Coverage for pygeodesy/trf.py: 95%

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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, -4) 

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, -5) 

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

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

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

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

69''' 

70 

71from pygeodesy.basics import map1, neg, isstr, _xinstanceof, _xisscalar, _zip 

72from pygeodesy.constants import _0_0s, _0_0, _0_001, _0_5, _1_0, _float as _F 

73from pygeodesy.datums import Datums, _earth_datum, _minus, Transform, _WGS84 

74from pygeodesy.errors import TRFError, _xkwds 

75from pygeodesy.interns import MISSING, NN, _AT_, _COMMASPACE_, _conversion_, _datum_, \ 

76 _DOT_, _exists_, _invalid_, _MINUS_, _NAD83_, _no_, \ 

77 _PLUS_, _reframe_, _s_, _SPACE_, _sx_, _sy_, _sz_, _to_, \ 

78 _tx_, _ty_, _tz_, _WGS84_, _x_, _intern as _i 

79from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS 

80from pygeodesy.named import ADict, classname, _lazyNamedEnumItem as _lazy, _Named, \ 

81 _NamedEnum, _NamedEnumItem, _NamedTuple, Fmt, unstr 

82from pygeodesy.props import Property, Property_RO, property_RO 

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

84from pygeodesy.units import Epoch, Float 

85 

86from math import ceil 

87 

88__all__ = _ALL_LAZY.trf 

89__version__ = '24.02.06' 

90 

91_EP0CH = Epoch(0, low=0) 

92_Es = {_EP0CH: _EP0CH} # L{Epoch} de_dup 

93_Ps = {} # L{TRFXform7Tuple} de-dup, deleted below 

94 

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_v_ = 'v' 

102 

103_ETRF88_ = _i('ETRF88') 

104_ETRF89_ = _i('ETRF89') 

105_ETRF90_ = _i('ETRF90') 

106_ETRF91_ = _i('ETRF91') 

107_ETRF92_ = _i('ETRF92') 

108_ETRF93_ = _i('ETRF93') 

109_ETRF94_ = _i('ETRF94') 

110_ETRF96_ = _i('ETRF96') 

111_ETRF97_ = _i('ETRF97') 

112_ETRF2000_ = _i('ETRF2000') 

113_ETRF2005_ = _i('ETRF2005') 

114_ETRF2008_ = _i('ETRF2008') 

115_ETRF2014_ = _i('ETRF2014') 

116_ETRF2020_ = _i('ETRF2020') 

117_GDA94_ = _i('GDA94') 

118_GDA2020_ = _i('GDA2020') 

119_ITRF_ = _i('ITRF') 

120_ITRF88_ = _i('ITRF88') 

121_ITRF89_ = _i('ITRF89') 

122_ITRF90_ = _i('ITRF90') 

123_ITRF91_ = _i('ITRF91') 

124_ITRF92_ = _i('ITRF92') 

125_ITRF93_ = _i('ITRF93') 

126_ITRF94_ = _i('ITRF94') 

127_ITRF96_ = _i('ITRF96') 

128_ITRF97_ = _i('ITRF97') 

129_ITRF2000_ = _i('ITRF2000') 

130_ITRF2005_ = _i('ITRF2005') 

131_ITRF2008_ = _i('ITRF2008') 

132_ITRF2014_ = _i('ITRF2014') 

133_ITRF2020_ = _i('ITRF2020') 

134_WGS84g1150_ = _i('WGS84g1150') 

135_WGS84g1674_ = _i('WGS84g1674') 

136_WGS84g1762_ = _i('WGS84g1762') 

137# del _i 

138 

139 

140def _E(epoch): 

141 '''(INTERNAL) De-dup L{Epochs}s. 

142 ''' 

143 e = Epoch(_F(epoch)) 

144 return _Es.setdefault(e, e) 

145 

146 

147def _xellipsoidal(point): 

148 '''(INTERNAL) Check an ellipsoidal position. 

149 ''' 

150 m = _MODS.ellipsoidalBase 

151 _xinstanceof(m.CartesianEllipsoidalBase, 

152 m.LatLonEllipsoidalBase, point=point) 

153 return isinstance(point, m.CartesianEllipsoidalBase) 

154 

155 

156class RefFrame(_NamedEnumItem): 

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

158 ''' 

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

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

161 

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

163 '''New L{RefFrame}. 

164 

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

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

167 or L{a_f2Tuple}). 

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

169 

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

171 

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

173 

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

175 ''' 

176 if datum is not _GRS80: 

177 _earth_datum(self, datum, raiser=_datum_) 

178 self._epoch = _Epoch(epoch) 

179 self._Xs = {} # dict of Xforms 

180 if name: 

181 self._register(RefFrames, name) 

182 

183 def __eq__(self, other): 

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

185 and other.datum == self.datum 

186 

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

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

189 or self.epoch < other.epoch) 

190 

191 def __matmul__(self, point): # PYCHOK Python 3.5+ 

192 '''Convert an ellipsoidal B{C{point}} to this reframe and epoch. 

193 

194 @see: Method C{toRefFrame}. 

195 ''' 

196 _xellipsoidal(point) 

197 return point.toRefFrame(self) 

198 

199 @property_RO 

200 def datum(self): 

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

202 ''' 

203 return self._datum 

204 

205 @Property_RO 

206 def ellipsoid(self): 

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

208 ''' 

209 return self._datum.ellipsoid 

210 

211 @Property_RO 

212 def epoch(self): 

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

214 ''' 

215 return self._epoch 

216 

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

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

219 to an other C{reframe2} and C{epoch2 or epoch}. 

220 

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

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

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

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

225 

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

227 

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

229 

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

231 this reframe and B{C{epoch}} or this reframe's epoch. 

232 

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

234 and L{Cartesian.toRefFrame<ellipsoidalBase.CartesianEllipsoidalBase.toRefFrame>} 

235 for more details. 

236 ''' 

237 _xellipsoidal(point) 

238 kwds = _xkwds(epoch2_epoch_name, name=self.name) 

239 p = point.dup(reframe=self) if point.reframe != self else point 

240 return p.toRefFrame(reframe2, reframe=self, **kwds) 

241 

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

243 '''Return this reference frame as a text string. 

244 

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

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

247 reframe's name. 

248 

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

250 ''' 

251 D = self.datum 

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

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

254 Fmt.EQUAL(epoch=e), 

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

256 return _COMMASPACE_.join(t[1:] if name is None else t) 

257 

258 def Xform(self, reframe2): 

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

260 

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

262 

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

264 

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

266 ''' 

267 _xinstanceof(RefFrame, str, reframe2=reframe2) 

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

269 return self._Xs.get(n2, None) 

270 

271 def Xforms(self, inverse=False): 

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

273 

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

275 

276 @return: An L{ADict} of I{from} C{[refName2]=}L{TRFXform}s) or if 

277 C{B{inverse}=True} of I{to} C{[refName1]=}L{TRFXform}s). 

278 ''' 

279 def _Xi(n2): 

280 for n1, r in RefFrames.items(): 

281 if n2 in r._Xs: 

282 yield n1, r 

283 

284 return ADict(_Xi(self.name)) if inverse else ADict(self._Xs) 

285 

286 

287class RefFrames(_NamedEnum): 

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

289 to accommodate the L{_LazyNamedEnumItem} properties. 

290 ''' 

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

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

293 ''' 

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

295 

296RefFrames = RefFrames(RefFrame) # PYCHOK singleton 

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

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

299RefFrames._assert( 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

330 NAD83 = _lazy(_NAD83_, _E(1997)), # aka CORS96 

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

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

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

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

335 

336 

337class TransformXform(Transform): 

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

339 

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

341 ''' 

342 _Xform = None 

343 

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

345 '''New L{TransformXform}. 

346 

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

348 

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

350 

351 @note: The name of this L{TransformXform} starts with C{"-"} 

352 if its C{Xform} was I{inversed}. 

353 ''' 

354 Transform.__init__(self, **tx_ty_tz_s_sx_sy_sz) 

355 if name: 

356 self.name = name 

357 

358 def __eq__(self, other): 

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

360 

361 def rename(self, name=NN): 

362 '''Change this transform and its Xform's name. 

363 

364 @arg name: The new name (C{str}), overriding 

365 the base name. 

366 

367 @return: The old name (C{str}). 

368 ''' 

369 X = self.Xform 

370 return Transform.rename(self, name or (X.toStr() if X else NN)) 

371 

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

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

374 

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

376 

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

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

379 

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

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

382 but I{not} taken into account. 

383 ''' 

384 C = _xellipsoidal(point) 

385 c = point.dup() if C else point.toCartesian() 

386 r = c.toTransforms_(self) 

387 if not C: # i.e. back to LatLon 

388 r = r.toLatLon(datum=point.datum, height=point.height, 

389 LatLon=point.classof) 

390 X = self.Xform 

391 if X: 

392 r.reframe = X.reframe2 

393 r.epoch = X.epoch 

394 

395 r.rename(name or self.name) 

396 return r 

397 

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

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

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

401 

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

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

404 @kwarg epoch2_inverse: Optional C{B{epoch2}=None} and 

405 C{B{inverse}=False}, see class Xform's method 

406 L{toTransform<TRFXform.toTransform>}. 

407 

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

409 

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

411 missing Xform. 

412 ''' 

413 X = self.Xform 

414 if not X: 

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

416 X = X.dup(epoch=epoch1) 

417 _ = X.rename() 

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

419 

420 def velocities(self, factor=_MM2M): 

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

422 

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

424 from C{milli-meter-} to C{meter-per-year}. 

425 

426 @return: A L{Vector3Tuple}C{(x, y, z)} or C{None}. 

427 

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

429 

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

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

432 ''' 

433 v = self.Xform 

434 if v is not None: 

435 r = v.rates * factor # eq (3) ... 

436 t = self.dup(tx=r.sx, ty=r.sy, tz=r.sz, # Xyy-dot 

437 s1=0, name=NN(self.name, _v_)) 

438 v = t.transform(r.tx, r.ty, r.tz) # Xyy 

439 return v 

440 

441 @Property 

442 def Xform(self): 

443 '''Get the Xform of this Helmert (L{TRFXform} or C{None}). 

444 ''' 

445 return self._Xform 

446 

447 @Xform.setter # PYCHOK setter! 

448 def Xform(self, Xform): 

449 '''Set the Xform of this Helmert (L{TRFXform}). 

450 

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

452 ''' 

453 _xinstanceof(TRFXform, Xform=Xform) 

454 self._Xform = Xform 

455 

456 

457class TRFXform7Tuple(_NamedTuple): 

458 '''7-Tuple C{(tx, ty, tz, s, sx, sy, sz)} of conversion parameters with 

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

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

461 

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

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

464 

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

466 ''' 

467 _Names_ = (_tx_, _ty_, _tz_, _s_, _sx_, _sy_, _sz_) # == kwds 

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

469 

470 def __add__(self, other): 

471 '''Return the sum of this and an other L{TRFXform7Tuple}. 

472 ''' 

473 _xinstanceof(TRFXform7Tuple, other=other) 

474 return type(self)(((s + t) for s, t in _zip(self, other)), 

475 name=_PLUS_) # .fsums._add_op_ 

476 

477 def __eq__(self, other): 

478 return isinstance(other, TRFXform7Tuple) and all(s == t for s, t in 

479 _zip(self, other)) 

480 

481 def __hash__(self): 

482 return self._hash # memoized 

483 

484 def __mul__(self, factor): 

485 _xisscalar(factor=factor) 

486 return type(self)(s * factor for s in self) 

487 

488 def __neg__(self): 

489 return self.inverse() 

490 

491 @Property_RO 

492 def _hash(self): 

493 return hash(s for s in self) 

494 

495 def inverse(self, name=NN): 

496 '''Return the inverse of this transform. 

497 

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

499 

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

501 ''' 

502 n = name or _minus(self.name) 

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

504 

505 @Property_RO 

506 def isunity(self): 

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

508 ''' 

509 return not any(self) 

510 

511 

512class TRFXform(_Named): 

513 '''Terrestrial Reference Frame (TRF) converter between two 

514 reference frames observed at an C{epoch}. 

515 ''' 

516 _epoch = _EP0CH 

517 refName1 = \ 

518 refName2 = NN 

519 rates = \ 

520 xform = TRFXform7Tuple(_0_0s(len( 

521 TRFXform7Tuple._Names_))) 

522 

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

524 xform=None, 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}), as B{C{xform}}, 

532 but in C{units-per-year}. 

533 @kwarg name: Optional name (C{str}) 

534 

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

536 

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

538 ''' 

539 self.refName1 = str(refName1) 

540 self.refName2 = str(refName2) 

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

542 self.epoch = epoch 

543 self.xform = xform 

544 self.rates = rates 

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

546 

547 def __eq__(self, other): 

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

549 self.xform == other.xform and self.rates == other.rates 

550 

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

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

553 or self.refName2 < other.refName2 

554 or self.epoch < other.epoch) 

555 

556 def __neg__(self): 

557 return self.inverse() 

558 

559 def __repr__(self): 

560 return self.toRepr() 

561 

562 def _at(self, epoch): 

563 '''(INTERNAL) Return C{self.name@epoch}. 

564 ''' 

565 n = self.name 

566 if epoch != self.epoch: 

567 _e = _AT_(NN, epoch) 

568 if not n.endswith(_e): 

569 n = NN(n, _e) 

570 return n 

571 

572 @Property 

573 def epoch(self): 

574 '''Get the epoch (L{Epoch}). 

575 ''' 

576 return self._epoch 

577 

578 @epoch.setter # PYCHOK setter! 

579 def epoch(self, epoch): 

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

581 

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

583 ''' 

584 e = _Epoch(epoch) 

585 if self._epoch != e: 

586 self._epoch = e 

587 self.rename(self._at(e)) 

588 

589 def _7Helmert(self, epoch, factor): 

590 '''(INTERNAL) Get the Helmert parameters observed at C{epoch} 

591 converted by factor C{factor}, I{signed} (C{dict}). 

592 ''' 

593 e = epoch - self.epoch # delta in fractional years 

594 t = (self.xform + self.rates * e) * factor 

595 return dict(t.items()) 

596 

597 def inverse(self, name=NN): 

598 '''Return the inverse of this Xform. 

599 

600 @return: Inverse (L{TRFXform}). 

601 ''' 

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

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

604 name=name or _minus(self.name)) 

605 

606 def _range(self, *e1_e2): 

607 '''(INTERNAL) Epoch "range", distance. 

608 ''' 

609 def _r(e): 

610 e -= self.epoch 

611 return (-e) if e < 0 else (e * 2) 

612 

613 return sum(map(_r, e1_e2)) if e1_e2 else self.epoch 

614 

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

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

617 ''' 

618 r = RefFrames.get(name) 

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

620 r = RefFrame(self.epoch, datum) 

621 r.name = name # unregistered 

622 return r 

623 

624 @property_RO 

625 def reframe1(self): 

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

627 ''' 

628 return self._reframe(self.refName1) 

629 

630 @property_RO 

631 def reframe2(self): 

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

633 ''' 

634 return self._reframe(self.refName2) 

635 

636 def rename(self, name=NN): 

637 '''Change this Xform's name. 

638 

639 @arg name: The new name (C{str}), overriding the 

640 base name C{"refName1@epochxrefName2"}. 

641 

642 @return: The old name (C{str}). 

643 ''' 

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

645 

646 def toEpoch(self, epoch): 

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

648 

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

650 or C{str}). 

651 

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

653 

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

655 ''' 

656 e = _Epoch(epoch) - self.epoch 

657 if e: 

658 t = self.xform + self.rates * e 

659 X = self.dup(epoch=epoch, xform=t) 

660 else: 

661 X = self 

662 return X 

663 

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

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

666 C{epoch} to this Xform's C{refName1} and C{epoch2 or epoch}. 

667 

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

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

670 this Xform's C{epoch}. 

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

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

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

674 C{B{name}=NN}. 

675 

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

677 

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

679 ''' 

680 def _r(name): 

681 r = RefFrames.get(name) 

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

683 r = RefFrame(self.epoch, datum) 

684 r.name = name # unregistered 

685 return r 

686 

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

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

689 

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

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

692 ''' 

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

694 

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

696 '''Return this Xform as C{"refName1@epochxrefName2"} (C{str}). 

697 

698 @kwarg epoch: Epoch (C{scalar}), overriding this Xform's epoch. 

699 ''' 

700 e = epoch or self.epoch 

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

702 

703 def toTransform(self, epoch1, epoch2=None, inverse=False): 

704 '''Combine this Xform observed at B{C{epoch1}} into a Helmert 

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

706 

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

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

709 @kwarg inverse: Invert the Helmert tranform (C{bool}). 

710 

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

712 

713 @raise TRFError: Invalid B{C{epoch1}} or B{C{epoch2}}. 

714 

715 @note: Translations are converted from C{milli-meter} to 

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

717 C{arc-seconds} and scale from C{ppb} to C{ppM}. 

718 ''' 

719 e = Epoch(epoch2=epoch1 if epoch2 is None else epoch2) 

720 X = self.dup() if e == epoch1 else self.toEpoch(epoch1) 

721 if inverse: 

722 X = X.inverse() 

723 H = TransformXform(name=X._at(e), **X._7Helmert(e, _MM2M)) 

724 X.epoch = e 

725 H.Xform = X 

726 return H 

727 

728 

729def date2epoch(year, month, day): 

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

731 

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

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

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

735 

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

737 

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

739 

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

741 29 days in February. 

742 ''' 

743 try: 

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

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

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

747 return Epoch(e, low=0) 

748 

749 raise ValueError # _invalid_ 

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

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

752 

753 

754def epoch2date(epoch): 

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

756 

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

758 

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

760 

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

762 

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

764 29 days in February. 

765 ''' 

766 e = _Epoch(epoch, low=0) 

767 y = int(e) 

768 d = int(ceil(_366_0 * (e - y))) 

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

770 if d > n: 

771 d -= n 

772 else: 

773 break 

774 return y, (m + 1), max(1, d) 

775 

776 

777def _Epoch(e, **kwds): 

778 '''(INTERNAL) Get an C{Epoch(B{e})}. 

779 ''' 

780 return Epoch(e, **kwds) if kwds or not isinstance(e, Epoch) else e 

781 

782 

783def _eT0Ds4(inst, reframe, epoch, reframe2, epoch2): 

784 '''(INTERNAL) Get epoch, a Helmert L{Transform}s or 0-tuple, datum 

785 and datum2 to convert B{C{refFrame}} observed at B{C{epoch}} 

786 into B{C{refFrame2}} observed at C{epoch2 or epoch}. 

787 ''' 

788 r = reframe or inst.reframe 

789 if not r: 

790 t = _SPACE_(_DOT_(repr(inst), _reframe_), MISSING) 

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

792 

793 _xinstanceof(RefFrame, reframe2=reframe2, reframe=r) 

794 

795 e1 = _Epoch(epoch or inst.epoch or r.epoch) 

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

797 

798 t0 = _toTransform0(r.name, e1, reframe2.name, e2) 

799 if t0 is None: 

800 t = _SPACE_(RefFrame.__name__, _AT_(r.name, e1), 

801 _to_, _AT_(reframe2.name, e2)) 

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

803 

804 if t0: 

805 e2 = t0.Xform.epoch 

806 return e2, t0, r.datum, reframe2.datum 

807 

808 

809def _immediate(n1, n2, *unused): 

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

811 ''' 

812 X = RefFrames.get(n1) 

813 if X: 

814 X = X._Xs.get(n2, None) 

815 return X 

816 

817 

818def _intermediate(n1, n2, *e1_e2): 

819 '''(INTERNAL) Find an Xform "between" C{n1} and C{n2}. 

820 ''' 

821 def _e(e1=0, e2=0): 

822 return e1 - e2 

823 

824 def _X4(_Xs): 

825 for n, X1 in _Xs.items(): 

826 X2 = _immediate(n, n2) 

827 if X2: 

828 yield (X1._range(*e1_e2) + X2._range(*e1_e2)), X1, X2, True 

829 X2 = _immediate(n2, n) 

830 if X2: 

831 yield (X1._range(*e1_e2) + X2._range(*e1_e2)), X1, X2, False 

832 

833 X, r = None, RefFrames.get(n1) 

834 if r: 

835 i = sorted(_X4(r._Xs)) 

836 if i: 

837 _, X1, X2, f = i.pop(0) 

838 e1, e2 = X1.epoch, X2.epoch 

839 if e1 > e2 and _e(*e1_e2) < 0: # X1 to e2 

840 X1 = X1.toEpoch(e2) 

841 e1 = e2 

842 elif e1 != e2: # X2 to e1 

843 X2 = X2.toEpoch(e1) 

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

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

846 X = TRFXform(n1, n2, epoch=e1, 

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

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

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

850 X2._at(e1))) 

851 return X 

852 

853 

854def _P(*ps): # deleted below 

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

856 ''' 

857 t = TRFXform7Tuple(map(_F, ps)) 

858 return _Ps.setdefault(t, t) # PYCHOK del 

859 

860 

861def _reframe(**name_reframe): 

862 '''(INTERNAL) Get a C{reframe}. 

863 ''' 

864 if len(name_reframe) == 1: 

865 for n, r in name_reframe.items(): 

866 break 

867 if isstr(r): 

868 r = RefFrames.get(r) 

869 if r and isinstance(r, RefFrame): 

870 return r 

871 raise TRFError(**name_reframe) # _invalid_ 

872 

873 

874def _toTransform0(n1, e1, n2, e2): 

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

876 ''' 

877 if (n1 == n2 and e1 == e2) or \ 

878 (n1.startswith(_ITRF_) and n2.startswith(_WGS84_)) or \ 

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

880 return () 

881 

882 for _f in (_immediate, _intermediate): 

883 X = _f(n1, n2, e1, e2) 

884 Y = _f(n2, n1, e1, e2) 

885 if X and Y: 

886 if X._range(e1, e2) < Y._range(e1, e2): 

887 Y = None 

888 else: 

889 X = None 

890 if X: 

891 return X.toTransform(e1, epoch2=e2) 

892 if Y: 

893 return Y.toTransform(e1, epoch2=e2, inverse=True) 

894 

895 return None 

896 

897 

898def trfTransform0(reframe, reframe2, epoch=None, epoch2=None): 

899 '''Get the L{TransformXform} to convert a C{reframe} observed at C{epoch} to 

900 C{reframe2} at observed at C{epoch2 or epoch}. 

901 

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

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

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

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

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

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

908 

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

910 C{None} if no conversion exists. 

911 

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

913 B{C{epoch2}}. 

914 

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

916 ''' 

917 r1 = _reframe(reframe=reframe) 

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

919 r2 = _reframe(reframe2=reframe2) 

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

921 return _toTransform0(r1.name, e1, r2.name, e2) 

922 

923 

924def trfXform(reframe1, reframe2, epoch=None, xform=None, rates=None): 

925 '''Define a new Terrestrial Reference Frame (TRF) converter. 

926 

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

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

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

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

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

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

933 but in C{units-per-year}. 

934 

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

936 

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

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

939 already exists. 

940 ''' 

941 r1 = _reframe(reframe1=reframe1) 

942 r2 = _reframe(reframe2=reframe2) 

943 e = r2.epoch if epoch is None else _Epoch(epoch) 

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

945 return _trfX(r1.name, r2.name, epoch=e, xform=xform, rates=rates) 

946 

947 

948def _trfX(n1, n2, **epoch_xform_rates): 

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

950 ''' 

951 r1 = RefFrames.get(n1) 

952 r2 = RefFrames.get(n2) 

953 if r1 and r2: 

954 if n2 in r1._Xs: 

955 t = _exists_ 

956 elif n1 in r2._Xs: 

957 t = _SPACE_(_inverse_, _exists_) 

958 else: 

959 r1._Xs[n2] = X = TRFXform(n1, n2, **epoch_xform_rates) 

960 return X 

961 else: 

962 t = _invalid_ 

963 raise TRFError(trfX=_SPACE_(n1, _to_, n2), txt=t) # _NameError 

964 

965 

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

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

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

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

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

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

972_trfX(_ITRF2020_, _ITRF2014_, epoch=_E(2015), # <https://ITRF.IGN.Fr/docs/solutions/itrf2020/Transfo-ITRF2020_TRFs.txt> 

973 xform=_P( -1.4, -0.9, 1.4, -0.42, _0_0, _0_0, _0_0), 

974 rates=_P( _0_0, -0.1, 0.2, _0_0, _0_0, _0_0, _0_0)) 

975_trfX(_ITRF2020_, _ITRF2008_, epoch=_E(2015), 

976 xform=_P( 0.2, 1.0, 3.3, -0.29, _0_0, _0_0, _0_0), 

977 rates=_P( _0_0, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0)) 

978_trfX(_ITRF2020_, _ITRF2005_, epoch=_E(2015), 

979 xform=_P( 2.7, 0.1, -1.4, 0.65, _0_0, _0_0, _0_0), 

980 rates=_P( 0.3, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0)) 

981_trfX(_ITRF2020_, _ITRF2000_, epoch=_E(2015), 

982 xform=_P( -0.2, 0.8, -34.2, 2.25, _0_0, _0_0, _0_0), 

983 rates=_P( 0.1, _0_0, -1.7, 0.11, _0_0, _0_0, _0_0)) 

984_trfX(_ITRF2020_, _ITRF97_, epoch=_E(2015), 

985 xform=_P( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36), 

986 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

987_trfX(_ITRF2020_, _ITRF96_, epoch=_E(2015), 

988 xform=_P( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36), 

989 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

990_trfX(_ITRF2020_, _ITRF94_, epoch=_E(2015), 

991 xform=_P( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36), 

992 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

993_trfX(_ITRF2020_, _ITRF93_, epoch=_E(2015), 

994 xform=_P( -65.8, 1.9, -71.3, 4.47, -3.36, -4.33, 0.75), 

995 rates=_P( -2.8, -0.2, -2.3, 0.12, -0.11, -0.19, 0.07)) 

996_trfX(_ITRF2020_, _ITRF92_, epoch=_E(2015), 

997 xform=_P( 14.5, -1.9, -85.9, 3.27, _0_0, _0_0, 0.36), 

998 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

999_trfX(_ITRF2020_, _ITRF91_, epoch=_E(2015), 

1000 xform=_P( 26.5, 12.1, -91.9, 4.67, _0_0, _0_0, 0.36), 

1001 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1002_trfX(_ITRF2020_, _ITRF90_, epoch=_E(2015), 

1003 xform=_P( 24.5, 8.1, -107.9, 4.97, _0_0, _0_0, 0.36), 

1004 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1005_trfX(_ITRF2020_, _ITRF89_, epoch=_E(2015), 

1006 xform=_P( 29.5, 32.1, -145.9, 8.37, _0_0, _0_0, 0.36), 

1007 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1008_trfX(_ITRF2020_, _ITRF88_, epoch=_E(2015), 

1009 xform=_P( 24.5, -3.9, -169.9, 11.47, 0.1, _0_0, 0.36), 

1010 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1011 

1012# see U{Transformation Parameters ITRF2014<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2014_ITRFs.txt>} and 

1013# Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and 

1014# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1.pdf>} Appendix A. 

1015_trfX(_ITRF2014_, _ITRF2008_, epoch=(2010), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2014/tp_14-08.php> 

1016 xform=_P( 1.6, 1.9, 2.4, -0.02, _0_0, _0_0, _0_0), 

1017 rates=_P( _0_0, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0)) 

1018_trfX(_ITRF2014_, _ITRF2005_, epoch=_E(2010), 

1019 xform=_P( 2.6, _1_0, -2.3, 0.92, _0_0, _0_0, _0_0), 

1020 rates=_P( 0.3, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0)) 

1021_trfX(_ITRF2014_, _ITRF2000_, epoch=_E(2010), 

1022 xform=_P( 0.7, 1.2, -26.1, 2.12, _0_0, _0_0, _0_0), 

1023 rates=_P( 0.1, 0.1, -1.9, 0.11, _0_0, _0_0, _0_0)) 

1024_trfX(_ITRF2014_, _ITRF97_, epoch=_E(2010), 

1025 xform=_P( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26), 

1026 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1027_trfX(_ITRF2014_, _ITRF96_, epoch=_E(2010), 

1028 xform=_P( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26), 

1029 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1030_trfX(_ITRF2014_, _ITRF94_, epoch=_E(2010), 

1031 xform=_P( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26), 

1032 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1033_trfX(_ITRF2014_, _ITRF93_, epoch=_E(2010), 

1034 xform=_P( -50.4, 3.3, -60.2, 4.29, -2.81, -3.38, 0.4), 

1035 rates=_P( -2.8, -0.1, -2.5, 0.12, -0.11, -0.19, 0.07)) 

1036_trfX(_ITRF2014_, _ITRF92_, epoch=_E(2010), 

1037 xform=_P( 15.4, 1.5, -70.8, 3.09, _0_0, _0_0, 0.26), 

1038 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1039_trfX(_ITRF2014_, _ITRF91_, epoch=_E(2010), 

1040 xform=_P( 27.4, 15.5, -76.8, 4.49, _0_0, _0_0, 0.26), 

1041 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1042_trfX(_ITRF2014_, _ITRF90_, epoch=_E(2010), 

1043 xform=_P( 25.4, 11.5, -92.8, 4.79, _0_0, _0_0, 0.26), 

1044 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1045_trfX(_ITRF2014_, _ITRF89_, epoch=_E(2010), 

1046 xform=_P( 30.4, 35.5, -130.8, 8.19, _0_0, _0_0, 0.26), 

1047 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1048_trfX(_ITRF2014_, _ITRF88_, epoch=_E(2010), 

1049 xform=_P( 25.4, -0.5, -154.8, 11.29, 0.1, _0_0, 0.26), 

1050 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1051 

1052# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference 

1053# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 1st and 2nd column 

1054_trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2005), 

1055 xform=_P( -0.5, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0), 

1056 rates=_P( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0)) 

1057# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(1997), 

1058# xform=_P( -2.9, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0), 

1059# rates=_P( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0)) 

1060# see U{Transformation Parameters ITRF2008<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2008_ITRFs.txt>} 

1061# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2008/tp_08-05.php> 

1062# xform=_P( -2.0, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0), 

1063# rates=_P( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0)) 

1064_trfX(_ITRF2008_, _ITRF2000_, epoch=_E(2000), 

1065 xform=_P( -1.9, -1.7, -10.5, 1.34, _0_0, _0_0, _0_0), 

1066 rates=_P( 0.1, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0)) 

1067_trfX(_ITRF2008_, _ITRF97_, epoch=_E(2000), 

1068 xform=_P( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06), 

1069 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1070_trfX(_ITRF2008_, _ITRF96_, epoch=_E(2000), 

1071 xform=_P( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06), 

1072 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1073_trfX(_ITRF2008_, _ITRF94_, epoch=_E(2000), 

1074 xform=_P( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06), 

1075 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1076_trfX(_ITRF2008_, _ITRF93_, epoch=_E(2000), 

1077 xform=_P( -24.0, 2.4, -38.6, 3.41, -1.71, -1.48, -0.3), 

1078 rates=_P( -2.8, -0.1, -2.4, 0.09, -0.11, -0.19, 0.07)) 

1079_trfX(_ITRF2008_, _ITRF92_, epoch=_E(2000), 

1080 xform=_P( 12.8, 4.6, -41.2, 2.21, _0_0, _0_0, 0.06), 

1081 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1082_trfX(_ITRF2008_, _ITRF91_, epoch=_E(2000), 

1083 xform=_P( 24.8, 18.6, -47.2, 3.61, _0_0, _0_0, 0.06), 

1084 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1085_trfX(_ITRF2008_, _ITRF90_, epoch=_E(2000), 

1086 xform=_P( 22.8, 14.6, -63.2, 3.91, _0_0, _0_0, 0.06), 

1087 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1088_trfX(_ITRF2008_, _ITRF89_, epoch=_E(2000), 

1089 xform=_P( 27.8, 38.6, -101.2, 7.31, _0_0, _0_0, 0.06), 

1090 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1091_trfX(_ITRF2008_, _ITRF88_, epoch=_E(2000), 

1092 xform=_P( 22.8, 2.6, -125.2, 10.41, 0.1, _0_0, 0.06), 

1093 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1094 

1095# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference 

1096# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 3rd column 

1097# _trfX(_ITRF2005_, _ITRF2000_, epoch=_E(1997), 

1098# xform=_P( 0.7, -1.1, -0.4, 0.16, -0.2, 0.1 -1.8), 

1099# rates=_P( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0)) 

1100_trfX(_ITRF2005_, _ITRF2000_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2005/tp_05-00.php> 

1101 xform=_P( 0.1, -0.8, -5.8, 0.4, _0_0, _0_0, _0_0), 

1102 rates=_P( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0)) 

1103 

1104_trfX(_ITRF2000_, _ITRF97_, epoch=_E(1997), 

1105 xform=_P( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0), 

1106 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, -0.02)) # 0.02? 

1107_trfX(_ITRF2000_, _ITRF96_, epoch=_E(1997), 

1108 xform=_P( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0), 

1109 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1110_trfX(_ITRF2000_, _ITRF94_, epoch=_E(1997), 

1111 xform=_P( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0), 

1112 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1113_trfX(_ITRF2000_, _ITRF93_, epoch=_E(1988), 

1114 xform=_P( 12.7, 6.5, -20.9, 1.95, -0.39, 0.8, -1.14), 

1115 rates=_P( -2.9, -0.2, -0.6, 0.01, -0.11, -0.19, 0.07)) 

1116_trfX(_ITRF2000_, _ITRF92_, epoch=_E(1988), 

1117 xform=_P( 1.47, 1.35, -1.39, 0.75, _0_0, _0_0, -0.18), 

1118 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1119_trfX(_ITRF2000_, _ITRF91_, epoch=_E(1988), 

1120 xform=_P( 26.7, 27.5, -19.9, 2.15, _0_0, _0_0, -0.18), 

1121 rates=_P( _0_0, -0.6, -1.4, 0.01, _0_0, _0_0, 0.02)) 

1122_trfX(_ITRF2000_, _ITRF90_, epoch=_E(1988), 

1123 xform=_P( 2.47, 2.35, -3.59, 2.45, _0_0, _0_0, -0.18), 

1124 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1125_trfX(_ITRF2000_, _ITRF89_, epoch=_E(1988), 

1126 xform=_P( 2.97, 4.75, -7.39, 5.85, _0_0, _0_0, -0.18), 

1127 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1128_trfX(_ITRF2000_, _ITRF88_, epoch=_E(1988), 

1129 xform=_P( 2.47, 1.15, -9.79, 8.95, 0.1, _0_0, -0.18), 

1130 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1131 

1132# Soler, T .& Snay R.A. U{"Transforming Positions and Velocities between the International Terrestrial 

1133# Reference Frame of 2000 and North American Datum of 1983"<https://www.ResearchGate.net/publication/245291390>}, 

1134# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference 

1135# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 5th and 6th column 

1136_trfX(_ITRF97_, _ITRF96_, epoch=_E(1997), 

1137 xform=_P( -2.07, -0.21, 9.95, -0.93496, 0.1267, -0.22355, -0.06065,), 

1138 rates=_P( 0.69, -0.1, 1.86, -0.19201, 0.01347, -0.01514, 0.00027)) 

1139_trfX(_ITRF96_, _NAD83_, epoch=_E(1997), 

1140 xform=_P( 991.0, -190.72, -512.9, _0_0, 25.79, 9.65, 11.66,), 

1141 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.0532, -0.7423, -0.0316,)) 

1142 

1143# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and 

1144# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 1. 

1145# _trfX(_ITRF2020_, _ETRF2020_, epoch=_E(1989), # see Table 2 below 

1146# xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0), 

1147# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753)) 

1148# _trfX(_ITRF2014_, _ETRF2014_, epoch=_E(1989), # see Table 3 below 

1149# xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0), 

1150# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77)) 

1151_trfX(_ITRF2005_, _ETRF2005_, epoch=_E(1989), 

1152 xform=_P( 56.0, 48.0, -37.0, _0_0, _0_0, _0_0, _0_0), 

1153 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.054, 0.518, -0.781)) 

1154# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(1989), # see Table 4 below 

1155# xform=_P( 54.0, 51.0, -48.0, _0_0, _0_0, _0_0, _0_0), 

1156# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792)) 

1157_trfX(_ITRF97_, _ETRF97_, epoch=_E(1989), 

1158 xform=_P( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0), 

1159 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65)) 

1160_trfX(_ITRF96_, _ETRF96_, epoch=_E(1989), 

1161 xform=_P( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0), 

1162 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65)) 

1163_trfX(_ITRF94_, _ETRF94_, epoch=_E(1989), 

1164 xform=_P( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0), 

1165 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65)) 

1166_trfX(_ITRF93_, _ETRF93_, epoch=_E(1989), 

1167 xform=_P( 19.0, 53.0, -21.0, _0_0, _0_0, _0_0, _0_0), 

1168 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.32, 0.78, -0.67)) 

1169_trfX(_ITRF92_, _ETRF92_, epoch=_E(1989), 

1170 xform=_P( 38.0, 40.0, -37.0, 0.0, 0.0, 0.0, 0.0), 

1171 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68)) 

1172_trfX(_ITRF91_, _ETRF91_, epoch=_E(1989), 

1173 xform=_P( 21.0, 25.0, -37.0, _0_0, _0_0, _0_0, _0_0), 

1174 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68)) 

1175_trfX(_ITRF90_, _ETRF90_, epoch=_E(1989), 

1176 xform=_P( 19.0, 28.0, -23.0, _0_0, _0_0, _0_0, _0_0), 

1177 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71)) 

1178_trfX(_ITRF89_, _ETRF89_, epoch=_E(1989), 

1179 xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0), 

1180 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71)) 

1181 

1182# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and 

1183# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 2. 

1184_trfX(_ITRF2020_, _ETRF2020_, epoch=_E(2015), 

1185 xform=_P( _0_0, _0_0, _0_0, _0_0, 2.236, 13.494, -19.578), 

1186 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753)) 

1187_trfX(_ITRF2014_, _ETRF2020_, epoch=_E(2015), 

1188 xform=_P( 1.4, 0.9, -1.4, 0.42, 2.236, 13.494, -19.578), 

1189 rates=_P( _0_0, 0.1, -0.2, _0_0, 0.086, 0.519, -0.753)) 

1190_trfX(_ITRF2008_, _ETRF2020_, epoch=_E(2015), 

1191 xform=_P( 3.0, 2.8, 0.5, 0.55, 2.236, 13.494, -19.578), 

1192 rates=_P( _0_0, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753)) 

1193_trfX(_ITRF2005_, _ETRF2020_, epoch=_E(2015), 

1194 xform=_P( 5.5, 1.9, -4.2, 1.49, 2.236, 13.494, -19.578), 

1195 rates=_P( 0.3, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753)) 

1196_trfX(_ITRF2000_, _ETRF2020_, epoch=_E(2015), 

1197 xform=_P( 2.6, 2.6, -37.0, 3.09, 2.236, 13.494, -19.578), 

1198 rates=_P( 0.1, 0.2, -2.1, 0.11, 0.086, 0.519, -0.753)) 

1199_trfX(_ITRF97_, _ETRF2020_, epoch=_E(2015), 

1200 xform=_P( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218), 

1201 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1202_trfX(_ITRF96_, _ETRF2020_, epoch=_E(2015), 

1203 xform=_P( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218), 

1204 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1205_trfX(_ITRF94_, _ETRF2020_, epoch=_E(2015), 

1206 xform=_P( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218), 

1207 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1208_trfX(_ITRF93_, _ETRF2020_, epoch=_E(2015), 

1209 xform=_P( -63.0, 3.7, -74.1, 5.31, -1.124, 9.164, -18.828), 

1210 rates=_P( -2.8, _0_0, -2.7, 0.12, -0.024, 0.329, -0.683)) 

1211_trfX(_ITRF92_, _ETRF2020_, epoch=_E(2015), 

1212 xform=_P( 17.3, -0.1, -88.7, 4.11, 2.236, 13.494, -19.218), 

1213 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1214_trfX(_ITRF91_, _ETRF2020_, epoch=_E(2015), 

1215 xform=_P( 29.3, 13.9, -94.7, 5.51, 2.236, 13.494, -19.218), 

1216 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1217_trfX(_ITRF90_, _ETRF2020_, epoch=_E(2015), 

1218 xform=_P( 27.3, 9.9, -110.7, 5.81, 2.236, 13.494, -19.218), 

1219 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1220_trfX(_ITRF89_, _ETRF2020_, epoch=_E(2015), 

1221 xform=_P( 32.3, 33.9, -148.7, 9.21, 2.236, 13.494, -19.218), 

1222 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1223_trfX(_ITRF88_, _ETRF2020_, epoch=_E(2015), 

1224 xform=_P( 27.3, -2.1, -172.7, 12.31, 2.336, 13.494, -19.218), 

1225 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1226 

1227# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and 

1228# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 3. 

1229_trfX(_ITRF2020_, _ETRF2014_, epoch=_E(2015), 

1230 xform=_P( -1.4, -0.9, 1.4, 0.42, 2.21, 13.806, -20.02), 

1231 rates=_P( _0_0, -0.1, 0.2, _0_0, 0.085, 0.531, -0.77)) 

1232_trfX(_ITRF2014_, _ETRF2014_, epoch=_E(2015), 

1233 xform=_P( _0_0, _0_0, _0_0, _0_0, 2.21, 13.806, -20.02), 

1234 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77)) 

1235_trfX(_ITRF2008_, _ETRF2014_, epoch=_E(2015), 

1236 xform=_P( -1.6, -1.9, -1.9, -0.13, 2.21, 13.806, -20.02), 

1237 rates=_P( _0_0, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77)) 

1238_trfX(_ITRF2005_, _ETRF2014_, epoch=_E(2015), 

1239 xform=_P( -4.1, -1.0, 2.8, -1.07, 2.21, 13.806, -20.02), 

1240 rates=_P( -0.3, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77)) 

1241_trfX(_ITRF2000_, _ETRF2014_, epoch=_E(2015), 

1242 xform=_P( -1.2, -1.7, 35.6, -2.67, 2.21, 13.806, -20.02), 

1243 rates=_P( -0.1, -0.1, 1.9, -0.11, 0.085, 0.531, -0.77)) 

1244_trfX(_ITRF97_, _ETRF2014_, epoch=_E(2015), 

1245 xform=_P( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38), 

1246 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1247_trfX(_ITRF96_, _ETRF2014_, epoch=_E(2015), 

1248 xform=_P( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38), 

1249 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1250_trfX(_ITRF94_, _ETRF2014_, epoch=_E(2015), 

1251 xform=_P( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38), 

1252 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1253_trfX(_ITRF93_, _ETRF2014_, epoch=_E(2015), 

1254 xform=_P( 64.4, -2.8, 72.7, -4.89, 5.570, 18.136, -20.77), 

1255 rates=_P( 2.8, 0.1, 2.5, -0.12, 0.195, 0.721, -0.84)) 

1256_trfX(_ITRF92_, _ETRF2014_, epoch=_E(2015), 

1257 xform=_P( -15.9, 1.0, 87.3, -3.69, 2.21, 13.806, -20.38), 

1258 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1259_trfX(_ITRF91_, _ETRF2014_, epoch=_E(2015), 

1260 xform=_P( -27.9, -13.0, 93.3, -5.09, 2.21, 13.806, -20.38), 

1261 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1262_trfX(_ITRF90_, _ETRF2014_, epoch=_E(2015), 

1263 xform=_P( -25.9, -9.0, 109.3, -5.39, 2.21, 13.806, -20.38), 

1264 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1265_trfX(_ITRF89_, _ETRF2014_, epoch=_E(2015), 

1266 xform=_P( -30.9, -33.0, 147.3, -8.79, 2.21, 13.806, -20.38), 

1267 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1268_trfX(_ITRF88_, _ETRF2014_, epoch=_E(2015), 

1269 xform=_P( -25.9, 3.0, 171.3, -11.89, 2.11, 13.806, -20.38), 

1270 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1271 

1272# see U{Altamimi, Z. "EUREF Technical Note 1: Relationship and Transformation between the International and 

1273# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 4, 

1274# U{Boucher, C. & Altamimi, Z. "Memo: Specifications for reference frame fixing in the analysis of a EUREF GPS 

1275# campaign" (2011) <https://ETRS89.ENSG.IGN.Fr/memo-V8.pdf>} and U{Altamimi, Z. "Key results of ITRF2014 and 

1276# implication to ETRS89 realization", EUREF2016<https://www.EUREF.EU/symposia/2016SanSebastian/01-02-Altamimi.pdf>}. 

1277_trfX(_ITRF2020_, _ETRF2000_, epoch=_E(2015), 

1278 xform=_P( 53.8, 51.8, -82.2, 2.25, 2.106, 12.74, -20.592), 

1279 rates=_P( 0.1, _0_0, -1.7, 0.11, 0.081, 0.49, -0.792)) 

1280# _trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2000), 

1281# xform=_P( 53.7, 51.2, -55.1, 1.02, 0.891, 5.39, -8.712), 

1282# rates=_P( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792)) 

1283_trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2015), 

1284 xform=_P( 55.2, 52.7, -83.6, 2.67, 2.106, 12.74, -20.592), 

1285 rates=_P( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792)) 

1286# _trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2000), 

1287# xform=_P( 52.1, 49.3, -58.5, 1.34, 0.891, 5.39, -8.712), 

1288# rates=_P( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)) 

1289_trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2015), 

1290 xform=_P( 53.6, 50.8, -85.5, 2.54, 2.106, 12.74, -20.592), 

1291 rates=_P( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)) 

1292# _trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2000), 

1293# xform=_P( 54.1, 50.2, -53.8, 0.4, 0.891, 5.39, -8.712), 

1294# rates=_P( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)) 

1295_trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2015), 

1296 xform=_P( 51.1, 51.7, -80.8, 1.6, 2.106, 12.74, -20.592), 

1297 rates=_P( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)) 

1298# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2000), 

1299# xform=_P( 54.0, 51.0, -48.0, _0_0, 0.891, 5.39, -8.712), 

1300# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792)) 

1301_trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2015), 

1302 xform=_P( 54.0, 51.0, -48.0, _0_0, 2.106, 12.74, -20.592), 

1303 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792)) 

1304_trfX(_ITRF97_, _ETRF2000_, epoch=_E(2015), 

1305 xform=_P( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952), 

1306 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1307_trfX(_ITRF96_, _ETRF2000_, epoch=_E(2015), 

1308 xform=_P( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952), 

1309 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1310_trfX(_ITRF94_, _ETRF2000_, epoch=_E(2015), 

1311 xform=_P( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952), 

1312 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1313_trfX(_ITRF93_, _ETRF2000_, epoch=_E(2015), 

1314 xform=_P( 119.6, 49.9, -10.9, -2.22, 5.466, 17.07, -21.342), 

1315 rates=_P( 2.9, 0.2, 0.6, -0.01, 0.191, 0.68, -0.862)) 

1316_trfX(_ITRF92_, _ETRF2000_, epoch=_E(2015), 

1317 xform=_P( 39.3, 53.7, 3.7, -1.02, 2.106, 12.74, -20.952), 

1318 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1319_trfX(_ITRF91_, _ETRF2000_, epoch=_E(2015), 

1320 xform=_P( 27.3, 39.7, 9.7, -2.42, 2.106, 12.74, -20.952), 

1321 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1322_trfX(_ITRF90_, _ETRF2000_, epoch=_E(2015), 

1323 xform=_P( 29.3, 43.7, 25.7, -2.72, 2.106, 12.74, -20.952), 

1324 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1325_trfX(_ITRF89_, _ETRF2000_, epoch=_E(2015), 

1326 xform=_P( 24.3, 19.7, 63.7, -6.12, 2.106, 12.74, -20.952), 

1327 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1328_trfX(_ITRF88_, _ETRF2000_, epoch=_E(2015), 

1329 xform=_P( 29.3, 55.7, 87.7, -9.22, 2.006, 12.74, -20.952), 

1330 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1331 

1332# GDA2020 "Geocentric Datum of Australia 2020 Technical Manual", v1.5, 2020-12-09, Table 3.3 and 3.4 

1333# <https://www.ICSM.gov.AU/sites/default/files/2020-12/GDA2020%20Technical%20Manual%20V1.5_4.pdf> 

1334# (the GDA2020 xforms are different but the rates are the same as GDA94, further below) 

1335_trfX(_ITRF2014_, _GDA2020_, epoch=_E(2020), 

1336 xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0), 

1337 rates=_P( _0_0, _0_0, _0_0, _0_0, 1.50379, 1.18346, 1.20716)) 

1338_trfX(_ITRF2008_, _GDA2020_, epoch=_E(2020), 

1339 xform=_P( 13.79, 4.55, 15.22, 2.5, 0.2808, 0.2677, -0.4638), 

1340 rates=_P( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551)) 

1341_trfX(_ITRF2005_, _GDA2020_, epoch=_E(2020), 

1342 xform=_P( 40.32, -33.85, -16.72, 4.286, -1.2893, -0.8492, -0.3342), 

1343 rates=_P( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701)) 

1344_trfX(_ITRF2000_, _GDA2020_, epoch=_E(2020), 

1345 xform=_P(-105.52, 51.58, 231.68, 3.55, 4.2175, 6.3941, 0.8617), 

1346 rates=_P( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224)) 

1347 

1348# see Table 2 in U{Dawson, J. & Woods, A. "ITRF to GDA94 coordinate transformations", Journal of Applied 

1349# Geodesy 4 (2010), 189-199<https://www.ResearchGate.net/publication/258401581_ITRF_to_GDA94_coordinate_transformations>} 

1350# (note, sign of rotations for GDA94 reversed as "Australia assumes rotation to be of coordinate axes", 

1351# rather than the more conventional "position around the coordinate axes") 

1352_trfX(_ITRF2008_, _GDA94_, epoch=_E(1994), 

1353 xform=_P( -84.68, -19.42, 32.01, 9.71, -0.4254, 2.2578, 2.4015), 

1354 rates=_P( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551)) 

1355_trfX(_ITRF2005_, _GDA94_, epoch=_E(1994), 

1356 xform=_P( -79.73, -6.86, 38.03, 6.636, 0.0351, -2.1211, -2.1411), 

1357 rates=_P( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701)) 

1358_trfX(_ITRF2000_, _GDA94_, epoch=_E(1994), 

1359 xform=_P( -45.91, -29.85, -20.37, 7.07, -1.6705, 0.4594, 1.9356), 

1360 rates=_P( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224)) 

1361 

1362# see U{Solar, T. & Snay, R.A. "Transforming Positions and Velocities between the 

1363# International Terrestrial Reference Frame of 2000 and North American Datum of 1983" 

1364# (2004)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>} 

1365_trfX(_ITRF2000_, _NAD83_, epoch=_E(1997), # note NAD83(CORS96) 

1366 xform=_P( 995.6, -1901.3, -521.5, 0.615, -25.915, -9.426, -11.599), 

1367 rates=_P( 0.7, -0.7, _0_5, -0.182, -0.06667, 0.75744, 0.05133)) 

1368 

1369# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ 

1370# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83 and Pearson, C. & Snay, R. U{"Introducing 

1371# HTDP 3.1 to transform coordinates across time and spatial reference frames"<https://Geodesy.NOAA.gov/ 

1372# TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 7th column 

1373_trfX(_ITRF2008_, _NAD83_, epoch=_E(1997), 

1374 xform=_P( 993.43, -1903.31, -526.55, 1.71504, -25.91467, -9.42645, -11.59935), 

1375 rates=_P( 0.79, -0.6, -1.34, -0.10201, -0.06667, 0.75744, 0.05133)) 

1376# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ 

1377# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83 

1378_trfX(_ITRF2005_, _NAD83_, epoch=_E(1997), 

1379 xform=_P( 996.3, -1902.4, -521.9, 0.775, -25.915, -9.426, -11.599), 

1380 rates=_P( 0.5, -0.6, -1.3, -0.10201, -0.06667, 0.75744, 0.05133)) 

1381_trfX(_ITRF90_, _NAD83_, epoch=_E(1997), 

1382 xform=_P( 973.0, -1919.2, -482.9, -0.9, -25.79, -9.65, -11.66), 

1383 rates=_P( _0_0, _0_0, _0_0, _0_0, -0.053, 0.742, 0.032)) 

1384_trfX(_ITRF90_, _WGS84_, epoch=_E(1984), 

1385 xform=_P( 60.0, -517.0, -223.0, -11.0, 18.3, -0.3, 7.0), 

1386 rates=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0)) 

1387 

1388del _P, _Ps # keep _E, _Es 

1389 

1390if __name__ == '__main__': 

1391 

1392 from pygeodesy.interns import _COLONSPACE_,_COMMA_, _NL_, _NLATvar_, _STAR_ 

1393 from pygeodesy.lazily import printf 

1394 from time import localtime 

1395 

1396 D = date2epoch.__name__ 

1397 E = epoch2date.__name__ 

1398 y = localtime()[0] 

1399 for m in range(1, 13): 

1400 for d in (1, 15, _mDays[m] - 1, _mDays[m]): 

1401 f = '%s(%d,%3d,%3d)' % (D, y, m, d) 

1402 e = date2epoch(y, m, d) 

1403 t = epoch2date(e) 

1404 x = NN if t == (y, m, d) else _STAR_ 

1405 e = '%.3f' % (e,) 

1406 e = '%s, %s(%s)' % (e, E, e) 

1407 t = '%d,%3d,%3d' % t 

1408 printf('# %s = %s = %s %s', f, e, t, x) 

1409 

1410 # __doc__ of this file, force all into registery 

1411 def _RFs(): 

1412 yield NN 

1413 for t in RefFrames.toRepr(all=True).split(_NL_): 

1414 t = t.strip(_COMMA_) 

1415 n = t.split(_COLONSPACE_)[0].split(_DOT_)[1] 

1416 r = RefFrames.get(n) 

1417 x = len(r.Xforms()), -len(r.Xforms(inverse=True)) 

1418 yield '%s .Xforms=%s' % (t, x) 

1419 

1420 printf(_NLATvar_.join(sorted(_RFs())), nt=1) 

1421 

1422 X, t = (), 0 # all form 

1423 for r in RefFrames.values(): 

1424 X += tuple(r._Xs.values()) 

1425 for X in sorted(X): 

1426 t += 1 

1427 printf('#%4d %-22s xform=%r', t, X.name, X.xform) 

1428 printf('#%27s rates=%r', _SPACE_, X.rates) 

1429 

1430# **) MIT License 

1431# 

1432# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1433# 

1434# Permission is hereby granted, free of charge, to any person obtaining a 

1435# copy of this software and associated documentation files (the "Software"), 

1436# to deal in the Software without restriction, including without limitation 

1437# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1438# and/or sell copies of the Software, and to permit persons to whom the 

1439# Software is furnished to do so, subject to the following conditions: 

1440# 

1441# The above copyright notice and this permission notice shall be included 

1442# in all copies or substantial portions of the Software. 

1443# 

1444# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1445# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1446# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1447# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1448# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1449# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1450# OTHER DEALINGS IN THE SOFTWARE. 

1451 

1452# % python -m pygeodesy.trf 

1453# 

1454# date2epoch(2024, 1, 1) = 2024.003, epoch2date(2024.003) = 2024, 1, 1 

1455# date2epoch(2024, 1, 15) = 2024.041, epoch2date(2024.041) = 2024, 1, 15 

1456# date2epoch(2024, 1, 30) = 2024.082, epoch2date(2024.082) = 2024, 1, 30 

1457# date2epoch(2024, 1, 31) = 2024.085, epoch2date(2024.085) = 2024, 1, 31 

1458# date2epoch(2024, 2, 1) = 2024.087, epoch2date(2024.087) = 2024, 2, 2 * 

1459# date2epoch(2024, 2, 15) = 2024.126, epoch2date(2024.126) = 2024, 2, 16 * 

1460# date2epoch(2024, 2, 28) = 2024.161, epoch2date(2024.161) = 2024, 2, 28 

1461# date2epoch(2024, 2, 29) = 2024.164, epoch2date(2024.164) = 2024, 3, 1 * 

1462# date2epoch(2024, 3, 1) = 2024.167, epoch2date(2024.167) = 2024, 3, 2 * 

1463# date2epoch(2024, 3, 15) = 2024.205, epoch2date(2024.205) = 2024, 3, 16 * 

1464# date2epoch(2024, 3, 30) = 2024.246, epoch2date(2024.246) = 2024, 3, 31 * 

1465# date2epoch(2024, 3, 31) = 2024.249, epoch2date(2024.249) = 2024, 4, 1 * 

1466# date2epoch(2024, 4, 1) = 2024.251, epoch2date(2024.251) = 2024, 4, 1 

1467# date2epoch(2024, 4, 15) = 2024.290, epoch2date(2024.290) = 2024, 4, 15 

1468# date2epoch(2024, 4, 29) = 2024.328, epoch2date(2024.328) = 2024, 4, 29 

1469# date2epoch(2024, 4, 30) = 2024.331, epoch2date(2024.331) = 2024, 4, 30 

1470# date2epoch(2024, 5, 1) = 2024.333, epoch2date(2024.333) = 2024, 5, 1 

1471# date2epoch(2024, 5, 15) = 2024.372, epoch2date(2024.372) = 2024, 5, 15 

1472# date2epoch(2024, 5, 30) = 2024.413, epoch2date(2024.413) = 2024, 5, 30 

1473# date2epoch(2024, 5, 31) = 2024.415, epoch2date(2024.415) = 2024, 6, 1 * 

1474# date2epoch(2024, 6, 1) = 2024.418, epoch2date(2024.418) = 2024, 6, 2 * 

1475# date2epoch(2024, 6, 15) = 2024.456, epoch2date(2024.456) = 2024, 6, 16 * 

1476# date2epoch(2024, 6, 29) = 2024.495, epoch2date(2024.495) = 2024, 6, 30 * 

1477# date2epoch(2024, 6, 30) = 2024.497, epoch2date(2024.497) = 2024, 7, 1 * 

1478# date2epoch(2024, 7, 1) = 2024.500, epoch2date(2024.500) = 2024, 7, 1 

1479# date2epoch(2024, 7, 15) = 2024.538, epoch2date(2024.538) = 2024, 7, 16 * 

1480# date2epoch(2024, 7, 30) = 2024.579, epoch2date(2024.579) = 2024, 7, 30 

1481# date2epoch(2024, 7, 31) = 2024.582, epoch2date(2024.582) = 2024, 7, 31 

1482# date2epoch(2024, 8, 1) = 2024.585, epoch2date(2024.585) = 2024, 8, 1 

1483# date2epoch(2024, 8, 15) = 2024.623, epoch2date(2024.623) = 2024, 8, 15 

1484# date2epoch(2024, 8, 30) = 2024.664, epoch2date(2024.664) = 2024, 8, 31 * 

1485# date2epoch(2024, 8, 31) = 2024.667, epoch2date(2024.667) = 2024, 9, 1 * 

1486# date2epoch(2024, 9, 1) = 2024.669, epoch2date(2024.669) = 2024, 9, 2 * 

1487# date2epoch(2024, 9, 15) = 2024.708, epoch2date(2024.708) = 2024, 9, 16 * 

1488# date2epoch(2024, 9, 29) = 2024.746, epoch2date(2024.746) = 2024, 9, 30 * 

1489# date2epoch(2024, 9, 30) = 2024.749, epoch2date(2024.749) = 2024, 10, 1 * 

1490# date2epoch(2024, 10, 1) = 2024.751, epoch2date(2024.751) = 2024, 10, 1 

1491# date2epoch(2024, 10, 15) = 2024.790, epoch2date(2024.790) = 2024, 10, 15 

1492# date2epoch(2024, 10, 30) = 2024.831, epoch2date(2024.831) = 2024, 10, 30 

1493# date2epoch(2024, 10, 31) = 2024.833, epoch2date(2024.833) = 2024, 10, 31 

1494# date2epoch(2024, 11, 1) = 2024.836, epoch2date(2024.836) = 2024, 11, 1 

1495# date2epoch(2024, 11, 15) = 2024.874, epoch2date(2024.874) = 2024, 11, 15 

1496# date2epoch(2024, 11, 29) = 2024.913, epoch2date(2024.913) = 2024, 11, 29 

1497# date2epoch(2024, 11, 30) = 2024.915, epoch2date(2024.915) = 2024, 12, 1 * 

1498# date2epoch(2024, 12, 1) = 2024.918, epoch2date(2024.918) = 2024, 12, 2 * 

1499# date2epoch(2024, 12, 15) = 2024.956, epoch2date(2024.956) = 2024, 12, 16 * 

1500# date2epoch(2024, 12, 30) = 2024.997, epoch2date(2024.997) = 2024, 12, 31 * 

1501# date2epoch(2024, 12, 31) = 2025.000, epoch2date(2025.000) = 2025, 1, 1 * 

1502 

1503# 1 ITRF2005@2015xETRF2000 xform=TRFXform7Tuple(tx=51.1, ty=51.7, tz=-80.8, s=1.6, sx=2.106, sy=12.74, sz=-20.592) 

1504# rates=TRFXform7Tuple(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792) 

1505# 2 ITRF88@2015xETRF2000 xform=TRFXform7Tuple(tx=29.3, ty=55.7, tz=87.7, s=-9.22, sx=2.006, sy=12.74, sz=-20.952) 

1506# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1507# 3 ITRF2005@1989xETRF2005 xform=TRFXform7Tuple(tx=56.0, ty=48.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1508# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.054, sy=0.518, sz=-0.781) 

1509# 4 ITRF88@2015xETRF2014 xform=TRFXform7Tuple(tx=-25.9, ty=3.0, tz=171.3, s=-11.89, sx=2.11, sy=13.806, sz=-20.38) 

1510# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1511# 5 ITRF88@2015xETRF2020 xform=TRFXform7Tuple(tx=27.3, ty=-2.1, tz=-172.7, s=12.31, sx=2.336, sy=13.494, sz=-19.218) 

1512# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1513# 6 ITRF89@2015xETRF2000 xform=TRFXform7Tuple(tx=24.3, ty=19.7, tz=63.7, s=-6.12, sx=2.106, sy=12.74, sz=-20.952) 

1514# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1515# 7 ITRF89@2015xETRF2014 xform=TRFXform7Tuple(tx=-30.9, ty=-33.0, tz=147.3, s=-8.79, sx=2.21, sy=13.806, sz=-20.38) 

1516# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1517# 8 ITRF89@2015xETRF2020 xform=TRFXform7Tuple(tx=32.3, ty=33.9, tz=-148.7, s=9.21, sx=2.236, sy=13.494, sz=-19.218) 

1518# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1519# 9 ITRF89@1989xETRF89 xform=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1520# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71) 

1521# 10 ITRF90@1984xWGS84 xform=TRFXform7Tuple(tx=60.0, ty=-517.0, tz=-223.0, s=-11.0, sx=18.3, sy=-0.3, sz=7.0) 

1522# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1523# 11 ITRF2005@1994xGDA94 xform=TRFXform7Tuple(tx=-79.73, ty=-6.86, tz=38.03, s=6.636, sx=0.0351, sy=-2.1211, sz=-2.1411) 

1524# rates=TRFXform7Tuple(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701) 

1525# 12 ITRF90@1997xNAD83 xform=TRFXform7Tuple(tx=973.0, ty=-1919.2, tz=-482.9, s=-0.9, sx=-25.79, sy=-9.65, sz=-11.66) 

1526# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=-0.053, sy=0.742, sz=0.032) 

1527# 13 ITRF90@2015xETRF2000 xform=TRFXform7Tuple(tx=29.3, ty=43.7, tz=25.7, s=-2.72, sx=2.106, sy=12.74, sz=-20.952) 

1528# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1529# 14 ITRF2005@2015xETRF2014 xform=TRFXform7Tuple(tx=-4.1, ty=-1.0, tz=2.8, s=-1.07, sx=2.21, sy=13.806, sz=-20.02) 

1530# rates=TRFXform7Tuple(tx=-0.3, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77) 

1531# 15 ITRF90@2015xETRF2014 xform=TRFXform7Tuple(tx=-25.9, ty=-9.0, tz=109.3, s=-5.39, sx=2.21, sy=13.806, sz=-20.38) 

1532# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1533# 16 ITRF2005@2015xETRF2020 xform=TRFXform7Tuple(tx=5.5, ty=1.9, tz=-4.2, s=1.49, sx=2.236, sy=13.494, sz=-19.578) 

1534# rates=TRFXform7Tuple(tx=0.3, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753) 

1535# 17 ITRF90@2015xETRF2020 xform=TRFXform7Tuple(tx=27.3, ty=9.9, tz=-110.7, s=5.81, sx=2.236, sy=13.494, sz=-19.218) 

1536# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1537# 18 ITRF90@1989xETRF90 xform=TRFXform7Tuple(tx=19.0, ty=28.0, tz=-23.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1538# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71) 

1539# 19 ITRF91@2015xETRF2000 xform=TRFXform7Tuple(tx=27.3, ty=39.7, tz=9.7, s=-2.42, sx=2.106, sy=12.74, sz=-20.952) 

1540# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1541# 20 ITRF91@2015xETRF2014 xform=TRFXform7Tuple(tx=-27.9, ty=-13.0, tz=93.3, s=-5.09, sx=2.21, sy=13.806, sz=-20.38) 

1542# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1543# 21 ITRF91@1989xETRF91 xform=TRFXform7Tuple(tx=21.0, ty=25.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1544# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68) 

1545# 22 ITRF92@2015xETRF2000 xform=TRFXform7Tuple(tx=39.3, ty=53.7, tz=3.7, s=-1.02, sx=2.106, sy=12.74, sz=-20.952) 

1546# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1547# 23 ITRF92@2015xETRF2014 xform=TRFXform7Tuple(tx=-15.9, ty=1.0, tz=87.3, s=-3.69, sx=2.21, sy=13.806, sz=-20.38) 

1548# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1549# 24 ITRF92@2015xETRF2020 xform=TRFXform7Tuple(tx=17.3, ty=-0.1, tz=-88.7, s=4.11, sx=2.236, sy=13.494, sz=-19.218) 

1550# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1551# 25 ITRF92@1989xETRF92 xform=TRFXform7Tuple(tx=38.0, ty=40.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1552# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68) 

1553# 26 ITRF93@2015xETRF2000 xform=TRFXform7Tuple(tx=119.6, ty=49.9, tz=-10.9, s=-2.22, sx=5.466, sy=17.07, sz=-21.342) 

1554# rates=TRFXform7Tuple(tx=2.9, ty=0.2, tz=0.6, s=-0.01, sx=0.191, sy=0.68, sz=-0.862) 

1555# 27 ITRF93@2015xETRF2014 xform=TRFXform7Tuple(tx=64.4, ty=-2.8, tz=72.7, s=-4.89, sx=5.57, sy=18.136, sz=-20.77) 

1556# rates=TRFXform7Tuple(tx=2.8, ty=0.1, tz=2.5, s=-0.12, sx=0.195, sy=0.721, sz=-0.84) 

1557# 28 ITRF93@2015xETRF2020 xform=TRFXform7Tuple(tx=-63.0, ty=3.7, tz=-74.1, s=5.31, sx=-1.124, sy=9.164, sz=-18.828) 

1558# rates=TRFXform7Tuple(tx=-2.8, ty=0.0, tz=-2.7, s=0.12, sx=-0.024, sy=0.329, sz=-0.683) 

1559# 29 ITRF93@1989xETRF93 xform=TRFXform7Tuple(tx=19.0, ty=53.0, tz=-21.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1560# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.32, sy=0.78, sz=-0.67) 

1561# 30 ITRF94@2015xETRF2000 xform=TRFXform7Tuple(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952) 

1562# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1563# 31 ITRF94@2015xETRF2014 xform=TRFXform7Tuple(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38) 

1564# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1565# 32 ITRF94@2015xETRF2020 xform=TRFXform7Tuple(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218) 

1566# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1567# 33 ITRF94@1989xETRF94 xform=TRFXform7Tuple(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1568# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65) 

1569# 34 ITRF96@1989xETRF96 xform=TRFXform7Tuple(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1570# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65) 

1571# 35 ITRF97@1989xETRF97 xform=TRFXform7Tuple(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1572# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65) 

1573# 36 ITRF2000@1994xGDA94 xform=TRFXform7Tuple(tx=-45.91, ty=-29.85, tz=-20.37, s=7.07, sx=-1.6705, sy=0.4594, sz=1.9356) 

1574# rates=TRFXform7Tuple(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224) 

1575# 37 ITRF2000@2015xETRF2000 xform=TRFXform7Tuple(tx=54.0, ty=51.0, tz=-48.0, s=0.0, sx=2.106, sy=12.74, sz=-20.592) 

1576# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.081, sy=0.49, sz=-0.792) 

1577# 38 ITRF96@2015xETRF2000 xform=TRFXform7Tuple(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952) 

1578# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1579# 39 ITRF97@2015xETRF2000 xform=TRFXform7Tuple(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952) 

1580# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1581# 40 ITRF2000@2015xETRF2014 xform=TRFXform7Tuple(tx=-1.2, ty=-1.7, tz=35.6, s=-2.67, sx=2.21, sy=13.806, sz=-20.02) 

1582# rates=TRFXform7Tuple(tx=-0.1, ty=-0.1, tz=1.9, s=-0.11, sx=0.085, sy=0.531, sz=-0.77) 

1583# 41 ITRF96@2015xETRF2014 xform=TRFXform7Tuple(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38) 

1584# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1585# 42 ITRF97@2015xETRF2014 xform=TRFXform7Tuple(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38) 

1586# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1587# 43 ITRF2000@2015xETRF2020 xform=TRFXform7Tuple(tx=2.6, ty=2.6, tz=-37.0, s=3.09, sx=2.236, sy=13.494, sz=-19.578) 

1588# rates=TRFXform7Tuple(tx=0.1, ty=0.2, tz=-2.1, s=0.11, sx=0.086, sy=0.519, sz=-0.753) 

1589# 44 ITRF91@2015xETRF2020 xform=TRFXform7Tuple(tx=29.3, ty=13.9, tz=-94.7, s=5.51, sx=2.236, sy=13.494, sz=-19.218) 

1590# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1591# 45 ITRF96@2015xETRF2020 xform=TRFXform7Tuple(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218) 

1592# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1593# 46 ITRF97@2015xETRF2020 xform=TRFXform7Tuple(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218) 

1594# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1595# 47 ITRF2000@2020xGDA2020 xform=TRFXform7Tuple(tx=-105.52, ty=51.58, tz=231.68, s=3.55, sx=4.2175, sy=6.3941, sz=0.8617) 

1596# rates=TRFXform7Tuple(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224) 

1597# 48 ITRF2000@1988xITRF88 xform=TRFXform7Tuple(tx=2.47, ty=1.15, tz=-9.79, s=8.95, sx=0.1, sy=0.0, sz=-0.18) 

1598# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1599# 49 ITRF2000@1988xITRF89 xform=TRFXform7Tuple(tx=2.97, ty=4.75, tz=-7.39, s=5.85, sx=0.0, sy=0.0, sz=-0.18) 

1600# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1601# 50 ITRF2000@1988xITRF90 xform=TRFXform7Tuple(tx=2.47, ty=2.35, tz=-3.59, s=2.45, sx=0.0, sy=0.0, sz=-0.18) 

1602# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1603# 51 ITRF2000@1988xITRF91 xform=TRFXform7Tuple(tx=26.7, ty=27.5, tz=-19.9, s=2.15, sx=0.0, sy=0.0, sz=-0.18) 

1604# rates=TRFXform7Tuple(tx=0.0, ty=-0.6, tz=-1.4, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1605# 52 ITRF2000@1988xITRF92 xform=TRFXform7Tuple(tx=1.47, ty=1.35, tz=-1.39, s=0.75, sx=0.0, sy=0.0, sz=-0.18) 

1606# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1607# 53 ITRF2000@1988xITRF93 xform=TRFXform7Tuple(tx=12.7, ty=6.5, tz=-20.9, s=1.95, sx=-0.39, sy=0.8, sz=-1.14) 

1608# rates=TRFXform7Tuple(tx=-2.9, ty=-0.2, tz=-0.6, s=0.01, sx=-0.11, sy=-0.19, sz=0.07) 

1609# 54 ITRF2000@1997xITRF94 xform=TRFXform7Tuple(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0) 

1610# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1611# 55 ITRF2000@1997xITRF96 xform=TRFXform7Tuple(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0) 

1612# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1613# 56 ITRF97@1997xITRF96 xform=TRFXform7Tuple(tx=-2.07, ty=-0.21, tz=9.95, s=-0.93496, sx=0.1267, sy=-0.22355, sz=-0.06065) 

1614# rates=TRFXform7Tuple(tx=0.69, ty=-0.1, tz=1.86, s=-0.19201, sx=0.01347, sy=-0.01514, sz=0.00027) 

1615# 57 ITRF2000@1997xITRF97 xform=TRFXform7Tuple(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0) 

1616# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=-0.02) 

1617# 58 ITRF2000@1997xNAD83 xform=TRFXform7Tuple(tx=995.6, ty=-1901.3, tz=-521.5, s=0.615, sx=-25.915, sy=-9.426, sz=-11.599) 

1618# rates=TRFXform7Tuple(tx=0.7, ty=-0.7, tz=0.5, s=-0.182, sx=-0.06667, sy=0.75744, sz=0.05133) 

1619# 59 ITRF2005@1997xNAD83 xform=TRFXform7Tuple(tx=996.3, ty=-1902.4, tz=-521.9, s=0.775, sx=-25.915, sy=-9.426, sz=-11.599) 

1620# rates=TRFXform7Tuple(tx=0.5, ty=-0.6, tz=-1.3, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133) 

1621# 60 ITRF96@1997xNAD83 xform=TRFXform7Tuple(tx=991.0, ty=-190.72, tz=-512.9, s=0.0, sx=25.79, sy=9.65, sz=11.66) 

1622# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0532, sy=-0.7423, sz=-0.0316) 

1623# 61 ITRF2005@2020xGDA2020 xform=TRFXform7Tuple(tx=40.32, ty=-33.85, tz=-16.72, s=4.286, sx=-1.2893, sy=-0.8492, sz=-0.3342) 

1624# rates=TRFXform7Tuple(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701) 

1625# 62 ITRF2005@2000xITRF2000 xform=TRFXform7Tuple(tx=0.1, ty=-0.8, tz=-5.8, s=0.4, sx=0.0, sy=0.0, sz=0.0) 

1626# rates=TRFXform7Tuple(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0) 

1627# 63 ITRF2008@1994xGDA94 xform=TRFXform7Tuple(tx=-84.68, ty=-19.42, tz=32.01, s=9.71, sx=-0.4254, sy=2.2578, sz=2.4015) 

1628# rates=TRFXform7Tuple(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551) 

1629# 64 ITRF2008@1997xNAD83 xform=TRFXform7Tuple(tx=993.43, ty=-1903.31, tz=-526.55, s=1.71504, sx=-25.91467, sy=-9.42645, sz=-11.59935) 

1630# rates=TRFXform7Tuple(tx=0.79, ty=-0.6, tz=-1.34, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133) 

1631# 65 ITRF2008@2015xETRF2000 xform=TRFXform7Tuple(tx=53.6, ty=50.8, tz=-85.5, s=2.54, sx=2.106, sy=12.74, sz=-20.592) 

1632# rates=TRFXform7Tuple(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792) 

1633# 66 ITRF2008@2015xETRF2014 xform=TRFXform7Tuple(tx=-1.6, ty=-1.9, tz=-1.9, s=-0.13, sx=2.21, sy=13.806, sz=-20.02) 

1634# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77) 

1635# 67 ITRF2008@2015xETRF2020 xform=TRFXform7Tuple(tx=3.0, ty=2.8, tz=0.5, s=0.55, sx=2.236, sy=13.494, sz=-19.578) 

1636# rates=TRFXform7Tuple(tx=0.0, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753) 

1637# 68 ITRF2008@2020xGDA2020 xform=TRFXform7Tuple(tx=13.79, ty=4.55, tz=15.22, s=2.5, sx=0.2808, sy=0.2677, sz=-0.4638) 

1638# rates=TRFXform7Tuple(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551) 

1639# 69 ITRF2008@2000xITRF2000 xform=TRFXform7Tuple(tx=-1.9, ty=-1.7, tz=-10.5, s=1.34, sx=0.0, sy=0.0, sz=0.0) 

1640# rates=TRFXform7Tuple(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0) 

1641# 70 ITRF2008@2000xITRF88 xform=TRFXform7Tuple(tx=22.8, ty=2.6, tz=-125.2, s=10.41, sx=0.1, sy=0.0, sz=0.06) 

1642# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1643# 71 ITRF2008@2000xITRF89 xform=TRFXform7Tuple(tx=27.8, ty=38.6, tz=-101.2, s=7.31, sx=0.0, sy=0.0, sz=0.06) 

1644# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1645# 72 ITRF2008@2000xITRF90 xform=TRFXform7Tuple(tx=22.8, ty=14.6, tz=-63.2, s=3.91, sx=0.0, sy=0.0, sz=0.06) 

1646# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1647# 73 ITRF2008@2000xITRF91 xform=TRFXform7Tuple(tx=24.8, ty=18.6, tz=-47.2, s=3.61, sx=0.0, sy=0.0, sz=0.06) 

1648# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1649# 74 ITRF2008@2000xITRF92 xform=TRFXform7Tuple(tx=12.8, ty=4.6, tz=-41.2, s=2.21, sx=0.0, sy=0.0, sz=0.06) 

1650# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1651# 75 ITRF2008@2000xITRF93 xform=TRFXform7Tuple(tx=-24.0, ty=2.4, tz=-38.6, s=3.41, sx=-1.71, sy=-1.48, sz=-0.3) 

1652# rates=TRFXform7Tuple(tx=-2.8, ty=-0.1, tz=-2.4, s=0.09, sx=-0.11, sy=-0.19, sz=0.07) 

1653# 76 ITRF2008@2000xITRF94 xform=TRFXform7Tuple(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06) 

1654# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1655# 77 ITRF2008@2000xITRF96 xform=TRFXform7Tuple(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06) 

1656# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1657# 78 ITRF2008@2000xITRF97 xform=TRFXform7Tuple(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06) 

1658# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1659# 79 ITRF2008@2005xITRF2005 xform=TRFXform7Tuple(tx=-0.5, ty=-0.9, tz=-4.7, s=0.94, sx=0.0, sy=0.0, sz=0.0) 

1660# rates=TRFXform7Tuple(tx=0.3, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1661# 80 ITRF2014@2015xETRF2000 xform=TRFXform7Tuple(tx=55.2, ty=52.7, tz=-83.6, s=2.67, sx=2.106, sy=12.74, sz=-20.592) 

1662# rates=TRFXform7Tuple(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.081, sy=0.49, sz=-0.792) 

1663# 81 ITRF2014@2015xETRF2014 xform=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=2.21, sy=13.806, sz=-20.02) 

1664# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.085, sy=0.531, sz=-0.77) 

1665# 82 ITRF2014@2015xETRF2020 xform=TRFXform7Tuple(tx=1.4, ty=0.9, tz=-1.4, s=0.42, sx=2.236, sy=13.494, sz=-19.578) 

1666# rates=TRFXform7Tuple(tx=0.0, ty=0.1, tz=-0.2, s=0.0, sx=0.086, sy=0.519, sz=-0.753) 

1667# 83 ITRF2014@2020xGDA2020 xform=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1668# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=1.50379, sy=1.18346, sz=1.20716) 

1669# 84 ITRF2014@2010xITRF2000 xform=TRFXform7Tuple(tx=0.7, ty=1.2, tz=-26.1, s=2.12, sx=0.0, sy=0.0, sz=0.0) 

1670# rates=TRFXform7Tuple(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.0, sy=0.0, sz=0.0) 

1671# 85 ITRF2014@2010xITRF2005 xform=TRFXform7Tuple(tx=2.6, ty=1.0, tz=-2.3, s=0.92, sx=0.0, sy=0.0, sz=0.0) 

1672# rates=TRFXform7Tuple(tx=0.3, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0) 

1673# 86 ITRF2014@2010xITRF2008 xform=TRFXform7Tuple(tx=1.6, ty=1.9, tz=2.4, s=-0.02, sx=0.0, sy=0.0, sz=0.0) 

1674# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0) 

1675# 87 ITRF2014@2010xITRF88 xform=TRFXform7Tuple(tx=25.4, ty=-0.5, tz=-154.8, s=11.29, sx=0.1, sy=0.0, sz=0.26) 

1676# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1677# 88 ITRF2014@2010xITRF89 xform=TRFXform7Tuple(tx=30.4, ty=35.5, tz=-130.8, s=8.19, sx=0.0, sy=0.0, sz=0.26) 

1678# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1679# 89 ITRF2014@2010xITRF90 xform=TRFXform7Tuple(tx=25.4, ty=11.5, tz=-92.8, s=4.79, sx=0.0, sy=0.0, sz=0.26) 

1680# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1681# 90 ITRF2014@2010xITRF91 xform=TRFXform7Tuple(tx=27.4, ty=15.5, tz=-76.8, s=4.49, sx=0.0, sy=0.0, sz=0.26) 

1682# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1683# 91 ITRF2014@2010xITRF92 xform=TRFXform7Tuple(tx=15.4, ty=1.5, tz=-70.8, s=3.09, sx=0.0, sy=0.0, sz=0.26) 

1684# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1685# 92 ITRF2014@2010xITRF93 xform=TRFXform7Tuple(tx=-50.4, ty=3.3, tz=-60.2, s=4.29, sx=-2.81, sy=-3.38, sz=0.4) 

1686# rates=TRFXform7Tuple(tx=-2.8, ty=-0.1, tz=-2.5, s=0.12, sx=-0.11, sy=-0.19, sz=0.07) 

1687# 93 ITRF2014@2010xITRF94 xform=TRFXform7Tuple(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26) 

1688# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1689# 94 ITRF2014@2010xITRF96 xform=TRFXform7Tuple(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26) 

1690# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1691# 95 ITRF2014@2010xITRF97 xform=TRFXform7Tuple(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26) 

1692# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1693# 96 ITRF2020@2015xETRF2000 xform=TRFXform7Tuple(tx=53.8, ty=51.8, tz=-82.2, s=2.25, sx=2.106, sy=12.74, sz=-20.592) 

1694# rates=TRFXform7Tuple(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.081, sy=0.49, sz=-0.792) 

1695# 97 ITRF2020@2015xETRF2014 xform=TRFXform7Tuple(tx=-1.4, ty=-0.9, tz=1.4, s=0.42, sx=2.21, sy=13.806, sz=-20.02) 

1696# rates=TRFXform7Tuple(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.085, sy=0.531, sz=-0.77) 

1697# 98 ITRF2020@2015xETRF2020 xform=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=2.236, sy=13.494, sz=-19.578) 

1698# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.086, sy=0.519, sz=-0.753) 

1699# 99 ITRF2020@2015xITRF2000 xform=TRFXform7Tuple(tx=-0.2, ty=0.8, tz=-34.2, s=2.25, sx=0.0, sy=0.0, sz=0.0) 

1700# rates=TRFXform7Tuple(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.0, sy=0.0, sz=0.0) 

1701# 100 ITRF2020@2015xITRF2005 xform=TRFXform7Tuple(tx=2.7, ty=0.1, tz=-1.4, s=0.65, sx=0.0, sy=0.0, sz=0.0) 

1702# rates=TRFXform7Tuple(tx=0.3, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0) 

1703# 101 ITRF2020@2015xITRF2008 xform=TRFXform7Tuple(tx=0.2, ty=1.0, tz=3.3, s=-0.29, sx=0.0, sy=0.0, sz=0.0) 

1704# rates=TRFXform7Tuple(tx=0.0, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0) 

1705# 102 ITRF2020@2015xITRF2014 xform=TRFXform7Tuple(tx=-1.4, ty=-0.9, tz=1.4, s=-0.42, sx=0.0, sy=0.0, sz=0.0) 

1706# rates=TRFXform7Tuple(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1707# 103 ITRF2020@2015xITRF88 xform=TRFXform7Tuple(tx=24.5, ty=-3.9, tz=-169.9, s=11.47, sx=0.1, sy=0.0, sz=0.36) 

1708# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1709# 104 ITRF2020@2015xITRF89 xform=TRFXform7Tuple(tx=29.5, ty=32.1, tz=-145.9, s=8.37, sx=0.0, sy=0.0, sz=0.36) 

1710# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1711# 105 ITRF2020@2015xITRF90 xform=TRFXform7Tuple(tx=24.5, ty=8.1, tz=-107.9, s=4.97, sx=0.0, sy=0.0, sz=0.36) 

1712# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1713# 106 ITRF2020@2015xITRF91 xform=TRFXform7Tuple(tx=26.5, ty=12.1, tz=-91.9, s=4.67, sx=0.0, sy=0.0, sz=0.36) 

1714# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1715# 107 ITRF2020@2015xITRF92 xform=TRFXform7Tuple(tx=14.5, ty=-1.9, tz=-85.9, s=3.27, sx=0.0, sy=0.0, sz=0.36) 

1716# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1717# 108 ITRF2020@2015xITRF93 xform=TRFXform7Tuple(tx=-65.8, ty=1.9, tz=-71.3, s=4.47, sx=-3.36, sy=-4.33, sz=0.75) 

1718# rates=TRFXform7Tuple(tx=-2.8, ty=-0.2, tz=-2.3, s=0.12, sx=-0.11, sy=-0.19, sz=0.07) 

1719# 109 ITRF2020@2015xITRF94 xform=TRFXform7Tuple(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36) 

1720# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1721# 110 ITRF2020@2015xITRF96 xform=TRFXform7Tuple(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36) 

1722# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1723# 111 ITRF2020@2015xITRF97 xform=TRFXform7Tuple(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36) 

1724# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)