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 _float as _F, _0_0s, _0_0, _0_001, _0_5, _1_0 

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__ = '24.02.09' 

90 

91_EP0CH = Epoch(0, low=0) 

92_Es = {_EP0CH: _EP0CH} # L{Epoch}s de_dup, deleted below 

93_GRS80 = Datums.GRS80 

94_inverse_ = 'inverse' 

95_MAS = _MM = _PPB = Float # Units 

96_MM2M = _0_001 # scale mm2m, ppb2ppM, mas2as 

97_mDays = (0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 0) 

98_366_0 = _F(sum(_mDays)) 

99_Ps = {} # L{TRFXform7Tuple}s de-dup, deleted below 

100_v_ = 'v' 

101 

102_ETRF88_ = _i('ETRF88') 

103_ETRF89_ = _i('ETRF89') 

104_ETRF90_ = _i('ETRF90') 

105_ETRF91_ = _i('ETRF91') 

106_ETRF92_ = _i('ETRF92') 

107_ETRF93_ = _i('ETRF93') 

108_ETRF94_ = _i('ETRF94') 

109_ETRF96_ = _i('ETRF96') 

110_ETRF97_ = _i('ETRF97') 

111_ETRF2000_ = _i('ETRF2000') 

112_ETRF2005_ = _i('ETRF2005') 

113_ETRF2008_ = _i('ETRF2008') 

114_ETRF2014_ = _i('ETRF2014') 

115_ETRF2020_ = _i('ETRF2020') 

116_GDA94_ = _i('GDA94') 

117_GDA2020_ = _i('GDA2020') 

118_ITRF_ = _i('ITRF') 

119_ITRF88_ = _i('ITRF88') 

120_ITRF89_ = _i('ITRF89') 

121_ITRF90_ = _i('ITRF90') 

122_ITRF91_ = _i('ITRF91') 

123_ITRF92_ = _i('ITRF92') 

124_ITRF93_ = _i('ITRF93') 

125_ITRF94_ = _i('ITRF94') 

126_ITRF96_ = _i('ITRF96') 

127_ITRF97_ = _i('ITRF97') 

128_ITRF2000_ = _i('ITRF2000') 

129_ITRF2005_ = _i('ITRF2005') 

130_ITRF2008_ = _i('ITRF2008') 

131_ITRF2014_ = _i('ITRF2014') 

132_ITRF2020_ = _i('ITRF2020') 

133_WGS84g1150_ = _i('WGS84g1150') 

134_WGS84g1674_ = _i('WGS84g1674') 

135_WGS84g1762_ = _i('WGS84g1762') 

136# del _i 

137 

138 

139def _E(epoch): # deleted below 

140 '''(INTERNAL) De-dup L{Epochs}s. 

141 ''' 

142 e = Epoch(_F(epoch)) 

143 return _Es.setdefault(e, e) # PYCHOK deleted 

144 

145 

146def _xellipsoidal(point): 

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

148 ''' 

149 m = _MODS.ellipsoidalBase 

150 _xinstanceof(m.CartesianEllipsoidalBase, 

151 m.LatLonEllipsoidalBase, point=point) 

152 return isinstance(point, m.CartesianEllipsoidalBase) 

153 

154 

155class RefFrame(_NamedEnumItem): 

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

157 ''' 

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

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

160 

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

162 '''New L{RefFrame}. 

163 

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

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

166 or L{a_f2Tuple}). 

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

168 

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

170 

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

172 

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

174 ''' 

175 if datum is not _GRS80: 

176 _earth_datum(self, datum, raiser=_datum_) 

177 self._epoch = _Epoch(epoch) 

178 self._Xs = {} # dict of Xforms 

179 if name: 

180 self._register(RefFrames, name) 

181 

182 def __eq__(self, other): 

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

184 and other.datum == self.datum 

185 

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

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

188 or self.epoch < other.epoch) 

189 

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

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

192 

193 @see: Method C{toRefFrame}. 

194 ''' 

195 _xellipsoidal(point) 

196 return point.toRefFrame(self) 

197 

198 @property_RO 

199 def datum(self): 

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

201 ''' 

202 return self._datum 

203 

204 @Property_RO 

205 def ellipsoid(self): 

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

207 ''' 

208 return self._datum.ellipsoid 

209 

210 @Property_RO 

211 def epoch(self): 

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

213 ''' 

214 return self._epoch 

215 

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

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

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

219 

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

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

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

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

224 

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

226 

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

228 

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

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

231 

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

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

234 for more details. 

235 ''' 

236 _xellipsoidal(point) 

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

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

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

240 

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

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

243 

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

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

246 reframe's name. 

247 

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

249 ''' 

250 D = self.datum 

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

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

253 Fmt.EQUAL(epoch=e), 

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

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

256 

257 def Xform(self, reframe2): 

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

259 

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

261 

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

263 

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

265 ''' 

266 _xinstanceof(RefFrame, str, reframe2=reframe2) 

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

268 return self._Xs.get(n2, None) 

269 

270 def Xforms(self, inverse=False): 

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

272 

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

274 

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

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

277 ''' 

278 def _Xi(n2): 

279 for n1, r in RefFrames.items(): 

280 if n2 in r._Xs: 

281 yield n1, r 

282 

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

284 

285 

286class RefFrames(_NamedEnum): 

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

288 to accommodate the L{_LazyNamedEnumItem} properties. 

289 ''' 

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

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

292 ''' 

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

294 

295RefFrames = RefFrames(RefFrame) # PYCHOK singleton 

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

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

298RefFrames._assert( 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

334 

335 

336class TransformXform(Transform): 

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

338 

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

340 ''' 

341 _Xform = None 

342 

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

344 '''New L{TransformXform}. 

345 

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

347 

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

349 

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

351 if its C{Xform} was I{inversed}. 

352 ''' 

353 Transform.__init__(self, **tx_ty_tz_s_sx_sy_sz) 

354 if name: 

355 self.name = name 

356 

357 def __eq__(self, other): 

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

359 

360 def rename(self, name=NN): 

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

362 

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

364 the base name. 

365 

366 @return: The old name (C{str}). 

367 ''' 

368 X = self.Xform 

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

370 

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

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

373 

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

375 

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

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

378 

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

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

381 but I{not} taken into account. 

382 ''' 

383 C = _xellipsoidal(point) 

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

385 r = c.toTransforms_(self) 

386 if not C: # i.e. back to LatLon 

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

388 LatLon=point.classof) 

389 X = self.Xform 

390 if X: 

391 r.reframe = X.reframe2 

392 r.epoch = X.epoch 

393 

394 r.rename(name or self.name) 

395 return r 

396 

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

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

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

400 

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

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

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

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

405 L{toTransform<TRFXform.toTransform>}. 

406 

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

408 

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

410 missing Xform. 

411 ''' 

412 X = self.Xform 

413 if not X: 

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

415 X = X.dup(epoch=epoch1) 

416 _ = X.rename() 

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

418 

419 def velocities(self, factor=_MM2M): 

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

421 

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

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

424 

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

426 

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

428 

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

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

431 ''' 

432 v = self.Xform 

433 if v is not None: 

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

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

436 s1=0, name=NN(self.name, _v_)) 

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

438 return v 

439 

440 @Property 

441 def Xform(self): 

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

443 ''' 

444 return self._Xform 

445 

446 @Xform.setter # PYCHOK setter! 

447 def Xform(self, Xform): 

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

449 

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

451 ''' 

452 _xinstanceof(TRFXform, Xform=Xform) 

453 self._Xform = Xform 

454 

455 

456class TRFXform7Tuple(_NamedTuple): 

457 '''7-Tuple C{(tx, ty, tz, s, sx, sy, sz)} of conversion parameters with 

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

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

460 

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

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

463 

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

465 ''' 

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

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

468 

469 def __add__(self, other): 

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

471 ''' 

472 _xinstanceof(TRFXform7Tuple, other=other) 

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

474 name=_PLUS_) # .fsums._add_op_ 

475 

476 def __eq__(self, other): 

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

478 _zip(self, other)) 

479 

480 def __hash__(self): 

481 return self._hash # memoized 

482 

483 def __mul__(self, factor): 

484 _xisscalar(factor=factor) 

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

486 

487 def __neg__(self): 

488 return self.inverse() 

489 

490 @Property_RO 

491 def _hash(self): 

492 return hash(s for s in self) 

493 

494 def inverse(self, name=NN): 

495 '''Return the inverse of this transform. 

496 

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

498 

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

500 ''' 

501 n = name or _minus(self.name) 

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

503 

504 @Property_RO 

505 def isunity(self): 

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

507 ''' 

508 return not any(self) 

509 

510 

511class TRFXform(_Named): 

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

513 reference frames observed at an C{epoch}. 

514 ''' 

515 _epoch = _EP0CH 

516 _epoch_d = _0_0 

517 _indir_d = \ 

518 _inver_d = False 

519 refName1 = \ 

520 refName2 = NN 

521 rates = \ 

522 xform = TRFXform7Tuple(_0_0s(len( 

523 TRFXform7Tuple._Names_))) 

524 

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

526 xform=None, rates=None, name=NN): 

527 '''New L{trfXform}. 

528 

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

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

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

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

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

534 but in C{units-per-year}. 

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

536 

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

538 

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

540 ''' 

541 self.refName1 = str(refName1) 

542 self.refName2 = str(refName2) 

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

544 self.epoch = epoch 

545 self.xform = xform 

546 self.rates = rates 

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

548 

549 def __eq__(self, other): 

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

551 self.xform == other.xform and self.rates == other.rates 

552 

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

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

555 or self.refName2 < other.refName2 

556 or self.epoch < other.epoch) 

557 

558 def __neg__(self): 

559 return self.inverse() 

560 

561 def __repr__(self): 

562 return self.toRepr() 

563 

564 def _at(self, epoch): 

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

566 ''' 

567 n = self.name 

568 if epoch != self.epoch: 

569 _e = _AT_(NN, epoch) 

570 if not n.endswith(_e): 

571 n = NN(n, _e) 

572 return n 

573 

574 @Property 

575 def epoch(self): 

576 '''Get the epoch (L{Epoch}). 

577 ''' 

578 return self._epoch 

579 

580 @epoch.setter # PYCHOK setter! 

581 def epoch(self, epoch): 

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

583 

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

585 ''' 

586 e = _Epoch(epoch) 

587 if self._epoch != e: 

588 self._epoch = e 

589 self.rename(self._at(e)) 

590 

591 @property_RO 

592 def epoched(self): 

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

594 ''' 

595 return self._epoch_d 

596 

597 def _7Helmert(self, epoch, factor=_MM2M): 

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

599 and converted by I{signed} factor C{factor} (C{dict}). 

600 ''' 

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

602 # dict((self.toEpoch(epoch).xform * factor).items()) 

603 return dict((n, (x + r * e) * factor) for n, x, r in 

604 _zip(TRFXform7Tuple._Names_, self.xform, self.rates)) 

605 

606 def inverse(self, name=NN): 

607 '''Return the inverse of this Xform. 

608 

609 @return: Inverse (L{TRFXform}). 

610 ''' 

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

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

613 name=name or _minus(self.name), 

614 _inver_d=not self.inversed) 

615 

616 @property_RO 

617 def indirected(self): 

618 '''Is this an I{indirected} Xform? (C{bool}). 

619 ''' 

620 return self._indir_d 

621 

622 @property_RO 

623 def inversed(self): 

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

625 ''' 

626 return self._inver_d 

627 

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

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

630 ''' 

631 r = RefFrames.get(name) 

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

633 r = RefFrame(self.epoch, datum) 

634 r.name = name # unregistered 

635 return r 

636 

637 @property_RO 

638 def reframe1(self): 

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

640 ''' 

641 return self._reframe(self.refName1) 

642 

643 @property_RO 

644 def reframe2(self): 

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

646 ''' 

647 return self._reframe(self.refName2) 

648 

649 def rename(self, name=NN): 

650 '''Change this Xform's name. 

651 

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

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

654 

655 @return: The old name (C{str}). 

656 ''' 

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

658 

659 def toEpoch(self, epoch): 

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

661 

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

663 or C{str}). 

664 

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

666 

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

668 ''' 

669 e = _Epoch(epoch) - self.epoch 

670 if e: 

671 t = self.xform + self.rates * e 

672 X = self.dup(epoch=epoch, xform=t, 

673 name=self._at(epoch)) 

674 X._epoch_d += e 

675 else: 

676 X = self 

677 return X 

678 

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

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

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

682 

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

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

685 this Xform's C{epoch}. 

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

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

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

689 C{B{name}=NN}. 

690 

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

692 

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

694 ''' 

695 def _r(name): 

696 r = RefFrames.get(name) 

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

698 r = RefFrame(self.epoch, datum) 

699 r.name = name # unregistered 

700 return r 

701 

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

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

704 

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

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

707 ''' 

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

709 

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

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

712 

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

714 ''' 

715 e = epoch or self.epoch 

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

717 

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

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

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

721 

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

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

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

725 

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

727 

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

729 

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

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

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

733 ''' 

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

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

736 if inverse: 

737 X = X.inverse() 

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

739 H.Xform = X 

740 X.epoch = e 

741 return H 

742 

743 

744def date2epoch(year, month, day): 

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

746 

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

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

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

750 

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

752 

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

754 

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

756 29 days in February. 

757 ''' 

758 try: 

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

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

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

762 return Epoch(e, low=0) 

763 

764 raise ValueError # _invalid_ 

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

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

767 

768 

769def epoch2date(epoch): 

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

771 

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

773 

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

775 

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

777 

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

779 29 days in February. 

780 ''' 

781 e = _Epoch(epoch, low=0) 

782 y = int(e) 

783 d = int(ceil(_366_0 * (e - y))) 

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

785 if d > n: 

786 d -= n 

787 else: 

788 break 

789 return y, (m + 1), max(1, d) 

790 

791 

792def _Epoch(e, **kwds): 

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

794 ''' 

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

796 

797 

798def _eT0Ds4(inst, reframe, epoch, reframe2, epoch2): 

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

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

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

802 ''' 

803 r = reframe or inst.reframe 

804 if not r: 

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

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

807 

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

809 

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

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

812 

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

814 if t0 is None: 

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

816 _to_, _AT_(reframe2.name, e2)) 

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

818 

819 if t0: # not () 

820 e2 = t0.Xform.epoch 

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

822 

823 

824def _direct(n1, n2): 

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

826 ''' 

827 X = RefFrames.get(n1) 

828 if X: 

829 X = X._Xs.get(n2, None) 

830 return X 

831 

832 

833def _indirects(n1, n2): 

834 '''(INTERNAL) Yield all Xforms "between" C{n1} and C{n2}. 

835 ''' 

836 def _X3(_Xs, n2): 

837 for n, X1 in _Xs.items(): 

838 X2 = _direct(n, n2) 

839 if X2: 

840 yield X1, X2, True # + 

841 X2 = _direct(n2, n) 

842 if X2: 

843 yield X1, X2, False # - 

844 

845 r = RefFrames.get(n1) 

846 if r: 

847 for X1, X2, f in _X3(r._Xs, n2): 

848 e1, e2 = X1.epoch, X2.epoch 

849 if e1 < e2: # X1 to e2 

850 X1 = X1.toEpoch(e2) 

851 e1 = e2 

852 elif e1 > e2: # X2 to e1 

853 X2 = X2.toEpoch(e1) 

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

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

856 X = TRFXform(n1, n2, epoch=e1, 

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

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

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

860 X2._at(e1))) 

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

862 X._indir_d = True # reframe? 

863 yield X 

864 

865 

866def _P(*ps): # deleted below 

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

868 ''' 

869 t = TRFXform7Tuple(map(_F, ps)) 

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

871 

872 

873def _reframe(**name_reframe): 

874 '''(INTERNAL) Get a C{reframe}. 

875 ''' 

876 if len(name_reframe) == 1: 

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

878 break 

879 if isstr(r): 

880 r = RefFrames.get(r) 

881 if r and isinstance(r, RefFrame): 

882 return r 

883 raise TRFError(**name_reframe) # _invalid_ 

884 

885 

886def _toTransform0(n1, e1, n2, e2, **indirect_inverse): 

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

888 ''' 

889 if (n1 == n2 and e1 == e2): 

890 return () # unity? 

891 

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

893 return X # first OK? 

894 

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

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

897 return () # unity? 

898 

899 return None 

900 

901 

902def _toTransforms(n1, e1, n2, e2, indirect=True, inverse=True): 

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

904 ''' 

905 def _k(X): 

906 return -X.epoch 

907 

908 X = _direct(n1, n2) 

909 if X: 

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

911 

912 if inverse: 

913 X = _direct(n2, n1) 

914 if X: 

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

916 

917 if indirect: 

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

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

920 

921 if inverse: 

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

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

924 

925 

926def trfTransform0(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True): 

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

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

929 

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

931 C{None} if no conversion exists. 

932 

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

934 ''' 

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

936 indirect=indirect, inverse=inverse) 

937 

938 

939def trfTransforms(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True): 

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

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

942 

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

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

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

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

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

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

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

950 reframe, otherwise only direct transforms between B{C{reframe1} 

951 and B{C{reframe2}} (C{bool}). 

952 @kwarg inverse: If C{True}, include inverse, otherwise only foward transforms 

953 (C{bool}). 

954 

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

956 

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

958 B{C{epoch2}}. 

959 

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

961 ''' 

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

963 indirect=indirect, inverse=inverse) 

964 

965 

966def _trfT0s(_toT0s, reframe, reframe2, epoch, epoch2, **indirect_inverse): 

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

968 ''' 

969 r1 = _reframe(reframe=reframe) 

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

971 r2 = _reframe(reframe2=reframe2) 

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

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

974 

975 

976def trfXform(reframe1, reframe2, epoch=None, xform=None, rates=None): 

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

978 

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

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

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

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

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

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

985 but in C{units-per-year}. 

986 

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

988 

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

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

991 already exists. 

992 ''' 

993 r1 = _reframe(reframe1=reframe1) 

994 r2 = _reframe(reframe2=reframe2) 

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

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

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

998 

999 

1000def _trfX(n1, n2, **epoch_xform_rates): 

1001 '''(INTERNAL) New, I{unique} L{TRFXform} converter. 

1002 ''' 

1003 r1 = RefFrames.get(n1) 

1004 r2 = RefFrames.get(n2) 

1005 if r1 and r2: 

1006 if n2 in r1._Xs: 

1007 t = _exists_ 

1008 elif n1 in r2._Xs: 

1009 t = _SPACE_(_inverse_, _exists_) 

1010 else: 

1011 r1._Xs[n2] = X = TRFXform(n1, n2, **epoch_xform_rates) 

1012 return X 

1013 else: 

1014 t = _invalid_ 

1015 raise TRFError(TRFXform=_SPACE_(n1, _to_, n2), txt=t) # _NameError 

1016 

1017 

1018# TRF conversions specified as an epoch and 2 sets of 7-parameters. Most from Altamimi, Z. U{"EUREF Technical 

1019# Note 1: Relationship and Transformation between the International and the European Terrestrial Reference 

1020# Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Appendix A, more at U{Quinsy QPS <https:// 

1021# confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ITRF_Transformation_Parameters.xlsx>}. 

1022# See also U{Quinsy International Terrestrial Reference Frame 2014 (ITRF2014)<https://confluence.QPS.NL/qinsy/latest/ 

1023# en/international-terrestrial-reference-frame-2014-itrf2014-182618383.html>}. 

1024_trfX(_ITRF2020_, _ITRF2014_, epoch=_E(2015), # <https://ITRF.IGN.Fr/docs/solutions/itrf2020/Transfo-ITRF2020_TRFs.txt> 

1025 xform=_P( -1.4, -0.9, 1.4, -0.42, _0_0, _0_0, _0_0), 

1026 rates=_P( _0_0, -0.1, 0.2, _0_0, _0_0, _0_0, _0_0)) 

1027_trfX(_ITRF2020_, _ITRF2008_, epoch=_E(2015), 

1028 xform=_P( 0.2, 1.0, 3.3, -0.29, _0_0, _0_0, _0_0), 

1029 rates=_P( _0_0, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0)) 

1030_trfX(_ITRF2020_, _ITRF2005_, epoch=_E(2015), 

1031 xform=_P( 2.7, 0.1, -1.4, 0.65, _0_0, _0_0, _0_0), 

1032 rates=_P( 0.3, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0)) 

1033_trfX(_ITRF2020_, _ITRF2000_, epoch=_E(2015), 

1034 xform=_P( -0.2, 0.8, -34.2, 2.25, _0_0, _0_0, _0_0), 

1035 rates=_P( 0.1, _0_0, -1.7, 0.11, _0_0, _0_0, _0_0)) 

1036_trfX(_ITRF2020_, _ITRF97_, epoch=_E(2015), 

1037 xform=_P( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36), 

1038 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1039_trfX(_ITRF2020_, _ITRF96_, epoch=_E(2015), 

1040 xform=_P( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36), 

1041 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1042_trfX(_ITRF2020_, _ITRF94_, epoch=_E(2015), 

1043 xform=_P( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36), 

1044 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1045_trfX(_ITRF2020_, _ITRF93_, epoch=_E(2015), 

1046 xform=_P( -65.8, 1.9, -71.3, 4.47, -3.36, -4.33, 0.75), 

1047 rates=_P( -2.8, -0.2, -2.3, 0.12, -0.11, -0.19, 0.07)) 

1048_trfX(_ITRF2020_, _ITRF92_, epoch=_E(2015), 

1049 xform=_P( 14.5, -1.9, -85.9, 3.27, _0_0, _0_0, 0.36), 

1050 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1051_trfX(_ITRF2020_, _ITRF91_, epoch=_E(2015), 

1052 xform=_P( 26.5, 12.1, -91.9, 4.67, _0_0, _0_0, 0.36), 

1053 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1054_trfX(_ITRF2020_, _ITRF90_, epoch=_E(2015), 

1055 xform=_P( 24.5, 8.1, -107.9, 4.97, _0_0, _0_0, 0.36), 

1056 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1057_trfX(_ITRF2020_, _ITRF89_, epoch=_E(2015), 

1058 xform=_P( 29.5, 32.1, -145.9, 8.37, _0_0, _0_0, 0.36), 

1059 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1060_trfX(_ITRF2020_, _ITRF88_, epoch=_E(2015), 

1061 xform=_P( 24.5, -3.9, -169.9, 11.47, 0.1, _0_0, 0.36), 

1062 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02)) 

1063 

1064# see U{Transformation Parameters ITRF2014<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2014_ITRFs.txt>} and 

1065# Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and 

1066# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1.pdf>} Appendix A. 

1067_trfX(_ITRF2014_, _ITRF2008_, epoch=(2010), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2014/tp_14-08.php> 

1068 xform=_P( 1.6, 1.9, 2.4, -0.02, _0_0, _0_0, _0_0), 

1069 rates=_P( _0_0, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0)) 

1070_trfX(_ITRF2014_, _ITRF2005_, epoch=_E(2010), 

1071 xform=_P( 2.6, _1_0, -2.3, 0.92, _0_0, _0_0, _0_0), 

1072 rates=_P( 0.3, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0)) 

1073_trfX(_ITRF2014_, _ITRF2000_, epoch=_E(2010), 

1074 xform=_P( 0.7, 1.2, -26.1, 2.12, _0_0, _0_0, _0_0), 

1075 rates=_P( 0.1, 0.1, -1.9, 0.11, _0_0, _0_0, _0_0)) 

1076_trfX(_ITRF2014_, _ITRF97_, epoch=_E(2010), 

1077 xform=_P( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26), 

1078 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1079_trfX(_ITRF2014_, _ITRF96_, epoch=_E(2010), 

1080 xform=_P( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26), 

1081 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1082_trfX(_ITRF2014_, _ITRF94_, epoch=_E(2010), 

1083 xform=_P( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26), 

1084 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1085_trfX(_ITRF2014_, _ITRF93_, epoch=_E(2010), 

1086 xform=_P( -50.4, 3.3, -60.2, 4.29, -2.81, -3.38, 0.4), 

1087 rates=_P( -2.8, -0.1, -2.5, 0.12, -0.11, -0.19, 0.07)) 

1088_trfX(_ITRF2014_, _ITRF92_, epoch=_E(2010), 

1089 xform=_P( 15.4, 1.5, -70.8, 3.09, _0_0, _0_0, 0.26), 

1090 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1091_trfX(_ITRF2014_, _ITRF91_, epoch=_E(2010), 

1092 xform=_P( 27.4, 15.5, -76.8, 4.49, _0_0, _0_0, 0.26), 

1093 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1094_trfX(_ITRF2014_, _ITRF90_, epoch=_E(2010), 

1095 xform=_P( 25.4, 11.5, -92.8, 4.79, _0_0, _0_0, 0.26), 

1096 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1097_trfX(_ITRF2014_, _ITRF89_, epoch=_E(2010), 

1098 xform=_P( 30.4, 35.5, -130.8, 8.19, _0_0, _0_0, 0.26), 

1099 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1100_trfX(_ITRF2014_, _ITRF88_, epoch=_E(2010), 

1101 xform=_P( 25.4, -0.5, -154.8, 11.29, 0.1, _0_0, 0.26), 

1102 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02)) 

1103 

1104# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference 

1105# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 1st and 2nd column 

1106_trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2005), 

1107 xform=_P( -0.5, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0), 

1108 rates=_P( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0)) 

1109# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(1997), 

1110# xform=_P( -2.9, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0), 

1111# rates=_P( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0)) 

1112# see U{Transformation Parameters ITRF2008<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2008_ITRFs.txt>} 

1113# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2008/tp_08-05.php> 

1114# xform=_P( -2.0, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0), 

1115# rates=_P( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0)) 

1116_trfX(_ITRF2008_, _ITRF2000_, epoch=_E(2000), 

1117 xform=_P( -1.9, -1.7, -10.5, 1.34, _0_0, _0_0, _0_0), 

1118 rates=_P( 0.1, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0)) 

1119_trfX(_ITRF2008_, _ITRF97_, epoch=_E(2000), 

1120 xform=_P( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06), 

1121 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1122_trfX(_ITRF2008_, _ITRF96_, epoch=_E(2000), 

1123 xform=_P( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06), 

1124 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1125_trfX(_ITRF2008_, _ITRF94_, epoch=_E(2000), 

1126 xform=_P( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06), 

1127 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1128_trfX(_ITRF2008_, _ITRF93_, epoch=_E(2000), 

1129 xform=_P( -24.0, 2.4, -38.6, 3.41, -1.71, -1.48, -0.3), 

1130 rates=_P( -2.8, -0.1, -2.4, 0.09, -0.11, -0.19, 0.07)) 

1131_trfX(_ITRF2008_, _ITRF92_, epoch=_E(2000), 

1132 xform=_P( 12.8, 4.6, -41.2, 2.21, _0_0, _0_0, 0.06), 

1133 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1134_trfX(_ITRF2008_, _ITRF91_, epoch=_E(2000), 

1135 xform=_P( 24.8, 18.6, -47.2, 3.61, _0_0, _0_0, 0.06), 

1136 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1137_trfX(_ITRF2008_, _ITRF90_, epoch=_E(2000), 

1138 xform=_P( 22.8, 14.6, -63.2, 3.91, _0_0, _0_0, 0.06), 

1139 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1140_trfX(_ITRF2008_, _ITRF89_, epoch=_E(2000), 

1141 xform=_P( 27.8, 38.6, -101.2, 7.31, _0_0, _0_0, 0.06), 

1142 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1143_trfX(_ITRF2008_, _ITRF88_, epoch=_E(2000), 

1144 xform=_P( 22.8, 2.6, -125.2, 10.41, 0.1, _0_0, 0.06), 

1145 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02)) 

1146 

1147# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference 

1148# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 3rd column 

1149# _trfX(_ITRF2005_, _ITRF2000_, epoch=_E(1997), 

1150# xform=_P( 0.7, -1.1, -0.4, 0.16, -0.2, 0.1 -1.8), 

1151# rates=_P( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0)) 

1152_trfX(_ITRF2005_, _ITRF2000_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2005/tp_05-00.php> 

1153 xform=_P( 0.1, -0.8, -5.8, 0.4, _0_0, _0_0, _0_0), 

1154 rates=_P( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0)) 

1155 

1156_trfX(_ITRF2000_, _ITRF97_, epoch=_E(1997), 

1157 xform=_P( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0), 

1158 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, -0.02)) # 0.02? 

1159_trfX(_ITRF2000_, _ITRF96_, epoch=_E(1997), 

1160 xform=_P( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0), 

1161 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1162_trfX(_ITRF2000_, _ITRF94_, epoch=_E(1997), 

1163 xform=_P( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0), 

1164 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1165_trfX(_ITRF2000_, _ITRF93_, epoch=_E(1988), 

1166 xform=_P( 12.7, 6.5, -20.9, 1.95, -0.39, 0.8, -1.14), 

1167 rates=_P( -2.9, -0.2, -0.6, 0.01, -0.11, -0.19, 0.07)) 

1168_trfX(_ITRF2000_, _ITRF92_, epoch=_E(1988), 

1169 xform=_P( 1.47, 1.35, -1.39, 0.75, _0_0, _0_0, -0.18), 

1170 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1171_trfX(_ITRF2000_, _ITRF91_, epoch=_E(1988), 

1172 xform=_P( 26.7, 27.5, -19.9, 2.15, _0_0, _0_0, -0.18), 

1173 rates=_P( _0_0, -0.6, -1.4, 0.01, _0_0, _0_0, 0.02)) 

1174_trfX(_ITRF2000_, _ITRF90_, epoch=_E(1988), 

1175 xform=_P( 2.47, 2.35, -3.59, 2.45, _0_0, _0_0, -0.18), 

1176 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1177_trfX(_ITRF2000_, _ITRF89_, epoch=_E(1988), 

1178 xform=_P( 2.97, 4.75, -7.39, 5.85, _0_0, _0_0, -0.18), 

1179 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1180_trfX(_ITRF2000_, _ITRF88_, epoch=_E(1988), 

1181 xform=_P( 2.47, 1.15, -9.79, 8.95, 0.1, _0_0, -0.18), 

1182 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02)) 

1183 

1184# Soler, T .& Snay R.A. U{"Transforming Positions and Velocities between the International Terrestrial 

1185# Reference Frame of 2000 and North American Datum of 1983"<https://www.ResearchGate.net/publication/245291390>}, 

1186# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference 

1187# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 5th and 6th column 

1188_trfX(_ITRF97_, _ITRF96_, epoch=_E(1997), 

1189 xform=_P( -2.07, -0.21, 9.95, -0.93496, 0.1267, -0.22355, -0.06065,), 

1190 rates=_P( 0.69, -0.1, 1.86, -0.19201, 0.01347, -0.01514, 0.00027)) 

1191_trfX(_ITRF96_, _NAD83_, epoch=_E(1997), 

1192 xform=_P( 991.0, -190.72, -512.9, _0_0, 25.79, 9.65, 11.66,), 

1193 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.0532, -0.7423, -0.0316,)) 

1194 

1195# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and 

1196# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 1. 

1197# _trfX(_ITRF2020_, _ETRF2020_, epoch=_E(1989), # see Table 2 below 

1198# xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0), 

1199# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753)) 

1200# _trfX(_ITRF2014_, _ETRF2014_, epoch=_E(1989), # see Table 3 below 

1201# xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0), 

1202# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77)) 

1203_trfX(_ITRF2005_, _ETRF2005_, epoch=_E(1989), 

1204 xform=_P( 56.0, 48.0, -37.0, _0_0, _0_0, _0_0, _0_0), 

1205 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.054, 0.518, -0.781)) 

1206# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(1989), # see Table 4 below 

1207# xform=_P( 54.0, 51.0, -48.0, _0_0, _0_0, _0_0, _0_0), 

1208# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792)) 

1209_trfX(_ITRF97_, _ETRF97_, epoch=_E(1989), 

1210 xform=_P( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0), 

1211 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65)) 

1212_trfX(_ITRF96_, _ETRF96_, epoch=_E(1989), 

1213 xform=_P( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0), 

1214 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65)) 

1215_trfX(_ITRF94_, _ETRF94_, epoch=_E(1989), 

1216 xform=_P( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0), 

1217 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65)) 

1218_trfX(_ITRF93_, _ETRF93_, epoch=_E(1989), 

1219 xform=_P( 19.0, 53.0, -21.0, _0_0, _0_0, _0_0, _0_0), 

1220 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.32, 0.78, -0.67)) 

1221_trfX(_ITRF92_, _ETRF92_, epoch=_E(1989), 

1222 xform=_P( 38.0, 40.0, -37.0, 0.0, 0.0, 0.0, 0.0), 

1223 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68)) 

1224_trfX(_ITRF91_, _ETRF91_, epoch=_E(1989), 

1225 xform=_P( 21.0, 25.0, -37.0, _0_0, _0_0, _0_0, _0_0), 

1226 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68)) 

1227_trfX(_ITRF90_, _ETRF90_, epoch=_E(1989), 

1228 xform=_P( 19.0, 28.0, -23.0, _0_0, _0_0, _0_0, _0_0), 

1229 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71)) 

1230_trfX(_ITRF89_, _ETRF89_, epoch=_E(1989), 

1231 xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0), 

1232 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71)) 

1233 

1234# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and 

1235# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 2. 

1236_trfX(_ITRF2020_, _ETRF2020_, epoch=_E(2015), 

1237 xform=_P( _0_0, _0_0, _0_0, _0_0, 2.236, 13.494, -19.578), 

1238 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753)) 

1239_trfX(_ITRF2014_, _ETRF2020_, epoch=_E(2015), 

1240 xform=_P( 1.4, 0.9, -1.4, 0.42, 2.236, 13.494, -19.578), 

1241 rates=_P( _0_0, 0.1, -0.2, _0_0, 0.086, 0.519, -0.753)) 

1242_trfX(_ITRF2008_, _ETRF2020_, epoch=_E(2015), 

1243 xform=_P( 3.0, 2.8, 0.5, 0.55, 2.236, 13.494, -19.578), 

1244 rates=_P( _0_0, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753)) 

1245_trfX(_ITRF2005_, _ETRF2020_, epoch=_E(2015), 

1246 xform=_P( 5.5, 1.9, -4.2, 1.49, 2.236, 13.494, -19.578), 

1247 rates=_P( 0.3, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753)) 

1248_trfX(_ITRF2000_, _ETRF2020_, epoch=_E(2015), 

1249 xform=_P( 2.6, 2.6, -37.0, 3.09, 2.236, 13.494, -19.578), 

1250 rates=_P( 0.1, 0.2, -2.1, 0.11, 0.086, 0.519, -0.753)) 

1251_trfX(_ITRF97_, _ETRF2020_, epoch=_E(2015), 

1252 xform=_P( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218), 

1253 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1254_trfX(_ITRF96_, _ETRF2020_, epoch=_E(2015), 

1255 xform=_P( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218), 

1256 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1257_trfX(_ITRF94_, _ETRF2020_, epoch=_E(2015), 

1258 xform=_P( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218), 

1259 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1260_trfX(_ITRF93_, _ETRF2020_, epoch=_E(2015), 

1261 xform=_P( -63.0, 3.7, -74.1, 5.31, -1.124, 9.164, -18.828), 

1262 rates=_P( -2.8, _0_0, -2.7, 0.12, -0.024, 0.329, -0.683)) 

1263_trfX(_ITRF92_, _ETRF2020_, epoch=_E(2015), 

1264 xform=_P( 17.3, -0.1, -88.7, 4.11, 2.236, 13.494, -19.218), 

1265 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1266_trfX(_ITRF91_, _ETRF2020_, epoch=_E(2015), 

1267 xform=_P( 29.3, 13.9, -94.7, 5.51, 2.236, 13.494, -19.218), 

1268 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1269_trfX(_ITRF90_, _ETRF2020_, epoch=_E(2015), 

1270 xform=_P( 27.3, 9.9, -110.7, 5.81, 2.236, 13.494, -19.218), 

1271 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1272_trfX(_ITRF89_, _ETRF2020_, epoch=_E(2015), 

1273 xform=_P( 32.3, 33.9, -148.7, 9.21, 2.236, 13.494, -19.218), 

1274 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1275_trfX(_ITRF88_, _ETRF2020_, epoch=_E(2015), 

1276 xform=_P( 27.3, -2.1, -172.7, 12.31, 2.336, 13.494, -19.218), 

1277 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733)) 

1278 

1279# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and 

1280# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 3. 

1281_trfX(_ITRF2020_, _ETRF2014_, epoch=_E(2015), 

1282 xform=_P( -1.4, -0.9, 1.4, 0.42, 2.21, 13.806, -20.02), 

1283 rates=_P( _0_0, -0.1, 0.2, _0_0, 0.085, 0.531, -0.77)) 

1284_trfX(_ITRF2014_, _ETRF2014_, epoch=_E(2015), 

1285 xform=_P( _0_0, _0_0, _0_0, _0_0, 2.21, 13.806, -20.02), 

1286 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77)) 

1287_trfX(_ITRF2008_, _ETRF2014_, epoch=_E(2015), 

1288 xform=_P( -1.6, -1.9, -1.9, -0.13, 2.21, 13.806, -20.02), 

1289 rates=_P( _0_0, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77)) 

1290_trfX(_ITRF2005_, _ETRF2014_, epoch=_E(2015), 

1291 xform=_P( -4.1, -1.0, 2.8, -1.07, 2.21, 13.806, -20.02), 

1292 rates=_P( -0.3, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77)) 

1293_trfX(_ITRF2000_, _ETRF2014_, epoch=_E(2015), 

1294 xform=_P( -1.2, -1.7, 35.6, -2.67, 2.21, 13.806, -20.02), 

1295 rates=_P( -0.1, -0.1, 1.9, -0.11, 0.085, 0.531, -0.77)) 

1296_trfX(_ITRF97_, _ETRF2014_, epoch=_E(2015), 

1297 xform=_P( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38), 

1298 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1299_trfX(_ITRF96_, _ETRF2014_, epoch=_E(2015), 

1300 xform=_P( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38), 

1301 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1302_trfX(_ITRF94_, _ETRF2014_, epoch=_E(2015), 

1303 xform=_P( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38), 

1304 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1305_trfX(_ITRF93_, _ETRF2014_, epoch=_E(2015), 

1306 xform=_P( 64.4, -2.8, 72.7, -4.89, 5.570, 18.136, -20.77), 

1307 rates=_P( 2.8, 0.1, 2.5, -0.12, 0.195, 0.721, -0.84)) 

1308_trfX(_ITRF92_, _ETRF2014_, epoch=_E(2015), 

1309 xform=_P( -15.9, 1.0, 87.3, -3.69, 2.21, 13.806, -20.38), 

1310 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1311_trfX(_ITRF91_, _ETRF2014_, epoch=_E(2015), 

1312 xform=_P( -27.9, -13.0, 93.3, -5.09, 2.21, 13.806, -20.38), 

1313 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1314_trfX(_ITRF90_, _ETRF2014_, epoch=_E(2015), 

1315 xform=_P( -25.9, -9.0, 109.3, -5.39, 2.21, 13.806, -20.38), 

1316 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1317_trfX(_ITRF89_, _ETRF2014_, epoch=_E(2015), 

1318 xform=_P( -30.9, -33.0, 147.3, -8.79, 2.21, 13.806, -20.38), 

1319 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1320_trfX(_ITRF88_, _ETRF2014_, epoch=_E(2015), 

1321 xform=_P( -25.9, 3.0, 171.3, -11.89, 2.11, 13.806, -20.38), 

1322 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79)) 

1323 

1324# see U{Altamimi, Z. "EUREF Technical Note 1: Relationship and Transformation between the International and 

1325# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 4, 

1326# U{Boucher, C. & Altamimi, Z. "Memo: Specifications for reference frame fixing in the analysis of a EUREF GPS 

1327# campaign" (2011) <https://ETRS89.ENSG.IGN.Fr/memo-V8.pdf>} and U{Altamimi, Z. "Key results of ITRF2014 and 

1328# implication to ETRS89 realization", EUREF2016<https://www.EUREF.EU/symposia/2016SanSebastian/01-02-Altamimi.pdf>}. 

1329_trfX(_ITRF2020_, _ETRF2000_, epoch=_E(2015), 

1330 xform=_P( 53.8, 51.8, -82.2, 2.25, 2.106, 12.74, -20.592), 

1331 rates=_P( 0.1, _0_0, -1.7, 0.11, 0.081, 0.49, -0.792)) 

1332# _trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2000), 

1333# xform=_P( 53.7, 51.2, -55.1, 1.02, 0.891, 5.39, -8.712), 

1334# rates=_P( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792)) 

1335_trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2015), 

1336 xform=_P( 55.2, 52.7, -83.6, 2.67, 2.106, 12.74, -20.592), 

1337 rates=_P( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792)) 

1338# _trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2000), 

1339# xform=_P( 52.1, 49.3, -58.5, 1.34, 0.891, 5.39, -8.712), 

1340# rates=_P( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)) 

1341_trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2015), 

1342 xform=_P( 53.6, 50.8, -85.5, 2.54, 2.106, 12.74, -20.592), 

1343 rates=_P( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)) 

1344# _trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2000), 

1345# xform=_P( 54.1, 50.2, -53.8, 0.4, 0.891, 5.39, -8.712), 

1346# rates=_P( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)) 

1347_trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2015), 

1348 xform=_P( 51.1, 51.7, -80.8, 1.6, 2.106, 12.74, -20.592), 

1349 rates=_P( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792)) 

1350# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2000), 

1351# xform=_P( 54.0, 51.0, -48.0, _0_0, 0.891, 5.39, -8.712), 

1352# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792)) 

1353_trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2015), 

1354 xform=_P( 54.0, 51.0, -48.0, _0_0, 2.106, 12.74, -20.592), 

1355 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792)) 

1356_trfX(_ITRF97_, _ETRF2000_, epoch=_E(2015), 

1357 xform=_P( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952), 

1358 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1359_trfX(_ITRF96_, _ETRF2000_, epoch=_E(2015), 

1360 xform=_P( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952), 

1361 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1362_trfX(_ITRF94_, _ETRF2000_, epoch=_E(2015), 

1363 xform=_P( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952), 

1364 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1365_trfX(_ITRF93_, _ETRF2000_, epoch=_E(2015), 

1366 xform=_P( 119.6, 49.9, -10.9, -2.22, 5.466, 17.07, -21.342), 

1367 rates=_P( 2.9, 0.2, 0.6, -0.01, 0.191, 0.68, -0.862)) 

1368_trfX(_ITRF92_, _ETRF2000_, epoch=_E(2015), 

1369 xform=_P( 39.3, 53.7, 3.7, -1.02, 2.106, 12.74, -20.952), 

1370 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1371_trfX(_ITRF91_, _ETRF2000_, epoch=_E(2015), 

1372 xform=_P( 27.3, 39.7, 9.7, -2.42, 2.106, 12.74, -20.952), 

1373 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1374_trfX(_ITRF90_, _ETRF2000_, epoch=_E(2015), 

1375 xform=_P( 29.3, 43.7, 25.7, -2.72, 2.106, 12.74, -20.952), 

1376 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1377_trfX(_ITRF89_, _ETRF2000_, epoch=_E(2015), 

1378 xform=_P( 24.3, 19.7, 63.7, -6.12, 2.106, 12.74, -20.952), 

1379 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1380_trfX(_ITRF88_, _ETRF2000_, epoch=_E(2015), 

1381 xform=_P( 29.3, 55.7, 87.7, -9.22, 2.006, 12.74, -20.952), 

1382 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812)) 

1383 

1384# GDA2020 "Geocentric Datum of Australia 2020 Technical Manual", v1.5, 2020-12-09, Table 3.3 and 3.4 

1385# <https://www.ICSM.gov.AU/sites/default/files/2020-12/GDA2020%20Technical%20Manual%20V1.5_4.pdf> 

1386# (the GDA2020 xforms are different but the rates are the same as GDA94, further below) 

1387_trfX(_ITRF2014_, _GDA2020_, epoch=_E(2020), 

1388 xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0), 

1389 rates=_P( _0_0, _0_0, _0_0, _0_0, 1.50379, 1.18346, 1.20716)) 

1390_trfX(_ITRF2008_, _GDA2020_, epoch=_E(2020), 

1391 xform=_P( 13.79, 4.55, 15.22, 2.5, 0.2808, 0.2677, -0.4638), 

1392 rates=_P( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551)) 

1393_trfX(_ITRF2005_, _GDA2020_, epoch=_E(2020), 

1394 xform=_P( 40.32, -33.85, -16.72, 4.286, -1.2893, -0.8492, -0.3342), 

1395 rates=_P( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701)) 

1396_trfX(_ITRF2000_, _GDA2020_, epoch=_E(2020), 

1397 xform=_P(-105.52, 51.58, 231.68, 3.55, 4.2175, 6.3941, 0.8617), 

1398 rates=_P( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224)) 

1399 

1400# see Table 2 in U{Dawson, J. & Woods, A. "ITRF to GDA94 coordinate transformations", Journal of Applied 

1401# Geodesy 4 (2010), 189-199<https://www.ResearchGate.net/publication/258401581_ITRF_to_GDA94_coordinate_transformations>} 

1402# (note, sign of rotations for GDA94 reversed as "Australia assumes rotation to be of coordinate axes", 

1403# rather than the more conventional "position around the coordinate axes") 

1404_trfX(_ITRF2008_, _GDA94_, epoch=_E(1994), 

1405 xform=_P( -84.68, -19.42, 32.01, 9.71, -0.4254, 2.2578, 2.4015), 

1406 rates=_P( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551)) 

1407_trfX(_ITRF2005_, _GDA94_, epoch=_E(1994), 

1408 xform=_P( -79.73, -6.86, 38.03, 6.636, 0.0351, -2.1211, -2.1411), 

1409 rates=_P( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701)) 

1410_trfX(_ITRF2000_, _GDA94_, epoch=_E(1994), 

1411 xform=_P( -45.91, -29.85, -20.37, 7.07, -1.6705, 0.4594, 1.9356), 

1412 rates=_P( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224)) 

1413 

1414# see U{Solar, T. & Snay, R.A. "Transforming Positions and Velocities between the International Terrestrial Reference 

1415# Frame of 2000 and North American Datum of 1983" (2004)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>} 

1416_trfX(_ITRF2000_, _NAD83_, epoch=_E(1997), # note NAD83(CORS96) 

1417 xform=_P( 995.6, -1901.3, -521.5, 0.615, -25.915, -9.426, -11.599), 

1418 rates=_P( 0.7, -0.7, _0_5, -0.182, -0.06667, 0.75744, 0.05133)) 

1419 

1420# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ 

1421# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83 and Pearson, C. & Snay, R. U{"Introducing 

1422# HTDP 3.1 to transform coordinates across time and spatial reference frames"<https://Geodesy.NOAA.gov/ 

1423# TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 7th column 

1424trfXform(_ITRF2008_, _NAD83_, epoch=_E(1997), # coverage 

1425 xform=_P( 993.43, -1903.31, -526.55, 1.71504, -25.91467, -9.42645, -11.59935), 

1426 rates=_P( 0.79, -0.6, -1.34, -0.10201, -0.06667, 0.75744, 0.05133)) 

1427# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ 

1428# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83 

1429_trfX(_ITRF2005_, _NAD83_, epoch=_E(1997), 

1430 xform=_P( 996.3, -1902.4, -521.9, 0.775, -25.915, -9.426, -11.599), 

1431 rates=_P( 0.5, -0.6, -1.3, -0.10201, -0.06667, 0.75744, 0.05133)) 

1432_trfX(_ITRF90_, _NAD83_, epoch=_E(1997), 

1433 xform=_P( 973.0, -1919.2, -482.9, -0.9, -25.79, -9.65, -11.66), 

1434 rates=_P( _0_0, _0_0, _0_0, _0_0, -0.053, 0.742, 0.032)) 

1435_trfX(_ITRF90_, _WGS84_, epoch=_E(1984), 

1436 xform=_P( 60.0, -517.0, -223.0, -11.0, 18.3, -0.3, 7.0), 

1437 rates=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0)) 

1438 

1439del _E, _Es, _P, _Ps 

1440 

1441if __name__ == '__main__': 

1442 

1443 from pygeodesy.interns import _COLONSPACE_,_COMMA_, _NL_, _NLATvar_, _STAR_ 

1444 from pygeodesy.lazily import printf 

1445 from time import localtime 

1446 

1447 D = date2epoch.__name__ 

1448 E = epoch2date.__name__ 

1449 y = localtime()[0] 

1450 for m in range(1, 13): 

1451 for d in (1, 15, _mDays[m] - 1, _mDays[m]): 

1452 f = '%s(%d,%3d,%3d)' % (D, y, m, d) 

1453 e = date2epoch(y, m, d) 

1454 t = epoch2date(e) 

1455 x = NN if t == (y, m, d) else _STAR_ 

1456 e = '%.3f' % (e,) 

1457 e = '%s, %s(%s)' % (e, E, e) 

1458 t = '%d,%3d,%3d' % t 

1459 printf('# %s = %s = %s %s', f, e, t, x) 

1460 

1461 # __doc__ of this file, force all into registery 

1462 def _RFs(): 

1463 yield NN 

1464 for t in RefFrames.toRepr(all=True).split(_NL_): 

1465 t = t.strip(_COMMA_) 

1466 n = t.split(_COLONSPACE_)[0].split(_DOT_)[1] 

1467 r = RefFrames.get(n) 

1468 x = len(r.Xforms()), -len(r.Xforms(inverse=True)) 

1469 yield '%s .Xforms=%s' % (t, x) 

1470 

1471 printf(_NLATvar_.join(sorted(_RFs())), nt=1) 

1472 

1473 X, t = (), 0 # all form 

1474 for r in RefFrames.values(): 

1475 X += tuple(r._Xs.values()) 

1476 for X in sorted(X): 

1477 t += 1 

1478 printf('#%4d %-22s xform=%r', t, X.name, X.xform) 

1479 printf('#%27s rates=%r', _SPACE_, X.rates) 

1480 

1481# **) MIT License 

1482# 

1483# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1484# 

1485# Permission is hereby granted, free of charge, to any person obtaining a 

1486# copy of this software and associated documentation files (the "Software"), 

1487# to deal in the Software without restriction, including without limitation 

1488# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1489# and/or sell copies of the Software, and to permit persons to whom the 

1490# Software is furnished to do so, subject to the following conditions: 

1491# 

1492# The above copyright notice and this permission notice shall be included 

1493# in all copies or substantial portions of the Software. 

1494# 

1495# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1496# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1497# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1498# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1499# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1500# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1501# OTHER DEALINGS IN THE SOFTWARE. 

1502 

1503# % python -m pygeodesy.trf 

1504# 

1505# date2epoch(2024, 1, 1) = 2024.003, epoch2date(2024.003) = 2024, 1, 1 

1506# date2epoch(2024, 1, 15) = 2024.041, epoch2date(2024.041) = 2024, 1, 15 

1507# date2epoch(2024, 1, 30) = 2024.082, epoch2date(2024.082) = 2024, 1, 30 

1508# date2epoch(2024, 1, 31) = 2024.085, epoch2date(2024.085) = 2024, 1, 31 

1509# date2epoch(2024, 2, 1) = 2024.087, epoch2date(2024.087) = 2024, 2, 2 * 

1510# date2epoch(2024, 2, 15) = 2024.126, epoch2date(2024.126) = 2024, 2, 16 * 

1511# date2epoch(2024, 2, 28) = 2024.161, epoch2date(2024.161) = 2024, 2, 28 

1512# date2epoch(2024, 2, 29) = 2024.164, epoch2date(2024.164) = 2024, 3, 1 * 

1513# date2epoch(2024, 3, 1) = 2024.167, epoch2date(2024.167) = 2024, 3, 2 * 

1514# date2epoch(2024, 3, 15) = 2024.205, epoch2date(2024.205) = 2024, 3, 16 * 

1515# date2epoch(2024, 3, 30) = 2024.246, epoch2date(2024.246) = 2024, 3, 31 * 

1516# date2epoch(2024, 3, 31) = 2024.249, epoch2date(2024.249) = 2024, 4, 1 * 

1517# date2epoch(2024, 4, 1) = 2024.251, epoch2date(2024.251) = 2024, 4, 1 

1518# date2epoch(2024, 4, 15) = 2024.290, epoch2date(2024.290) = 2024, 4, 15 

1519# date2epoch(2024, 4, 29) = 2024.328, epoch2date(2024.328) = 2024, 4, 29 

1520# date2epoch(2024, 4, 30) = 2024.331, epoch2date(2024.331) = 2024, 4, 30 

1521# date2epoch(2024, 5, 1) = 2024.333, epoch2date(2024.333) = 2024, 5, 1 

1522# date2epoch(2024, 5, 15) = 2024.372, epoch2date(2024.372) = 2024, 5, 15 

1523# date2epoch(2024, 5, 30) = 2024.413, epoch2date(2024.413) = 2024, 5, 30 

1524# date2epoch(2024, 5, 31) = 2024.415, epoch2date(2024.415) = 2024, 6, 1 * 

1525# date2epoch(2024, 6, 1) = 2024.418, epoch2date(2024.418) = 2024, 6, 2 * 

1526# date2epoch(2024, 6, 15) = 2024.456, epoch2date(2024.456) = 2024, 6, 16 * 

1527# date2epoch(2024, 6, 29) = 2024.495, epoch2date(2024.495) = 2024, 6, 30 * 

1528# date2epoch(2024, 6, 30) = 2024.497, epoch2date(2024.497) = 2024, 7, 1 * 

1529# date2epoch(2024, 7, 1) = 2024.500, epoch2date(2024.500) = 2024, 7, 1 

1530# date2epoch(2024, 7, 15) = 2024.538, epoch2date(2024.538) = 2024, 7, 16 * 

1531# date2epoch(2024, 7, 30) = 2024.579, epoch2date(2024.579) = 2024, 7, 30 

1532# date2epoch(2024, 7, 31) = 2024.582, epoch2date(2024.582) = 2024, 7, 31 

1533# date2epoch(2024, 8, 1) = 2024.585, epoch2date(2024.585) = 2024, 8, 1 

1534# date2epoch(2024, 8, 15) = 2024.623, epoch2date(2024.623) = 2024, 8, 15 

1535# date2epoch(2024, 8, 30) = 2024.664, epoch2date(2024.664) = 2024, 8, 31 * 

1536# date2epoch(2024, 8, 31) = 2024.667, epoch2date(2024.667) = 2024, 9, 1 * 

1537# date2epoch(2024, 9, 1) = 2024.669, epoch2date(2024.669) = 2024, 9, 2 * 

1538# date2epoch(2024, 9, 15) = 2024.708, epoch2date(2024.708) = 2024, 9, 16 * 

1539# date2epoch(2024, 9, 29) = 2024.746, epoch2date(2024.746) = 2024, 9, 30 * 

1540# date2epoch(2024, 9, 30) = 2024.749, epoch2date(2024.749) = 2024, 10, 1 * 

1541# date2epoch(2024, 10, 1) = 2024.751, epoch2date(2024.751) = 2024, 10, 1 

1542# date2epoch(2024, 10, 15) = 2024.790, epoch2date(2024.790) = 2024, 10, 15 

1543# date2epoch(2024, 10, 30) = 2024.831, epoch2date(2024.831) = 2024, 10, 30 

1544# date2epoch(2024, 10, 31) = 2024.833, epoch2date(2024.833) = 2024, 10, 31 

1545# date2epoch(2024, 11, 1) = 2024.836, epoch2date(2024.836) = 2024, 11, 1 

1546# date2epoch(2024, 11, 15) = 2024.874, epoch2date(2024.874) = 2024, 11, 15 

1547# date2epoch(2024, 11, 29) = 2024.913, epoch2date(2024.913) = 2024, 11, 29 

1548# date2epoch(2024, 11, 30) = 2024.915, epoch2date(2024.915) = 2024, 12, 1 * 

1549# date2epoch(2024, 12, 1) = 2024.918, epoch2date(2024.918) = 2024, 12, 2 * 

1550# date2epoch(2024, 12, 15) = 2024.956, epoch2date(2024.956) = 2024, 12, 16 * 

1551# date2epoch(2024, 12, 30) = 2024.997, epoch2date(2024.997) = 2024, 12, 31 * 

1552# date2epoch(2024, 12, 31) = 2025.000, epoch2date(2025.000) = 2025, 1, 1 * 

1553 

1554# 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) 

1555# rates=TRFXform7Tuple(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792) 

1556# 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) 

1557# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1558# 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) 

1559# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.054, sy=0.518, sz=-0.781) 

1560# 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) 

1561# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1562# 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) 

1563# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1564# 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) 

1565# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1566# 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) 

1567# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1568# 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) 

1569# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1570# 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) 

1571# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71) 

1572# 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) 

1573# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1574# 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) 

1575# rates=TRFXform7Tuple(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701) 

1576# 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) 

1577# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=-0.053, sy=0.742, sz=0.032) 

1578# 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) 

1579# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1580# 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) 

1581# rates=TRFXform7Tuple(tx=-0.3, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77) 

1582# 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) 

1583# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1584# 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) 

1585# rates=TRFXform7Tuple(tx=0.3, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753) 

1586# 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) 

1587# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1588# 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) 

1589# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71) 

1590# 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) 

1591# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1592# 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) 

1593# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1594# 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) 

1595# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68) 

1596# 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) 

1597# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1598# 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) 

1599# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1600# 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) 

1601# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1602# 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) 

1603# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68) 

1604# 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) 

1605# rates=TRFXform7Tuple(tx=2.9, ty=0.2, tz=0.6, s=-0.01, sx=0.191, sy=0.68, sz=-0.862) 

1606# 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) 

1607# rates=TRFXform7Tuple(tx=2.8, ty=0.1, tz=2.5, s=-0.12, sx=0.195, sy=0.721, sz=-0.84) 

1608# 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) 

1609# rates=TRFXform7Tuple(tx=-2.8, ty=0.0, tz=-2.7, s=0.12, sx=-0.024, sy=0.329, sz=-0.683) 

1610# 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) 

1611# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.32, sy=0.78, sz=-0.67) 

1612# 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) 

1613# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1614# 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) 

1615# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1616# 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) 

1617# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1618# 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) 

1619# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65) 

1620# 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) 

1621# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65) 

1622# 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) 

1623# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65) 

1624# 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) 

1625# rates=TRFXform7Tuple(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224) 

1626# 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) 

1627# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.081, sy=0.49, sz=-0.792) 

1628# 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) 

1629# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1630# 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) 

1631# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812) 

1632# 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) 

1633# rates=TRFXform7Tuple(tx=-0.1, ty=-0.1, tz=1.9, s=-0.11, sx=0.085, sy=0.531, sz=-0.77) 

1634# 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) 

1635# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1636# 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) 

1637# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79) 

1638# 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) 

1639# rates=TRFXform7Tuple(tx=0.1, ty=0.2, tz=-2.1, s=0.11, sx=0.086, sy=0.519, sz=-0.753) 

1640# 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) 

1641# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1642# 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) 

1643# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1644# 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) 

1645# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733) 

1646# 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) 

1647# rates=TRFXform7Tuple(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224) 

1648# 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) 

1649# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1650# 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) 

1651# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1652# 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) 

1653# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1654# 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) 

1655# rates=TRFXform7Tuple(tx=0.0, ty=-0.6, tz=-1.4, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1656# 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) 

1657# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1658# 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) 

1659# rates=TRFXform7Tuple(tx=-2.9, ty=-0.2, tz=-0.6, s=0.01, sx=-0.11, sy=-0.19, sz=0.07) 

1660# 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) 

1661# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1662# 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) 

1663# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02) 

1664# 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) 

1665# rates=TRFXform7Tuple(tx=0.69, ty=-0.1, tz=1.86, s=-0.19201, sx=0.01347, sy=-0.01514, sz=0.00027) 

1666# 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) 

1667# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=-0.02) 

1668# 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) 

1669# rates=TRFXform7Tuple(tx=0.7, ty=-0.7, tz=0.5, s=-0.182, sx=-0.06667, sy=0.75744, sz=0.05133) 

1670# 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) 

1671# rates=TRFXform7Tuple(tx=0.5, ty=-0.6, tz=-1.3, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133) 

1672# 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) 

1673# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0532, sy=-0.7423, sz=-0.0316) 

1674# 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) 

1675# rates=TRFXform7Tuple(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701) 

1676# 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) 

1677# rates=TRFXform7Tuple(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0) 

1678# 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) 

1679# rates=TRFXform7Tuple(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551) 

1680# 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) 

1681# rates=TRFXform7Tuple(tx=0.79, ty=-0.6, tz=-1.34, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133) 

1682# 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) 

1683# rates=TRFXform7Tuple(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792) 

1684# 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) 

1685# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77) 

1686# 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) 

1687# rates=TRFXform7Tuple(tx=0.0, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753) 

1688# 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) 

1689# rates=TRFXform7Tuple(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551) 

1690# 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) 

1691# rates=TRFXform7Tuple(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0) 

1692# 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) 

1693# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1694# 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) 

1695# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1696# 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) 

1697# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1698# 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) 

1699# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1700# 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) 

1701# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1702# 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) 

1703# rates=TRFXform7Tuple(tx=-2.8, ty=-0.1, tz=-2.4, s=0.09, sx=-0.11, sy=-0.19, sz=0.07) 

1704# 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) 

1705# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1706# 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) 

1707# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1708# 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) 

1709# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02) 

1710# 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) 

1711# rates=TRFXform7Tuple(tx=0.3, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1712# 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) 

1713# rates=TRFXform7Tuple(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.081, sy=0.49, sz=-0.792) 

1714# 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) 

1715# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.085, sy=0.531, sz=-0.77) 

1716# 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) 

1717# rates=TRFXform7Tuple(tx=0.0, ty=0.1, tz=-0.2, s=0.0, sx=0.086, sy=0.519, sz=-0.753) 

1718# 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) 

1719# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=1.50379, sy=1.18346, sz=1.20716) 

1720# 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) 

1721# rates=TRFXform7Tuple(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.0, sy=0.0, sz=0.0) 

1722# 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) 

1723# rates=TRFXform7Tuple(tx=0.3, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0) 

1724# 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) 

1725# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0) 

1726# 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) 

1727# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1728# 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) 

1729# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1730# 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) 

1731# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1732# 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) 

1733# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1734# 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) 

1735# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1736# 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) 

1737# rates=TRFXform7Tuple(tx=-2.8, ty=-0.1, tz=-2.5, s=0.12, sx=-0.11, sy=-0.19, sz=0.07) 

1738# 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) 

1739# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1740# 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) 

1741# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1742# 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) 

1743# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1744# 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) 

1745# rates=TRFXform7Tuple(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.081, sy=0.49, sz=-0.792) 

1746# 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) 

1747# rates=TRFXform7Tuple(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.085, sy=0.531, sz=-0.77) 

1748# 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) 

1749# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.086, sy=0.519, sz=-0.753) 

1750# 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) 

1751# rates=TRFXform7Tuple(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.0, sy=0.0, sz=0.0) 

1752# 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) 

1753# rates=TRFXform7Tuple(tx=0.3, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0) 

1754# 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) 

1755# rates=TRFXform7Tuple(tx=0.0, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0) 

1756# 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) 

1757# rates=TRFXform7Tuple(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.0, sy=0.0, sz=0.0) 

1758# 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) 

1759# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1760# 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) 

1761# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1762# 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) 

1763# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1764# 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) 

1765# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1766# 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) 

1767# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1768# 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) 

1769# rates=TRFXform7Tuple(tx=-2.8, ty=-0.2, tz=-2.3, s=0.12, sx=-0.11, sy=-0.19, sz=0.07) 

1770# 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) 

1771# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1772# 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) 

1773# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02) 

1774# 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) 

1775# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)