.5, ty=8.1, tz=-107.9, s=4.97, sx=0.0, sy=0.0, sz=0.36) 

1874# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1875# 108 ITRF2020@2015xITRF91 xform=xform(tx=26.5, ty=12.1, tz=-91.9, s=4.67, sx=0.0, sy=0.0, sz=0.36) 

1876# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1877# 109 ITRF2020@2015xITRF92 xform=xform(tx=14.5, ty=-1.9, tz=-85.9, s=3.27, sx=0.0, sy=0.0, sz=0.36) 

1878# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1879# 110 ITRF2020@2015xITRF93 xform=xform(tx=-65.8, ty=1.9, tz=-71.3, s=4.47, sx=-3.36, sy=-4.33, sz=0.75) 

1880# rates=rates(tx=-2.8, ty=-0.2, tz=-2.3, s=0.12, sx=-0.11, sy=-0.19, sz=0.07) 

1881# 111 ITRF2020@2015xITRF94 xform=xform(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36) 

1882# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1883# 112 ITRF2020@2015xITRF96 xform=xform(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36) 

1884# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1885# 113 ITRF2020@2015xITRF97 xform=xform(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36) 

1886# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)