Coverage for pygeodesy/trf.py: 95%
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2# -*- coding: utf-8 -*-
4u'''I{Veness}' Terrestrial Reference Frames (TRF).
6Classes L{RefFrame}, registry L{RefFrames} and L{TRFError}.
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>}.
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>}.
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}.
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>}.
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.
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>}.
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'''
71from pygeodesy.basics import map1, neg, isstr, _xinstanceof, _xisscalar, _zip
72from pygeodesy.constants import _0_0s, _0_0, _0_001, _0_5, _1_0, _float as _F
73from pygeodesy.datums import Datums, _earth_datum, _minus, Transform, _WGS84
74from pygeodesy.errors import TRFError, _xkwds
75from pygeodesy.interns import MISSING, NN, _AT_, _COMMASPACE_, _conversion_, _datum_, \
76 _DOT_, _exists_, _invalid_, _MINUS_, _NAD83_, _no_, \
77 _PLUS_, _reframe_, _s_, _SPACE_, _sx_, _sy_, _sz_, _to_, \
78 _tx_, _ty_, _tz_, _WGS84_, _x_, _intern as _i
79from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS
80from pygeodesy.named import ADict, classname, _lazyNamedEnumItem as _lazy, _Named, \
81 _NamedEnum, _NamedEnumItem, _NamedTuple, Fmt, unstr
82from pygeodesy.props import Property, Property_RO, property_RO
83# from pygeodesy.streprs import Fmt, unstr # from .named
84from pygeodesy.units import Epoch, Float
86from math import ceil
88__all__ = _ALL_LAZY.trf
89__version__ = '24.02.06'
91_EP0CH = Epoch(0, low=0)
92_Es = {_EP0CH: _EP0CH} # L{Epoch} de_dup
93_Ps = {} # L{TRFXform7Tuple} de-dup, deleted below
95_GRS80 = Datums.GRS80
96_inverse_ = 'inverse'
97_MAS = _MM = _PPB = Float # Units
98_MM2M = _0_001 # scale mm2m, ppb2ppM, mas2as
99_mDays = (0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 0)
100_366_0 = _F(sum(_mDays))
101_v_ = 'v'
103_ETRF88_ = _i('ETRF88')
104_ETRF89_ = _i('ETRF89')
105_ETRF90_ = _i('ETRF90')
106_ETRF91_ = _i('ETRF91')
107_ETRF92_ = _i('ETRF92')
108_ETRF93_ = _i('ETRF93')
109_ETRF94_ = _i('ETRF94')
110_ETRF96_ = _i('ETRF96')
111_ETRF97_ = _i('ETRF97')
112_ETRF2000_ = _i('ETRF2000')
113_ETRF2005_ = _i('ETRF2005')
114_ETRF2008_ = _i('ETRF2008')
115_ETRF2014_ = _i('ETRF2014')
116_ETRF2020_ = _i('ETRF2020')
117_GDA94_ = _i('GDA94')
118_GDA2020_ = _i('GDA2020')
119_ITRF_ = _i('ITRF')
120_ITRF88_ = _i('ITRF88')
121_ITRF89_ = _i('ITRF89')
122_ITRF90_ = _i('ITRF90')
123_ITRF91_ = _i('ITRF91')
124_ITRF92_ = _i('ITRF92')
125_ITRF93_ = _i('ITRF93')
126_ITRF94_ = _i('ITRF94')
127_ITRF96_ = _i('ITRF96')
128_ITRF97_ = _i('ITRF97')
129_ITRF2000_ = _i('ITRF2000')
130_ITRF2005_ = _i('ITRF2005')
131_ITRF2008_ = _i('ITRF2008')
132_ITRF2014_ = _i('ITRF2014')
133_ITRF2020_ = _i('ITRF2020')
134_WGS84g1150_ = _i('WGS84g1150')
135_WGS84g1674_ = _i('WGS84g1674')
136_WGS84g1762_ = _i('WGS84g1762')
137# del _i
140def _E(epoch):
141 '''(INTERNAL) De-dup L{Epochs}s.
142 '''
143 e = Epoch(_F(epoch))
144 return _Es.setdefault(e, e)
147def _xellipsoidal(point):
148 '''(INTERNAL) Check an ellipsoidal position.
149 '''
150 m = _MODS.ellipsoidalBase
151 _xinstanceof(m.CartesianEllipsoidalBase,
152 m.LatLonEllipsoidalBase, point=point)
153 return isinstance(point, m.CartesianEllipsoidalBase)
156class RefFrame(_NamedEnumItem):
157 '''Terrestrial Reference Frame (TRF) parameters.
158 '''
159 _datum = _GRS80 # Datums.GRS80 or .WGS84 (L{Datum})
160 _epoch = _EP0CH # epoch, fractional year (L{Epoch})
162 def __init__(self, epoch, datum, name=NN):
163 '''New L{RefFrame}.
165 @arg epoch: Epoch, a fractional calendar year (C{scalar} or C{str}).
166 @arg datum: Datum or ellipsoid (L{Datum}, {Ellipsoid}, L{Ellipsoid2}
167 or L{a_f2Tuple}).
168 @kwarg name: Unique, non-empty name (C{str}).
170 @raise NameError: A L{RefFrame} with that B{C{name}} already exists.
172 @raise TRFError: Invalid B{C{epoch}}.
174 @raise TypeError: Invalid B{C{datum}}.
175 '''
176 if datum is not _GRS80:
177 _earth_datum(self, datum, raiser=_datum_)
178 self._epoch = _Epoch(epoch)
179 self._Xs = {} # dict of Xforms
180 if name:
181 self._register(RefFrames, name)
183 def __eq__(self, other):
184 return isinstance(other, RefFrame) and other.epoch == self.epoch \
185 and other.datum == self.datum
187 def __lt__(self, other): # for sorting
188 return isinstance(other, RefFrame) and (self.name < other.name
189 or self.epoch < other.epoch)
191 def __matmul__(self, point): # PYCHOK Python 3.5+
192 '''Convert an ellipsoidal B{C{point}} to this reframe and epoch.
194 @see: Method C{toRefFrame}.
195 '''
196 _xellipsoidal(point)
197 return point.toRefFrame(self)
199 @property_RO
200 def datum(self):
201 '''Get this reference frame's datum (L{Datum}).
202 '''
203 return self._datum
205 @Property_RO
206 def ellipsoid(self):
207 '''Get this reference frame's ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
208 '''
209 return self._datum.ellipsoid
211 @Property_RO
212 def epoch(self):
213 '''Get this reference frame's epoch (C{Epoch}).
214 '''
215 return self._epoch
217 def toRefFrame(self, point, reframe2, **epoch2_epoch_name):
218 '''Convert an ellipsoidal point from this reframe and from C{epoch}
219 to an other C{reframe2} and C{epoch2 or epoch}.
221 @arg point: The point to convert (C{Cartesian} or C{LatLon}).
222 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}).
223 @kwarg epoch2_epoch_name: Optional keyword arguments C{B{epoch2}=None},
224 C{B{epoch}=None} and C{B{name}=NN}.
226 @return: A copy of the B{C{point}}, converted or renamed.
228 @raise TypeError: Invalid B{C{point}}.
230 @note: The B{C{point}}'s C{reframe} and C{epoch} are overridden by
231 this reframe and B{C{epoch}} or this reframe's epoch.
233 @see: Ellipsoidal methods L{LatLon.toRefFrame<ellipsoidalBase.LatLonEllipsoidalBase.toRefFrame>}
234 and L{Cartesian.toRefFrame<ellipsoidalBase.CartesianEllipsoidalBase.toRefFrame>}
235 for more details.
236 '''
237 _xellipsoidal(point)
238 kwds = _xkwds(epoch2_epoch_name, name=self.name)
239 p = point.dup(reframe=self) if point.reframe != self else point
240 return p.toRefFrame(reframe2, reframe=self, **kwds)
242 def toStr(self, epoch=None, name=NN, **unused): # PYCHOK expected
243 '''Return this reference frame as a text string.
245 @kwarg epoch: Override this reframe's epoch (C{scalar} or C{str}).
246 @kwarg name: Override name (C{str}) or C{None} to exclude the
247 reframe's name.
249 @return: This L{RefFrame}'s attributes (C{str}).
250 '''
251 D = self.datum
252 e = self.epoch if epoch is None else _Epoch(epoch)
253 t = (Fmt.EQUAL(name=repr(name or self.name)),
254 Fmt.EQUAL(epoch=e),
255 Fmt.EQUAL(datum=_DOT_(classname(D) + _s_, D.name)))
256 return _COMMASPACE_.join(t[1:] if name is None else t)
258 def Xform(self, reframe2):
259 '''Get the converter Xform I{from} this reference frame I{to} C{reframe2}.
261 @arg reframe2: Destination frame to convert I{to} (L{RefFrame} or C{str}).
263 @return: The L{TRFXform} instance or C{None} if not available.
265 @raise TypeError: Invalid B{C{reframe2}}.
266 '''
267 _xinstanceof(RefFrame, str, reframe2=reframe2)
268 n2 = reframe2 if isstr(reframe2) else reframe2.name
269 return self._Xs.get(n2, None)
271 def Xforms(self, inverse=False):
272 '''Return all Xforms converting I{from} or I{to} this reference frame.
274 @kwarg inverse: If C{True}, get all I{inverse, to} Xforms (C{bool}).
276 @return: An L{ADict} of I{from} C{[refName2]=}L{TRFXform}s) or if
277 C{B{inverse}=True} of I{to} C{[refName1]=}L{TRFXform}s).
278 '''
279 def _Xi(n2):
280 for n1, r in RefFrames.items():
281 if n2 in r._Xs:
282 yield n1, r
284 return ADict(_Xi(self.name)) if inverse else ADict(self._Xs)
287class RefFrames(_NamedEnum):
288 '''(INTERNAL) L{RefFrame} registry, I{must} be a sub-class
289 to accommodate the L{_LazyNamedEnumItem} properties.
290 '''
291 def _Lazy(self, epoch, datum=_GRS80, name=NN):
292 '''(INTERNAL) Instantiate the L{RefFrame}.
293 '''
294 return RefFrame(epoch, datum, name=name)
296RefFrames = RefFrames(RefFrame) # PYCHOK singleton
297'''Some pre-defined L{RefFrame}s, all I{lazily} instantiated.'''
298# <https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe.js>
299RefFrames._assert(
300 ETRF88 = _lazy(_ETRF88_, _E(1988)), # epoch, datum?
301 ETRF89 = _lazy(_ETRF89_, _E(1989)), # epoch, datum?
302 ETRF90 = _lazy(_ETRF90_, _E(1990)), # epoch, datum?
303 ETRF91 = _lazy(_ETRF91_, _E(1991)), # epoch, datum?
304 ETRF92 = _lazy(_ETRF92_, _E(1992)), # epoch, datum?
305 ETRF93 = _lazy(_ETRF93_, _E(1993)), # epoch, datum?
306 ETRF94 = _lazy(_ETRF94_, _E(1994)), # epoch, datum?
307 ETRF96 = _lazy(_ETRF96_, _E(1996)), # epoch, datum?
308 ETRF97 = _lazy(_ETRF97_, _E(1997)), # epoch, datum?
309 ETRF2000 = _lazy(_ETRF2000_, _E(2005)),
310 ETRF2005 = _lazy(_ETRF2005_, _E(2005)), # epoch, datum?
311 ETRF2008 = _lazy(_ETRF2008_, _E(2008)), # epoch, datum?
312 ETRF2014 = _lazy(_ETRF2014_, _E(2014)), # epoch, datum?
313 ETRF2020 = _lazy(_ETRF2020_, _E(2020)), # epoch, datum?
314 GDA94 = _lazy(_GDA94_, _E(1994)), # Australia
315 GDA2020 = _lazy(_GDA2020_, _E(2020)), # Australia
316 ITRF88 = _lazy(_ITRF88_, _E(1988)),
317 ITRF89 = _lazy(_ITRF89_, _E(1989)),
318 ITRF90 = _lazy(_ITRF90_, _E(1988)),
319 ITRF91 = _lazy(_ITRF91_, _E(1988)),
320 ITRF92 = _lazy(_ITRF92_, _E(1988)),
321 ITRF93 = _lazy(_ITRF93_, _E(1988)),
322 ITRF94 = _lazy(_ITRF94_, _E(1993)),
323 ITRF96 = _lazy(_ITRF96_, _E(1997)),
324 ITRF97 = _lazy(_ITRF97_, _E(1997)),
325 ITRF2000 = _lazy(_ITRF2000_, _E(1997)), # aka ITRF00
326 ITRF2005 = _lazy(_ITRF2005_, _E(2000)),
327 ITRF2008 = _lazy(_ITRF2008_, _E(2005)), # aka ITRF08
328 ITRF2014 = _lazy(_ITRF2014_, _E(2010)),
329 ITRF2020 = _lazy(_ITRF2020_, _E(2015)),
330 NAD83 = _lazy(_NAD83_, _E(1997)), # aka CORS96
331 WGS84 = _lazy(_WGS84_, _E(1984), _WGS84),
332 WGS84g1150 = _lazy(_WGS84g1150_, _E(2001), _WGS84),
333 WGS84g1674 = _lazy(_WGS84g1674_, _E(2005), _WGS84),
334 WGS84g1762 = _lazy(_WGS84g1762_, _E(2005), _WGS84)) # same epoch
337class TransformXform(Transform):
338 '''Helmert transformation, extended with an C{Xform} converter.
340 @see: L{Transform<datums.Transform>} and L{Xform<TRFXform>}.
341 '''
342 _Xform = None
344 def __init__(self, name=NN, **tx_ty_tz_s_sx_sy_sz): # PYCHOK signature
345 '''New L{TransformXform}.
347 @kwarg name: Optional name (C{str}), I{not registered}.
349 @see: L{Transform<datums.Transform>} for details.
351 @note: The name of this L{TransformXform} starts with C{"-"}
352 if its C{Xform} was I{inversed}.
353 '''
354 Transform.__init__(self, **tx_ty_tz_s_sx_sy_sz)
355 if name:
356 self.name = name
358 def __eq__(self, other):
359 return isinstance(other, TransformXform) and Transform.__eq__(self, other)
361 def rename(self, name=NN):
362 '''Change this transform and its Xform's name.
364 @arg name: The new name (C{str}), overriding
365 the base name.
367 @return: The old name (C{str}).
368 '''
369 X = self.Xform
370 return Transform.rename(self, name or (X.toStr() if X else NN))
372 def toRefFrame(self, point, name=NN): # PYCHOK signature
373 '''Convert an ellipsoidal point using this transform and Xform.
375 @arg point: The point to convert (C{Cartesian} or C{LatLon}).
377 @return: A copy of the B{C{point}}, converted I{directly} to
378 this transform's Xform's C{refName2} and C{epoch}.
380 @note: The B{C{point}}'s original C{reframe} and C{epoch} are
381 I{ignored}, its C{datum} and C{height} are preserved
382 but I{not} taken into account.
383 '''
384 C = _xellipsoidal(point)
385 c = point.dup() if C else point.toCartesian()
386 r = c.toTransforms_(self)
387 if not C: # i.e. back to LatLon
388 r = r.toLatLon(datum=point.datum, height=point.height,
389 LatLon=point.classof)
390 X = self.Xform
391 if X:
392 r.reframe = X.reframe2
393 r.epoch = X.epoch
395 r.rename(name or self.name)
396 return r
398 def toTransform(self, epoch1, **epoch2_inverse):
399 '''Return this transform observed at B{C{epoch1}} as a Helmert
400 L{TransformXform}, optionally at B{C{epoch2 or epoch1}}.
402 @arg epoch1: Epoch to observe I{from} (C{scalar}).
403 @kwarg epoch2: Optional epoch to observe I{to} (C{scalar}).
404 @kwarg epoch2_inverse: Optional C{B{epoch2}=None} and
405 C{B{inverse}=False}, see class Xform's method
406 L{toTransform<TRFXform.toTransform>}.
408 @return: The Helmert transform (L{TransformXform}).
410 @raise TRFError: Invalid B{C{epoch1}}, B{C{epoch2}} or
411 missing Xform.
412 '''
413 X = self.Xform
414 if not X:
415 raise TRFError(Xform=X, txt=MISSING)
416 X = X.dup(epoch=epoch1)
417 _ = X.rename()
418 return X.toTransform(epoch1, **epoch2_inverse)
420 def velocities(self, factor=_MM2M):
421 '''Compute the X, Y and Z I{velocities} of this transform.
423 @kwarg factor: Factor to scale this Xform's C{rates} (C{scalar}), default
424 from C{milli-meter-} to C{meter-per-year}.
426 @return: A L{Vector3Tuple}C{(x, y, z)} or C{None}.
428 @raise TypeError: Non-scalar B{C{factor}}.
430 @see: Altamimi, Z. "EUREF-TN-1-Jan-31-2024", U{Appendix A, equation (3)
431 <http://ETRS89.ENSG.IGN.FR/pub/EUREF-TN-1-Jan-31-2024.pdf>}.
432 '''
433 v = self.Xform
434 if v is not None:
435 r = v.rates * factor # eq (3) ...
436 t = self.dup(tx=r.sx, ty=r.sy, tz=r.sz, # Xyy-dot
437 s1=0, name=NN(self.name, _v_))
438 v = t.transform(r.tx, r.ty, r.tz) # Xyy
439 return v
441 @Property
442 def Xform(self):
443 '''Get the Xform of this Helmert (L{TRFXform} or C{None}).
444 '''
445 return self._Xform
447 @Xform.setter # PYCHOK setter!
448 def Xform(self, Xform):
449 '''Set the Xform of this Helmert (L{TRFXform}).
451 @raise TypeError: Invalid B{C{Xform}}.
452 '''
453 _xinstanceof(TRFXform, Xform=Xform)
454 self._Xform = Xform
457class TRFXform7Tuple(_NamedTuple):
458 '''7-Tuple C{(tx, ty, tz, s, sx, sy, sz)} of conversion parameters with
459 translations C{tx}, C{ty} and C{tz} in C{milli-meter}, scale C{s} in
460 C{ppb} and rates C{sx}, C{sy} and C{sz} in C{milli-arc-seconds-per-year}.
462 @note: The parameters are also named as C{(Tx, Ty, Tz, D, Rx, Ry, Rz)}
463 or C{(T1, T2, T3, D, R1, R2, R3)}.
465 @see: Class L{TransformXform}'s matching keyword argument names.
466 '''
467 _Names_ = (_tx_, _ty_, _tz_, _s_, _sx_, _sy_, _sz_) # == kwds
468 _Units_ = (_MM, _MM, _MM, _PPB, _MAS, _MAS, _MAS)
470 def __add__(self, other):
471 '''Return the sum of this and an other L{TRFXform7Tuple}.
472 '''
473 _xinstanceof(TRFXform7Tuple, other=other)
474 return type(self)(((s + t) for s, t in _zip(self, other)),
475 name=_PLUS_) # .fsums._add_op_
477 def __eq__(self, other):
478 return isinstance(other, TRFXform7Tuple) and all(s == t for s, t in
479 _zip(self, other))
481 def __hash__(self):
482 return self._hash # memoized
484 def __mul__(self, factor):
485 _xisscalar(factor=factor)
486 return type(self)(s * factor for s in self)
488 def __neg__(self):
489 return self.inverse()
491 @Property_RO
492 def _hash(self):
493 return hash(s for s in self)
495 def inverse(self, name=NN):
496 '''Return the inverse of this transform.
498 @kwarg name: Optional name (C{str}).
500 @return: Inverse (L{TransformXform}).
501 '''
502 n = name or _minus(self.name)
503 return type(self)(map(neg, self), name=n)
505 @Property_RO
506 def isunity(self):
507 '''Is this a C{unity, identidy} transform (C{bool}).
508 '''
509 return not any(self)
512class TRFXform(_Named):
513 '''Terrestrial Reference Frame (TRF) converter between two
514 reference frames observed at an C{epoch}.
515 '''
516 _epoch = _EP0CH
517 refName1 = \
518 refName2 = NN
519 rates = \
520 xform = TRFXform7Tuple(_0_0s(len(
521 TRFXform7Tuple._Names_)))
523 def __init__(self, refName1, refName2, epoch=None,
524 xform=None, rates=None, name=NN):
525 '''New L{trfXform}.
527 @arg refName1: Source reframe (C{str}), converting I{from}.
528 @arg refName2: Destination reframe (C{str}), converting I{to}.
529 @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str}).
530 @kwarg xform: I{Transform} parameters (L{TRFXform7Tuple}).
531 @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), as B{C{xform}},
532 but in C{units-per-year}.
533 @kwarg name: Optional name (C{str})
535 @return: The new TRF converter (L{TRFXform}).
537 @raise TRFError: Invalid B{C{epoch}}, B{C{xform}} or B{C{rates}}.
538 '''
539 self.refName1 = str(refName1)
540 self.refName2 = str(refName2)
541 _xinstanceof(TRFXform7Tuple, xform=xform, rates=rates)
542 self.epoch = epoch
543 self.xform = xform
544 self.rates = rates
545 self.rename(name or self.toStr())
547 def __eq__(self, other):
548 return isinstance(other, TRFXform) and self.epoch == other.epoch and \
549 self.xform == other.xform and self.rates == other.rates
551 def __lt__(self, other): # for sorting
552 return isinstance(other, TRFXform) and (self.refName1 < other.refName1
553 or self.refName2 < other.refName2
554 or self.epoch < other.epoch)
556 def __neg__(self):
557 return self.inverse()
559 def __repr__(self):
560 return self.toRepr()
562 def _at(self, epoch):
563 '''(INTERNAL) Return C{self.name@epoch}.
564 '''
565 n = self.name
566 if epoch != self.epoch:
567 _e = _AT_(NN, epoch)
568 if not n.endswith(_e):
569 n = NN(n, _e)
570 return n
572 @Property
573 def epoch(self):
574 '''Get the epoch (L{Epoch}).
575 '''
576 return self._epoch
578 @epoch.setter # PYCHOK setter!
579 def epoch(self, epoch):
580 '''Set the epoch (L{Epoch}, C{scalar} or C{str}).
582 @raise TRFError: Invalid B{C{epoch}}.
583 '''
584 e = _Epoch(epoch)
585 if self._epoch != e:
586 self._epoch = e
587 self.rename(self._at(e))
589 def _7Helmert(self, epoch, factor):
590 '''(INTERNAL) Get the Helmert parameters observed at C{epoch}
591 converted by factor C{factor}, I{signed} (C{dict}).
592 '''
593 e = epoch - self.epoch # delta in fractional years
594 t = (self.xform + self.rates * e) * factor
595 return dict(t.items())
597 def inverse(self, name=NN):
598 '''Return the inverse of this Xform.
600 @return: Inverse (L{TRFXform}).
601 '''
602 return self.dup(refName1=self.refName2, xform=-self.xform,
603 refName2=self.refName1, rates=-self.rates,
604 name=name or _minus(self.name))
606 def _range(self, *e1_e2):
607 '''(INTERNAL) Epoch "range", distance.
608 '''
609 def _r(e):
610 e -= self.epoch
611 return (-e) if e < 0 else (e * 2)
613 return sum(map(_r, e1_e2)) if e1_e2 else self.epoch
615 def _reframe(self, name, datum=_GRS80):
616 '''(INTERNAL) Get an un-/registered frame.
617 '''
618 r = RefFrames.get(name)
619 if r is None or r.datum != datum:
620 r = RefFrame(self.epoch, datum)
621 r.name = name # unregistered
622 return r
624 @property_RO
625 def reframe1(self):
626 '''Get the un-/registered I{from} frame (C{RefFrame}).
627 '''
628 return self._reframe(self.refName1)
630 @property_RO
631 def reframe2(self):
632 '''Get the un-/registered I{to} frame (C{RefFrame}).
633 '''
634 return self._reframe(self.refName2)
636 def rename(self, name=NN):
637 '''Change this Xform's name.
639 @arg name: The new name (C{str}), overriding the
640 base name C{"refName1@epochxrefName2"}.
642 @return: The old name (C{str}).
643 '''
644 return _Named.rename(self, name or self.toStr())
646 def toEpoch(self, epoch):
647 '''Convert this Xform to B{C{epoch}}, if needed.
649 @arg epoch: Epoch, fractional year (C{Epoch}, C{scalar}
650 or C{str}).
652 @return: This Xform or a copy converted to B{C{epoch}}.
654 @raise TRFError: Invalid B{C{epoch}}.
655 '''
656 e = _Epoch(epoch) - self.epoch
657 if e:
658 t = self.xform + self.rates * e
659 X = self.dup(epoch=epoch, xform=t)
660 else:
661 X = self
662 return X
664 def toRefFrame(self, point, epoch=None, datum=_GRS80, **epoch2_name):
665 '''Convert an ellipsoidal point from this Xform's C{refName1} and
666 C{epoch} to this Xform's C{refName1} and C{epoch2 or epoch}.
668 @arg point: The point to convert (C{Cartesian} or C{LatLon}).
669 @kwarg epoch: Optional epoch ((L{Epoch}, C{scalar} or C{str})), overriding
670 this Xform's C{epoch}.
671 @kwarg datum: Optional datum to define a temporary L{RefFrame} from this
672 Xform's C{refName1} or C{refName2} (C{datum}).
673 @kwarg epoch2_name: Optional keyword arguments B{C{epoch2}=None} and
674 C{B{name}=NN}.
676 @return: A copy of the B{C{point}}, converted or renamed.
678 @see: Method L{RefFrame.toRefFrame} for more details.
679 '''
680 def _r(name):
681 r = RefFrames.get(name)
682 if r is None or r.datum != datum:
683 r = RefFrame(self.epoch, datum)
684 r.name = name # unregistered
685 return r
687 return _r(self.refName1).toRefFrame(point,
688 _r(self.refName2), epoch=epoch, **epoch2_name)
690 def toRepr(self, **unused): # PYCHOK signature
691 '''Return the represention of this Xform (C{str}).
692 '''
693 return unstr(self.classname, epoch=self.epoch, name=self.name)
695 def toStr(self, epoch=None, **unused): # PYCHOK signature
696 '''Return this Xform as C{"refName1@epochxrefName2"} (C{str}).
698 @kwarg epoch: Epoch (C{scalar}), overriding this Xform's epoch.
699 '''
700 e = epoch or self.epoch
701 return NN(_AT_(self.refName1, e), _x_, self.refName2)
703 def toTransform(self, epoch1, epoch2=None, inverse=False):
704 '''Combine this Xform observed at B{C{epoch1}} into a Helmert
705 L{TransformXform}, optionally at B{C{epoch2 or epoch1}}.
707 @arg epoch1: Epoch to observe I{from} (C{scalar}).
708 @kwarg epoch2: Optional epoch to observe I{to} (C{scalar}).
709 @kwarg inverse: Invert the Helmert tranform (C{bool}).
711 @return: The Helmert transform (L{TransformXform}).
713 @raise TRFError: Invalid B{C{epoch1}} or B{C{epoch2}}.
715 @note: Translations are converted from C{milli-meter} to
716 C{meter}, shift rates from C{milli-arc-seconds} to
717 C{arc-seconds} and scale from C{ppb} to C{ppM}.
718 '''
719 e = Epoch(epoch2=epoch1 if epoch2 is None else epoch2)
720 X = self.dup() if e == epoch1 else self.toEpoch(epoch1)
721 if inverse:
722 X = X.inverse()
723 H = TransformXform(name=X._at(e), **X._7Helmert(e, _MM2M))
724 X.epoch = e
725 H.Xform = X
726 return H
729def date2epoch(year, month, day):
730 '''Return the C{epoch} for a calendar day.
732 @arg year: Year of the date (C{scalar}).
733 @arg month: Month in the B{C{year}} (C{scalar}, 1..12).
734 @arg day: Day in the B{C{month}} (C{scalar}, 1..31).
736 @return: Epoch, the fractional year (C{float}).
738 @raise TRFError: Invalid B{C{year}}, B{C{month}} or B{C{day}}.
740 @note: Any B{C{year}} is considered a leap year, i.e. having
741 29 days in February.
742 '''
743 try:
744 y, m, d = map1(int, year, month, day)
745 if y > 0 and 1 <= m <= 12 and 1 <= d <= _mDays[m]:
746 e = y + float(sum(_mDays[:m]) + d) / _366_0
747 return Epoch(e, low=0)
749 raise ValueError # _invalid_
750 except (TRFError, TypeError, ValueError) as x:
751 raise TRFError(year=year, month=month, day=day, cause=x)
754def epoch2date(epoch):
755 '''Return the date for a reference frame C{epoch}.
757 @arg epoch: Fractional year (C{scalar}).
759 @return: 3-Tuple C{(year, month, day)}.
761 @raise TRFError: Invalid B{C{epoch}}.
763 @note: Any B{C{year}} is considered a leap year, i.e. having
764 29 days in February.
765 '''
766 e = _Epoch(epoch, low=0)
767 y = int(e)
768 d = int(ceil(_366_0 * (e - y)))
769 for m, n in enumerate(_mDays[1:]):
770 if d > n:
771 d -= n
772 else:
773 break
774 return y, (m + 1), max(1, d)
777def _Epoch(e, **kwds):
778 '''(INTERNAL) Get an C{Epoch(B{e})}.
779 '''
780 return Epoch(e, **kwds) if kwds or not isinstance(e, Epoch) else e
783def _eT0Ds4(inst, reframe, epoch, reframe2, epoch2):
784 '''(INTERNAL) Get epoch, a Helmert L{Transform}s or 0-tuple, datum
785 and datum2 to convert B{C{refFrame}} observed at B{C{epoch}}
786 into B{C{refFrame2}} observed at C{epoch2 or epoch}.
787 '''
788 r = reframe or inst.reframe
789 if not r:
790 t = _SPACE_(_DOT_(repr(inst), _reframe_), MISSING)
791 raise TRFError(_no_(_conversion_), txt=t)
793 _xinstanceof(RefFrame, reframe2=reframe2, reframe=r)
795 e1 = _Epoch(epoch or inst.epoch or r.epoch)
796 e2 = e1 if epoch2 is None else Epoch(epoch2=epoch2)
798 t0 = _toTransform0(r.name, e1, reframe2.name, e2)
799 if t0 is None:
800 t = _SPACE_(RefFrame.__name__, _AT_(r.name, e1),
801 _to_, _AT_(reframe2.name, e2))
802 raise TRFError(_no_(_conversion_), txt=t)
804 if t0:
805 e2 = t0.Xform.epoch
806 return e2, t0, r.datum, reframe2.datum
809def _immediate(n1, n2, *unused):
810 '''(INTERNAL) Get the C{n1} to C{n2} Xform or C{None}.
811 '''
812 X = RefFrames.get(n1)
813 if X:
814 X = X._Xs.get(n2, None)
815 return X
818def _intermediate(n1, n2, *e1_e2):
819 '''(INTERNAL) Find an Xform "between" C{n1} and C{n2}.
820 '''
821 def _e(e1=0, e2=0):
822 return e1 - e2
824 def _X4(_Xs):
825 for n, X1 in _Xs.items():
826 X2 = _immediate(n, n2)
827 if X2:
828 yield (X1._range(*e1_e2) + X2._range(*e1_e2)), X1, X2, True
829 X2 = _immediate(n2, n)
830 if X2:
831 yield (X1._range(*e1_e2) + X2._range(*e1_e2)), X1, X2, False
833 X, r = None, RefFrames.get(n1)
834 if r:
835 i = sorted(_X4(r._Xs))
836 if i:
837 _, X1, X2, f = i.pop(0)
838 e1, e2 = X1.epoch, X2.epoch
839 if e1 > e2 and _e(*e1_e2) < 0: # X1 to e2
840 X1 = X1.toEpoch(e2)
841 e1 = e2
842 elif e1 != e2: # X2 to e1
843 X2 = X2.toEpoch(e1)
844 # U{Appendix, Table 7, last column "Sum of the previous ..."
845 # <https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf">}
846 X = TRFXform(n1, n2, epoch=e1,
847 xform=X1.xform + (X2.xform if f else -X2.xform),
848 rates=X1.rates + (X2.rates if f else -X2.rates),
849 name=NN(X1._at(e1), _PLUS_ if f else _MINUS_,
850 X2._at(e1)))
851 return X
854def _P(*ps): # deleted below
855 '''(INTERNAL) De-dup L{TRFXform7Tuple}s.
856 '''
857 t = TRFXform7Tuple(map(_F, ps))
858 return _Ps.setdefault(t, t) # PYCHOK del
861def _reframe(**name_reframe):
862 '''(INTERNAL) Get a C{reframe}.
863 '''
864 if len(name_reframe) == 1:
865 for n, r in name_reframe.items():
866 break
867 if isstr(r):
868 r = RefFrames.get(r)
869 if r and isinstance(r, RefFrame):
870 return r
871 raise TRFError(**name_reframe) # _invalid_
874def _toTransform0(n1, e1, n2, e2):
875 '''(INTERNAL) Return a L{TransformXform}, 0-tuple or C{None}.
876 '''
877 if (n1 == n2 and e1 == e2) or \
878 (n1.startswith(_ITRF_) and n2.startswith(_WGS84_)) or \
879 (n2.startswith(_ITRF_) and n1.startswith(_WGS84_)):
880 return ()
882 for _f in (_immediate, _intermediate):
883 X = _f(n1, n2, e1, e2)
884 Y = _f(n2, n1, e1, e2)
885 if X and Y:
886 if X._range(e1, e2) < Y._range(e1, e2):
887 Y = None
888 else:
889 X = None
890 if X:
891 return X.toTransform(e1, epoch2=e2)
892 if Y:
893 return Y.toTransform(e1, epoch2=e2, inverse=True)
895 return None
898def trfTransform0(reframe, reframe2, epoch=None, epoch2=None):
899 '''Get the L{TransformXform} to convert a C{reframe} observed at C{epoch} to
900 C{reframe2} at observed at C{epoch2 or epoch}.
902 @arg reframe: Reference frame to convert I{from} (L{RefFrame} or C{str}).
903 @arg reframe2: Reference frame to convert I{to} (L{RefFrame} or C{str}).
904 @arg epoch: Epoch to observe I{from} (L{Epoch}, C{scalar} or C{str}),
905 otherwise C{B{reframe}}'s C{epoch}.
906 @kwarg epoch2: Optional epoch to observe to observe I{to} (L{Epoch}, C{scalar}
907 or C{str}), otherwise B{C{epoch}} or C{B{reframe}}'s C{epoch}.
909 @return: A L{TransformXform} instance, a C{0-tuple} for I{unity, identity} or
910 C{None} if no conversion exists.
912 @raise TRFError: Invalid B{C{reframe}}, B{C{epoch}}, B{C{reframe2}} or
913 B{C{epoch2}}.
915 @raise TypeError: Invalid B{C{reframe}} or B{C{reframe2}}.
916 '''
917 r1 = _reframe(reframe=reframe)
918 e1 = r1.epoch if epoch is None else _Epoch(epoch)
919 r2 = _reframe(reframe2=reframe2)
920 e2 = e1 if epoch2 is None else Epoch(epoch2=epoch2)
921 return _toTransform0(r1.name, e1, r2.name, e2)
924def trfXform(reframe1, reframe2, epoch=None, xform=None, rates=None):
925 '''Define a new Terrestrial Reference Frame (TRF) converter.
927 @arg reframe1: Source reframe (L{RefFrame} or C{str}), converting I{from}.
928 @arg reframe2: Destination reframe (L{RefFrame} or C{str}), converting I{to}.
929 @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str})
930 or C{None} for C{B{reframe2}}'s epoch.
931 @kwarg xform: I{Transform} parameters (L{TRFXform7Tuple}).
932 @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), as B{C{xform}},
933 but in C{units-per-year}.
935 @return: The new TRF converter (L{TRFXform}).
937 @raise TRFError: Invalid B{C{reframe1}}, B{C{reframe2}}, B{C{epoch}},
938 B{C{xform}} or B{C{rates}} or the TRF converter
939 already exists.
940 '''
941 r1 = _reframe(reframe1=reframe1)
942 r2 = _reframe(reframe2=reframe2)
943 e = r2.epoch if epoch is None else _Epoch(epoch)
944 _xinstanceof(TRFXform7Tuple, xform=xform, rates=rates)
945 return _trfX(r1.name, r2.name, epoch=e, xform=xform, rates=rates)
948def _trfX(n1, n2, **epoch_xform_rates):
949 '''(INTERNAL) New, I{unique} L{TRFXform} converter.
950 '''
951 r1 = RefFrames.get(n1)
952 r2 = RefFrames.get(n2)
953 if r1 and r2:
954 if n2 in r1._Xs:
955 t = _exists_
956 elif n1 in r2._Xs:
957 t = _SPACE_(_inverse_, _exists_)
958 else:
959 r1._Xs[n2] = X = TRFXform(n1, n2, **epoch_xform_rates)
960 return X
961 else:
962 t = _invalid_
963 raise TRFError(trfX=_SPACE_(n1, _to_, n2), txt=t) # _NameError
966# TRF conversions specified as an epoch and 2 sets of 7-parameters. Most from Altamimi, Z. U{"EUREF Technical
967# Note 1: Relationship and Transformation between the International and the European Terrestrial Reference
968# Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Appendix A, more at U{Quinsy QPS <https://
969# confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ITRF_Transformation_Parameters.xlsx>}.
970# See also U{Quinsy International Terrestrial Reference Frame 2014 (ITRF2014)<https://confluence.QPS.NL/qinsy/latest/
971# en/international-terrestrial-reference-frame-2014-itrf2014-182618383.html>}.
972_trfX(_ITRF2020_, _ITRF2014_, epoch=_E(2015), # <https://ITRF.IGN.Fr/docs/solutions/itrf2020/Transfo-ITRF2020_TRFs.txt>
973 xform=_P( -1.4, -0.9, 1.4, -0.42, _0_0, _0_0, _0_0),
974 rates=_P( _0_0, -0.1, 0.2, _0_0, _0_0, _0_0, _0_0))
975_trfX(_ITRF2020_, _ITRF2008_, epoch=_E(2015),
976 xform=_P( 0.2, 1.0, 3.3, -0.29, _0_0, _0_0, _0_0),
977 rates=_P( _0_0, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0))
978_trfX(_ITRF2020_, _ITRF2005_, epoch=_E(2015),
979 xform=_P( 2.7, 0.1, -1.4, 0.65, _0_0, _0_0, _0_0),
980 rates=_P( 0.3, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0))
981_trfX(_ITRF2020_, _ITRF2000_, epoch=_E(2015),
982 xform=_P( -0.2, 0.8, -34.2, 2.25, _0_0, _0_0, _0_0),
983 rates=_P( 0.1, _0_0, -1.7, 0.11, _0_0, _0_0, _0_0))
984_trfX(_ITRF2020_, _ITRF97_, epoch=_E(2015),
985 xform=_P( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
986 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
987_trfX(_ITRF2020_, _ITRF96_, epoch=_E(2015),
988 xform=_P( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
989 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
990_trfX(_ITRF2020_, _ITRF94_, epoch=_E(2015),
991 xform=_P( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
992 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
993_trfX(_ITRF2020_, _ITRF93_, epoch=_E(2015),
994 xform=_P( -65.8, 1.9, -71.3, 4.47, -3.36, -4.33, 0.75),
995 rates=_P( -2.8, -0.2, -2.3, 0.12, -0.11, -0.19, 0.07))
996_trfX(_ITRF2020_, _ITRF92_, epoch=_E(2015),
997 xform=_P( 14.5, -1.9, -85.9, 3.27, _0_0, _0_0, 0.36),
998 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
999_trfX(_ITRF2020_, _ITRF91_, epoch=_E(2015),
1000 xform=_P( 26.5, 12.1, -91.9, 4.67, _0_0, _0_0, 0.36),
1001 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1002_trfX(_ITRF2020_, _ITRF90_, epoch=_E(2015),
1003 xform=_P( 24.5, 8.1, -107.9, 4.97, _0_0, _0_0, 0.36),
1004 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1005_trfX(_ITRF2020_, _ITRF89_, epoch=_E(2015),
1006 xform=_P( 29.5, 32.1, -145.9, 8.37, _0_0, _0_0, 0.36),
1007 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1008_trfX(_ITRF2020_, _ITRF88_, epoch=_E(2015),
1009 xform=_P( 24.5, -3.9, -169.9, 11.47, 0.1, _0_0, 0.36),
1010 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
1012# see U{Transformation Parameters ITRF2014<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2014_ITRFs.txt>} and
1013# Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1014# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1.pdf>} Appendix A.
1015_trfX(_ITRF2014_, _ITRF2008_, epoch=(2010), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2014/tp_14-08.php>
1016 xform=_P( 1.6, 1.9, 2.4, -0.02, _0_0, _0_0, _0_0),
1017 rates=_P( _0_0, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0))
1018_trfX(_ITRF2014_, _ITRF2005_, epoch=_E(2010),
1019 xform=_P( 2.6, _1_0, -2.3, 0.92, _0_0, _0_0, _0_0),
1020 rates=_P( 0.3, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0))
1021_trfX(_ITRF2014_, _ITRF2000_, epoch=_E(2010),
1022 xform=_P( 0.7, 1.2, -26.1, 2.12, _0_0, _0_0, _0_0),
1023 rates=_P( 0.1, 0.1, -1.9, 0.11, _0_0, _0_0, _0_0))
1024_trfX(_ITRF2014_, _ITRF97_, epoch=_E(2010),
1025 xform=_P( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1026 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1027_trfX(_ITRF2014_, _ITRF96_, epoch=_E(2010),
1028 xform=_P( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1029 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1030_trfX(_ITRF2014_, _ITRF94_, epoch=_E(2010),
1031 xform=_P( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
1032 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1033_trfX(_ITRF2014_, _ITRF93_, epoch=_E(2010),
1034 xform=_P( -50.4, 3.3, -60.2, 4.29, -2.81, -3.38, 0.4),
1035 rates=_P( -2.8, -0.1, -2.5, 0.12, -0.11, -0.19, 0.07))
1036_trfX(_ITRF2014_, _ITRF92_, epoch=_E(2010),
1037 xform=_P( 15.4, 1.5, -70.8, 3.09, _0_0, _0_0, 0.26),
1038 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1039_trfX(_ITRF2014_, _ITRF91_, epoch=_E(2010),
1040 xform=_P( 27.4, 15.5, -76.8, 4.49, _0_0, _0_0, 0.26),
1041 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1042_trfX(_ITRF2014_, _ITRF90_, epoch=_E(2010),
1043 xform=_P( 25.4, 11.5, -92.8, 4.79, _0_0, _0_0, 0.26),
1044 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1045_trfX(_ITRF2014_, _ITRF89_, epoch=_E(2010),
1046 xform=_P( 30.4, 35.5, -130.8, 8.19, _0_0, _0_0, 0.26),
1047 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1048_trfX(_ITRF2014_, _ITRF88_, epoch=_E(2010),
1049 xform=_P( 25.4, -0.5, -154.8, 11.29, 0.1, _0_0, 0.26),
1050 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
1052# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1053# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 1st and 2nd column
1054_trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2005),
1055 xform=_P( -0.5, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1056 rates=_P( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1057# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(1997),
1058# xform=_P( -2.9, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1059# rates=_P( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1060# see U{Transformation Parameters ITRF2008<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2008_ITRFs.txt>}
1061# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2008/tp_08-05.php>
1062# xform=_P( -2.0, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
1063# rates=_P( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1064_trfX(_ITRF2008_, _ITRF2000_, epoch=_E(2000),
1065 xform=_P( -1.9, -1.7, -10.5, 1.34, _0_0, _0_0, _0_0),
1066 rates=_P( 0.1, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1067_trfX(_ITRF2008_, _ITRF97_, epoch=_E(2000),
1068 xform=_P( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1069 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1070_trfX(_ITRF2008_, _ITRF96_, epoch=_E(2000),
1071 xform=_P( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1072 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1073_trfX(_ITRF2008_, _ITRF94_, epoch=_E(2000),
1074 xform=_P( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
1075 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1076_trfX(_ITRF2008_, _ITRF93_, epoch=_E(2000),
1077 xform=_P( -24.0, 2.4, -38.6, 3.41, -1.71, -1.48, -0.3),
1078 rates=_P( -2.8, -0.1, -2.4, 0.09, -0.11, -0.19, 0.07))
1079_trfX(_ITRF2008_, _ITRF92_, epoch=_E(2000),
1080 xform=_P( 12.8, 4.6, -41.2, 2.21, _0_0, _0_0, 0.06),
1081 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1082_trfX(_ITRF2008_, _ITRF91_, epoch=_E(2000),
1083 xform=_P( 24.8, 18.6, -47.2, 3.61, _0_0, _0_0, 0.06),
1084 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1085_trfX(_ITRF2008_, _ITRF90_, epoch=_E(2000),
1086 xform=_P( 22.8, 14.6, -63.2, 3.91, _0_0, _0_0, 0.06),
1087 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1088_trfX(_ITRF2008_, _ITRF89_, epoch=_E(2000),
1089 xform=_P( 27.8, 38.6, -101.2, 7.31, _0_0, _0_0, 0.06),
1090 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1091_trfX(_ITRF2008_, _ITRF88_, epoch=_E(2000),
1092 xform=_P( 22.8, 2.6, -125.2, 10.41, 0.1, _0_0, 0.06),
1093 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
1095# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1096# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 3rd column
1097# _trfX(_ITRF2005_, _ITRF2000_, epoch=_E(1997),
1098# xform=_P( 0.7, -1.1, -0.4, 0.16, -0.2, 0.1 -1.8),
1099# rates=_P( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1100_trfX(_ITRF2005_, _ITRF2000_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2005/tp_05-00.php>
1101 xform=_P( 0.1, -0.8, -5.8, 0.4, _0_0, _0_0, _0_0),
1102 rates=_P( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
1104_trfX(_ITRF2000_, _ITRF97_, epoch=_E(1997),
1105 xform=_P( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1106 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, -0.02)) # 0.02?
1107_trfX(_ITRF2000_, _ITRF96_, epoch=_E(1997),
1108 xform=_P( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1109 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1110_trfX(_ITRF2000_, _ITRF94_, epoch=_E(1997),
1111 xform=_P( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
1112 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1113_trfX(_ITRF2000_, _ITRF93_, epoch=_E(1988),
1114 xform=_P( 12.7, 6.5, -20.9, 1.95, -0.39, 0.8, -1.14),
1115 rates=_P( -2.9, -0.2, -0.6, 0.01, -0.11, -0.19, 0.07))
1116_trfX(_ITRF2000_, _ITRF92_, epoch=_E(1988),
1117 xform=_P( 1.47, 1.35, -1.39, 0.75, _0_0, _0_0, -0.18),
1118 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1119_trfX(_ITRF2000_, _ITRF91_, epoch=_E(1988),
1120 xform=_P( 26.7, 27.5, -19.9, 2.15, _0_0, _0_0, -0.18),
1121 rates=_P( _0_0, -0.6, -1.4, 0.01, _0_0, _0_0, 0.02))
1122_trfX(_ITRF2000_, _ITRF90_, epoch=_E(1988),
1123 xform=_P( 2.47, 2.35, -3.59, 2.45, _0_0, _0_0, -0.18),
1124 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1125_trfX(_ITRF2000_, _ITRF89_, epoch=_E(1988),
1126 xform=_P( 2.97, 4.75, -7.39, 5.85, _0_0, _0_0, -0.18),
1127 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1128_trfX(_ITRF2000_, _ITRF88_, epoch=_E(1988),
1129 xform=_P( 2.47, 1.15, -9.79, 8.95, 0.1, _0_0, -0.18),
1130 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1132# Soler, T .& Snay R.A. U{"Transforming Positions and Velocities between the International Terrestrial
1133# Reference Frame of 2000 and North American Datum of 1983"<https://www.ResearchGate.net/publication/245291390>},
1134# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1135# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 5th and 6th column
1136_trfX(_ITRF97_, _ITRF96_, epoch=_E(1997),
1137 xform=_P( -2.07, -0.21, 9.95, -0.93496, 0.1267, -0.22355, -0.06065,),
1138 rates=_P( 0.69, -0.1, 1.86, -0.19201, 0.01347, -0.01514, 0.00027))
1139_trfX(_ITRF96_, _NAD83_, epoch=_E(1997),
1140 xform=_P( 991.0, -190.72, -512.9, _0_0, 25.79, 9.65, 11.66,),
1141 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.0532, -0.7423, -0.0316,))
1143# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1144# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 1.
1145# _trfX(_ITRF2020_, _ETRF2020_, epoch=_E(1989), # see Table 2 below
1146# xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0),
1147# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753))
1148# _trfX(_ITRF2014_, _ETRF2014_, epoch=_E(1989), # see Table 3 below
1149# xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0),
1150# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77))
1151_trfX(_ITRF2005_, _ETRF2005_, epoch=_E(1989),
1152 xform=_P( 56.0, 48.0, -37.0, _0_0, _0_0, _0_0, _0_0),
1153 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.054, 0.518, -0.781))
1154# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(1989), # see Table 4 below
1155# xform=_P( 54.0, 51.0, -48.0, _0_0, _0_0, _0_0, _0_0),
1156# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1157_trfX(_ITRF97_, _ETRF97_, epoch=_E(1989),
1158 xform=_P( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1159 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1160_trfX(_ITRF96_, _ETRF96_, epoch=_E(1989),
1161 xform=_P( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1162 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1163_trfX(_ITRF94_, _ETRF94_, epoch=_E(1989),
1164 xform=_P( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1165 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1166_trfX(_ITRF93_, _ETRF93_, epoch=_E(1989),
1167 xform=_P( 19.0, 53.0, -21.0, _0_0, _0_0, _0_0, _0_0),
1168 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.32, 0.78, -0.67))
1169_trfX(_ITRF92_, _ETRF92_, epoch=_E(1989),
1170 xform=_P( 38.0, 40.0, -37.0, 0.0, 0.0, 0.0, 0.0),
1171 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68))
1172_trfX(_ITRF91_, _ETRF91_, epoch=_E(1989),
1173 xform=_P( 21.0, 25.0, -37.0, _0_0, _0_0, _0_0, _0_0),
1174 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68))
1175_trfX(_ITRF90_, _ETRF90_, epoch=_E(1989),
1176 xform=_P( 19.0, 28.0, -23.0, _0_0, _0_0, _0_0, _0_0),
1177 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71))
1178_trfX(_ITRF89_, _ETRF89_, epoch=_E(1989),
1179 xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0),
1180 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71))
1182# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1183# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 2.
1184_trfX(_ITRF2020_, _ETRF2020_, epoch=_E(2015),
1185 xform=_P( _0_0, _0_0, _0_0, _0_0, 2.236, 13.494, -19.578),
1186 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753))
1187_trfX(_ITRF2014_, _ETRF2020_, epoch=_E(2015),
1188 xform=_P( 1.4, 0.9, -1.4, 0.42, 2.236, 13.494, -19.578),
1189 rates=_P( _0_0, 0.1, -0.2, _0_0, 0.086, 0.519, -0.753))
1190_trfX(_ITRF2008_, _ETRF2020_, epoch=_E(2015),
1191 xform=_P( 3.0, 2.8, 0.5, 0.55, 2.236, 13.494, -19.578),
1192 rates=_P( _0_0, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753))
1193_trfX(_ITRF2005_, _ETRF2020_, epoch=_E(2015),
1194 xform=_P( 5.5, 1.9, -4.2, 1.49, 2.236, 13.494, -19.578),
1195 rates=_P( 0.3, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753))
1196_trfX(_ITRF2000_, _ETRF2020_, epoch=_E(2015),
1197 xform=_P( 2.6, 2.6, -37.0, 3.09, 2.236, 13.494, -19.578),
1198 rates=_P( 0.1, 0.2, -2.1, 0.11, 0.086, 0.519, -0.753))
1199_trfX(_ITRF97_, _ETRF2020_, epoch=_E(2015),
1200 xform=_P( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1201 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1202_trfX(_ITRF96_, _ETRF2020_, epoch=_E(2015),
1203 xform=_P( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1204 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1205_trfX(_ITRF94_, _ETRF2020_, epoch=_E(2015),
1206 xform=_P( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1207 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1208_trfX(_ITRF93_, _ETRF2020_, epoch=_E(2015),
1209 xform=_P( -63.0, 3.7, -74.1, 5.31, -1.124, 9.164, -18.828),
1210 rates=_P( -2.8, _0_0, -2.7, 0.12, -0.024, 0.329, -0.683))
1211_trfX(_ITRF92_, _ETRF2020_, epoch=_E(2015),
1212 xform=_P( 17.3, -0.1, -88.7, 4.11, 2.236, 13.494, -19.218),
1213 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1214_trfX(_ITRF91_, _ETRF2020_, epoch=_E(2015),
1215 xform=_P( 29.3, 13.9, -94.7, 5.51, 2.236, 13.494, -19.218),
1216 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1217_trfX(_ITRF90_, _ETRF2020_, epoch=_E(2015),
1218 xform=_P( 27.3, 9.9, -110.7, 5.81, 2.236, 13.494, -19.218),
1219 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1220_trfX(_ITRF89_, _ETRF2020_, epoch=_E(2015),
1221 xform=_P( 32.3, 33.9, -148.7, 9.21, 2.236, 13.494, -19.218),
1222 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1223_trfX(_ITRF88_, _ETRF2020_, epoch=_E(2015),
1224 xform=_P( 27.3, -2.1, -172.7, 12.31, 2.336, 13.494, -19.218),
1225 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1227# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1228# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 3.
1229_trfX(_ITRF2020_, _ETRF2014_, epoch=_E(2015),
1230 xform=_P( -1.4, -0.9, 1.4, 0.42, 2.21, 13.806, -20.02),
1231 rates=_P( _0_0, -0.1, 0.2, _0_0, 0.085, 0.531, -0.77))
1232_trfX(_ITRF2014_, _ETRF2014_, epoch=_E(2015),
1233 xform=_P( _0_0, _0_0, _0_0, _0_0, 2.21, 13.806, -20.02),
1234 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77))
1235_trfX(_ITRF2008_, _ETRF2014_, epoch=_E(2015),
1236 xform=_P( -1.6, -1.9, -1.9, -0.13, 2.21, 13.806, -20.02),
1237 rates=_P( _0_0, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77))
1238_trfX(_ITRF2005_, _ETRF2014_, epoch=_E(2015),
1239 xform=_P( -4.1, -1.0, 2.8, -1.07, 2.21, 13.806, -20.02),
1240 rates=_P( -0.3, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77))
1241_trfX(_ITRF2000_, _ETRF2014_, epoch=_E(2015),
1242 xform=_P( -1.2, -1.7, 35.6, -2.67, 2.21, 13.806, -20.02),
1243 rates=_P( -0.1, -0.1, 1.9, -0.11, 0.085, 0.531, -0.77))
1244_trfX(_ITRF97_, _ETRF2014_, epoch=_E(2015),
1245 xform=_P( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1246 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1247_trfX(_ITRF96_, _ETRF2014_, epoch=_E(2015),
1248 xform=_P( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1249 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1250_trfX(_ITRF94_, _ETRF2014_, epoch=_E(2015),
1251 xform=_P( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1252 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1253_trfX(_ITRF93_, _ETRF2014_, epoch=_E(2015),
1254 xform=_P( 64.4, -2.8, 72.7, -4.89, 5.570, 18.136, -20.77),
1255 rates=_P( 2.8, 0.1, 2.5, -0.12, 0.195, 0.721, -0.84))
1256_trfX(_ITRF92_, _ETRF2014_, epoch=_E(2015),
1257 xform=_P( -15.9, 1.0, 87.3, -3.69, 2.21, 13.806, -20.38),
1258 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1259_trfX(_ITRF91_, _ETRF2014_, epoch=_E(2015),
1260 xform=_P( -27.9, -13.0, 93.3, -5.09, 2.21, 13.806, -20.38),
1261 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1262_trfX(_ITRF90_, _ETRF2014_, epoch=_E(2015),
1263 xform=_P( -25.9, -9.0, 109.3, -5.39, 2.21, 13.806, -20.38),
1264 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1265_trfX(_ITRF89_, _ETRF2014_, epoch=_E(2015),
1266 xform=_P( -30.9, -33.0, 147.3, -8.79, 2.21, 13.806, -20.38),
1267 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1268_trfX(_ITRF88_, _ETRF2014_, epoch=_E(2015),
1269 xform=_P( -25.9, 3.0, 171.3, -11.89, 2.11, 13.806, -20.38),
1270 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1272# see U{Altamimi, Z. "EUREF Technical Note 1: Relationship and Transformation between the International and
1273# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 4,
1274# U{Boucher, C. & Altamimi, Z. "Memo: Specifications for reference frame fixing in the analysis of a EUREF GPS
1275# campaign" (2011) <https://ETRS89.ENSG.IGN.Fr/memo-V8.pdf>} and U{Altamimi, Z. "Key results of ITRF2014 and
1276# implication to ETRS89 realization", EUREF2016<https://www.EUREF.EU/symposia/2016SanSebastian/01-02-Altamimi.pdf>}.
1277_trfX(_ITRF2020_, _ETRF2000_, epoch=_E(2015),
1278 xform=_P( 53.8, 51.8, -82.2, 2.25, 2.106, 12.74, -20.592),
1279 rates=_P( 0.1, _0_0, -1.7, 0.11, 0.081, 0.49, -0.792))
1280# _trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2000),
1281# xform=_P( 53.7, 51.2, -55.1, 1.02, 0.891, 5.39, -8.712),
1282# rates=_P( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792))
1283_trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2015),
1284 xform=_P( 55.2, 52.7, -83.6, 2.67, 2.106, 12.74, -20.592),
1285 rates=_P( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792))
1286# _trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2000),
1287# xform=_P( 52.1, 49.3, -58.5, 1.34, 0.891, 5.39, -8.712),
1288# rates=_P( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1289_trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2015),
1290 xform=_P( 53.6, 50.8, -85.5, 2.54, 2.106, 12.74, -20.592),
1291 rates=_P( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1292# _trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2000),
1293# xform=_P( 54.1, 50.2, -53.8, 0.4, 0.891, 5.39, -8.712),
1294# rates=_P( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1295_trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2015),
1296 xform=_P( 51.1, 51.7, -80.8, 1.6, 2.106, 12.74, -20.592),
1297 rates=_P( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1298# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2000),
1299# xform=_P( 54.0, 51.0, -48.0, _0_0, 0.891, 5.39, -8.712),
1300# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1301_trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2015),
1302 xform=_P( 54.0, 51.0, -48.0, _0_0, 2.106, 12.74, -20.592),
1303 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1304_trfX(_ITRF97_, _ETRF2000_, epoch=_E(2015),
1305 xform=_P( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1306 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1307_trfX(_ITRF96_, _ETRF2000_, epoch=_E(2015),
1308 xform=_P( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1309 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1310_trfX(_ITRF94_, _ETRF2000_, epoch=_E(2015),
1311 xform=_P( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1312 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1313_trfX(_ITRF93_, _ETRF2000_, epoch=_E(2015),
1314 xform=_P( 119.6, 49.9, -10.9, -2.22, 5.466, 17.07, -21.342),
1315 rates=_P( 2.9, 0.2, 0.6, -0.01, 0.191, 0.68, -0.862))
1316_trfX(_ITRF92_, _ETRF2000_, epoch=_E(2015),
1317 xform=_P( 39.3, 53.7, 3.7, -1.02, 2.106, 12.74, -20.952),
1318 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1319_trfX(_ITRF91_, _ETRF2000_, epoch=_E(2015),
1320 xform=_P( 27.3, 39.7, 9.7, -2.42, 2.106, 12.74, -20.952),
1321 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1322_trfX(_ITRF90_, _ETRF2000_, epoch=_E(2015),
1323 xform=_P( 29.3, 43.7, 25.7, -2.72, 2.106, 12.74, -20.952),
1324 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1325_trfX(_ITRF89_, _ETRF2000_, epoch=_E(2015),
1326 xform=_P( 24.3, 19.7, 63.7, -6.12, 2.106, 12.74, -20.952),
1327 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1328_trfX(_ITRF88_, _ETRF2000_, epoch=_E(2015),
1329 xform=_P( 29.3, 55.7, 87.7, -9.22, 2.006, 12.74, -20.952),
1330 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1332# GDA2020 "Geocentric Datum of Australia 2020 Technical Manual", v1.5, 2020-12-09, Table 3.3 and 3.4
1333# <https://www.ICSM.gov.AU/sites/default/files/2020-12/GDA2020%20Technical%20Manual%20V1.5_4.pdf>
1334# (the GDA2020 xforms are different but the rates are the same as GDA94, further below)
1335_trfX(_ITRF2014_, _GDA2020_, epoch=_E(2020),
1336 xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0),
1337 rates=_P( _0_0, _0_0, _0_0, _0_0, 1.50379, 1.18346, 1.20716))
1338_trfX(_ITRF2008_, _GDA2020_, epoch=_E(2020),
1339 xform=_P( 13.79, 4.55, 15.22, 2.5, 0.2808, 0.2677, -0.4638),
1340 rates=_P( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551))
1341_trfX(_ITRF2005_, _GDA2020_, epoch=_E(2020),
1342 xform=_P( 40.32, -33.85, -16.72, 4.286, -1.2893, -0.8492, -0.3342),
1343 rates=_P( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701))
1344_trfX(_ITRF2000_, _GDA2020_, epoch=_E(2020),
1345 xform=_P(-105.52, 51.58, 231.68, 3.55, 4.2175, 6.3941, 0.8617),
1346 rates=_P( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224))
1348# see Table 2 in U{Dawson, J. & Woods, A. "ITRF to GDA94 coordinate transformations", Journal of Applied
1349# Geodesy 4 (2010), 189-199<https://www.ResearchGate.net/publication/258401581_ITRF_to_GDA94_coordinate_transformations>}
1350# (note, sign of rotations for GDA94 reversed as "Australia assumes rotation to be of coordinate axes",
1351# rather than the more conventional "position around the coordinate axes")
1352_trfX(_ITRF2008_, _GDA94_, epoch=_E(1994),
1353 xform=_P( -84.68, -19.42, 32.01, 9.71, -0.4254, 2.2578, 2.4015),
1354 rates=_P( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551))
1355_trfX(_ITRF2005_, _GDA94_, epoch=_E(1994),
1356 xform=_P( -79.73, -6.86, 38.03, 6.636, 0.0351, -2.1211, -2.1411),
1357 rates=_P( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701))
1358_trfX(_ITRF2000_, _GDA94_, epoch=_E(1994),
1359 xform=_P( -45.91, -29.85, -20.37, 7.07, -1.6705, 0.4594, 1.9356),
1360 rates=_P( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224))
1362# see U{Solar, T. & Snay, R.A. "Transforming Positions and Velocities between the
1363# International Terrestrial Reference Frame of 2000 and North American Datum of 1983"
1364# (2004)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>}
1365_trfX(_ITRF2000_, _NAD83_, epoch=_E(1997), # note NAD83(CORS96)
1366 xform=_P( 995.6, -1901.3, -521.5, 0.615, -25.915, -9.426, -11.599),
1367 rates=_P( 0.7, -0.7, _0_5, -0.182, -0.06667, 0.75744, 0.05133))
1369# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/
1370# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83 and Pearson, C. & Snay, R. U{"Introducing
1371# HTDP 3.1 to transform coordinates across time and spatial reference frames"<https://Geodesy.NOAA.gov/
1372# TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 7th column
1373_trfX(_ITRF2008_, _NAD83_, epoch=_E(1997),
1374 xform=_P( 993.43, -1903.31, -526.55, 1.71504, -25.91467, -9.42645, -11.59935),
1375 rates=_P( 0.79, -0.6, -1.34, -0.10201, -0.06667, 0.75744, 0.05133))
1376# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/
1377# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83
1378_trfX(_ITRF2005_, _NAD83_, epoch=_E(1997),
1379 xform=_P( 996.3, -1902.4, -521.9, 0.775, -25.915, -9.426, -11.599),
1380 rates=_P( 0.5, -0.6, -1.3, -0.10201, -0.06667, 0.75744, 0.05133))
1381_trfX(_ITRF90_, _NAD83_, epoch=_E(1997),
1382 xform=_P( 973.0, -1919.2, -482.9, -0.9, -25.79, -9.65, -11.66),
1383 rates=_P( _0_0, _0_0, _0_0, _0_0, -0.053, 0.742, 0.032))
1384_trfX(_ITRF90_, _WGS84_, epoch=_E(1984),
1385 xform=_P( 60.0, -517.0, -223.0, -11.0, 18.3, -0.3, 7.0),
1386 rates=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1388del _P, _Ps # keep _E, _Es
1390if __name__ == '__main__':
1392 from pygeodesy.interns import _COLONSPACE_,_COMMA_, _NL_, _NLATvar_, _STAR_
1393 from pygeodesy.lazily import printf
1394 from time import localtime
1396 D = date2epoch.__name__
1397 E = epoch2date.__name__
1398 y = localtime()[0]
1399 for m in range(1, 13):
1400 for d in (1, 15, _mDays[m] - 1, _mDays[m]):
1401 f = '%s(%d,%3d,%3d)' % (D, y, m, d)
1402 e = date2epoch(y, m, d)
1403 t = epoch2date(e)
1404 x = NN if t == (y, m, d) else _STAR_
1405 e = '%.3f' % (e,)
1406 e = '%s, %s(%s)' % (e, E, e)
1407 t = '%d,%3d,%3d' % t
1408 printf('# %s = %s = %s %s', f, e, t, x)
1410 # __doc__ of this file, force all into registery
1411 def _RFs():
1412 yield NN
1413 for t in RefFrames.toRepr(all=True).split(_NL_):
1414 t = t.strip(_COMMA_)
1415 n = t.split(_COLONSPACE_)[0].split(_DOT_)[1]
1416 r = RefFrames.get(n)
1417 x = len(r.Xforms()), -len(r.Xforms(inverse=True))
1418 yield '%s .Xforms=%s' % (t, x)
1420 printf(_NLATvar_.join(sorted(_RFs())), nt=1)
1422 X, t = (), 0 # all form
1423 for r in RefFrames.values():
1424 X += tuple(r._Xs.values())
1425 for X in sorted(X):
1426 t += 1
1427 printf('#%4d %-22s xform=%r', t, X.name, X.xform)
1428 printf('#%27s rates=%r', _SPACE_, X.rates)
1430# **) MIT License
1431#
1432# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1433#
1434# Permission is hereby granted, free of charge, to any person obtaining a
1435# copy of this software and associated documentation files (the "Software"),
1436# to deal in the Software without restriction, including without limitation
1437# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1438# and/or sell copies of the Software, and to permit persons to whom the
1439# Software is furnished to do so, subject to the following conditions:
1440#
1441# The above copyright notice and this permission notice shall be included
1442# in all copies or substantial portions of the Software.
1443#
1444# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1445# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1446# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1447# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1448# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1449# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1450# OTHER DEALINGS IN THE SOFTWARE.
1452# % python -m pygeodesy.trf
1453#
1454# date2epoch(2024, 1, 1) = 2024.003, epoch2date(2024.003) = 2024, 1, 1
1455# date2epoch(2024, 1, 15) = 2024.041, epoch2date(2024.041) = 2024, 1, 15
1456# date2epoch(2024, 1, 30) = 2024.082, epoch2date(2024.082) = 2024, 1, 30
1457# date2epoch(2024, 1, 31) = 2024.085, epoch2date(2024.085) = 2024, 1, 31
1458# date2epoch(2024, 2, 1) = 2024.087, epoch2date(2024.087) = 2024, 2, 2 *
1459# date2epoch(2024, 2, 15) = 2024.126, epoch2date(2024.126) = 2024, 2, 16 *
1460# date2epoch(2024, 2, 28) = 2024.161, epoch2date(2024.161) = 2024, 2, 28
1461# date2epoch(2024, 2, 29) = 2024.164, epoch2date(2024.164) = 2024, 3, 1 *
1462# date2epoch(2024, 3, 1) = 2024.167, epoch2date(2024.167) = 2024, 3, 2 *
1463# date2epoch(2024, 3, 15) = 2024.205, epoch2date(2024.205) = 2024, 3, 16 *
1464# date2epoch(2024, 3, 30) = 2024.246, epoch2date(2024.246) = 2024, 3, 31 *
1465# date2epoch(2024, 3, 31) = 2024.249, epoch2date(2024.249) = 2024, 4, 1 *
1466# date2epoch(2024, 4, 1) = 2024.251, epoch2date(2024.251) = 2024, 4, 1
1467# date2epoch(2024, 4, 15) = 2024.290, epoch2date(2024.290) = 2024, 4, 15
1468# date2epoch(2024, 4, 29) = 2024.328, epoch2date(2024.328) = 2024, 4, 29
1469# date2epoch(2024, 4, 30) = 2024.331, epoch2date(2024.331) = 2024, 4, 30
1470# date2epoch(2024, 5, 1) = 2024.333, epoch2date(2024.333) = 2024, 5, 1
1471# date2epoch(2024, 5, 15) = 2024.372, epoch2date(2024.372) = 2024, 5, 15
1472# date2epoch(2024, 5, 30) = 2024.413, epoch2date(2024.413) = 2024, 5, 30
1473# date2epoch(2024, 5, 31) = 2024.415, epoch2date(2024.415) = 2024, 6, 1 *
1474# date2epoch(2024, 6, 1) = 2024.418, epoch2date(2024.418) = 2024, 6, 2 *
1475# date2epoch(2024, 6, 15) = 2024.456, epoch2date(2024.456) = 2024, 6, 16 *
1476# date2epoch(2024, 6, 29) = 2024.495, epoch2date(2024.495) = 2024, 6, 30 *
1477# date2epoch(2024, 6, 30) = 2024.497, epoch2date(2024.497) = 2024, 7, 1 *
1478# date2epoch(2024, 7, 1) = 2024.500, epoch2date(2024.500) = 2024, 7, 1
1479# date2epoch(2024, 7, 15) = 2024.538, epoch2date(2024.538) = 2024, 7, 16 *
1480# date2epoch(2024, 7, 30) = 2024.579, epoch2date(2024.579) = 2024, 7, 30
1481# date2epoch(2024, 7, 31) = 2024.582, epoch2date(2024.582) = 2024, 7, 31
1482# date2epoch(2024, 8, 1) = 2024.585, epoch2date(2024.585) = 2024, 8, 1
1483# date2epoch(2024, 8, 15) = 2024.623, epoch2date(2024.623) = 2024, 8, 15
1484# date2epoch(2024, 8, 30) = 2024.664, epoch2date(2024.664) = 2024, 8, 31 *
1485# date2epoch(2024, 8, 31) = 2024.667, epoch2date(2024.667) = 2024, 9, 1 *
1486# date2epoch(2024, 9, 1) = 2024.669, epoch2date(2024.669) = 2024, 9, 2 *
1487# date2epoch(2024, 9, 15) = 2024.708, epoch2date(2024.708) = 2024, 9, 16 *
1488# date2epoch(2024, 9, 29) = 2024.746, epoch2date(2024.746) = 2024, 9, 30 *
1489# date2epoch(2024, 9, 30) = 2024.749, epoch2date(2024.749) = 2024, 10, 1 *
1490# date2epoch(2024, 10, 1) = 2024.751, epoch2date(2024.751) = 2024, 10, 1
1491# date2epoch(2024, 10, 15) = 2024.790, epoch2date(2024.790) = 2024, 10, 15
1492# date2epoch(2024, 10, 30) = 2024.831, epoch2date(2024.831) = 2024, 10, 30
1493# date2epoch(2024, 10, 31) = 2024.833, epoch2date(2024.833) = 2024, 10, 31
1494# date2epoch(2024, 11, 1) = 2024.836, epoch2date(2024.836) = 2024, 11, 1
1495# date2epoch(2024, 11, 15) = 2024.874, epoch2date(2024.874) = 2024, 11, 15
1496# date2epoch(2024, 11, 29) = 2024.913, epoch2date(2024.913) = 2024, 11, 29
1497# date2epoch(2024, 11, 30) = 2024.915, epoch2date(2024.915) = 2024, 12, 1 *
1498# date2epoch(2024, 12, 1) = 2024.918, epoch2date(2024.918) = 2024, 12, 2 *
1499# date2epoch(2024, 12, 15) = 2024.956, epoch2date(2024.956) = 2024, 12, 16 *
1500# date2epoch(2024, 12, 30) = 2024.997, epoch2date(2024.997) = 2024, 12, 31 *
1501# date2epoch(2024, 12, 31) = 2025.000, epoch2date(2025.000) = 2025, 1, 1 *
1503# 1 ITRF2005@2015xETRF2000 xform=TRFXform7Tuple(tx=51.1, ty=51.7, tz=-80.8, s=1.6, sx=2.106, sy=12.74, sz=-20.592)
1504# rates=TRFXform7Tuple(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792)
1505# 2 ITRF88@2015xETRF2000 xform=TRFXform7Tuple(tx=29.3, ty=55.7, tz=87.7, s=-9.22, sx=2.006, sy=12.74, sz=-20.952)
1506# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1507# 3 ITRF2005@1989xETRF2005 xform=TRFXform7Tuple(tx=56.0, ty=48.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1508# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.054, sy=0.518, sz=-0.781)
1509# 4 ITRF88@2015xETRF2014 xform=TRFXform7Tuple(tx=-25.9, ty=3.0, tz=171.3, s=-11.89, sx=2.11, sy=13.806, sz=-20.38)
1510# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1511# 5 ITRF88@2015xETRF2020 xform=TRFXform7Tuple(tx=27.3, ty=-2.1, tz=-172.7, s=12.31, sx=2.336, sy=13.494, sz=-19.218)
1512# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1513# 6 ITRF89@2015xETRF2000 xform=TRFXform7Tuple(tx=24.3, ty=19.7, tz=63.7, s=-6.12, sx=2.106, sy=12.74, sz=-20.952)
1514# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1515# 7 ITRF89@2015xETRF2014 xform=TRFXform7Tuple(tx=-30.9, ty=-33.0, tz=147.3, s=-8.79, sx=2.21, sy=13.806, sz=-20.38)
1516# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1517# 8 ITRF89@2015xETRF2020 xform=TRFXform7Tuple(tx=32.3, ty=33.9, tz=-148.7, s=9.21, sx=2.236, sy=13.494, sz=-19.218)
1518# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1519# 9 ITRF89@1989xETRF89 xform=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1520# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71)
1521# 10 ITRF90@1984xWGS84 xform=TRFXform7Tuple(tx=60.0, ty=-517.0, tz=-223.0, s=-11.0, sx=18.3, sy=-0.3, sz=7.0)
1522# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1523# 11 ITRF2005@1994xGDA94 xform=TRFXform7Tuple(tx=-79.73, ty=-6.86, tz=38.03, s=6.636, sx=0.0351, sy=-2.1211, sz=-2.1411)
1524# rates=TRFXform7Tuple(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701)
1525# 12 ITRF90@1997xNAD83 xform=TRFXform7Tuple(tx=973.0, ty=-1919.2, tz=-482.9, s=-0.9, sx=-25.79, sy=-9.65, sz=-11.66)
1526# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=-0.053, sy=0.742, sz=0.032)
1527# 13 ITRF90@2015xETRF2000 xform=TRFXform7Tuple(tx=29.3, ty=43.7, tz=25.7, s=-2.72, sx=2.106, sy=12.74, sz=-20.952)
1528# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1529# 14 ITRF2005@2015xETRF2014 xform=TRFXform7Tuple(tx=-4.1, ty=-1.0, tz=2.8, s=-1.07, sx=2.21, sy=13.806, sz=-20.02)
1530# rates=TRFXform7Tuple(tx=-0.3, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77)
1531# 15 ITRF90@2015xETRF2014 xform=TRFXform7Tuple(tx=-25.9, ty=-9.0, tz=109.3, s=-5.39, sx=2.21, sy=13.806, sz=-20.38)
1532# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1533# 16 ITRF2005@2015xETRF2020 xform=TRFXform7Tuple(tx=5.5, ty=1.9, tz=-4.2, s=1.49, sx=2.236, sy=13.494, sz=-19.578)
1534# rates=TRFXform7Tuple(tx=0.3, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753)
1535# 17 ITRF90@2015xETRF2020 xform=TRFXform7Tuple(tx=27.3, ty=9.9, tz=-110.7, s=5.81, sx=2.236, sy=13.494, sz=-19.218)
1536# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1537# 18 ITRF90@1989xETRF90 xform=TRFXform7Tuple(tx=19.0, ty=28.0, tz=-23.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1538# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71)
1539# 19 ITRF91@2015xETRF2000 xform=TRFXform7Tuple(tx=27.3, ty=39.7, tz=9.7, s=-2.42, sx=2.106, sy=12.74, sz=-20.952)
1540# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1541# 20 ITRF91@2015xETRF2014 xform=TRFXform7Tuple(tx=-27.9, ty=-13.0, tz=93.3, s=-5.09, sx=2.21, sy=13.806, sz=-20.38)
1542# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1543# 21 ITRF91@1989xETRF91 xform=TRFXform7Tuple(tx=21.0, ty=25.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1544# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68)
1545# 22 ITRF92@2015xETRF2000 xform=TRFXform7Tuple(tx=39.3, ty=53.7, tz=3.7, s=-1.02, sx=2.106, sy=12.74, sz=-20.952)
1546# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1547# 23 ITRF92@2015xETRF2014 xform=TRFXform7Tuple(tx=-15.9, ty=1.0, tz=87.3, s=-3.69, sx=2.21, sy=13.806, sz=-20.38)
1548# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1549# 24 ITRF92@2015xETRF2020 xform=TRFXform7Tuple(tx=17.3, ty=-0.1, tz=-88.7, s=4.11, sx=2.236, sy=13.494, sz=-19.218)
1550# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1551# 25 ITRF92@1989xETRF92 xform=TRFXform7Tuple(tx=38.0, ty=40.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1552# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68)
1553# 26 ITRF93@2015xETRF2000 xform=TRFXform7Tuple(tx=119.6, ty=49.9, tz=-10.9, s=-2.22, sx=5.466, sy=17.07, sz=-21.342)
1554# rates=TRFXform7Tuple(tx=2.9, ty=0.2, tz=0.6, s=-0.01, sx=0.191, sy=0.68, sz=-0.862)
1555# 27 ITRF93@2015xETRF2014 xform=TRFXform7Tuple(tx=64.4, ty=-2.8, tz=72.7, s=-4.89, sx=5.57, sy=18.136, sz=-20.77)
1556# rates=TRFXform7Tuple(tx=2.8, ty=0.1, tz=2.5, s=-0.12, sx=0.195, sy=0.721, sz=-0.84)
1557# 28 ITRF93@2015xETRF2020 xform=TRFXform7Tuple(tx=-63.0, ty=3.7, tz=-74.1, s=5.31, sx=-1.124, sy=9.164, sz=-18.828)
1558# rates=TRFXform7Tuple(tx=-2.8, ty=0.0, tz=-2.7, s=0.12, sx=-0.024, sy=0.329, sz=-0.683)
1559# 29 ITRF93@1989xETRF93 xform=TRFXform7Tuple(tx=19.0, ty=53.0, tz=-21.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1560# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.32, sy=0.78, sz=-0.67)
1561# 30 ITRF94@2015xETRF2000 xform=TRFXform7Tuple(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
1562# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1563# 31 ITRF94@2015xETRF2014 xform=TRFXform7Tuple(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
1564# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1565# 32 ITRF94@2015xETRF2020 xform=TRFXform7Tuple(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
1566# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1567# 33 ITRF94@1989xETRF94 xform=TRFXform7Tuple(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1568# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1569# 34 ITRF96@1989xETRF96 xform=TRFXform7Tuple(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1570# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1571# 35 ITRF97@1989xETRF97 xform=TRFXform7Tuple(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1572# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1573# 36 ITRF2000@1994xGDA94 xform=TRFXform7Tuple(tx=-45.91, ty=-29.85, tz=-20.37, s=7.07, sx=-1.6705, sy=0.4594, sz=1.9356)
1574# rates=TRFXform7Tuple(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224)
1575# 37 ITRF2000@2015xETRF2000 xform=TRFXform7Tuple(tx=54.0, ty=51.0, tz=-48.0, s=0.0, sx=2.106, sy=12.74, sz=-20.592)
1576# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.081, sy=0.49, sz=-0.792)
1577# 38 ITRF96@2015xETRF2000 xform=TRFXform7Tuple(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
1578# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1579# 39 ITRF97@2015xETRF2000 xform=TRFXform7Tuple(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
1580# rates=TRFXform7Tuple(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1581# 40 ITRF2000@2015xETRF2014 xform=TRFXform7Tuple(tx=-1.2, ty=-1.7, tz=35.6, s=-2.67, sx=2.21, sy=13.806, sz=-20.02)
1582# rates=TRFXform7Tuple(tx=-0.1, ty=-0.1, tz=1.9, s=-0.11, sx=0.085, sy=0.531, sz=-0.77)
1583# 41 ITRF96@2015xETRF2014 xform=TRFXform7Tuple(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
1584# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1585# 42 ITRF97@2015xETRF2014 xform=TRFXform7Tuple(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
1586# rates=TRFXform7Tuple(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1587# 43 ITRF2000@2015xETRF2020 xform=TRFXform7Tuple(tx=2.6, ty=2.6, tz=-37.0, s=3.09, sx=2.236, sy=13.494, sz=-19.578)
1588# rates=TRFXform7Tuple(tx=0.1, ty=0.2, tz=-2.1, s=0.11, sx=0.086, sy=0.519, sz=-0.753)
1589# 44 ITRF91@2015xETRF2020 xform=TRFXform7Tuple(tx=29.3, ty=13.9, tz=-94.7, s=5.51, sx=2.236, sy=13.494, sz=-19.218)
1590# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1591# 45 ITRF96@2015xETRF2020 xform=TRFXform7Tuple(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
1592# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1593# 46 ITRF97@2015xETRF2020 xform=TRFXform7Tuple(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
1594# rates=TRFXform7Tuple(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1595# 47 ITRF2000@2020xGDA2020 xform=TRFXform7Tuple(tx=-105.52, ty=51.58, tz=231.68, s=3.55, sx=4.2175, sy=6.3941, sz=0.8617)
1596# rates=TRFXform7Tuple(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224)
1597# 48 ITRF2000@1988xITRF88 xform=TRFXform7Tuple(tx=2.47, ty=1.15, tz=-9.79, s=8.95, sx=0.1, sy=0.0, sz=-0.18)
1598# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1599# 49 ITRF2000@1988xITRF89 xform=TRFXform7Tuple(tx=2.97, ty=4.75, tz=-7.39, s=5.85, sx=0.0, sy=0.0, sz=-0.18)
1600# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1601# 50 ITRF2000@1988xITRF90 xform=TRFXform7Tuple(tx=2.47, ty=2.35, tz=-3.59, s=2.45, sx=0.0, sy=0.0, sz=-0.18)
1602# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1603# 51 ITRF2000@1988xITRF91 xform=TRFXform7Tuple(tx=26.7, ty=27.5, tz=-19.9, s=2.15, sx=0.0, sy=0.0, sz=-0.18)
1604# rates=TRFXform7Tuple(tx=0.0, ty=-0.6, tz=-1.4, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1605# 52 ITRF2000@1988xITRF92 xform=TRFXform7Tuple(tx=1.47, ty=1.35, tz=-1.39, s=0.75, sx=0.0, sy=0.0, sz=-0.18)
1606# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1607# 53 ITRF2000@1988xITRF93 xform=TRFXform7Tuple(tx=12.7, ty=6.5, tz=-20.9, s=1.95, sx=-0.39, sy=0.8, sz=-1.14)
1608# rates=TRFXform7Tuple(tx=-2.9, ty=-0.2, tz=-0.6, s=0.01, sx=-0.11, sy=-0.19, sz=0.07)
1609# 54 ITRF2000@1997xITRF94 xform=TRFXform7Tuple(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
1610# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1611# 55 ITRF2000@1997xITRF96 xform=TRFXform7Tuple(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
1612# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1613# 56 ITRF97@1997xITRF96 xform=TRFXform7Tuple(tx=-2.07, ty=-0.21, tz=9.95, s=-0.93496, sx=0.1267, sy=-0.22355, sz=-0.06065)
1614# rates=TRFXform7Tuple(tx=0.69, ty=-0.1, tz=1.86, s=-0.19201, sx=0.01347, sy=-0.01514, sz=0.00027)
1615# 57 ITRF2000@1997xITRF97 xform=TRFXform7Tuple(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
1616# rates=TRFXform7Tuple(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=-0.02)
1617# 58 ITRF2000@1997xNAD83 xform=TRFXform7Tuple(tx=995.6, ty=-1901.3, tz=-521.5, s=0.615, sx=-25.915, sy=-9.426, sz=-11.599)
1618# rates=TRFXform7Tuple(tx=0.7, ty=-0.7, tz=0.5, s=-0.182, sx=-0.06667, sy=0.75744, sz=0.05133)
1619# 59 ITRF2005@1997xNAD83 xform=TRFXform7Tuple(tx=996.3, ty=-1902.4, tz=-521.9, s=0.775, sx=-25.915, sy=-9.426, sz=-11.599)
1620# rates=TRFXform7Tuple(tx=0.5, ty=-0.6, tz=-1.3, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133)
1621# 60 ITRF96@1997xNAD83 xform=TRFXform7Tuple(tx=991.0, ty=-190.72, tz=-512.9, s=0.0, sx=25.79, sy=9.65, sz=11.66)
1622# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0532, sy=-0.7423, sz=-0.0316)
1623# 61 ITRF2005@2020xGDA2020 xform=TRFXform7Tuple(tx=40.32, ty=-33.85, tz=-16.72, s=4.286, sx=-1.2893, sy=-0.8492, sz=-0.3342)
1624# rates=TRFXform7Tuple(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701)
1625# 62 ITRF2005@2000xITRF2000 xform=TRFXform7Tuple(tx=0.1, ty=-0.8, tz=-5.8, s=0.4, sx=0.0, sy=0.0, sz=0.0)
1626# rates=TRFXform7Tuple(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0)
1627# 63 ITRF2008@1994xGDA94 xform=TRFXform7Tuple(tx=-84.68, ty=-19.42, tz=32.01, s=9.71, sx=-0.4254, sy=2.2578, sz=2.4015)
1628# rates=TRFXform7Tuple(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551)
1629# 64 ITRF2008@1997xNAD83 xform=TRFXform7Tuple(tx=993.43, ty=-1903.31, tz=-526.55, s=1.71504, sx=-25.91467, sy=-9.42645, sz=-11.59935)
1630# rates=TRFXform7Tuple(tx=0.79, ty=-0.6, tz=-1.34, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133)
1631# 65 ITRF2008@2015xETRF2000 xform=TRFXform7Tuple(tx=53.6, ty=50.8, tz=-85.5, s=2.54, sx=2.106, sy=12.74, sz=-20.592)
1632# rates=TRFXform7Tuple(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792)
1633# 66 ITRF2008@2015xETRF2014 xform=TRFXform7Tuple(tx=-1.6, ty=-1.9, tz=-1.9, s=-0.13, sx=2.21, sy=13.806, sz=-20.02)
1634# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77)
1635# 67 ITRF2008@2015xETRF2020 xform=TRFXform7Tuple(tx=3.0, ty=2.8, tz=0.5, s=0.55, sx=2.236, sy=13.494, sz=-19.578)
1636# rates=TRFXform7Tuple(tx=0.0, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753)
1637# 68 ITRF2008@2020xGDA2020 xform=TRFXform7Tuple(tx=13.79, ty=4.55, tz=15.22, s=2.5, sx=0.2808, sy=0.2677, sz=-0.4638)
1638# rates=TRFXform7Tuple(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551)
1639# 69 ITRF2008@2000xITRF2000 xform=TRFXform7Tuple(tx=-1.9, ty=-1.7, tz=-10.5, s=1.34, sx=0.0, sy=0.0, sz=0.0)
1640# rates=TRFXform7Tuple(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0)
1641# 70 ITRF2008@2000xITRF88 xform=TRFXform7Tuple(tx=22.8, ty=2.6, tz=-125.2, s=10.41, sx=0.1, sy=0.0, sz=0.06)
1642# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1643# 71 ITRF2008@2000xITRF89 xform=TRFXform7Tuple(tx=27.8, ty=38.6, tz=-101.2, s=7.31, sx=0.0, sy=0.0, sz=0.06)
1644# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1645# 72 ITRF2008@2000xITRF90 xform=TRFXform7Tuple(tx=22.8, ty=14.6, tz=-63.2, s=3.91, sx=0.0, sy=0.0, sz=0.06)
1646# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1647# 73 ITRF2008@2000xITRF91 xform=TRFXform7Tuple(tx=24.8, ty=18.6, tz=-47.2, s=3.61, sx=0.0, sy=0.0, sz=0.06)
1648# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1649# 74 ITRF2008@2000xITRF92 xform=TRFXform7Tuple(tx=12.8, ty=4.6, tz=-41.2, s=2.21, sx=0.0, sy=0.0, sz=0.06)
1650# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1651# 75 ITRF2008@2000xITRF93 xform=TRFXform7Tuple(tx=-24.0, ty=2.4, tz=-38.6, s=3.41, sx=-1.71, sy=-1.48, sz=-0.3)
1652# rates=TRFXform7Tuple(tx=-2.8, ty=-0.1, tz=-2.4, s=0.09, sx=-0.11, sy=-0.19, sz=0.07)
1653# 76 ITRF2008@2000xITRF94 xform=TRFXform7Tuple(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
1654# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1655# 77 ITRF2008@2000xITRF96 xform=TRFXform7Tuple(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
1656# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1657# 78 ITRF2008@2000xITRF97 xform=TRFXform7Tuple(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
1658# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1659# 79 ITRF2008@2005xITRF2005 xform=TRFXform7Tuple(tx=-0.5, ty=-0.9, tz=-4.7, s=0.94, sx=0.0, sy=0.0, sz=0.0)
1660# rates=TRFXform7Tuple(tx=0.3, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1661# 80 ITRF2014@2015xETRF2000 xform=TRFXform7Tuple(tx=55.2, ty=52.7, tz=-83.6, s=2.67, sx=2.106, sy=12.74, sz=-20.592)
1662# rates=TRFXform7Tuple(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.081, sy=0.49, sz=-0.792)
1663# 81 ITRF2014@2015xETRF2014 xform=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=2.21, sy=13.806, sz=-20.02)
1664# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.085, sy=0.531, sz=-0.77)
1665# 82 ITRF2014@2015xETRF2020 xform=TRFXform7Tuple(tx=1.4, ty=0.9, tz=-1.4, s=0.42, sx=2.236, sy=13.494, sz=-19.578)
1666# rates=TRFXform7Tuple(tx=0.0, ty=0.1, tz=-0.2, s=0.0, sx=0.086, sy=0.519, sz=-0.753)
1667# 83 ITRF2014@2020xGDA2020 xform=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1668# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=1.50379, sy=1.18346, sz=1.20716)
1669# 84 ITRF2014@2010xITRF2000 xform=TRFXform7Tuple(tx=0.7, ty=1.2, tz=-26.1, s=2.12, sx=0.0, sy=0.0, sz=0.0)
1670# rates=TRFXform7Tuple(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.0, sy=0.0, sz=0.0)
1671# 85 ITRF2014@2010xITRF2005 xform=TRFXform7Tuple(tx=2.6, ty=1.0, tz=-2.3, s=0.92, sx=0.0, sy=0.0, sz=0.0)
1672# rates=TRFXform7Tuple(tx=0.3, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1673# 86 ITRF2014@2010xITRF2008 xform=TRFXform7Tuple(tx=1.6, ty=1.9, tz=2.4, s=-0.02, sx=0.0, sy=0.0, sz=0.0)
1674# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1675# 87 ITRF2014@2010xITRF88 xform=TRFXform7Tuple(tx=25.4, ty=-0.5, tz=-154.8, s=11.29, sx=0.1, sy=0.0, sz=0.26)
1676# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1677# 88 ITRF2014@2010xITRF89 xform=TRFXform7Tuple(tx=30.4, ty=35.5, tz=-130.8, s=8.19, sx=0.0, sy=0.0, sz=0.26)
1678# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1679# 89 ITRF2014@2010xITRF90 xform=TRFXform7Tuple(tx=25.4, ty=11.5, tz=-92.8, s=4.79, sx=0.0, sy=0.0, sz=0.26)
1680# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1681# 90 ITRF2014@2010xITRF91 xform=TRFXform7Tuple(tx=27.4, ty=15.5, tz=-76.8, s=4.49, sx=0.0, sy=0.0, sz=0.26)
1682# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1683# 91 ITRF2014@2010xITRF92 xform=TRFXform7Tuple(tx=15.4, ty=1.5, tz=-70.8, s=3.09, sx=0.0, sy=0.0, sz=0.26)
1684# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1685# 92 ITRF2014@2010xITRF93 xform=TRFXform7Tuple(tx=-50.4, ty=3.3, tz=-60.2, s=4.29, sx=-2.81, sy=-3.38, sz=0.4)
1686# rates=TRFXform7Tuple(tx=-2.8, ty=-0.1, tz=-2.5, s=0.12, sx=-0.11, sy=-0.19, sz=0.07)
1687# 93 ITRF2014@2010xITRF94 xform=TRFXform7Tuple(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
1688# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1689# 94 ITRF2014@2010xITRF96 xform=TRFXform7Tuple(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
1690# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1691# 95 ITRF2014@2010xITRF97 xform=TRFXform7Tuple(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
1692# rates=TRFXform7Tuple(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1693# 96 ITRF2020@2015xETRF2000 xform=TRFXform7Tuple(tx=53.8, ty=51.8, tz=-82.2, s=2.25, sx=2.106, sy=12.74, sz=-20.592)
1694# rates=TRFXform7Tuple(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.081, sy=0.49, sz=-0.792)
1695# 97 ITRF2020@2015xETRF2014 xform=TRFXform7Tuple(tx=-1.4, ty=-0.9, tz=1.4, s=0.42, sx=2.21, sy=13.806, sz=-20.02)
1696# rates=TRFXform7Tuple(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.085, sy=0.531, sz=-0.77)
1697# 98 ITRF2020@2015xETRF2020 xform=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=2.236, sy=13.494, sz=-19.578)
1698# rates=TRFXform7Tuple(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.086, sy=0.519, sz=-0.753)
1699# 99 ITRF2020@2015xITRF2000 xform=TRFXform7Tuple(tx=-0.2, ty=0.8, tz=-34.2, s=2.25, sx=0.0, sy=0.0, sz=0.0)
1700# rates=TRFXform7Tuple(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.0, sy=0.0, sz=0.0)
1701# 100 ITRF2020@2015xITRF2005 xform=TRFXform7Tuple(tx=2.7, ty=0.1, tz=-1.4, s=0.65, sx=0.0, sy=0.0, sz=0.0)
1702# rates=TRFXform7Tuple(tx=0.3, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1703# 101 ITRF2020@2015xITRF2008 xform=TRFXform7Tuple(tx=0.2, ty=1.0, tz=3.3, s=-0.29, sx=0.0, sy=0.0, sz=0.0)
1704# rates=TRFXform7Tuple(tx=0.0, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1705# 102 ITRF2020@2015xITRF2014 xform=TRFXform7Tuple(tx=-1.4, ty=-0.9, tz=1.4, s=-0.42, sx=0.0, sy=0.0, sz=0.0)
1706# rates=TRFXform7Tuple(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1707# 103 ITRF2020@2015xITRF88 xform=TRFXform7Tuple(tx=24.5, ty=-3.9, tz=-169.9, s=11.47, sx=0.1, sy=0.0, sz=0.36)
1708# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1709# 104 ITRF2020@2015xITRF89 xform=TRFXform7Tuple(tx=29.5, ty=32.1, tz=-145.9, s=8.37, sx=0.0, sy=0.0, sz=0.36)
1710# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1711# 105 ITRF2020@2015xITRF90 xform=TRFXform7Tuple(tx=24.5, ty=8.1, tz=-107.9, s=4.97, sx=0.0, sy=0.0, sz=0.36)
1712# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1713# 106 ITRF2020@2015xITRF91 xform=TRFXform7Tuple(tx=26.5, ty=12.1, tz=-91.9, s=4.67, sx=0.0, sy=0.0, sz=0.36)
1714# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1715# 107 ITRF2020@2015xITRF92 xform=TRFXform7Tuple(tx=14.5, ty=-1.9, tz=-85.9, s=3.27, sx=0.0, sy=0.0, sz=0.36)
1716# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1717# 108 ITRF2020@2015xITRF93 xform=TRFXform7Tuple(tx=-65.8, ty=1.9, tz=-71.3, s=4.47, sx=-3.36, sy=-4.33, sz=0.75)
1718# rates=TRFXform7Tuple(tx=-2.8, ty=-0.2, tz=-2.3, s=0.12, sx=-0.11, sy=-0.19, sz=0.07)
1719# 109 ITRF2020@2015xITRF94 xform=TRFXform7Tuple(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
1720# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1721# 110 ITRF2020@2015xITRF96 xform=TRFXform7Tuple(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
1722# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1723# 111 ITRF2020@2015xITRF97 xform=TRFXform7Tuple(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
1724# rates=TRFXform7Tuple(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)