Coverage for pygeodesy/trf.py: 94%

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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__ = '24.02.22' 

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, 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, 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. 

270 

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

272 

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

274 if C{B{inverse}=True} I{to} this reframe. 

275 ''' 

276 def _Xi(n2): 

277 for n1, r in RefFrames.items(): 

278 if n2 in r._Xto: 

279 yield n1, r 

280 

281 return ADict(_Xi(self.name) if inverse else self._Xto) 

282 

283 

284class RefFrames(_NamedEnum): 

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

286 to accommodate the L{_LazyNamedEnumItem} properties. 

287 ''' 

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

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

290 ''' 

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

292 

293RefFrames = RefFrames(RefFrame) # PYCHOK singleton 

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

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

296RefFrames._assert( 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

333 

334 

335class TransformXform(Transform): 

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

337 

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

339 ''' 

340 _Xform = None 

341 

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

343 '''New L{TransformXform}. 

344 

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

346 

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

348 

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

350 I{inversed}. 

351 ''' 

352 Transform.__init__(self, **tx_ty_tz_s_sx_sy_sz) 

353 if name: 

354 self.name = name 

355 

356 def __eq__(self, other): 

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

358 

359 def rename(self, name=NN): 

360 '''Change this transform's name. 

361 

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

363 

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

365 ''' 

366 X = self.Xform 

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

368 return Transform.rename(self, n) 

369 

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

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

372 

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

374 

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

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

377 

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

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

380 but I{not} taken into account. 

381 ''' 

382 _ = _xellipsoidall(point) 

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

384 X = self.Xform 

385 if X: # see _toRefFrame below 

386 p._reframe = X.reframe2 

387 p._epoch = X.epoch 

388 p.rename(name or self.name) 

389 return p 

390 

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

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

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

394 

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

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

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

398 L{toTransform<TRFXform.toTransform>} from 

399 L{TRFXform}. 

400 

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

402 

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

404 missing Xform. 

405 ''' 

406 X = self.Xform 

407 if X is None: 

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

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

410 

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

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

413 

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

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

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

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

418 keyword arguments to return the I{velocities}. 

419 

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

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

422 

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

424 

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

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

427 ''' 

428 v = X = self.Xform 

429 if X is not None: 

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

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

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

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

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

435 **Vector_and_kwds) 

436 return v 

437 

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

439 def Xform(self): 

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

441 ''' 

442 return self._Xform 

443 

444 @Xform.setter # PYCHOK setter! 

445 def Xform(self, Xform): 

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

447 

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

449 ''' 

450 _xinstanceof(TRFXform, Xform=Xform) 

451 self._Xform = Xform 

452 

453 

454class TRFXform7Tuple(_NamedTuple): 

455 '''7-Tuple C{(tx, ty, tz, s, sx, sy, sz)} of conversion parameters with 

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

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

458 

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

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

461 

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

463 ''' 

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

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

466 

467 def __add__(self, other): 

468 _xinstanceof(TRFXform7Tuple, other=other) 

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

470 

471 def __eq__(self, other): 

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

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

474 

475 def __hash__(self): 

476 return self._hash # memoized 

477 

478 def __mul__(self, factor): 

479 _xisscalar(factor=factor) 

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

481 

482 def __neg__(self): 

483 return self.inverse() 

484 

485 def __sub__(self, other): 

486 _xinstanceof(TRFXform7Tuple, other=other) 

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

488 

489 @Property_RO 

490 def _hash(self): 

491 return hash(s for s in self) 

492 

493 def inverse(self, name=NN): 

494 '''Return the inverse of this transform. 

495 

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

497 

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

499 ''' 

500 n = name or _minus(self.name) 

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

502 

503 @Property_RO 

504 def isunity(self): 

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

506 ''' 

507 return not any(self) 

508 

509 

510class TRFXform(_Named): 

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

512 reference frames observed at an C{epoch}. 

513 ''' 

514 _epoch = _EP0CH 

515 _epoch_d = _0_0 

516 _indir_d = NN # refName 

517 _inver_d = False 

518 refName1 = \ 

519 refName2 = NN 

520 rates = \ 

521 xform = None 

522 

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

524 rates=None, name=NN): 

525 '''New L{trfXform}. 

526 

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

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

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

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

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

532 but in C{units-per-year}. 

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

534 method L{toStr<TRFXform.toStr>}. 

535 

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

537 

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

539 ''' 

540 self.refName1 = str(refName1) 

541 self.refName2 = str(refName2) 

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

543 self.epoch = epoch 

544 self.xform = xform 

545 self.rates = rates 

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

547 

548 def __eq__(self, other): 

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

550 self.xform == other.xform and self.rates == other.rates 

551 

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

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

554 or self.refName2 < other.refName2 

555 or self.epoch < other.epoch) 

556 

557 def __neg__(self): 

558 return self.inverse() 

559 

560 def __repr__(self): 

561 return self.toRepr() 

562 

563 def __str__(self): 

564 return self.toStr() 

565 

566 def _at(self, epoch): 

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

568 ''' 

569 n = self.name 

570 if epoch != self.epoch: 

571 _e = _AT_(NN, epoch) 

572 if not n.endswith(_e): 

573 n = NN(n, _e) 

574 return n 

575 

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

577 def epoch(self): 

578 '''Get the epoch (L{Epoch}). 

579 ''' 

580 return self._epoch 

581 

582 @epoch.setter # PYCHOK setter! 

583 def epoch(self, epoch): 

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

585 

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

587 ''' 

588 e = _Epoch(epoch) 

589 if self._epoch != e: 

590 self.rename(self._at(e)) 

591 self._epoch = e 

592 

593 @property_RO 

594 def epoched(self): 

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

596 ''' 

597 return self._epoch_d 

598 

599 @property_RO 

600 def indirected(self): 

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

602 ''' 

603 return self._indir_d 

604 

605 def inverse(self, name=NN): 

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

607 

608 @return: Inverse (L{TRFXform}). 

609 ''' 

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

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

612 name=name or _minus(self.name), 

613 _inver_d=not self.inversed) 

614 

615 @property_RO 

616 def inversed(self): 

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

618 ''' 

619 return self._inver_d 

620 

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

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

623 ''' 

624 r = RefFrames.get(name) 

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

626 r = RefFrame(self.epoch, datum) 

627 r.name = name # unregistered 

628 return r 

629 

630 @property_RO 

631 def reframe1(self): 

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

633 ''' 

634 return self._reframe(self.refName1) 

635 

636 @property_RO 

637 def reframe2(self): 

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

639 ''' 

640 return self._reframe(self.refName2) 

641 

642 def rename(self, name=NN): 

643 '''Change this Xform's name. 

644 

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

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

647 

648 @return: The old name (C{str}). 

649 ''' 

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

651 

652 def toEpoch(self, epoch): 

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

654 

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

656 or C{str}). 

657 

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

659 

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

661 ''' 

662 e = _Epoch(epoch) 

663 X, d = self, e - self.epoch 

664 if d: 

665 t = X.xform + X.rates * d 

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

667 X._epoch_d += d # abs(d)? 

668 return X 

669 

670 def toHelmert(self, factor=_MM2M): 

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

672 

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

674 

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

676 

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

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

679 and scale from C{ppb} to C{ppM}. 

680 ''' 

681 h = self.xform * factor 

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

683 H.Xform = self 

684 return H 

685 

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

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

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

689 

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

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

692 overriding this Xform's C{epoch}. 

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

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

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

696 and C{B{name}=refName1}. 

697 

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

699 

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

701 ''' 

702 def _r(name): 

703 r = RefFrames.get(name) 

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

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

706 r.name = name # unregistered 

707 return r 

708 

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

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

711 

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

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

714 ''' 

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

716 

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

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

719 

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

721 this Xform's epoch. 

722 ''' 

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

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

725 

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

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

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

729 

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

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

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

733 

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

735 

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

737 

738 @see: Method L{toHelmert}. 

739 ''' 

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

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

742 X = self.toEpoch(e) 

743 if inverse: 

744 X = X.inverse() 

745 return X.toHelmert() 

746 

747 

748def date2epoch(year, month, day): 

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

750 

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

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

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

754 

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

756 

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

758 

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

760 29 days in February. 

761 ''' 

762 try: 

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

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

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

766 return Epoch(e, low=0) 

767 

768 raise ValueError # _invalid_ 

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

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

771 

772 

773def _direct(n1, n2): 

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

775 ''' 

776 r = RefFrames.get(n1) 

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

778 

779 

780def _Epoch(e, **kwds): 

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

782 ''' 

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

784 

785 

786def epoch2date(epoch): 

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

788 

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

790 

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

792 

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

794 

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

796 29 days in February. 

797 ''' 

798 e = Epoch(epoch, low=0) 

799 y = int(e) 

800 d = int(_ceil((e - y) * _366_0)) 

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

802 if d > n: 

803 d -= n 

804 else: 

805 break 

806 return y, (m + 1), max(1, d) 

807 

808 

809def _indirects(n1, n2): 

810 '''(INTERNAL) Yield all Xforms between C{n1} and C{n2} via C{n}. 

811 ''' 

812 def _X4(_Xto, n2): 

813 _d = _direct 

814 for n, X1 in _Xto.items(): 

815 X2 = _d(n, n2) 

816 if X2: 

817 yield X1, X2, n, True # + 

818 X2 = _d(n2, n) 

819 if X2: 

820 yield X1, X2, n, False # - 

821 

822 r1 = RefFrames.get(n1) 

823 if r1: 

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

825 e1, e2 = X1.epoch, X2.epoch 

826 if e1 < e2: # X1 to e2 

827 X1 = X1.toEpoch(e2) 

828 e1 = e2 

829 elif e1 > e2: # X2 to e1 

830 X2 = X2.toEpoch(e1) 

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

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

833 X = TRFXform(n1, n2, epoch=e1, 

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

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

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

837 X2._at(e1))) 

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

839 X._indir_d = n # reframe? 

840 yield X 

841 

842 

843def _reframe(**name_reframe): 

844 '''(INTERNAL) Get a C{reframe}. 

845 ''' 

846 if len(name_reframe) == 1: 

847 for r in name_reframe.values(): 

848 break 

849 if isstr(r) and r: # not NN 

850 r = RefFrames.get(r) 

851 if r and isinstance(r, RefFrame): 

852 return r 

853 raise TRFError(**name_reframe) # _invalid_ 

854 

855 

856def _toRefFrame(point, reframe2, reframe=None, epoch=None, 

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

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

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

860 ''' 

861 ll = _xellipsoidall(point) 

862 r1 = reframe or point.reframe 

863 if not r1: 

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

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

866 

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

868 

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

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

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

872 if t0 is None: 

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

874 _to_, _AT_(reframe2.name, e2)) 

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

876 

877 if t0: # is not () 

878 if t0.isunity: 

879 p = point.dup() 

880 elif point.datum: 

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

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

883 .toDatum(reframe2.datum).toDatum(point.datum) 

884 if ll: 

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

886 elif ll: # and LatLon_kwds 

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

888 else: 

889 p = point.toTransform(t0) 

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

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

892 p.rename(name or reframe2.name) 

893 else: 

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

895 return p 

896 

897 

898def _toTransform0(n1, e1, n2, e2, **indirect_inverse): 

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

900 ''' 

901 if n1 == n2 and e1 == e2: 

902 return () # unity? 

903 

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

905 return X # first OK? 

906 

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

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

909 return () # unity? 

910 

911 return None 

912 

913 

914def _toTransforms(n1, e1, n2, e2, indirect=True, inverse=True): 

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

916 ''' 

917 def _k(X): 

918 return -X.epoch 

919 

920 X = _direct(n1, n2) 

921 if X: 

922 yield X.toTransform(e1, epoch2=e2) 

923 

924 if inverse: 

925 X = _direct(n2, n1) 

926 if X: 

927 yield X.toTransform(e1, epoch2=e2, inverse=True) 

928 

929 if indirect: 

930 for X in sorted(_indirects(n1, n2), key=_k): 

931 yield X.toTransform(e1, epoch2=e2) 

932 

933 if inverse: 

934 for X in sorted(_indirects(n2, n1), key=_k): 

935 yield X.toTransform(e1, epoch2=e2, inverse=True) 

936 

937 

938def trfTransform0(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True): 

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

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

941 

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

943 C{None} if no conversion exists. 

944 

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

946 ''' 

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

948 indirect=indirect, inverse=inverse) 

949 

950 

951def trfTransforms(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True): 

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

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

954 

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

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

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

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

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

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

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

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

963 transforms (C{bool}). 

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

965 (C{bool}). 

966 

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

968 

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

970 B{C{epoch2}}. 

971 

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

973 ''' 

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

975 indirect=indirect, inverse=inverse) 

976 

977 

978def _trfT0s(_toT0s, reframe, reframe2, epoch, epoch2, **indirect_inverse): 

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

980 ''' 

981 r1 = _reframe(reframe=reframe) 

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

983 r2 = _reframe(reframe2=reframe2) 

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

985 return _toT0s(r1.name, e1, r2.name, e2, **indirect_inverse) 

986 

987 

988def trfXform(reframe1, reframe2, epoch=None, xform=None, rates=None, raiser=True): 

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

990 existing one. 

991 

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

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

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

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

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

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

998 but in C{units-per-year}. 

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

1000 exists, replace it (C{bool}). 

1001 

1002 @return: The new TRF converter (L{TRFXform}) or if no B{C{epoch}}, 

1003 B{C{xform}} and B{C{rates}} are given, return the existing 

1004 one (L{TRFXform}) or C{None} if not available. 

1005 

1006 @raise TRFError: Invalid B{C{reframe1}}, B{C{reframe2}}, B{C{epoch}}, 

1007 B{C{xform}} or B{C{rates}} or the TRF converter 

1008 already exists. 

1009 ''' 

1010 try: 

1011 r1 = _reframe(reframe1=reframe1) 

1012 r2 = _reframe(reframe2=reframe2) 

1013 if epoch is None: 

1014 if xform is rates is None: 

1015 return r1._Xto.get(r2.name, None) 

1016 e = r2.epoch 

1017 else: 

1018 e = _Epoch(epoch) 

1019 return _trfX(r1.name, r2.name, raiser=raiser, epoch=e, 

1020 xform=xform, rates=rates) 

1021 except (TypeError, ValueError) as x: 

1022 t = unstr(trfXform, reframe1, reframe2, epoch=epoch) 

1023 raise TRFError(t, cause=x) 

1024 

1025 

1026def _trfX(n1, n2, raiser=True, **epoch_xform_rates): 

1027 '''(INTERNAL) New, I{unique} L{TRFXform} converter. 

1028 ''' 

1029 r1 = RefFrames.get(n1) 

1030 if r1 is None: 

1031 raise ValueError(_invalid_) 

1032 r2 = RefFrames.get(n2) 

1033 if r2 is None: 

1034 raise ValueError(_invalid_) 

1035 if raiser: 

1036 if n2 in r1._Xto: 

1037 raise ValueError(_exists_) 

1038 if n1 in r2._Xto: 

1039 raise ValueError(_SPACE_(_inverse_, _exists_)) 

1040 r1._Xto[n2] = X = TRFXform(n1, n2, **epoch_xform_rates) 

1041 return X 

1042 

1043 

1044def _X(*ps): # deleted below 

1045 return _P(ps, _xform_, _Xs) # PYCHOK del 

1046 

1047 

1048def _R(*ps): # deleted below 

1049 return _P(ps, _rates_, _Rs) # PYCHOK del 

1050 

1051 

1052_P_0_0s = TRFXform7Tuple(_0_0s(len(_Names7)), name='unity') 

1053 

1054# TRF conversions specified as an epoch and 2 sets of 7 parameters. Most from Altamimi, Z. U{"EUREF Technical 

1055# Note 1: Relationship and Transformation between the International and the European Terrestrial Reference 

1056# Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Appendix A, more at U{Quinsy QPS <https:// 

1057# confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ITRF_Transformation_Parameters.xlsx>}. 

1058# See also U{Quinsy International Terrestrial Reference Frame 2014 (ITRF2014)<https://confluence.QPS.NL/qinsy/latest/ 

1059# en/international-terrestrial-reference-frame-2014-itrf2014-182618383.html>}. 

1060_trfX(_ITRF2020_, _ITRF2014_, epoch=_E(2015), # <https://ITRF.IGN.Fr/docs/solutions/itrf2020/Transfo-ITRF2020_TRFs.txt> 

1061 xform=_X( -1.4, -0.9, 1.4, -0.42, _0_0, _0_0, _0_0), 

1062 rates=_R( _0_0, -0.1, 0.2, _0_0, _0_0, _0_0, _0_0)) 

1063_trfX(_ITRF2020_, _ITRF2008_, epoch=_E(2015), 

1064 xform=_X( 0.2, 1.0, 3.3, -0.29, _0_0, _0_0, _0_0), 

1065 rates=_R( _0_0, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0)) 

1066_trfX(_ITRF2020_, _ITRF2005_, epoch=_E(2015), 

1067 xform=_X( 2.7, 0.1, -1.4, 0.65, _0_0, _0_0, _0_0), 

1068 rates=_R( 0.3, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0)) 

1069_trfX(_ITRF2020_, _ITRF2000_, epoch=_E(2015), 

1070 xform=_X( -0.2, 0.8, -34.2, 2.25, _0_0, _0_0, _0_0), 

1071 rates=_R( 0.1, _0_0, -1.7, 0.11, _0_0, _0_0, _0_0)) 

1072_trfX(_ITRF2020_, _ITRF97_, epoch=_E(2015), 

1073 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36), 

1074 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1075_trfX(_ITRF2020_, _ITRF96_, epoch=_E(2015), 

1076 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36), 

1077 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1078_trfX(_ITRF2020_, _ITRF94_, epoch=_E(2015), 

1079 xform=_X( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36), 

1080 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1081_trfX(_ITRF2020_, _ITRF93_, epoch=_E(2015), 

1082 xform=_X( -65.8, 1.9, -71.3, 4.47, -3.36, -4.33, 0.75), 

1083 rates=_R( -2.8, -0.2, -2.3, 0.12, -0.11, -0.19, 0.07)) 

1084_trfX(_ITRF2020_, _ITRF92_, epoch=_E(2015), 

1085 xform=_X( 14.5, -1.9, -85.9, 3.27, _0_0, _0_0, 0.36), 

1086 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1087_trfX(_ITRF2020_, _ITRF91_, epoch=_E(2015), 

1088 xform=_X( 26.5, 12.1, -91.9, 4.67, _0_0, _0_0, 0.36), 

1089 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1090_trfX(_ITRF2020_, _ITRF90_, epoch=_E(2015), 

1091 xform=_X( 24.5, 8.1, -107.9, 4.97, _0_0, _0_0, 0.36), 

1092 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1093_trfX(_ITRF2020_, _ITRF89_, epoch=_E(2015), 

1094 xform=_X( 29.5, 32.1, -145.9, 8.37, _0_0, _0_0, 0.36), 

1095 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1096_trfX(_ITRF2020_, _ITRF88_, epoch=_E(2015), 

1097 xform=_X( 24.5, -3.9, -169.9, 11.47, 0.1, _0_0, 0.36), 

1098 rates=_R( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1099 

1100# see U{Transformation Parameters ITRF2014<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2014_ITRFs.txt>} and 

1101# Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and 

1102# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1.pdf>} Appendix A. 

1103_trfX(_ITRF2014_, _ITRF2008_, epoch=(2010), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2014/tp_14-08.php> 

1104 xform=_X( 1.6, 1.9, 2.4, -0.02, _0_0, _0_0, _0_0), 

1105 rates=_R( _0_0, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0)) 

1106_trfX(_ITRF2014_, _ITRF2005_, epoch=_E(2010), 

1107 xform=_X( 2.6, _1_0, -2.3, 0.92, _0_0, _0_0, _0_0), 

1108 rates=_R( 0.3, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0)) 

1109_trfX(_ITRF2014_, _ITRF2000_, epoch=_E(2010), 

1110 xform=_X( 0.7, 1.2, -26.1, 2.12, _0_0, _0_0, _0_0), 

1111 rates=_R( 0.1, 0.1, -1.9, 0.11, _0_0, _0_0, _0_0)) 

1112_trfX(_ITRF2014_, _ITRF97_, epoch=_E(2010), 

1113 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26), 

1114 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1115_trfX(_ITRF2014_, _ITRF96_, epoch=_E(2010), 

1116 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26), 

1117 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1118_trfX(_ITRF2014_, _ITRF94_, epoch=_E(2010), 

1119 xform=_X( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26), 

1120 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1121_trfX(_ITRF2014_, _ITRF93_, epoch=_E(2010), 

1122 xform=_X( -50.4, 3.3, -60.2, 4.29, -2.81, -3.38, 0.4), 

1123 rates=_R( -2.8, -0.1, -2.5, 0.12, -0.11, -0.19, 0.07)) 

1124_trfX(_ITRF2014_, _ITRF92_, epoch=_E(2010), 

1125 xform=_X( 15.4, 1.5, -70.8, 3.09, _0_0, _0_0, 0.26), 

1126 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1127_trfX(_ITRF2014_, _ITRF91_, epoch=_E(2010), 

1128 xform=_X( 27.4, 15.5, -76.8, 4.49, _0_0, _0_0, 0.26), 

1129 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1130_trfX(_ITRF2014_, _ITRF90_, epoch=_E(2010), 

1131 xform=_X( 25.4, 11.5, -92.8, 4.79, _0_0, _0_0, 0.26), 

1132 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1133_trfX(_ITRF2014_, _ITRF89_, epoch=_E(2010), 

1134 xform=_X( 30.4, 35.5, -130.8, 8.19, _0_0, _0_0, 0.26), 

1135 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1136_trfX(_ITRF2014_, _ITRF88_, epoch=_E(2010), 

1137 xform=_X( 25.4, -0.5, -154.8, 11.29, 0.1, _0_0, 0.26), 

1138 rates=_R( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1139 

1140# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference 

1141# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 1st and 2nd column 

1142_trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2005), 

1143 xform=_X( -0.5, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0), 

1144 rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0)) 

1145# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(1997), 

1146# xform=_X( -2.9, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0), 

1147# rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0)) 

1148# see U{Transformation Parameters ITRF2008<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2008_ITRFs.txt>} 

1149# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2008/tp_08-05.php> 

1150# xform=_X( -2.0, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0), 

1151# rates=_R( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0)) 

1152_trfX(_ITRF2008_, _ITRF2000_, epoch=_E(2000), 

1153 xform=_X( -1.9, -1.7, -10.5, 1.34, _0_0, _0_0, _0_0), 

1154 rates=_R( 0.1, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0)) 

1155_trfX(_ITRF2008_, _ITRF97_, epoch=_E(2000), 

1156 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06), 

1157 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1158_trfX(_ITRF2008_, _ITRF96_, epoch=_E(2000), 

1159 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06), 

1160 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1161_trfX(_ITRF2008_, _ITRF94_, epoch=_E(2000), 

1162 xform=_X( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06), 

1163 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1164_trfX(_ITRF2008_, _ITRF93_, epoch=_E(2000), 

1165 xform=_X( -24.0, 2.4, -38.6, 3.41, -1.71, -1.48, -0.3), 

1166 rates=_R( -2.8, -0.1, -2.4, 0.09, -0.11, -0.19, 0.07)) 

1167_trfX(_ITRF2008_, _ITRF92_, epoch=_E(2000), 

1168 xform=_X( 12.8, 4.6, -41.2, 2.21, _0_0, _0_0, 0.06), 

1169 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1170_trfX(_ITRF2008_, _ITRF91_, epoch=_E(2000), 

1171 xform=_X( 24.8, 18.6, -47.2, 3.61, _0_0, _0_0, 0.06), 

1172 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1173_trfX(_ITRF2008_, _ITRF90_, epoch=_E(2000), 

1174 xform=_X( 22.8, 14.6, -63.2, 3.91, _0_0, _0_0, 0.06), 

1175 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1176_trfX(_ITRF2008_, _ITRF89_, epoch=_E(2000), 

1177 xform=_X( 27.8, 38.6, -101.2, 7.31, _0_0, _0_0, 0.06), 

1178 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1179_trfX(_ITRF2008_, _ITRF88_, epoch=_E(2000), 

1180 xform=_X( 22.8, 2.6, -125.2, 10.41, 0.1, _0_0, 0.06), 

1181 rates=_R( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1182 

1183# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference 

1184# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 3rd column 

1185# _trfX(_ITRF2005_, _ITRF2000_, epoch=_E(1997), 

1186# xform=_X( 0.7, -1.1, -0.4, 0.16, -0.2, 0.1 -1.8), 

1187# rates=_R( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0)) 

1188_trfX(_ITRF2005_, _ITRF2000_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2005/tp_05-00.php> 

1189 xform=_X( 0.1, -0.8, -5.8, 0.4, _0_0, _0_0, _0_0), 

1190 rates=_R( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0)) 

1191 

1192_trfX(_ITRF2000_, _ITRF97_, epoch=_E(1997), 

1193 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0), 

1194 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, -0.02)) # 0.02? 

1195_trfX(_ITRF2000_, _ITRF96_, epoch=_E(1997), 

1196 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0), 

1197 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1198_trfX(_ITRF2000_, _ITRF94_, epoch=_E(1997), 

1199 xform=_X( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0), 

1200 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1201_trfX(_ITRF2000_, _ITRF93_, epoch=_E(1988), 

1202 xform=_X( 12.7, 6.5, -20.9, 1.95, -0.39, 0.8, -1.14), 

1203 rates=_R( -2.9, -0.2, -0.6, 0.01, -0.11, -0.19, 0.07)) 

1204_trfX(_ITRF2000_, _ITRF92_, epoch=_E(1988), 

1205 xform=_X( 1.47, 1.35, -1.39, 0.75, _0_0, _0_0, -0.18), 

1206 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1207_trfX(_ITRF2000_, _ITRF91_, epoch=_E(1988), 

1208 xform=_X( 26.7, 27.5, -19.9, 2.15, _0_0, _0_0, -0.18), 

1209 rates=_R( _0_0, -0.6, -1.4, 0.01, _0_0, _0_0, 0.02)) 

1210_trfX(_ITRF2000_, _ITRF90_, epoch=_E(1988), 

1211 xform=_X( 2.47, 2.35, -3.59, 2.45, _0_0, _0_0, -0.18), 

1212 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1213_trfX(_ITRF2000_, _ITRF89_, epoch=_E(1988), 

1214 xform=_X( 2.97, 4.75, -7.39, 5.85, _0_0, _0_0, -0.18), 

1215 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1216_trfX(_ITRF2000_, _ITRF88_, epoch=_E(1988), 

1217 xform=_X( 2.47, 1.15, -9.79, 8.95, 0.1, _0_0, -0.18), 

1218 rates=_R( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1219 

1220# Soler, T .& Snay R.A. U{"Transforming Positions and Velocities between the International Terrestrial 

1221# Reference Frame of 2000 and North American Datum of 1983"<https://www.ResearchGate.net/publication/245291390>}, 

1222# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference 

1223# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 5th and 6th column 

1224_trfX(_ITRF97_, _ITRF96_, epoch=_E(1997), 

1225 xform=_X( -2.07, -0.21, 9.95, -0.93496, 0.1267, -0.22355, -0.06065,), 

1226 rates=_R( 0.69, -0.1, 1.86, -0.19201, 0.01347, -0.01514, 0.00027)) 

1227_trfX(_ITRF96_, _NAD83_, epoch=_E(1997), 

1228 xform=_X( 991.0, -190.72, -512.9, _0_0, 25.79, 9.65, 11.66,), 

1229 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.0532, -0.7423, -0.0316,)) 

1230 

1231# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and 

1232# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 1. 

1233# _trfX(_ITRF2020_, _ETRF2020_, epoch=_E(1989), # see Table 2 below 

1234# xform=_P_0_0s, 

1235# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753)) 

1236# _trfX(_ITRF2014_, _ETRF2014_, epoch=_E(1989), # see Table 3 below 

1237# xform=_P_0_0s, 

1238# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77)) 

1239_trfX(_ITRF2005_, _ETRF2005_, epoch=_E(1989), 

1240 xform=_X( 56.0, 48.0, -37.0, _0_0, _0_0, _0_0, _0_0), 

1241 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.054, 0.518, -0.781)) 

1242# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(1989), # see Table 4 below 

1243# xform=_X( 54.0, 51.0, -48.0, _0_0, _0_0, _0_0, _0_0), 

1244# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792)) 

1245_trfX(_ITRF97_, _ETRF97_, epoch=_E(1989), 

1246 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0), 

1247 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65)) 

1248_trfX(_ITRF96_, _ETRF96_, epoch=_E(1989), 

1249 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0), 

1250 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65)) 

1251_trfX(_ITRF94_, _ETRF94_, epoch=_E(1989), 

1252 xform=_X( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0), 

1253 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65)) 

1254_trfX(_ITRF93_, _ETRF93_, epoch=_E(1989), 

1255 xform=_X( 19.0, 53.0, -21.0, _0_0, _0_0, _0_0, _0_0), 

1256 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.32, 0.78, -0.67)) 

1257_trfX(_ITRF92_, _ETRF92_, epoch=_E(1989), 

1258 xform=_X( 38.0, 40.0, -37.0, 0.0, 0.0, 0.0, 0.0), 

1259 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68)) 

1260_trfX(_ITRF91_, _ETRF91_, epoch=_E(1989), 

1261 xform=_X( 21.0, 25.0, -37.0, _0_0, _0_0, _0_0, _0_0), 

1262 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68)) 

1263_trfX(_ITRF90_, _ETRF90_, epoch=_E(1989), 

1264 xform=_X( 19.0, 28.0, -23.0, _0_0, _0_0, _0_0, _0_0), 

1265 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71)) 

1266_trfX(_ITRF89_, _ETRF89_, epoch=_E(1989), 

1267 xform=_P_0_0s, 

1268 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71)) 

1269 

1270# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and 

1271# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 2. 

1272_trfX(_ITRF2020_, _ETRF2020_, epoch=_E(2015), 

1273 xform=_X( _0_0, _0_0, _0_0, _0_0, 2.236, 13.494, -19.578), 

1274 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753)) 

1275_trfX(_ITRF2014_, _ETRF2020_, epoch=_E(2015), 

1276 xform=_X( 1.4, 0.9, -1.4, 0.42, 2.236, 13.494, -19.578), 

1277 rates=_R( _0_0, 0.1, -0.2, _0_0, 0.086, 0.519, -0.753)) 

1278_trfX(_ITRF2008_, _ETRF2020_, epoch=_E(2015), 

1279 xform=_X( 3.0, 2.8, 0.5, 0.55, 2.236, 13.494, -19.578), 

1280 rates=_R( _0_0, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753)) 

1281_trfX(_ITRF2005_, _ETRF2020_, epoch=_E(2015), 

1282 xform=_X( 5.5, 1.9, -4.2, 1.49, 2.236, 13.494, -19.578), 

1283 rates=_R( 0.3, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753)) 

1284_trfX(_ITRF2000_, _ETRF2020_, epoch=_E(2015), 

1285 xform=_X( 2.6, 2.6, -37.0, 3.09, 2.236, 13.494, -19.578), 

1286 rates=_R( 0.1, 0.2, -2.1, 0.11, 0.086, 0.519, -0.753)) 

1287_trfX(_ITRF97_, _ETRF2020_, epoch=_E(2015), 

1288 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218), 

1289 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1290_trfX(_ITRF96_, _ETRF2020_, epoch=_E(2015), 

1291 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218), 

1292 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1293_trfX(_ITRF94_, _ETRF2020_, epoch=_E(2015), 

1294 xform=_X( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218), 

1295 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1296_trfX(_ITRF93_, _ETRF2020_, epoch=_E(2015), 

1297 xform=_X( -63.0, 3.7, -74.1, 5.31, -1.124, 9.164, -18.828), 

1298 rates=_R( -2.8, _0_0, -2.7, 0.12, -0.024, 0.329, -0.683)) 

1299_trfX(_ITRF92_, _ETRF2020_, epoch=_E(2015), 

1300 xform=_X( 17.3, -0.1, -88.7, 4.11, 2.236, 13.494, -19.218), 

1301 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1302_trfX(_ITRF91_, _ETRF2020_, epoch=_E(2015), 

1303 xform=_X( 29.3, 13.9, -94.7, 5.51, 2.236, 13.494, -19.218), 

1304 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1305_trfX(_ITRF90_, _ETRF2020_, epoch=_E(2015), 

1306 xform=_X( 27.3, 9.9, -110.7, 5.81, 2.236, 13.494, -19.218), 

1307 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1308_trfX(_ITRF89_, _ETRF2020_, epoch=_E(2015), 

1309 xform=_X( 32.3, 33.9, -148.7, 9.21, 2.236, 13.494, -19.218), 

1310 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1311_trfX(_ITRF88_, _ETRF2020_, epoch=_E(2015), 

1312 xform=_X( 27.3, -2.1, -172.7, 12.31, 2.336, 13.494, -19.218), 

1313 rates=_R( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1314 

1315# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and 

1316# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 3. 

1317_trfX(_ITRF2020_, _ETRF2014_, epoch=_E(2015), 

1318 xform=_X( -1.4, -0.9, 1.4, 0.42, 2.21, 13.806, -20.02), 

1319 rates=_R( _0_0, -0.1, 0.2, _0_0, 0.085, 0.531, -0.77)) 

1320_trfX(_ITRF2014_, _ETRF2014_, epoch=_E(2015), 

1321 xform=_X( _0_0, _0_0, _0_0, _0_0, 2.21, 13.806, -20.02), 

1322 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77)) 

1323_trfX(_ITRF2008_, _ETRF2014_, epoch=_E(2015), 

1324 xform=_X( -1.6, -1.9, -1.9, -0.13, 2.21, 13.806, -20.02), 

1325 rates=_R( _0_0, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77)) 

1326_trfX(_ITRF2005_, _ETRF2014_, epoch=_E(2015), 

1327 xform=_X( -4.1, -1.0, 2.8, -1.07, 2.21, 13.806, -20.02), 

1328 rates=_R( -0.3, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77)) 

1329_trfX(_ITRF2000_, _ETRF2014_, epoch=_E(2015), 

1330 xform=_X( -1.2, -1.7, 35.6, -2.67, 2.21, 13.806, -20.02), 

1331 rates=_R( -0.1, -0.1, 1.9, -0.11, 0.085, 0.531, -0.77)) 

1332_trfX(_ITRF97_, _ETRF2014_, epoch=_E(2015), 

1333 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38), 

1334 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1335_trfX(_ITRF96_, _ETRF2014_, epoch=_E(2015), 

1336 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38), 

1337 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1338_trfX(_ITRF94_, _ETRF2014_, epoch=_E(2015), 

1339 xform=_X( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38), 

1340 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1341_trfX(_ITRF93_, _ETRF2014_, epoch=_E(2015), 

1342 xform=_X( 64.4, -2.8, 72.7, -4.89, 5.570, 18.136, -20.77), 

1343 rates=_R( 2.8, 0.1, 2.5, -0.12, 0.195, 0.721, -0.84)) 

1344_trfX(_ITRF92_, _ETRF2014_, epoch=_E(2015), 

1345 xform=_X( -15.9, 1.0, 87.3, -3.69, 2.21, 13.806, -20.38), 

1346 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1347_trfX(_ITRF91_, _ETRF2014_, epoch=_E(2015), 

1348 xform=_X( -27.9, -13.0, 93.3, -5.09, 2.21, 13.806, -20.38), 

1349 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1350_trfX(_ITRF90_, _ETRF2014_, epoch=_E(2015), 

1351 xform=_X( -25.9, -9.0, 109.3, -5.39, 2.21, 13.806, -20.38), 

1352 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1353_trfX(_ITRF89_, _ETRF2014_, epoch=_E(2015), 

1354 xform=_X( -30.9, -33.0, 147.3, -8.79, 2.21, 13.806, -20.38), 

1355 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1356_trfX(_ITRF88_, _ETRF2014_, epoch=_E(2015), 

1357 xform=_X( -25.9, 3.0, 171.3, -11.89, 2.11, 13.806, -20.38), 

1358 rates=_R( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1359 

1360# see U{Altamimi, Z. "EUREF Technical Note 1: Relationship and Transformation between the International and 

1361# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 4, 

1362# U{Boucher, C. & Altamimi, Z. "Memo: Specifications for reference frame fixing in the analysis of a EUREF GPS 

1363# campaign" (2011) <https://ETRS89.ENSG.IGN.Fr/memo-V8.pdf>} and U{Altamimi, Z. "Key results of ITRF2014 and 

1364# implication to ETRS89 realization", EUREF2016<https://www.EUREF.EU/symposia/2016SanSebastian/01-02-Altamimi.pdf>}. 

1365_trfX(_ITRF2020_, _ETRF2000_, epoch=_E(2015), 

1366 xform=_X( 53.8, 51.8, -82.2, 2.25, 2.106, 12.74, -20.592), 

1367 rates=_R( 0.1, _0_0, -1.7, 0.11, 0.081, 0.49, -0.792)) 

1368# _trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2000), 

1369# xform=_X( 53.7, 51.2, -55.1, 1.02, 0.891, 5.39, -8.712), 

1370# rates=_R( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792)) 

1371_trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2015), 

1372 xform=_X( 55.2, 52.7, -83.6, 2.67, 2.106, 12.74, -20.592), 

1373 rates=_R( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792)) 

1374# _trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2000), 

1375# xform=_X( 52.1, 49.3, -58.5, 1.34, 0.891, 5.39, -8.712), 

1376# rates=_R( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)) 

1377_trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2015), 

1378 xform=_X( 53.6, 50.8, -85.5, 2.54, 2.106, 12.74, -20.592), 

1379 rates=_R( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)) 

1380# _trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2000), 

1381# xform=_X( 54.1, 50.2, -53.8, 0.4, 0.891, 5.39, -8.712), 

1382# rates=_R( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)) 

1383_trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2015), 

1384 xform=_X( 51.1, 51.7, -80.8, 1.6, 2.106, 12.74, -20.592), 

1385 rates=_R( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)) 

1386# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2000), 

1387# xform=_X( 54.0, 51.0, -48.0, _0_0, 0.891, 5.39, -8.712), 

1388# rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792)) 

1389_trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2015), 

1390 xform=_X( 54.0, 51.0, -48.0, _0_0, 2.106, 12.74, -20.592), 

1391 rates=_R( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792)) 

1392_trfX(_ITRF97_, _ETRF2000_, epoch=_E(2015), 

1393 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952), 

1394 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1395_trfX(_ITRF96_, _ETRF2000_, epoch=_E(2015), 

1396 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952), 

1397 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1398_trfX(_ITRF94_, _ETRF2000_, epoch=_E(2015), 

1399 xform=_X( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952), 

1400 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1401_trfX(_ITRF93_, _ETRF2000_, epoch=_E(2015), 

1402 xform=_X( 119.6, 49.9, -10.9, -2.22, 5.466, 17.07, -21.342), 

1403 rates=_R( 2.9, 0.2, 0.6, -0.01, 0.191, 0.68, -0.862)) 

1404_trfX(_ITRF92_, _ETRF2000_, epoch=_E(2015), 

1405 xform=_X( 39.3, 53.7, 3.7, -1.02, 2.106, 12.74, -20.952), 

1406 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1407_trfX(_ITRF91_, _ETRF2000_, epoch=_E(2015), 

1408 xform=_X( 27.3, 39.7, 9.7, -2.42, 2.106, 12.74, -20.952), 

1409 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1410_trfX(_ITRF90_, _ETRF2000_, epoch=_E(2015), 

1411 xform=_X( 29.3, 43.7, 25.7, -2.72, 2.106, 12.74, -20.952), 

1412 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1413_trfX(_ITRF89_, _ETRF2000_, epoch=_E(2015), 

1414 xform=_X( 24.3, 19.7, 63.7, -6.12, 2.106, 12.74, -20.952), 

1415 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1416_trfX(_ITRF88_, _ETRF2000_, epoch=_E(2015), 

1417 xform=_X( 29.3, 55.7, 87.7, -9.22, 2.006, 12.74, -20.952), 

1418 rates=_R( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1419 

1420# GDA2020 "Geocentric Datum of Australia 2020 Technical Manual", v1.5, 2020-12-09, Table 3.3 and 3.4 

1421# <https://www.ICSM.gov.AU/sites/default/files/2020-12/GDA2020%20Technical%20Manual%20V1.5_4.pdf> 

1422# (the GDA2020 xforms are different but the rates are the same as GDA94, further below) 

1423_trfX(_ITRF2014_, _GDA2020_, epoch=_E(2020), 

1424 xform=_P_0_0s, 

1425 rates=_R( _0_0, _0_0, _0_0, _0_0, 1.50379, 1.18346, 1.20716)) 

1426_trfX(_ITRF2008_, _GDA2020_, epoch=_E(2020), 

1427 xform=_X( 13.79, 4.55, 15.22, 2.5, 0.2808, 0.2677, -0.4638), 

1428 rates=_R( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551)) 

1429_trfX(_ITRF2005_, _GDA2020_, epoch=_E(2020), 

1430 xform=_X( 40.32, -33.85, -16.72, 4.286, -1.2893, -0.8492, -0.3342), 

1431 rates=_R( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701)) 

1432_trfX(_ITRF2000_, _GDA2020_, epoch=_E(2020), 

1433 xform=_X(-105.52, 51.58, 231.68, 3.55, 4.2175, 6.3941, 0.8617), 

1434 rates=_R( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224)) 

1435 

1436# see Table 2 in U{Dawson, J. & Woods, A. "ITRF to GDA94 coordinate transformations", Journal of Applied 

1437# Geodesy 4 (2010), 189-199<https://www.ResearchGate.net/publication/258401581_ITRF_to_GDA94_coordinate_transformations>} 

1438# (note, sign of rotations for GDA94 reversed as "Australia assumes rotation to be of coordinate axes", 

1439# rather than the more conventional "position around the coordinate axes") 

1440_trfX(_ITRF2008_, _GDA94_, epoch=_E(1994), 

1441 xform=_X( -84.68, -19.42, 32.01, 9.71, -0.4254, 2.2578, 2.4015), 

1442 rates=_R( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551)) 

1443_trfX(_ITRF2005_, _GDA94_, epoch=_E(1994), 

1444 xform=_X( -79.73, -6.86, 38.03, 6.636, 0.0351, -2.1211, -2.1411), 

1445 rates=_R( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701)) 

1446_trfX(_ITRF2000_, _GDA94_, epoch=_E(1994), 

1447 xform=_X( -45.91, -29.85, -20.37, 7.07, -1.6705, 0.4594, 1.9356), 

1448 rates=_R( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224)) 

1449 

1450# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ 

1451# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83 and Pearson, C. & Snay, R. U{"Introducing 

1452# HTDP 3.1 to transform coordinates across time and spatial reference frames"<https://Geodesy.NOAA.gov/ 

1453# TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 7th column 

1454_trfX(_ITRF2008_, _NAD83_, epoch=_E(1997), 

1455 xform=_X( 993.43, -1903.31, -526.55, 1.71504, -25.91467, -9.42645, -11.59935), 

1456 rates=_R( 0.79, -0.6, -1.34, -0.10201, -0.06667, 0.75744, 0.05133)) 

1457# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ 

1458# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83 

1459_trfX(_ITRF2005_, _NAD83_, epoch=_E(1997), 

1460 xform=_X( 996.3, -1902.4, -521.9, 0.775, -25.915, -9.426, -11.599), 

1461 rates=_R( 0.5, -0.6, -1.3, -0.10201, -0.06667, 0.75744, 0.05133)) 

1462# see U{Solar, T. & Snay, R.A. "Transforming Positions and Velocities between the International Terrestrial Reference 

1463# Frame of 2000 and North American Datum of 1983" (2004)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>} 

1464_trfX(_ITRF2000_, _NAD83_, epoch=_E(1997), # note NAD83(CORS96) 

1465 xform=_X( 995.6, -1901.3, -521.5, 0.615, -25.915, -9.426, -11.599), 

1466 rates=_R( 0.7, -0.7, _0_5, -0.182, -0.06667, 0.75744, 0.05133)) 

1467_trfX(_ITRF90_, _NAD83_, epoch=_E(1997), 

1468 xform=_X( 973.0, -1919.2, -482.9, -0.9, -25.79, -9.65, -11.66), 

1469 rates=_R( _0_0, _0_0, _0_0, _0_0, -0.053, 0.742, 0.032)) 

1470_trfX(_ITRF90_, _WGS84_, epoch=_E(1984), # coverage 

1471 xform=_X( 60.0, -517.0, -223.0, -11.0, 18.3, -0.3, 7.0), 

1472 rates=_P_0_0s) 

1473 

1474# equivalents U{"Transformations Between NAD83 and WGS84"<https://www.NGS.NOAA.gov/CORS/Articles/WGS84NAD83.pdf>} 

1475trfXform(_NAD83cors96_, _NAD83_, epoch=_E(1997), xform=_P_0_0s, rates=_P_0_0s) 

1476trfXform(_WGS84g1150_, _ITRF2000_, epoch=_E(2004), xform=_P_0_0s, rates=_P_0_0s) 

1477 

1478del _E, _Es, _i, _P, _P_0_0s, _R, _Rs, _X, _Xs 

1479 

1480if __name__ == '__main__': 

1481 

1482 def _main(): 

1483 from pygeodesy.interns import _COLONSPACE_,_COMMA_, _NL_, _NLATvar_, _vs_ 

1484 from pygeodesy.lazily import printf 

1485 from time import localtime 

1486 

1487 D = date2epoch.__name__ 

1488 E = epoch2date.__name__ 

1489 y = localtime()[0] 

1490 for m in range(1, 13): 

1491 for d in (1, 15, _mDays[m] - 1, _mDays[m]): 

1492 f = '%s(%d,%3d,%3d)' % (D, y, m, d) 

1493 e = date2epoch(y, m, d) 

1494 t = epoch2date(e) 

1495 x = NN if t == (y, m, d) else _STAR_ 

1496 e = '%.3f' % (e,) 

1497 e = '%s, %s(%s)' % (e, E, e) 

1498 t = '%d,%3d,%3d' % t 

1499 printf('# %s = %s = %s %s', f, e, t, x) 

1500 

1501 # __doc__ of this file, force all into registery 

1502 def _RFs(): 

1503 yield NN 

1504 for t in RefFrames.toRepr(all=True).split(_NL_): 

1505 t = t.strip(_COMMA_) 

1506 n = t.split(_COLONSPACE_)[0].split(_DOT_)[1] 

1507 r = RefFrames.get(n) 

1508 x = len(r.Xforms()), -len(r.Xforms(inverse=True)) 

1509 yield '%s .Xforms=%s' % (t, x) 

1510 

1511 printf(_NLATvar_.join(sorted(_RFs())), nt=1) 

1512 

1513 X, t = (), 0 # all form 

1514 for r in RefFrames.values(): 

1515 X += tuple(r._Xto.values()) 

1516 for X in sorted(X): 

1517 t += 1 

1518 printf('#%4d %-24s xform=%r', t, X.name, X.xform) 

1519 printf('#%29s rates=%r', _SPACE_, X.rates) 

1520 

1521 t = _MODS.basics._args_kwds_names(Transform.__init__) 

1522 for n in TRFXform7Tuple._Names_: 

1523 if n not in t: 

1524 raise AssertionError(_SPACE_(n, _vs_, t)) 

1525 

1526 _main() 

1527 del _main 

1528 

1529# **) MIT License 

1530# 

1531# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1532# 

1533# Permission is hereby granted, free of charge, to any person obtaining a 

1534# copy of this software and associated documentation files (the "Software"), 

1535# to deal in the Software without restriction, including without limitation 

1536# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1537# and/or sell copies of the Software, and to permit persons to whom the 

1538# Software is furnished to do so, subject to the following conditions: 

1539# 

1540# The above copyright notice and this permission notice shall be included 

1541# in all copies or substantial portions of the Software. 

1542# 

1543# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1544# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1545# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1546# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1547# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1548# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1549# OTHER DEALINGS IN THE SOFTWARE. 

1550 

1551# % python -m pygeodesy.trf 

1552# 

1553# date2epoch(2024, 1, 1) = 2024.003, epoch2date(2024.003) = 2024, 1, 1 

1554# date2epoch(2024, 1, 15) = 2024.041, epoch2date(2024.041) = 2024, 1, 15 

1555# date2epoch(2024, 1, 30) = 2024.082, epoch2date(2024.082) = 2024, 1, 30 

1556# date2epoch(2024, 1, 31) = 2024.085, epoch2date(2024.085) = 2024, 1, 31 

1557# date2epoch(2024, 2, 1) = 2024.087, epoch2date(2024.087) = 2024, 2, 2 * 

1558# date2epoch(2024, 2, 15) = 2024.126, epoch2date(2024.126) = 2024, 2, 16 * 

1559# date2epoch(2024, 2, 28) = 2024.161, epoch2date(2024.161) = 2024, 2, 28 

1560# date2epoch(2024, 2, 29) = 2024.164, epoch2date(2024.164) = 2024, 3, 1 * 

1561# date2epoch(2024, 3, 1) = 2024.167, epoch2date(2024.167) = 2024, 3, 2 * 

1562# date2epoch(2024, 3, 15) = 2024.205, epoch2date(2024.205) = 2024, 3, 16 * 

1563# date2epoch(2024, 3, 30) = 2024.246, epoch2date(2024.246) = 2024, 3, 31 * 

1564# date2epoch(2024, 3, 31) = 2024.249, epoch2date(2024.249) = 2024, 4, 1 * 

1565# date2epoch(2024, 4, 1) = 2024.251, epoch2date(2024.251) = 2024, 4, 1 

1566# date2epoch(2024, 4, 15) = 2024.290, epoch2date(2024.290) = 2024, 4, 15 

1567# date2epoch(2024, 4, 29) = 2024.328, epoch2date(2024.328) = 2024, 4, 29 

1568# date2epoch(2024, 4, 30) = 2024.331, epoch2date(2024.331) = 2024, 4, 30 

1569# date2epoch(2024, 5, 1) = 2024.333, epoch2date(2024.333) = 2024, 5, 1 

1570# date2epoch(2024, 5, 15) = 2024.372, epoch2date(2024.372) = 2024, 5, 15 

1571# date2epoch(2024, 5, 30) = 2024.413, epoch2date(2024.413) = 2024, 5, 30 

1572# date2epoch(2024, 5, 31) = 2024.415, epoch2date(2024.415) = 2024, 6, 1 * 

1573# date2epoch(2024, 6, 1) = 2024.418, epoch2date(2024.418) = 2024, 6, 2 * 

1574# date2epoch(2024, 6, 15) = 2024.456, epoch2date(2024.456) = 2024, 6, 16 * 

1575# date2epoch(2024, 6, 29) = 2024.495, epoch2date(2024.495) = 2024, 6, 30 * 

1576# date2epoch(2024, 6, 30) = 2024.497, epoch2date(2024.497) = 2024, 7, 1 * 

1577# date2epoch(2024, 7, 1) = 2024.500, epoch2date(2024.500) = 2024, 7, 1 

1578# date2epoch(2024, 7, 15) = 2024.538, epoch2date(2024.538) = 2024, 7, 16 * 

1579# date2epoch(2024, 7, 30) = 2024.579, epoch2date(2024.579) = 2024, 7, 30 

1580# date2epoch(2024, 7, 31) = 2024.582, epoch2date(2024.582) = 2024, 7, 31 

1581# date2epoch(2024, 8, 1) = 2024.585, epoch2date(2024.585) = 2024, 8, 1 

1582# date2epoch(2024, 8, 15) = 2024.623, epoch2date(2024.623) = 2024, 8, 15 

1583# date2epoch(2024, 8, 30) = 2024.664, epoch2date(2024.664) = 2024, 8, 31 * 

1584# date2epoch(2024, 8, 31) = 2024.667, epoch2date(2024.667) = 2024, 9, 1 * 

1585# date2epoch(2024, 9, 1) = 2024.669, epoch2date(2024.669) = 2024, 9, 2 * 

1586# date2epoch(2024, 9, 15) = 2024.708, epoch2date(2024.708) = 2024, 9, 16 * 

1587# date2epoch(2024, 9, 29) = 2024.746, epoch2date(2024.746) = 2024, 9, 30 * 

1588# date2epoch(2024, 9, 30) = 2024.749, epoch2date(2024.749) = 2024, 10, 1 * 

1589# date2epoch(2024, 10, 1) = 2024.751, epoch2date(2024.751) = 2024, 10, 1 

1590# date2epoch(2024, 10, 15) = 2024.790, epoch2date(2024.790) = 2024, 10, 15 

1591# date2epoch(2024, 10, 30) = 2024.831, epoch2date(2024.831) = 2024, 10, 30 

1592# date2epoch(2024, 10, 31) = 2024.833, epoch2date(2024.833) = 2024, 10, 31 

1593# date2epoch(2024, 11, 1) = 2024.836, epoch2date(2024.836) = 2024, 11, 1 

1594# date2epoch(2024, 11, 15) = 2024.874, epoch2date(2024.874) = 2024, 11, 15 

1595# date2epoch(2024, 11, 29) = 2024.913, epoch2date(2024.913) = 2024, 11, 29 

1596# date2epoch(2024, 11, 30) = 2024.915, epoch2date(2024.915) = 2024, 12, 1 * 

1597# date2epoch(2024, 12, 1) = 2024.918, epoch2date(2024.918) = 2024, 12, 2 * 

1598# date2epoch(2024, 12, 15) = 2024.956, epoch2date(2024.956) = 2024, 12, 16 * 

1599# date2epoch(2024, 12, 30) = 2024.997, epoch2date(2024.997) = 2024, 12, 31 * 

1600# date2epoch(2024, 12, 31) = 2025.000, epoch2date(2025.000) = 2025, 1, 1 * 

1601 

1602# 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) 

1603# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1604# 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) 

1605# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1606# 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) 

1607# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1608# 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) 

1609# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1610# 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) 

1611# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1612# 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) 

1613# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1614# 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) 

1615# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71) 

1616# 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) 

1617# rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1618# 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) 

1619# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1620# 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) 

1621# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71) 

1622# 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) 

1623# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=-0.053, sy=0.742, sz=0.032) 

1624# 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) 

1625# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1626# 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) 

1627# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68) 

1628# 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) 

1629# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1630# 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) 

1631# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1632# 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) 

1633# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1634# 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) 

1635# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68) 

1636# 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) 

1637# rates=rates(tx=2.9, ty=0.2, tz=0.6, s=-0.01, sx=0.191, sy=0.68, sz=-0.862) 

1638# 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) 

1639# rates=rates(tx=2.8, ty=0.1, tz=2.5, s=-0.12, sx=0.195, sy=0.721, sz=-0.84) 

1640# 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) 

1641# rates=rates(tx=-2.8, ty=0.0, tz=-2.7, s=0.12, sx=-0.024, sy=0.329, sz=-0.683) 

1642# 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) 

1643# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.32, sy=0.78, sz=-0.67) 

1644# 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) 

1645# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1646# 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) 

1647# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1648# 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) 

1649# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1650# 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) 

1651# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65) 

1652# 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) 

1653# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65) 

1654# 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) 

1655# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65) 

1656# 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) 

1657# rates=rates(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224) 

1658# 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) 

1659# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.081, sy=0.49, sz=-0.792) 

1660# 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) 

1661# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1662# 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) 

1663# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1664# 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) 

1665# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1666# 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) 

1667# rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1668# 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) 

1669# rates=rates(tx=-0.1, ty=-0.1, tz=1.9, s=-0.11, sx=0.085, sy=0.531, sz=-0.77) 

1670# 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) 

1671# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1672# 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) 

1673# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1674# 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) 

1675# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1676# 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) 

1677# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1678# 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) 

1679# rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1680# 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) 

1681# rates=rates(tx=0.1, ty=0.2, tz=-2.1, s=0.11, sx=0.086, sy=0.519, sz=-0.753) 

1682# 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) 

1683# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1684# 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) 

1685# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1686# 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) 

1687# rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1688# 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) 

1689# rates=rates(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224) 

1690# 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) 

1691# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1692# 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) 

1693# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1694# 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) 

1695# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1696# 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) 

1697# rates=rates(tx=0.0, ty=-0.6, tz=-1.4, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1698# 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) 

1699# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1700# 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) 

1701# rates=rates(tx=-2.9, ty=-0.2, tz=-0.6, s=0.01, sx=-0.11, sy=-0.19, sz=0.07) 

1702# 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) 

1703# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1704# 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) 

1705# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1706# 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) 

1707# rates=rates(tx=0.69, ty=-0.1, tz=1.86, s=-0.19201, sx=0.01347, sy=-0.01514, sz=0.00027) 

1708# 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) 

1709# rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=-0.02) 

1710# 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) 

1711# rates=rates(tx=0.7, ty=-0.7, tz=0.5, s=-0.182, sx=-0.06667, sy=0.75744, sz=0.05133) 

1712# 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) 

1713# rates=rates(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792) 

1714# 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) 

1715# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.054, sy=0.518, sz=-0.781) 

1716# 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) 

1717# rates=rates(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701) 

1718# 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) 

1719# rates=rates(tx=0.5, ty=-0.6, tz=-1.3, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133) 

1720# 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) 

1721# rates=rates(tx=-0.3, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77) 

1722# 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) 

1723# rates=rates(tx=0.3, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753) 

1724# 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) 

1725# rates=rates(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701) 

1726# 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) 

1727# rates=rates(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0) 

1728# 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) 

1729# rates=rates(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551) 

1730# 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) 

1731# rates=rates(tx=0.79, ty=-0.6, tz=-1.34, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133) 

1732# 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) 

1733# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0532, sy=-0.7423, sz=-0.0316) 

1734# 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) 

1735# rates=rates(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792) 

1736# 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) 

1737# rates=rates(tx=0.0, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77) 

1738# 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) 

1739# rates=rates(tx=0.0, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753) 

1740# 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) 

1741# rates=rates(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551) 

1742# 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) 

1743# rates=rates(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0) 

1744# 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) 

1745# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1746# 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) 

1747# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1748# 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) 

1749# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1750# 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) 

1751# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1752# 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) 

1753# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1754# 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) 

1755# rates=rates(tx=-2.8, ty=-0.1, tz=-2.4, s=0.09, sx=-0.11, sy=-0.19, sz=0.07) 

1756# 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) 

1757# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1758# 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) 

1759# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1760# 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) 

1761# rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1762# 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) 

1763# rates=rates(tx=0.3, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1764# 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) 

1765# rates=rates(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.081, sy=0.49, sz=-0.792) 

1766# 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) 

1767# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.085, sy=0.531, sz=-0.77) 

1768# 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) 

1769# rates=rates(tx=0.0, ty=0.1, tz=-0.2, s=0.0, sx=0.086, sy=0.519, sz=-0.753) 

1770# 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) 

1771# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=1.50379, sy=1.18346, sz=1.20716) 

1772# 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) 

1773# rates=rates(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.0, sy=0.0, sz=0.0) 

1774# 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) 

1775# rates=rates(tx=0.3, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0) 

1776# 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) 

1777# rates=rates(tx=0.0, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0) 

1778# 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) 

1779# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1780# 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) 

1781# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1782# 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) 

1783# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1784# 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) 

1785# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1786# 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) 

1787# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1788# 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) 

1789# rates=rates(tx=-2.8, ty=-0.1, tz=-2.5, s=0.12, sx=-0.11, sy=-0.19, sz=0.07) 

1790# 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) 

1791# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1792# 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) 

1793# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1794# 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) 

1795# rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1796# 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) 

1797# rates=rates(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.081, sy=0.49, sz=-0.792) 

1798# 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) 

1799# rates=rates(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.085, sy=0.531, sz=-0.77) 

1800# 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) 

1801# rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.086, sy=0.519, sz=-0.753) 

1802# 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) 

1803# rates=rates(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.0, sy=0.0, sz=0.0) 

1804# 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) 

1805# rates=rates(tx=0.3, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0) 

1806# 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) 

1807# rates=rates(tx=0.0, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0) 

1808# 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) 

1809# rates=rates(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1810# 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) 

1811# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1812# 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) 

1813# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1814# 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) 

1815# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1816# 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) 

1817# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1818# 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) 

1819# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1820# 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) 

1821# rates=rates(tx=-2.8, ty=-0.2, tz=-2.3, s=0.12, sx=-0.11, sy=-0.19, sz=0.07) 

1822# 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) 

1823# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1824# 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) 

1825# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1826# 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) 

1827# rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)