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, isscalar, isstr, _xinstanceof, _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 _IsnotError, TRFError, _xkwds
75from pygeodesy.interns import MISSING, NN, _AT_, _COMMASPACE_, _cartesian_, _conversion_, \
76 _datum_, _DOT_, _ellipsoidal_, _exists_, _invalid_, _MINUS_, \
77 _NAD83_, _no_, _PLUS_, _reframe_, _s_, _scalar_, _SPACE_, \
78 _sx_, _sy_, _sz_, _to_, _tx_, _ty_, _tz_, _WGS84_, _x_, \
79 _intern as _i
80from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS
81from pygeodesy.named import ADict, classname, _lazyNamedEnumItem as _lazy, _Named, \
82 _NamedEnum, _NamedEnumItem, _NamedTuple, Fmt, unstr
83from pygeodesy.props import Property, Property_RO, property_RO
84# from pygeodesy.streprs import Fmt, unstr # from .named
85from pygeodesy.units import Epoch, Float
87from math import ceil
89__all__ = _ALL_LAZY.trf
90__version__ = '24.02.04'
92_EP0CH = Epoch(0, low=0)
93_Es = {_EP0CH: _EP0CH} # L{Epoch} de_dup
94_Ps = {} # L{TRFXform7Tuple} de-dup, deleted below
96_GRS80 = Datums.GRS80
97_inverse_ = 'inverse'
98_MAS = _MM = _PPB = Float # Units
99_MM2M = _0_001 # scale mm2m, ppb2ppM, mas2as
100_mDays = (0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 0)
101_366_0 = _F(sum(_mDays))
102_v_ = 'v'
104_ETRF88_ = _i('ETRF88')
105_ETRF89_ = _i('ETRF89')
106_ETRF90_ = _i('ETRF90')
107_ETRF91_ = _i('ETRF91')
108_ETRF92_ = _i('ETRF92')
109_ETRF93_ = _i('ETRF93')
110_ETRF94_ = _i('ETRF94')
111_ETRF96_ = _i('ETRF96')
112_ETRF97_ = _i('ETRF97')
113_ETRF2000_ = _i('ETRF2000')
114_ETRF2005_ = _i('ETRF2005')
115_ETRF2008_ = _i('ETRF2008')
116_ETRF2014_ = _i('ETRF2014')
117_ETRF2020_ = _i('ETRF2020')
118_GDA94_ = _i('GDA94')
119_GDA2020_ = _i('GDA2020')
120_ITRF_ = _i('ITRF')
121_ITRF88_ = _i('ITRF88')
122_ITRF89_ = _i('ITRF89')
123_ITRF90_ = _i('ITRF90')
124_ITRF91_ = _i('ITRF91')
125_ITRF92_ = _i('ITRF92')
126_ITRF93_ = _i('ITRF93')
127_ITRF94_ = _i('ITRF94')
128_ITRF96_ = _i('ITRF96')
129_ITRF97_ = _i('ITRF97')
130_ITRF2000_ = _i('ITRF2000')
131_ITRF2005_ = _i('ITRF2005')
132_ITRF2008_ = _i('ITRF2008')
133_ITRF2014_ = _i('ITRF2014')
134_ITRF2020_ = _i('ITRF2020')
135_WGS84g1150_ = _i('WGS84g1150')
136_WGS84g1674_ = _i('WGS84g1674')
137_WGS84g1762_ = _i('WGS84g1762')
138# del _i
141def _E(epoch):
142 '''(INTERNAL) De-dup L{Epochs}s.
143 '''
144 e = Epoch(_F(epoch))
145 return _Es.setdefault(e, e)
148class RefFrame(_NamedEnumItem):
149 '''Terrestrial Reference Frame (TRF) parameters.
150 '''
151 _datum = _GRS80 # Datums.GRS80 or .WGS84 (L{Datum})
152 _epoch = _EP0CH # epoch, fractional year (L{Epoch})
154 def __init__(self, epoch, datum, name=NN):
155 '''New L{RefFrame}.
157 @arg epoch: Epoch, a fractional calendar year (C{scalar} or C{str}).
158 @arg datum: Datum or ellipsoid (L{Datum}, {Ellipsoid}, L{Ellipsoid2}
159 or L{a_f2Tuple}).
160 @kwarg name: Unique, non-empty name (C{str}).
162 @raise NameError: A L{RefFrame} with that B{C{name}} already exists.
164 @raise TRFError: Invalid B{C{epoch}}.
166 @raise TypeError: Invalid B{C{datum}}.
167 '''
168 if datum is not _GRS80:
169 _earth_datum(self, datum, raiser=_datum_)
170 self._epoch = Epoch(epoch)
171 self._Xs = {}
172 if name:
173 self._register(RefFrames, name)
175 def __eq__(self, other):
176 return isinstance(other, RefFrame) and other.epoch == self.epoch \
177 and other.datum == self.datum
179 def __matmul__(self, other): # PYCHOK Python 3.5+
180 '''Convert cartesian or ellipsoidal B{C{other}} to this reframe.
182 @raise TypeError: Invalid B{C{other}}.
183 '''
184 try: # only Cartesian- and LatLonEllipsoidalBase
185 return other.toRefFrame(self)
186 except AttributeError:
187 pass
188 raise _IsnotError(_cartesian_, _ellipsoidal_, other=other)
190 @property_RO
191 def datum(self):
192 '''Get this reference frame's datum (L{Datum}).
193 '''
194 return self._datum
196 @Property_RO
197 def ellipsoid(self):
198 '''Get this reference frame's ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
199 '''
200 return self._datum.ellipsoid
202 @Property_RO
203 def epoch(self):
204 '''Get this reference frame's epoch (C{Epoch}).
205 '''
206 return self._epoch
208 def toRefFrame(self, point, reframe2, **epoch2_epoch_name):
209 '''Convert a cartesian or geodetic point from this to another reframe and epoch.
211 @return: A copy of the B{C{point}}, converted or renamed.
213 @see: Ellipsoidal methods L{LatLon.toRefFrame<ellipsoidalBase.LatLonEllipsoidalBase.toRefFrame>}
214 and L{Cartesian.toRefFrame<ellipsoidalBase.CartesianEllipsoidalBase.toRefFrame>}
215 for more details.
216 '''
217 b = _MODS.ellipsoidalBase
218 _xinstanceof(b.LatLonEllipsoidalBase, b.CartesianEllipsoidalBase, point=point)
219 p = point.dup(reframe=self) if point.reframe != self else point
220 return p.toRefFrame(reframe2, **_xkwds(epoch2_epoch_name, name=self.name))
222 def toStr(self, epoch=None, name=NN, **unused): # PYCHOK expected
223 '''Return this reference frame as a text string.
225 @kwarg epoch: Override this reframe's epoch (C{scalar} or C{str}).
226 @kwarg name: Override name (C{str}) or C{None} to exclude the
227 reframe's name.
229 @return: This L{RefFrame}'s attributes (C{str}).
230 '''
231 D = self.datum
232 e = self.epoch if epoch is None else _Epoch(epoch)
233 t = (Fmt.EQUAL(name=repr(name or self.name)),
234 Fmt.EQUAL(epoch=e),
235 Fmt.EQUAL(datum=_DOT_(classname(D) + _s_, D.name)))
236 return _COMMASPACE_.join(t[1:] if name is None else t)
238 def Xform(self, reframe2):
239 '''Get the converter Xform I{from} this reference frame I{to} C{reframe2}.
241 @arg reframe2: Destination frame to convert I{to} (L{RefFrame} or C{str}).
243 @return: The L{TRFXform} instance or C{None} if not available.
245 @raise TypeError: Invalid B{C{reframe2}}.
246 '''
247 _xinstanceof(RefFrame, str, reframe2=reframe2)
248 n2 = reframe2 if isstr(reframe2) else reframe2.name
249 return self._Xs.get(n2, None)
251 def Xforms(self, inverse=False):
252 '''Return all Xforms converting I{from} or I{to} this reference frame.
254 @kwarg inverse: If C{True}, get all I{inverse, to} Xforms (C{bool}).
256 @return: An L{ADict} of I{from} C{[refName2]=}L{TRFXform}s) or if
257 C{B{inverse}=True} of I{to} C{[refName1]=}L{TRFXform}s).
258 '''
259 def _Xi(n2):
260 for n1, r in RefFrames.items():
261 if n2 in r._Xs:
262 yield n1, r
264 return ADict(_Xi(self.name)) if inverse else ADict(self._Xs)
267class RefFrames(_NamedEnum):
268 '''(INTERNAL) L{RefFrame} registry, I{must} be a sub-class
269 to accommodate the L{_LazyNamedEnumItem} properties.
270 '''
271 def _Lazy(self, epoch, datum=_GRS80, name=NN):
272 '''(INTERNAL) Instantiate the L{RefFrame}.
273 '''
274 return RefFrame(epoch, datum, name=name)
276RefFrames = RefFrames(RefFrame) # PYCHOK singleton
277'''Some pre-defined L{RefFrame}s, all I{lazily} instantiated.'''
278# <https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe.js>
279RefFrames._assert(
280 ETRF88 = _lazy(_ETRF88_, _E(1988)), # epoch, datum?
281 ETRF89 = _lazy(_ETRF89_, _E(1989)), # epoch, datum?
282 ETRF90 = _lazy(_ETRF90_, _E(1990)), # epoch, datum?
283 ETRF91 = _lazy(_ETRF91_, _E(1991)), # epoch, datum?
284 ETRF92 = _lazy(_ETRF92_, _E(1992)), # epoch, datum?
285 ETRF93 = _lazy(_ETRF93_, _E(1993)), # epoch, datum?
286 ETRF94 = _lazy(_ETRF94_, _E(1994)), # epoch, datum?
287 ETRF96 = _lazy(_ETRF96_, _E(1996)), # epoch, datum?
288 ETRF97 = _lazy(_ETRF97_, _E(1997)), # epoch, datum?
289 ETRF2000 = _lazy(_ETRF2000_, _E(2005)),
290 ETRF2005 = _lazy(_ETRF2005_, _E(2005)), # epoch, datum?
291 ETRF2008 = _lazy(_ETRF2008_, _E(2008)), # epoch, datum?
292 ETRF2014 = _lazy(_ETRF2014_, _E(2014)), # epoch, datum?
293 ETRF2020 = _lazy(_ETRF2020_, _E(2020)), # epoch, datum?
294 GDA94 = _lazy(_GDA94_, _E(1994)), # Australia
295 GDA2020 = _lazy(_GDA2020_, _E(2020)), # Australia
296 ITRF88 = _lazy(_ITRF88_, _E(1988)),
297 ITRF89 = _lazy(_ITRF89_, _E(1989)),
298 ITRF90 = _lazy(_ITRF90_, _E(1988)),
299 ITRF91 = _lazy(_ITRF91_, _E(1988)),
300 ITRF92 = _lazy(_ITRF92_, _E(1988)),
301 ITRF93 = _lazy(_ITRF93_, _E(1988)),
302 ITRF94 = _lazy(_ITRF94_, _E(1993)),
303 ITRF96 = _lazy(_ITRF96_, _E(1997)),
304 ITRF97 = _lazy(_ITRF97_, _E(1997)),
305 ITRF2000 = _lazy(_ITRF2000_, _E(1997)), # aka ITRF00
306 ITRF2005 = _lazy(_ITRF2005_, _E(2000)),
307 ITRF2008 = _lazy(_ITRF2008_, _E(2005)), # aka ITRF08
308 ITRF2014 = _lazy(_ITRF2014_, _E(2010)),
309 ITRF2020 = _lazy(_ITRF2020_, _E(2015)),
310 NAD83 = _lazy(_NAD83_, _E(1997)), # aka CORS96
311 WGS84 = _lazy(_WGS84_, _E(1984), _WGS84),
312 WGS84g1150 = _lazy(_WGS84g1150_, _E(2001), _WGS84),
313 WGS84g1674 = _lazy(_WGS84g1674_, _E(2005), _WGS84),
314 WGS84g1762 = _lazy(_WGS84g1762_, _E(2005), _WGS84)) # same epoch
317class TransformXform(Transform):
318 '''Helmert transformation, extended with an C{Xform} converter.
320 @see: L{Transform<datums.Transform>} and L{Xform<TRFXform>}.
321 '''
322 _Xform = None
324 def __init__(self, name=NN, **tx_ty_tz_s_sx_sy_sz): # PYCHOK signature
325 '''New L{TransformXform}.
327 @kwarg name: Optional name (C{str}), I{not registered}.
329 @see: L{Transform<datums.Transform>} for details.
331 @note: The name of this L{TransformXform} starts with C{"-"}
332 if its C{Xform} was applied I{inversed}.
333 '''
334 Transform.__init__(self, **tx_ty_tz_s_sx_sy_sz)
335 if name:
336 self.name = name
338# def _rps2(self, s_):
339# '''(INTERNAL) Rate to rate.
340# '''
341# return s_, s_
343 def toRefFrame(self, point, epoch=None, **epoch2_datum_name): # PYCHOK signature
344 '''Convert a cartesian or geodetic point using this transform and C{refName1},
345 C{refName2} and C{epoch} of this transform's C{Xform}.
347 @kwarg epoch: Optional epoch ((L{Epoch}, C{scalar} or C{str})), overriding
348 this transform's Xform's C{epoch}.
350 @return: A copy of the B{C{point}}, converted or renamed.
352 @see: Method L{RefFrame.toRefFrame<trf.RefFrame.toRefFrame>} for more details.
353 '''
354 return self.Xform.toRefFrame(point, epoch=epoch, **_xkwds(epoch2_datum_name))
356 def velocities(self, factor=_MM2M):
357 '''Compute the X, Y and Z I{velocities} of this transform.
359 @kwarg factor: Factor to scale this Xform's C{rates} (C{scalar}), default
360 from C{milli-meter-} to C{meter-per-year}.
362 @return: A L{Vector3Tuple}C{(x, y, z)} or C{None}.
364 @raise TypeError: Invalid B{C{factor}}.
366 @see: Alamimi, Z. "EUREF-TN-1-Jan-31-2024", U{Appendix A, equation (3)
367 <http://ETRS89.ENSG.IGN.FR/pub/EUREF-TN-1-Jan-31-2024.pdf>}.
368 '''
369 v = self.Xform
370 if v is not None:
371 r = v.rates * factor # eq (3) ...
372 T = self.dup(tx=r.sx, ty=r.sy, tz=r.sz, # Xyy-dot?
373 s1=0, name=NN(self.name, _v_))
374 v = T.transform(r.tx, r.ty, r.tz) # Xyy?
375 return v
377 @Property
378 def Xform(self):
379 '''Get the Xform of this Helmert (L{TRFXform} or C{None}).
380 '''
381 return self._Xform
383 @Xform.setter # PYCHOK setter!
384 def Xform(self, Xform):
385 '''Set the Xform of this Helmert (L{TRFXform}).
387 @raise TypeError: Invalid B{C{Xform}}.
388 '''
389 _xinstanceof(TRFXform, Xform=Xform)
390 self._Xform = Xform
393class TRFXform7Tuple(_NamedTuple):
394 '''7-Tuple C{(tx, ty, tz, s, sx, sy, sz)} of conversion parameters with
395 translations C{tx}, C{ty} and C{tz} in C{milli-meter}, scale C{s} in
396 C{ppb} and rates C{sx}, C{sy} and C{sz} in C{milli-arc-seconds-per-year}.
398 @note: The parameters are also named as C{(Tx, Ty, Tz, D, Rx, Ry, Rz)}
399 or C{(T1, T2, T3, D, R1, R2, R3)}.
401 @see: Class L{TransformXform}'s matching keyword argument names.
402 '''
403 _Names_ = (_tx_, _ty_, _tz_, _s_, _sx_, _sy_, _sz_) # == kwds
404 _Units_ = (_MM, _MM, _MM, _PPB, _MAS, _MAS, _MAS)
406 def __add__(self, other):
407 '''Return the sum of this and an other L{TRFXform7Tuple}.
408 '''
409 _xinstanceof(TRFXform7Tuple, other=other)
410 return TRFXform7Tuple(((s + t) for s, t in _zip(self, other)),
411 name=_PLUS_) # .fsums._add_op_
413 def __mul__(self, factor):
414 if not isscalar(factor):
415 raise _IsnotError(_scalar_, factor=factor)
416 return type(self)(_ * factor for _ in self)
418 def __neg__(self):
419 return self.inverse()
421 def inverse(self, name=NN):
422 '''Return the inverse of this transform.
424 @kwarg name: Optional name (C{str}).
426 @return: Inverse (L{TransformXform}).
427 '''
428 n = name or _minus(self.name)
429 return type(self)(map(neg, self), name=n)
431 @Property_RO
432 def isunity(self):
433 '''Is this a C{unity, identidy} transform (C{bool}).
434 '''
435 return not any(self)
438class TRFXform(_Named):
439 '''Terrestrial Reference Frame (TRF) converter between two
440 reference frames observed at an C{epoch}.
441 '''
442 epoch = _EP0CH
443 refName1 = \
444 refName2 = NN
445 rates = \
446 xform = TRFXform7Tuple(_0_0s(len(
447 TRFXform7Tuple._Names_)))
449 def __init__(self, refName1, refName2, epoch=None,
450 xform=None, rates=None, name=NN):
451 '''New L{trfXform}.
453 @arg refName1: Source reframe (C{str}), converting I{from}.
454 @arg refName2: Destination reframe (C{str}), converting I{to}.
455 @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str}).
456 @kwarg xform: I{Transform} parameters (L{TRFXform7Tuple}).
457 @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), as B{C{xform}},
458 but in C{units-per-year}.
459 @kwarg name: Optional name (C{str})
461 @return: The new TRF converter (L{TRFXform}).
463 @raise TRFError: Invalid B{C{epoch}}, B{C{xform}} or B{C{rates}}.
464 '''
465 self.refName1 = str(refName1)
466 self.refName2 = str(refName2)
467 _xinstanceof(TRFXform7Tuple, xform=xform, rates=rates)
468 self.epoch = _Epoch(epoch)
469 self.xform = xform
470 self.rates = rates
471 self.name = name or self.toStr()
473 def __lt__(self, other):
474 _xinstanceof(TRFXform, other=other)
475 return self.refName1 < other.refName1 or \
476 self.refName2 < other.refName2 or \
477 self.epoch < other.epoch
479 def __neg__(self):
480 return self.inverse()
482 def __repr__(self):
483 return self.toRepr()
485 def _at(self, epoch):
486 '''(INTERNAL) Return C{self.name@epoch}.
487 '''
488 n = self.name
489 if epoch != self.epoch:
490 _t = _AT_(NN, epoch)
491 if not n.endswith(_t):
492 n = NN(n, _t)
493 return n
495 def _7Helmert(self, epoch, mm2m):
496 '''(INTERNAL) Get the named Helmert parameters observed
497 at C{epoch} converted by C{mm2m}, I{signed}.
498 '''
499 e = epoch - self.epoch # delta in fractional years
500 ns = TRFXform7Tuple._Names_
501 return dict((n, (x + e * r) * mm2m) for n, x, r in
502 _zip(ns, self.xform, self.rates)) # strict=True
504 def inverse(self, name=NN):
505 '''Return the inverse of this Xform.
507 @kwarg name: Optional name (C{str}).
509 @return: Inverse (L{TRFXform}).
510 '''
511 return self.dup(refName1=self.refName2, xform=-self.xform,
512 refName2=self.refName1, rates=-self.rates,
513 name=name or _minus(self.name))
515 def _range(self, *e1_e2):
516 '''(INTERNAL) Epoch "range", distance.
517 '''
518 def _r(e):
519 e -= self.epoch
520 return (-e) if e < 0 else (e * 2)
522 return sum(map(_r, e1_e2)) if e1_e2 else self.epoch
524 def toEpoch(self, epoch):
525 '''Convert this Xform to B{C{epoch}}, if needed.
527 @arg epoch: Epoch, fractional year (C{Epoch}, C{scalar}
528 or C{str}).
530 @return: This Xform or a copy converted to B{C{epoch}}.
532 @raise TRFError: Invalid B{C{epoch}}.
533 '''
534 e = _Epoch(epoch) - self.epoch
535 if e:
536 t = TRFXform7Tuple((x + e * r) for x, r in
537 _zip(self.xform, self.rates))
538 X = self.dup(epoch=epoch, xform=t, name=self._at(epoch))
539 else:
540 X = self
541 return X
543 def toRefFrame(self, point, epoch=None, datum=_GRS80, **epoch2_name):
544 '''Convert a cartesian or geodetic point using this Xform's C{refName1},
545 C{refName2}, C{epoch} and L{Transform<trf.TransformXform>}.
547 @kwarg epoch: Optional epoch ((L{Epoch}, C{scalar} or C{str})), overriding
548 this transform's Xform's C{epoch}.
550 @return: A copy of the B{C{point}}, converted or renamed.
552 @see: Method L{RefFrame.toRefFrame<trf.RefFrame.toRefFrame>} for more details.
553 '''
554 def _r(name):
555 r = RefFrames.get(name)
556 if r is None or r.datum != datum:
557 r = RefFrame(self.epoch, datum)
558 r.name = name # unregistered
559 return r
561 return _r(self.refName1).toRefFrame(point,
562 _r(self.refName2), epoch=epoch, **_xkwds(epoch2_name))
564 def toRepr(self, **unused): # PYCHOK signature
565 '''Return the represention of this Xform (C{str}).
566 '''
567 return unstr(self.classname, epoch=self.epoch, name=self.name)
569 def toStr(self, epoch=None, **unused): # PYCHOK signature
570 '''Return this Xform as C{"fromRef@epoch_toRef"} (C{str}).
572 @kwarg epoch: Epoch (C{scalar}), overriding this Xform's epoch.
573 '''
574 e = epoch or self.epoch
575 return NN(_AT_(self.refName1, e), _x_, self.refName2)
577 def toTransform(self, epoch1, epoch2=None, inverse=False):
578 '''Combine this Xform observed at B{C{epoch1}} into a Helmert
579 L{TransformXform}, optionally at B{C{epoch2 or epoch1}}.
581 @arg epoch1: Epoch to observe I{from} (C{scalar}).
582 @kwarg epoch2: Optional epoch to observe I{to} (C{scalar}).
583 @kwarg inverse: Invert the Helmert tranformation (C{bool}).
585 @raise TRFError: Invalid B{C{epoch1}} or B{C{epoch2}}.
587 @note: Translations are converted from C{milli-meter} to
588 C{meter}, shift rates from C{milli-arc-seconds} to
589 C{arc-seconds} and scale from C{ppb} to C{ppM}.
590 '''
591 e = Epoch(epoch2=epoch1 if epoch2 is None else epoch2)
592 X = self if e == epoch1 else self.toEpoch(epoch1)
593 if inverse:
594 X = X.inverse()
595 H = TransformXform(name=X._at(e), **X._7Helmert(e, _MM2M))
596 H.Xform = X
597 return H
600def date2epoch(year, month, day):
601 '''Return the C{epoch} for a calendar day.
603 @arg year: Year of the date (C{scalar}).
604 @arg month: Month in the B{C{year}} (C{scalar}, 1..12).
605 @arg day: Day in the B{C{month}} (C{scalar}, 1..31).
607 @return: Epoch, the fractional year (C{float}).
609 @raise TRFError: Invalid B{C{year}}, B{C{month}} or B{C{day}}.
611 @note: Any B{C{year}} is considered a leap year, i.e. having
612 29 days in February.
613 '''
614 try:
615 y, m, d = map1(int, year, month, day)
616 if y > 0 and 1 <= m <= 12 and 1 <= d <= _mDays[m]:
617 e = y + float(sum(_mDays[:m]) + d) / _366_0
618 return Epoch(e, low=0)
620 raise ValueError # _invalid_
621 except (TRFError, TypeError, ValueError) as x:
622 raise TRFError(year=year, month=month, day=day, cause=x)
625def epoch2date(epoch):
626 '''Return the date for a reference frame C{epoch}.
628 @arg epoch: Fractional year (C{scalar}).
630 @return: 3-Tuple C{(year, month, day)}.
632 @raise TRFError: Invalid B{C{epoch}}.
634 @note: Any B{C{year}} is considered a leap year, i.e. having
635 29 days in February.
636 '''
637 e = _Epoch(epoch, low=0)
638 y = int(e)
639 d = int(ceil(_366_0 * (e - y)))
640 for m, n in enumerate(_mDays[1:]):
641 if d > n:
642 d -= n
643 else:
644 break
645 return y, (m + 1), max(1, d)
648def _Epoch(e, **kwds):
649 '''(INTERNAL) Get an C{Epoch(B{e})}.
650 '''
651 return Epoch(e, **kwds) if kwds or not isinstance(e, Epoch) else e
654def _eT0Ds4(inst, reframe, epoch, reframe2, epoch2):
655 '''(INTERNAL) Get epoch, a Helmert L{Transform}s or 0-tuple, datum
656 and datum2 to convert B{C{refFrame}} observed at B{C{epoch}}
657 into B{C{refFrame2}} observed at C{epoch2 or epoch}.
658 '''
659 r = reframe or inst.reframe
660 if not r:
661 t = _SPACE_(_DOT_(repr(inst), _reframe_), MISSING)
662 raise TRFError(_no_(_conversion_), txt=t)
664 _xinstanceof(RefFrame, reframe2=reframe2, reframe=r)
666 e1 = _Epoch(epoch or inst.epoch or r.epoch)
667 e2 = e1 if epoch2 is None else Epoch(epoch2=epoch2)
669 t0 = _toTransform0(r.name, e1, reframe2.name, e2)
670 if t0 is None:
671 t = _SPACE_(RefFrame.__name__, _AT_(r.name, e1),
672 _to_, _AT_(reframe2.name, e2))
673 raise TRFError(_no_(_conversion_), txt=t)
675 return e2, t0, r.datum, reframe2.datum
678def _immediate(n1, n2, *unused):
679 '''(INTERNAL) Get the C{n1} to C{n2} Xform or C{None}.
680 '''
681 X = RefFrames.get(n1)
682 if X:
683 X = X._Xs.get(n2, None)
684 return X
687def _intermediate(n1, n2, *e1_e2):
688 '''(INTERNAL) Find an Xform "between" C{n1} and C{n2}.
689 '''
690 def _e(e1=0, e2=0):
691 return e1 - e2
693 def _X4(_Xs):
694 for n, X1 in _Xs.items():
695 X2 = _immediate(n, n2)
696 if X2:
697 yield (X1._range(*e1_e2) + X2._range(*e1_e2)), X1, X2, True
698 X2 = _immediate(n2, n)
699 if X2:
700 yield (X1._range(*e1_e2) + X2._range(*e1_e2)), X1, X2, False
702 X, r = None, RefFrames.get(n1)
703 if r:
704 i = sorted(_X4(r._Xs))
705 if i:
706 _, X1, X2, f = i.pop(0)
707 e1, e2 = X1.epoch, X2.epoch
708 if e1 > e2 and _e(*e1_e2) < 0: # X1 to e2
709 X1 = X1.toEpoch(e2)
710 e1 = e2
711 elif e1 != e2: # X2 to e1
712 X2 = X2.toEpoch(e1)
713 # <https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf,
714 # Apendix, Table 7, last column "Sum of the previous ..."
715 X = TRFXform(n1, n2, epoch=e1,
716 xform=X1.xform + (X2.xform if f else -X2.xform),
717 rates=X1.rates + (X2.rates if f else -X2.rates),
718 name=NN(X1._at(e1), _PLUS_ if f else _MINUS_,
719 X2._at(e1)))
720 return X
723def _P(*ps): # deleted below
724 '''(INTERNAL) De-dup L{TRFXform7Tuple}s.
725 '''
726 t = TRFXform7Tuple(map(_F, ps))
727 return _Ps.setdefault(t, t) # PYCHOK del
730def _reframe(**name_reframe):
731 '''(INTERNAL) Get a C{reframe}.
732 '''
733 if len(name_reframe) == 1:
734 for n, r in name_reframe.items():
735 break
736 if isstr(r):
737 r = RefFrames.get(r)
738 if r and isinstance(r, RefFrame):
739 return r
740 raise TRFError(**name_reframe) # _invalid_
743def _toTransform0(n1, e1, n2, e2):
744 '''(INTERNAL) Return a L{TransformXform}, 0-tuple or C{None}.
745 '''
746 if n1 == n2 or (n1.startswith(_ITRF_) and n2.startswith(_WGS84_)) \
747 or (n2.startswith(_ITRF_) and n1.startswith(_WGS84_)):
748 return ()
750 for _f in (_immediate, _intermediate):
751 X = _f(n1, n2, e1, e2)
752 Y = _f(n2, n1, e1, e2)
753 if X and Y:
754 if X._range(e1, e2) < Y._range(e1, e2):
755 Y = None
756 else:
757 X = None
758 if X:
759 return X.toTransform(e1, epoch2=e2)
760 if Y:
761 return Y.toTransform(e1, epoch2=e2, inverse=True)
763 return None
766def trfTransform0(reframe, reframe2, epoch=None, epoch2=None):
767 '''Get the L{TransformXform} to convert a C{reframe} observed at C{epoch} to
768 C{reframe2} at observed at C{epoch2 or epoch}.
770 @arg reframe: Reference frame to convert I{from} (L{RefFrame} or C{str}).
771 @arg reframe2: Reference frame to convert I{to} (L{RefFrame} or C{str}).
772 @arg epoch: Epoch to observe I{from} (L{Epoch}, C{scalar} or C{str}),
773 otherwise C{B{reframe}}'s C{epoch}.
774 @kwarg epoch2: Optional epoch to observe to observe I{to} (L{Epoch}, C{scalar}
775 or C{str}), otherwise B{C{epoch}} or C{B{reframe}}'s C{epoch}.
777 @return: A L{TransformXform} instance, a C{0-tuple} for I{unity, identity} or
778 C{None} if no conversion exists.
780 @raise TRFError: Invalid B{C{reframe}}, B{C{epoch}}, B{C{reframe2}} or
781 B{C{epoch2}}.
783 @raise TypeError: Invalid B{C{reframe}} or B{C{reframe2}}.
784 '''
785 r1 = _reframe(reframe=reframe)
786 e1 = r1.epoch if epoch is None else _Epoch(epoch)
787 r2 = _reframe(reframe2=reframe2)
788 e2 = e1 if epoch2 is None else Epoch(epoch2=epoch2)
789 return _toTransform0(r1.name, e1, r2.name, e2)
792def trfXform(reframe1, reframe2, epoch=None, xform=None, rates=None):
793 '''Define a new Terrestrial Reference Frame (TRF) converter.
795 @arg reframe1: Source reframe (L{RefFrame} or C{str}), converting I{from}.
796 @arg reframe2: Destination reframe (L{RefFrame} or C{str}), converting I{to}.
797 @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str})
798 or C{None} for C{B{reframe2}}'s epoch.
799 @kwarg xform: I{Transform} parameters (L{TRFXform7Tuple}).
800 @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), as B{C{xform}},
801 but in C{units-per-year}.
803 @return: The new TRF converter (L{TRFXform}).
805 @raise TRFError: Invalid B{C{reframe1}}, B{C{reframe2}}, B{C{epoch}},
806 B{C{xform}} or B{C{rates}} or the TRF converter
807 already exists.
808 '''
809 r1 = _reframe(reframe1=reframe1)
810 r2 = _reframe(reframe2=reframe2)
811 e = r2.epoch if epoch is None else _Epoch(epoch)
812 _xinstanceof(TRFXform7Tuple, xform=xform, rates=rates)
813 return _trfX(r1.name, r2.name, epoch=e, xform=xform, rates=rates)
816def _trfX(n1, n2, **epoch_xform_rates):
817 '''(INTERNAL) New, I{unique} L{TRFXform} converter.
818 '''
819 r1 = RefFrames.get(n1)
820 r2 = RefFrames.get(n2)
821 if r1 and r2:
822 if n2 in r1._Xs:
823 t = _exists_
824 elif n1 in r2._Xs:
825 t = _SPACE_(_inverse_, _exists_)
826 else:
827 r1._Xs[n2] = X = TRFXform(n1, n2, **epoch_xform_rates)
828 return X
829 else:
830 t = _invalid_
831 raise TRFError(trfX=_SPACE_(n1, _to_, n2), txt=t) # _NameError
834# TRF conversions specified as an epoch and 2 sets of 7-parameters. Most from Altamimi, Z. U{"EUREF Technical
835# Note 1: Relationship and Transformation between the International and the European Terrestrial Reference
836# Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Appendix A, more at U{Quinsy QPS <https://
837# confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ITRF_Transformation_Parameters.xlsx>}.
838# See also U{Quinsy International Terrestrial Reference Frame 2014 (ITRF2014)<https://confluence.QPS.NL/qinsy/latest/
839# en/international-terrestrial-reference-frame-2014-itrf2014-182618383.html>}.
840_trfX(_ITRF2020_, _ITRF2014_, epoch=_E(2015), # <https://ITRF.IGN.Fr/docs/solutions/itrf2020/Transfo-ITRF2020_TRFs.txt>
841 xform=_P( -1.4, -0.9, 1.4, -0.42, _0_0, _0_0, _0_0),
842 rates=_P( _0_0, -0.1, 0.2, _0_0, _0_0, _0_0, _0_0))
843_trfX(_ITRF2020_, _ITRF2008_, epoch=_E(2015),
844 xform=_P( 0.2, 1.0, 3.3, -0.29, _0_0, _0_0, _0_0),
845 rates=_P( _0_0, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0))
846_trfX(_ITRF2020_, _ITRF2005_, epoch=_E(2015),
847 xform=_P( 2.7, 0.1, -1.4, 0.65, _0_0, _0_0, _0_0),
848 rates=_P( 0.3, -0.1, 0.1, 0.03, _0_0, _0_0, _0_0))
849_trfX(_ITRF2020_, _ITRF2000_, epoch=_E(2015),
850 xform=_P( -0.2, 0.8, -34.2, 2.25, _0_0, _0_0, _0_0),
851 rates=_P( 0.1, _0_0, -1.7, 0.11, _0_0, _0_0, _0_0))
852_trfX(_ITRF2020_, _ITRF97_, epoch=_E(2015),
853 xform=_P( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
854 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
855_trfX(_ITRF2020_, _ITRF96_, epoch=_E(2015),
856 xform=_P( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
857 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
858_trfX(_ITRF2020_, _ITRF94_, epoch=_E(2015),
859 xform=_P( 6.5, -3.9, -77.9, 3.98, _0_0, _0_0, 0.36),
860 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
861_trfX(_ITRF2020_, _ITRF93_, epoch=_E(2015),
862 xform=_P( -65.8, 1.9, -71.3, 4.47, -3.36, -4.33, 0.75),
863 rates=_P( -2.8, -0.2, -2.3, 0.12, -0.11, -0.19, 0.07))
864_trfX(_ITRF2020_, _ITRF92_, epoch=_E(2015),
865 xform=_P( 14.5, -1.9, -85.9, 3.27, _0_0, _0_0, 0.36),
866 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
867_trfX(_ITRF2020_, _ITRF91_, epoch=_E(2015),
868 xform=_P( 26.5, 12.1, -91.9, 4.67, _0_0, _0_0, 0.36),
869 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
870_trfX(_ITRF2020_, _ITRF90_, epoch=_E(2015),
871 xform=_P( 24.5, 8.1, -107.9, 4.97, _0_0, _0_0, 0.36),
872 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
873_trfX(_ITRF2020_, _ITRF89_, epoch=_E(2015),
874 xform=_P( 29.5, 32.1, -145.9, 8.37, _0_0, _0_0, 0.36),
875 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
876_trfX(_ITRF2020_, _ITRF88_, epoch=_E(2015),
877 xform=_P( 24.5, -3.9, -169.9, 11.47, 0.1, _0_0, 0.36),
878 rates=_P( 0.1, -0.6, -3.1, 0.12, _0_0, _0_0, 0.02))
880# see U{Transformation Parameters ITRF2014<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2014_ITRFs.txt>} and
881# Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
882# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1.pdf>} Appendix A.
883_trfX(_ITRF2014_, _ITRF2008_, epoch=(2010), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2014/tp_14-08.php>
884 xform=_P( 1.6, 1.9, 2.4, -0.02, _0_0, _0_0, _0_0),
885 rates=_P( _0_0, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0))
886_trfX(_ITRF2014_, _ITRF2005_, epoch=_E(2010),
887 xform=_P( 2.6, _1_0, -2.3, 0.92, _0_0, _0_0, _0_0),
888 rates=_P( 0.3, _0_0, -0.1, 0.03, _0_0, _0_0, _0_0))
889_trfX(_ITRF2014_, _ITRF2000_, epoch=_E(2010),
890 xform=_P( 0.7, 1.2, -26.1, 2.12, _0_0, _0_0, _0_0),
891 rates=_P( 0.1, 0.1, -1.9, 0.11, _0_0, _0_0, _0_0))
892_trfX(_ITRF2014_, _ITRF97_, epoch=_E(2010),
893 xform=_P( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
894 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
895_trfX(_ITRF2014_, _ITRF96_, epoch=_E(2010),
896 xform=_P( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
897 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
898_trfX(_ITRF2014_, _ITRF94_, epoch=_E(2010),
899 xform=_P( 7.4, -0.5, -62.8, 3.8, _0_0, _0_0, 0.26),
900 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
901_trfX(_ITRF2014_, _ITRF93_, epoch=_E(2010),
902 xform=_P( -50.4, 3.3, -60.2, 4.29, -2.81, -3.38, 0.4),
903 rates=_P( -2.8, -0.1, -2.5, 0.12, -0.11, -0.19, 0.07))
904_trfX(_ITRF2014_, _ITRF92_, epoch=_E(2010),
905 xform=_P( 15.4, 1.5, -70.8, 3.09, _0_0, _0_0, 0.26),
906 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
907_trfX(_ITRF2014_, _ITRF91_, epoch=_E(2010),
908 xform=_P( 27.4, 15.5, -76.8, 4.49, _0_0, _0_0, 0.26),
909 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
910_trfX(_ITRF2014_, _ITRF90_, epoch=_E(2010),
911 xform=_P( 25.4, 11.5, -92.8, 4.79, _0_0, _0_0, 0.26),
912 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
913_trfX(_ITRF2014_, _ITRF89_, epoch=_E(2010),
914 xform=_P( 30.4, 35.5, -130.8, 8.19, _0_0, _0_0, 0.26),
915 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
916_trfX(_ITRF2014_, _ITRF88_, epoch=_E(2010),
917 xform=_P( 25.4, -0.5, -154.8, 11.29, 0.1, _0_0, 0.26),
918 rates=_P( 0.1, -0.5, -3.3, 0.12, _0_0, _0_0, 0.02))
920# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
921# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 1st and 2nd column
922_trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2005),
923 xform=_P( -0.5, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
924 rates=_P( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
925# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(1997),
926# xform=_P( -2.9, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
927# rates=_P( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
928# see U{Transformation Parameters ITRF2008<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2008_ITRFs.txt>}
929# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2008/tp_08-05.php>
930# xform=_P( -2.0, -0.9, -4.7, 0.94, _0_0, _0_0, _0_0),
931# rates=_P( 0.3, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
932_trfX(_ITRF2008_, _ITRF2000_, epoch=_E(2000),
933 xform=_P( -1.9, -1.7, -10.5, 1.34, _0_0, _0_0, _0_0),
934 rates=_P( 0.1, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
935_trfX(_ITRF2008_, _ITRF97_, epoch=_E(2000),
936 xform=_P( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
937 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
938_trfX(_ITRF2008_, _ITRF96_, epoch=_E(2000),
939 xform=_P( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
940 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
941_trfX(_ITRF2008_, _ITRF94_, epoch=_E(2000),
942 xform=_P( 4.8, 2.6, -33.2, 2.92, _0_0, _0_0, 0.06),
943 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
944_trfX(_ITRF2008_, _ITRF93_, epoch=_E(2000),
945 xform=_P( -24.0, 2.4, -38.6, 3.41, -1.71, -1.48, -0.3),
946 rates=_P( -2.8, -0.1, -2.4, 0.09, -0.11, -0.19, 0.07))
947_trfX(_ITRF2008_, _ITRF92_, epoch=_E(2000),
948 xform=_P( 12.8, 4.6, -41.2, 2.21, _0_0, _0_0, 0.06),
949 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
950_trfX(_ITRF2008_, _ITRF91_, epoch=_E(2000),
951 xform=_P( 24.8, 18.6, -47.2, 3.61, _0_0, _0_0, 0.06),
952 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
953_trfX(_ITRF2008_, _ITRF90_, epoch=_E(2000),
954 xform=_P( 22.8, 14.6, -63.2, 3.91, _0_0, _0_0, 0.06),
955 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
956_trfX(_ITRF2008_, _ITRF89_, epoch=_E(2000),
957 xform=_P( 27.8, 38.6, -101.2, 7.31, _0_0, _0_0, 0.06),
958 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
959_trfX(_ITRF2008_, _ITRF88_, epoch=_E(2000),
960 xform=_P( 22.8, 2.6, -125.2, 10.41, 0.1, _0_0, 0.06),
961 rates=_P( 0.1, -0.5, -3.2, 0.09, _0_0, _0_0, 0.02))
963# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
964# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 3rd column
965# _trfX(_ITRF2005_, _ITRF2000_, epoch=_E(1997),
966# xform=_P( 0.7, -1.1, -0.4, 0.16, -0.2, 0.1 -1.8),
967# rates=_P( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
968_trfX(_ITRF2005_, _ITRF2000_, epoch=_E(2000), # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2005/tp_05-00.php>
969 xform=_P( 0.1, -0.8, -5.8, 0.4, _0_0, _0_0, _0_0),
970 rates=_P( -0.2, 0.1, -1.8, 0.08, _0_0, _0_0, _0_0))
972_trfX(_ITRF2000_, _ITRF97_, epoch=_E(1997),
973 xform=_P( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
974 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, -0.02)) # 0.02?
975_trfX(_ITRF2000_, _ITRF96_, epoch=_E(1997),
976 xform=_P( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
977 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
978_trfX(_ITRF2000_, _ITRF94_, epoch=_E(1997),
979 xform=_P( 0.67, 0.61, -1.85, 1.55, _0_0, _0_0, _0_0),
980 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
981_trfX(_ITRF2000_, _ITRF93_, epoch=_E(1988),
982 xform=_P( 12.7, 6.5, -20.9, 1.95, -0.39, 0.8, -1.14),
983 rates=_P( -2.9, -0.2, -0.6, 0.01, -0.11, -0.19, 0.07))
984_trfX(_ITRF2000_, _ITRF92_, epoch=_E(1988),
985 xform=_P( 1.47, 1.35, -1.39, 0.75, _0_0, _0_0, -0.18),
986 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
987_trfX(_ITRF2000_, _ITRF91_, epoch=_E(1988),
988 xform=_P( 26.7, 27.5, -19.9, 2.15, _0_0, _0_0, -0.18),
989 rates=_P( _0_0, -0.6, -1.4, 0.01, _0_0, _0_0, 0.02))
990_trfX(_ITRF2000_, _ITRF90_, epoch=_E(1988),
991 xform=_P( 2.47, 2.35, -3.59, 2.45, _0_0, _0_0, -0.18),
992 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
993_trfX(_ITRF2000_, _ITRF89_, epoch=_E(1988),
994 xform=_P( 2.97, 4.75, -7.39, 5.85, _0_0, _0_0, -0.18),
995 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
996_trfX(_ITRF2000_, _ITRF88_, epoch=_E(1988),
997 xform=_P( 2.47, 1.15, -9.79, 8.95, 0.1, _0_0, -0.18),
998 rates=_P( _0_0, -0.06, -0.14, 0.01, _0_0, _0_0, 0.02))
1000# Soler, T .& Snay R.A. U{"Transforming Positions and Velocities between the International Terrestrial
1001# Reference Frame of 2000 and North American Datum of 1983"<https://www.ResearchGate.net/publication/245291390>},
1002# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
1003# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 5th and 6th column
1004_trfX(_ITRF97_, _ITRF96_, epoch=_E(1997),
1005 xform=_P( -2.07, -0.21, 9.95, -0.93496, 0.1267, -0.22355, -0.06065,),
1006 rates=_P( 0.69, -0.1, 1.86, -0.19201, 0.01347, -0.01514, 0.00027))
1007_trfX(_ITRF96_, _NAD83_, epoch=_E(1997),
1008 xform=_P( 991.0, -190.72, -512.9, _0_0, 25.79, 9.65, 11.66,),
1009 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.0532, -0.7423, -0.0316,))
1011# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1012# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 1.
1013# _trfX(_ITRF2020_, _ETRF2020_, epoch=_E(1989), # see Table 2 below
1014# xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0),
1015# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753))
1016# _trfX(_ITRF2014_, _ETRF2014_, epoch=_E(1989), # see Table 3 below
1017# xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0),
1018# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77))
1019_trfX(_ITRF2005_, _ETRF2005_, epoch=_E(1989),
1020 xform=_P( 56.0, 48.0, -37.0, _0_0, _0_0, _0_0, _0_0),
1021 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.054, 0.518, -0.781))
1022# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(1989), # see Table 4 below
1023# xform=_P( 54.0, 51.0, -48.0, _0_0, _0_0, _0_0, _0_0),
1024# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1025_trfX(_ITRF97_, _ETRF97_, epoch=_E(1989),
1026 xform=_P( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1027 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1028_trfX(_ITRF96_, _ETRF96_, epoch=_E(1989),
1029 xform=_P( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1030 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1031_trfX(_ITRF94_, _ETRF94_, epoch=_E(1989),
1032 xform=_P( 41.0, 41.0, -49.0, _0_0, _0_0, _0_0, _0_0),
1033 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.2, 0.5, -0.65))
1034_trfX(_ITRF93_, _ETRF93_, epoch=_E(1989),
1035 xform=_P( 19.0, 53.0, -21.0, _0_0, _0_0, _0_0, _0_0),
1036 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.32, 0.78, -0.67))
1037_trfX(_ITRF92_, _ETRF92_, epoch=_E(1989),
1038 xform=_P( 38.0, 40.0, -37.0, 0.0, 0.0, 0.0, 0.0),
1039 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68))
1040_trfX(_ITRF91_, _ETRF91_, epoch=_E(1989),
1041 xform=_P( 21.0, 25.0, -37.0, _0_0, _0_0, _0_0, _0_0),
1042 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.21, 0.52, -0.68))
1043_trfX(_ITRF90_, _ETRF90_, epoch=_E(1989),
1044 xform=_P( 19.0, 28.0, -23.0, _0_0, _0_0, _0_0, _0_0),
1045 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71))
1046_trfX(_ITRF89_, _ETRF89_, epoch=_E(1989),
1047 xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0),
1048 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.11, 0.57, -0.71))
1050# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1051# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 2.
1052_trfX(_ITRF2020_, _ETRF2020_, epoch=_E(2015),
1053 xform=_P( _0_0, _0_0, _0_0, _0_0, 2.236, 13.494, -19.578),
1054 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.086, 0.519, -0.753))
1055_trfX(_ITRF2014_, _ETRF2020_, epoch=_E(2015),
1056 xform=_P( 1.4, 0.9, -1.4, 0.42, 2.236, 13.494, -19.578),
1057 rates=_P( _0_0, 0.1, -0.2, _0_0, 0.086, 0.519, -0.753))
1058_trfX(_ITRF2008_, _ETRF2020_, epoch=_E(2015),
1059 xform=_P( 3.0, 2.8, 0.5, 0.55, 2.236, 13.494, -19.578),
1060 rates=_P( _0_0, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753))
1061_trfX(_ITRF2005_, _ETRF2020_, epoch=_E(2015),
1062 xform=_P( 5.5, 1.9, -4.2, 1.49, 2.236, 13.494, -19.578),
1063 rates=_P( 0.3, 0.1, -0.3, 0.03, 0.086, 0.519, -0.753))
1064_trfX(_ITRF2000_, _ETRF2020_, epoch=_E(2015),
1065 xform=_P( 2.6, 2.6, -37.0, 3.09, 2.236, 13.494, -19.578),
1066 rates=_P( 0.1, 0.2, -2.1, 0.11, 0.086, 0.519, -0.753))
1067_trfX(_ITRF97_, _ETRF2020_, epoch=_E(2015),
1068 xform=_P( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1069 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1070_trfX(_ITRF96_, _ETRF2020_, epoch=_E(2015),
1071 xform=_P( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1072 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1073_trfX(_ITRF94_, _ETRF2020_, epoch=_E(2015),
1074 xform=_P( 9.3, -2.1, -80.7, 4.82, 2.236, 13.494, -19.218),
1075 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1076_trfX(_ITRF93_, _ETRF2020_, epoch=_E(2015),
1077 xform=_P( -63.0, 3.7, -74.1, 5.31, -1.124, 9.164, -18.828),
1078 rates=_P( -2.8, _0_0, -2.7, 0.12, -0.024, 0.329, -0.683))
1079_trfX(_ITRF92_, _ETRF2020_, epoch=_E(2015),
1080 xform=_P( 17.3, -0.1, -88.7, 4.11, 2.236, 13.494, -19.218),
1081 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1082_trfX(_ITRF91_, _ETRF2020_, epoch=_E(2015),
1083 xform=_P( 29.3, 13.9, -94.7, 5.51, 2.236, 13.494, -19.218),
1084 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1085_trfX(_ITRF90_, _ETRF2020_, epoch=_E(2015),
1086 xform=_P( 27.3, 9.9, -110.7, 5.81, 2.236, 13.494, -19.218),
1087 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1088_trfX(_ITRF89_, _ETRF2020_, epoch=_E(2015),
1089 xform=_P( 32.3, 33.9, -148.7, 9.21, 2.236, 13.494, -19.218),
1090 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1091_trfX(_ITRF88_, _ETRF2020_, epoch=_E(2015),
1092 xform=_P( 27.3, -2.1, -172.7, 12.31, 2.336, 13.494, -19.218),
1093 rates=_P( 0.1, -0.4, -3.5, 0.12, 0.086, 0.519, -0.733))
1095# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
1096# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 3.
1097_trfX(_ITRF2020_, _ETRF2014_, epoch=_E(2015),
1098 xform=_P( -1.4, -0.9, 1.4, 0.42, 2.21, 13.806, -20.02),
1099 rates=_P( _0_0, -0.1, 0.2, _0_0, 0.085, 0.531, -0.77))
1100_trfX(_ITRF2014_, _ETRF2014_, epoch=_E(2015),
1101 xform=_P( _0_0, _0_0, _0_0, _0_0, 2.21, 13.806, -20.02),
1102 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.085, 0.531, -0.77))
1103_trfX(_ITRF2008_, _ETRF2014_, epoch=_E(2015),
1104 xform=_P( -1.6, -1.9, -1.9, -0.13, 2.21, 13.806, -20.02),
1105 rates=_P( _0_0, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77))
1106_trfX(_ITRF2005_, _ETRF2014_, epoch=_E(2015),
1107 xform=_P( -4.1, -1.0, 2.8, -1.07, 2.21, 13.806, -20.02),
1108 rates=_P( -0.3, _0_0, 0.1, -0.03, 0.085, 0.531, -0.77))
1109_trfX(_ITRF2000_, _ETRF2014_, epoch=_E(2015),
1110 xform=_P( -1.2, -1.7, 35.6, -2.67, 2.21, 13.806, -20.02),
1111 rates=_P( -0.1, -0.1, 1.9, -0.11, 0.085, 0.531, -0.77))
1112_trfX(_ITRF97_, _ETRF2014_, epoch=_E(2015),
1113 xform=_P( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1114 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1115_trfX(_ITRF96_, _ETRF2014_, epoch=_E(2015),
1116 xform=_P( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1117 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1118_trfX(_ITRF94_, _ETRF2014_, epoch=_E(2015),
1119 xform=_P( -7.9, 3.0, 79.3, -4.40, 2.210, 13.806, -20.38),
1120 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1121_trfX(_ITRF93_, _ETRF2014_, epoch=_E(2015),
1122 xform=_P( 64.4, -2.8, 72.7, -4.89, 5.570, 18.136, -20.77),
1123 rates=_P( 2.8, 0.1, 2.5, -0.12, 0.195, 0.721, -0.84))
1124_trfX(_ITRF92_, _ETRF2014_, epoch=_E(2015),
1125 xform=_P( -15.9, 1.0, 87.3, -3.69, 2.21, 13.806, -20.38),
1126 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1127_trfX(_ITRF91_, _ETRF2014_, epoch=_E(2015),
1128 xform=_P( -27.9, -13.0, 93.3, -5.09, 2.21, 13.806, -20.38),
1129 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1130_trfX(_ITRF90_, _ETRF2014_, epoch=_E(2015),
1131 xform=_P( -25.9, -9.0, 109.3, -5.39, 2.21, 13.806, -20.38),
1132 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1133_trfX(_ITRF89_, _ETRF2014_, epoch=_E(2015),
1134 xform=_P( -30.9, -33.0, 147.3, -8.79, 2.21, 13.806, -20.38),
1135 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1136_trfX(_ITRF88_, _ETRF2014_, epoch=_E(2015),
1137 xform=_P( -25.9, 3.0, 171.3, -11.89, 2.11, 13.806, -20.38),
1138 rates=_P( -0.1, 0.5, 3.3, -0.12, 0.085, 0.531, -0.79))
1140# see U{Altamimi, Z. "EUREF Technical Note 1: Relationship and Transformation between the International and
1141# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 4,
1142# U{Boucher, C. & Altamimi, Z. "Memo: Specifications for reference frame fixing in the analysis of a EUREF GPS
1143# campaign" (2011) <https://ETRS89.ENSG.IGN.Fr/memo-V8.pdf>} and U{Altamimi, Z. "Key results of ITRF2014 and
1144# implication to ETRS89 realization", EUREF2016<https://www.EUREF.EU/symposia/2016SanSebastian/01-02-Altamimi.pdf>}.
1145_trfX(_ITRF2020_, _ETRF2000_, epoch=_E(2015),
1146 xform=_P( 53.8, 51.8, -82.2, 2.25, 2.106, 12.74, -20.592),
1147 rates=_P( 0.1, _0_0, -1.7, 0.11, 0.081, 0.49, -0.792))
1148# _trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2000),
1149# xform=_P( 53.7, 51.2, -55.1, 1.02, 0.891, 5.39, -8.712),
1150# rates=_P( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792))
1151_trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2015),
1152 xform=_P( 55.2, 52.7, -83.6, 2.67, 2.106, 12.74, -20.592),
1153 rates=_P( 0.1, 0.1, -1.9, 0.11, 0.081, 0.49, -0.792))
1154# _trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2000),
1155# xform=_P( 52.1, 49.3, -58.5, 1.34, 0.891, 5.39, -8.712),
1156# rates=_P( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1157_trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2015),
1158 xform=_P( 53.6, 50.8, -85.5, 2.54, 2.106, 12.74, -20.592),
1159 rates=_P( 0.1, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1160# _trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2000),
1161# xform=_P( 54.1, 50.2, -53.8, 0.4, 0.891, 5.39, -8.712),
1162# rates=_P( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1163_trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2015),
1164 xform=_P( 51.1, 51.7, -80.8, 1.6, 2.106, 12.74, -20.592),
1165 rates=_P( -0.2, 0.1, -1.8, 0.08, 0.081, 0.49, -0.792))
1166# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2000),
1167# xform=_P( 54.0, 51.0, -48.0, _0_0, 0.891, 5.39, -8.712),
1168# rates=_P( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1169_trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2015),
1170 xform=_P( 54.0, 51.0, -48.0, _0_0, 2.106, 12.74, -20.592),
1171 rates=_P( _0_0, _0_0, _0_0, _0_0, 0.081, 0.49, -0.792))
1172_trfX(_ITRF97_, _ETRF2000_, epoch=_E(2015),
1173 xform=_P( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1174 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1175_trfX(_ITRF96_, _ETRF2000_, epoch=_E(2015),
1176 xform=_P( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1177 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1178_trfX(_ITRF94_, _ETRF2000_, epoch=_E(2015),
1179 xform=_P( 47.3, 55.7, -4.3, -1.73, 2.106, 12.74, -20.952),
1180 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1181_trfX(_ITRF93_, _ETRF2000_, epoch=_E(2015),
1182 xform=_P( 119.6, 49.9, -10.9, -2.22, 5.466, 17.07, -21.342),
1183 rates=_P( 2.9, 0.2, 0.6, -0.01, 0.191, 0.68, -0.862))
1184_trfX(_ITRF92_, _ETRF2000_, epoch=_E(2015),
1185 xform=_P( 39.3, 53.7, 3.7, -1.02, 2.106, 12.74, -20.952),
1186 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1187_trfX(_ITRF91_, _ETRF2000_, epoch=_E(2015),
1188 xform=_P( 27.3, 39.7, 9.7, -2.42, 2.106, 12.74, -20.952),
1189 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1190_trfX(_ITRF90_, _ETRF2000_, epoch=_E(2015),
1191 xform=_P( 29.3, 43.7, 25.7, -2.72, 2.106, 12.74, -20.952),
1192 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1193_trfX(_ITRF89_, _ETRF2000_, epoch=_E(2015),
1194 xform=_P( 24.3, 19.7, 63.7, -6.12, 2.106, 12.74, -20.952),
1195 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1196_trfX(_ITRF88_, _ETRF2000_, epoch=_E(2015),
1197 xform=_P( 29.3, 55.7, 87.7, -9.22, 2.006, 12.74, -20.952),
1198 rates=_P( _0_0, 0.6, 1.4, -0.01, 0.081, 0.49, -0.812))
1200# GDA2020 "Geocentric Datum of Australia 2020 Technical Manual", v1.5, 2020-12-09, Table 3.3 and 3.4
1201# <https://www.ICSM.gov.AU/sites/default/files/2020-12/GDA2020%20Technical%20Manual%20V1.5_4.pdf>
1202# (the GDA2020 xforms are different but the rates are the same as GDA94, further below)
1203_trfX(_ITRF2014_, _GDA2020_, epoch=_E(2020),
1204 xform=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0),
1205 rates=_P( _0_0, _0_0, _0_0, _0_0, 1.50379, 1.18346, 1.20716))
1206_trfX(_ITRF2008_, _GDA2020_, epoch=_E(2020),
1207 xform=_P( 13.79, 4.55, 15.22, 2.5, 0.2808, 0.2677, -0.4638),
1208 rates=_P( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551))
1209_trfX(_ITRF2005_, _GDA2020_, epoch=_E(2020),
1210 xform=_P( 40.32, -33.85, -16.72, 4.286, -1.2893, -0.8492, -0.3342),
1211 rates=_P( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701))
1212_trfX(_ITRF2000_, _GDA2020_, epoch=_E(2020),
1213 xform=_P(-105.52, 51.58, 231.68, 3.55, 4.2175, 6.3941, 0.8617),
1214 rates=_P( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224))
1216# see Table 2 in U{Dawson, J. & Woods, A. "ITRF to GDA94 coordinate transformations", Journal of Applied
1217# Geodesy 4 (2010), 189-199<https://www.ResearchGate.net/publication/258401581_ITRF_to_GDA94_coordinate_transformations>}
1218# (note, sign of rotations for GDA94 reversed as "Australia assumes rotation to be of coordinate axes",
1219# rather than the more conventional "position around the coordinate axes")
1220_trfX(_ITRF2008_, _GDA94_, epoch=_E(1994),
1221 xform=_P( -84.68, -19.42, 32.01, 9.71, -0.4254, 2.2578, 2.4015),
1222 rates=_P( 1.42, 1.34, 0.9, 0.109, 1.5461, 1.182, 1.1551))
1223_trfX(_ITRF2005_, _GDA94_, epoch=_E(1994),
1224 xform=_P( -79.73, -6.86, 38.03, 6.636, 0.0351, -2.1211, -2.1411),
1225 rates=_P( 2.25, -0.62, -0.56, 0.294, -1.4707, -1.1443, -1.1701))
1226_trfX(_ITRF2000_, _GDA94_, epoch=_E(1994),
1227 xform=_P( -45.91, -29.85, -20.37, 7.07, -1.6705, 0.4594, 1.9356),
1228 rates=_P( -4.66, 3.55, 11.24, 0.249, 1.7454, 1.4868, 1.224))
1230# see U{Solar, T. & Snay, R.A. "Transforming Positions and Velocities between the
1231# International Terrestrial Reference Frame of 2000 and North American Datum of 1983"
1232# (2004)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>}
1233_trfX(_ITRF2000_, _NAD83_, epoch=_E(1997), # note NAD83(CORS96)
1234 xform=_P( 995.6, -1901.3, -521.5, 0.615, -25.915, -9.426, -11.599),
1235 rates=_P( 0.7, -0.7, _0_5, -0.182, -0.06667, 0.75744, 0.05133))
1237# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/
1238# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83 and Pearson, C. & Snay, R. U{"Introducing
1239# HTDP 3.1 to transform coordinates across time and spatial reference frames"<https://Geodesy.NOAA.gov/
1240# TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 7th column
1241_trfX(_ITRF2008_, _NAD83_, epoch=_E(1997),
1242 xform=_P( 993.43, -1903.31, -526.55, 1.71504, -25.91467, -9.42645, -11.59935),
1243 rates=_P( 0.79, -0.6, -1.34, -0.10201, -0.06667, 0.75744, 0.05133))
1244# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/
1245# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83
1246_trfX(_ITRF2005_, _NAD83_, epoch=_E(1997),
1247 xform=_P( 996.3, -1902.4, -521.9, 0.775, -25.915, -9.426, -11.599),
1248 rates=_P( 0.5, -0.6, -1.3, -0.10201, -0.06667, 0.75744, 0.05133))
1249_trfX(_ITRF90_, _NAD83_, epoch=_E(1997),
1250 xform=_P( 973.0, -1919.2, -482.9, -0.9, -25.79, -9.65, -11.66),
1251 rates=_P( _0_0, _0_0, _0_0, _0_0, -0.053, 0.742, 0.032))
1252_trfX(_ITRF90_, _WGS84_, epoch=_E(1984),
1253 xform=_P( 60.0, -517.0, -223.0, -11.0, 18.3, -0.3, 7.0),
1254 rates=_P( _0_0, _0_0, _0_0, _0_0, _0_0, _0_0, _0_0))
1256del _P, _Ps # keep _E, _Es
1258if __name__ == '__main__':
1260 from pygeodesy.interns import _COLONSPACE_,_COMMA_, _NL_, _NLATvar_, _STAR_
1261 from pygeodesy.lazily import printf
1262 from time import localtime
1264 D = date2epoch.__name__
1265 E = epoch2date.__name__
1266 y = localtime()[0]
1267 for m in range(1, 13):
1268 for d in (1, 15, _mDays[m] - 1, _mDays[m]):
1269 f = '%s(%d,%3d,%3d)' % (D, y, m, d)
1270 e = date2epoch(y, m, d)
1271 t = epoch2date(e)
1272 x = NN if t == (y, m, d) else _STAR_
1273 e = '%.3f' % (e,)
1274 e = '%s, %s(%s)' % (e, E, e)
1275 t = '%d,%3d,%3d' % t
1276 printf('# %s = %s = %s %s', f, e, t, x)
1278 # __doc__ of this file, force all into registery
1279 def _RFs():
1280 yield NN
1281 for t in RefFrames.toRepr(all=True).split(_NL_):
1282 t = t.strip(_COMMA_)
1283 n = t.split(_COLONSPACE_)[0].split(_DOT_)[1]
1284 r = RefFrames.get(n)
1285 x = len(r.Xforms()), -len(r.Xforms(inverse=True))
1286 yield '%s .Xforms=%s' % (t, x)
1288 printf(_NLATvar_.join(sorted(_RFs())), nt=1)
1290 X, t = (), 0 # all form
1291 for r in RefFrames.values():
1292 X += tuple(r._Xs.values())
1293 for X in sorted(X):
1294 t += 1
1295 printf('#%4d %-27s xform=%r', t, X.name, X.xform)
1296 printf('#%32s rates=%r', _SPACE_, X.rates)
1298# **) MIT License
1299#
1300# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1301#
1302# Permission is hereby granted, free of charge, to any person obtaining a
1303# copy of this software and associated documentation files (the "Software"),
1304# to deal in the Software without restriction, including without limitation
1305# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1306# and/or sell copies of the Software, and to permit persons to whom the
1307# Software is furnished to do so, subject to the following conditions:
1308#
1309# The above copyright notice and this permission notice shall be included
1310# in all copies or substantial portions of the Software.
1311#
1312# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1313# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1314# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1315# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1316# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1317# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1318# OTHER DEALINGS IN THE SOFTWARE.
1320# % python -m pygeodesy.trf
1321#
1322# date2epoch(2024, 1, 1) = 2024.003, epoch2date(2024.003) = 2024, 1, 1
1323# date2epoch(2024, 1, 15) = 2024.041, epoch2date(2024.041) = 2024, 1, 15
1324# date2epoch(2024, 1, 30) = 2024.082, epoch2date(2024.082) = 2024, 1, 30
1325# date2epoch(2024, 1, 31) = 2024.085, epoch2date(2024.085) = 2024, 1, 31
1326# date2epoch(2024, 2, 1) = 2024.087, epoch2date(2024.087) = 2024, 2, 2 *
1327# date2epoch(2024, 2, 15) = 2024.126, epoch2date(2024.126) = 2024, 2, 16 *
1328# date2epoch(2024, 2, 28) = 2024.161, epoch2date(2024.161) = 2024, 2, 28
1329# date2epoch(2024, 2, 29) = 2024.164, epoch2date(2024.164) = 2024, 3, 1 *
1330# date2epoch(2024, 3, 1) = 2024.167, epoch2date(2024.167) = 2024, 3, 2 *
1331# date2epoch(2024, 3, 15) = 2024.205, epoch2date(2024.205) = 2024, 3, 16 *
1332# date2epoch(2024, 3, 30) = 2024.246, epoch2date(2024.246) = 2024, 3, 31 *
1333# date2epoch(2024, 3, 31) = 2024.249, epoch2date(2024.249) = 2024, 4, 1 *
1334# date2epoch(2024, 4, 1) = 2024.251, epoch2date(2024.251) = 2024, 4, 1
1335# date2epoch(2024, 4, 15) = 2024.290, epoch2date(2024.290) = 2024, 4, 15
1336# date2epoch(2024, 4, 29) = 2024.328, epoch2date(2024.328) = 2024, 4, 29
1337# date2epoch(2024, 4, 30) = 2024.331, epoch2date(2024.331) = 2024, 4, 30
1338# date2epoch(2024, 5, 1) = 2024.333, epoch2date(2024.333) = 2024, 5, 1
1339# date2epoch(2024, 5, 15) = 2024.372, epoch2date(2024.372) = 2024, 5, 15
1340# date2epoch(2024, 5, 30) = 2024.413, epoch2date(2024.413) = 2024, 5, 30
1341# date2epoch(2024, 5, 31) = 2024.415, epoch2date(2024.415) = 2024, 6, 1 *
1342# date2epoch(2024, 6, 1) = 2024.418, epoch2date(2024.418) = 2024, 6, 2 *
1343# date2epoch(2024, 6, 15) = 2024.456, epoch2date(2024.456) = 2024, 6, 16 *
1344# date2epoch(2024, 6, 29) = 2024.495, epoch2date(2024.495) = 2024, 6, 30 *
1345# date2epoch(2024, 6, 30) = 2024.497, epoch2date(2024.497) = 2024, 7, 1 *
1346# date2epoch(2024, 7, 1) = 2024.500, epoch2date(2024.500) = 2024, 7, 1
1347# date2epoch(2024, 7, 15) = 2024.538, epoch2date(2024.538) = 2024, 7, 16 *
1348# date2epoch(2024, 7, 30) = 2024.579, epoch2date(2024.579) = 2024, 7, 30
1349# date2epoch(2024, 7, 31) = 2024.582, epoch2date(2024.582) = 2024, 7, 31
1350# date2epoch(2024, 8, 1) = 2024.585, epoch2date(2024.585) = 2024, 8, 1
1351# date2epoch(2024, 8, 15) = 2024.623, epoch2date(2024.623) = 2024, 8, 15
1352# date2epoch(2024, 8, 30) = 2024.664, epoch2date(2024.664) = 2024, 8, 31 *
1353# date2epoch(2024, 8, 31) = 2024.667, epoch2date(2024.667) = 2024, 9, 1 *
1354# date2epoch(2024, 9, 1) = 2024.669, epoch2date(2024.669) = 2024, 9, 2 *
1355# date2epoch(2024, 9, 15) = 2024.708, epoch2date(2024.708) = 2024, 9, 16 *
1356# date2epoch(2024, 9, 29) = 2024.746, epoch2date(2024.746) = 2024, 9, 30 *
1357# date2epoch(2024, 9, 30) = 2024.749, epoch2date(2024.749) = 2024, 10, 1 *
1358# date2epoch(2024, 10, 1) = 2024.751, epoch2date(2024.751) = 2024, 10, 1
1359# date2epoch(2024, 10, 15) = 2024.790, epoch2date(2024.790) = 2024, 10, 15
1360# date2epoch(2024, 10, 30) = 2024.831, epoch2date(2024.831) = 2024, 10, 30
1361# date2epoch(2024, 10, 31) = 2024.833, epoch2date(2024.833) = 2024, 10, 31
1362# date2epoch(2024, 11, 1) = 2024.836, epoch2date(2024.836) = 2024, 11, 1
1363# date2epoch(2024, 11, 15) = 2024.874, epoch2date(2024.874) = 2024, 11, 15
1364# date2epoch(2024, 11, 29) = 2024.913, epoch2date(2024.913) = 2024, 11, 29
1365# date2epoch(2024, 11, 30) = 2024.915, epoch2date(2024.915) = 2024, 12, 1 *
1366# date2epoch(2024, 12, 1) = 2024.918, epoch2date(2024.918) = 2024, 12, 2 *
1367# date2epoch(2024, 12, 15) = 2024.956, epoch2date(2024.956) = 2024, 12, 16 *
1368# date2epoch(2024, 12, 30) = 2024.997, epoch2date(2024.997) = 2024, 12, 31 *
1369# date2epoch(2024, 12, 31) = 2025.000, epoch2date(2025.000) = 2025, 1, 1 *
1371# 1 ITRF2000@1988xITRF88@1988 xform=(tx=2.47, ty=1.15, tz=-9.79, s=8.95, sx=0.1, sy=0.0, sz=-0.18)
1372# rates=(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1373# 2 ITRF2000@1988xITRF89@1988 xform=(tx=2.97, ty=4.75, tz=-7.39, s=5.85, sx=0.0, sy=0.0, sz=-0.18)
1374# rates=(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1375# 3 ITRF2000@1988xITRF90@1988 xform=(tx=2.47, ty=2.35, tz=-3.59, s=2.45, sx=0.0, sy=0.0, sz=-0.18)
1376# rates=(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1377# 4 ITRF2000@1988xITRF91@1988 xform=(tx=26.7, ty=27.5, tz=-19.9, s=2.15, sx=0.0, sy=0.0, sz=-0.18)
1378# rates=(tx=0.0, ty=-0.6, tz=-1.4, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1379# 5 ITRF2000@1988xITRF92@1988 xform=(tx=1.47, ty=1.35, tz=-1.39, s=0.75, sx=0.0, sy=0.0, sz=-0.18)
1380# rates=(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1381# 6 ITRF2000@1988xITRF93@1988 xform=(tx=12.7, ty=6.5, tz=-20.9, s=1.95, sx=-0.39, sy=0.8, sz=-1.14)
1382# rates=(tx=-2.9, ty=-0.2, tz=-0.6, s=0.01, sx=-0.11, sy=-0.19, sz=0.07)
1383# 7 ITRF2000@1994xGDA94@1994 xform=(tx=-45.91, ty=-29.85, tz=-20.37, s=7.07, sx=-1.6705, sy=0.4594, sz=1.9356)
1384# rates=(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224)
1385# 8 ITRF2000@1997xITRF94@1997 xform=(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
1386# rates=(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1387# 9 ITRF2000@1997xITRF96@1997 xform=(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
1388# rates=(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
1389# 10 ITRF2000@1997xITRF97@1997 xform=(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
1390# rates=(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=-0.02)
1391# 11 ITRF2000@1997xNAD83@1997 xform=(tx=995.6, ty=-1901.3, tz=-521.5, s=0.615, sx=-25.915, sy=-9.426, sz=-11.599)
1392# rates=(tx=0.7, ty=-0.7, tz=0.5, s=-0.182, sx=-0.06667, sy=0.75744, sz=0.05133)
1393# 12 ITRF2000@2015xETRF2000@2015 xform=(tx=54.0, ty=51.0, tz=-48.0, s=0.0, sx=2.106, sy=12.74, sz=-20.592)
1394# rates=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.081, sy=0.49, sz=-0.792)
1395# 13 ITRF2000@2015xETRF2014@2015 xform=(tx=-1.2, ty=-1.7, tz=35.6, s=-2.67, sx=2.21, sy=13.806, sz=-20.02)
1396# rates=(tx=-0.1, ty=-0.1, tz=1.9, s=-0.11, sx=0.085, sy=0.531, sz=-0.77)
1397# 14 ITRF2000@2015xETRF2020@2015 xform=(tx=2.6, ty=2.6, tz=-37.0, s=3.09, sx=2.236, sy=13.494, sz=-19.578)
1398# rates=(tx=0.1, ty=0.2, tz=-2.1, s=0.11, sx=0.086, sy=0.519, sz=-0.753)
1399# 15 ITRF2000@2020xGDA2020@2020 xform=(tx=-105.52, ty=51.58, tz=231.68, s=3.55, sx=4.2175, sy=6.3941, sz=0.8617)
1400# rates=(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224)
1401# 16 ITRF2005@1989xETRF2005@1989 xform=(tx=56.0, ty=48.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1402# rates=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.054, sy=0.518, sz=-0.781)
1403# 17 ITRF2005@1994xGDA94@1994 xform=(tx=-79.73, ty=-6.86, tz=38.03, s=6.636, sx=0.0351, sy=-2.1211, sz=-2.1411)
1404# rates=(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701)
1405# 18 ITRF2005@1997xNAD83@1997 xform=(tx=996.3, ty=-1902.4, tz=-521.9, s=0.775, sx=-25.915, sy=-9.426, sz=-11.599)
1406# rates=(tx=0.5, ty=-0.6, tz=-1.3, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133)
1407# 19 ITRF2005@2000xITRF2000@2000 xform=(tx=0.1, ty=-0.8, tz=-5.8, s=0.4, sx=0.0, sy=0.0, sz=0.0)
1408# rates=(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0)
1409# 20 ITRF2005@2015xETRF2000@2015 xform=(tx=51.1, ty=51.7, tz=-80.8, s=1.6, sx=2.106, sy=12.74, sz=-20.592)
1410# rates=(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792)
1411# 21 ITRF2005@2015xETRF2014@2015 xform=(tx=-4.1, ty=-1.0, tz=2.8, s=-1.07, sx=2.21, sy=13.806, sz=-20.02)
1412# rates=(tx=-0.3, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77)
1413# 22 ITRF2005@2015xETRF2020@2015 xform=(tx=5.5, ty=1.9, tz=-4.2, s=1.49, sx=2.236, sy=13.494, sz=-19.578)
1414# rates=(tx=0.3, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753)
1415# 23 ITRF2005@2020xGDA2020@2020 xform=(tx=40.32, ty=-33.85, tz=-16.72, s=4.286, sx=-1.2893, sy=-0.8492, sz=-0.3342)
1416# rates=(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701)
1417# 24 ITRF2008@1994xGDA94@1994 xform=(tx=-84.68, ty=-19.42, tz=32.01, s=9.71, sx=-0.4254, sy=2.2578, sz=2.4015)
1418# rates=(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551)
1419# 25 ITRF2008@1997xNAD83@1997 xform=(tx=993.43, ty=-1903.31, tz=-526.55, s=1.71504, sx=-25.91467, sy=-9.42645, sz=-11.59935)
1420# rates=(tx=0.79, ty=-0.6, tz=-1.34, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133)
1421# 26 ITRF2008@2000xITRF2000@2000 xform=(tx=-1.9, ty=-1.7, tz=-10.5, s=1.34, sx=0.0, sy=0.0, sz=0.0)
1422# rates=(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0)
1423# 27 ITRF2008@2000xITRF88@2000 xform=(tx=22.8, ty=2.6, tz=-125.2, s=10.41, sx=0.1, sy=0.0, sz=0.06)
1424# rates=(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1425# 28 ITRF2008@2000xITRF89@2000 xform=(tx=27.8, ty=38.6, tz=-101.2, s=7.31, sx=0.0, sy=0.0, sz=0.06)
1426# rates=(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1427# 29 ITRF2008@2000xITRF90@2000 xform=(tx=22.8, ty=14.6, tz=-63.2, s=3.91, sx=0.0, sy=0.0, sz=0.06)
1428# rates=(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1429# 30 ITRF2008@2000xITRF91@2000 xform=(tx=24.8, ty=18.6, tz=-47.2, s=3.61, sx=0.0, sy=0.0, sz=0.06)
1430# rates=(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1431# 31 ITRF2008@2000xITRF92@2000 xform=(tx=12.8, ty=4.6, tz=-41.2, s=2.21, sx=0.0, sy=0.0, sz=0.06)
1432# rates=(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1433# 32 ITRF2008@2000xITRF93@2000 xform=(tx=-24.0, ty=2.4, tz=-38.6, s=3.41, sx=-1.71, sy=-1.48, sz=-0.3)
1434# rates=(tx=-2.8, ty=-0.1, tz=-2.4, s=0.09, sx=-0.11, sy=-0.19, sz=0.07)
1435# 33 ITRF2008@2000xITRF94@2000 xform=(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
1436# rates=(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1437# 34 ITRF2008@2000xITRF96@2000 xform=(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
1438# rates=(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1439# 35 ITRF2008@2000xITRF97@2000 xform=(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
1440# rates=(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
1441# 36 ITRF2008@2005xITRF2005@2005 xform=(tx=-0.5, ty=-0.9, tz=-4.7, s=0.94, sx=0.0, sy=0.0, sz=0.0)
1442# rates=(tx=0.3, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1443# 37 ITRF2008@2015xETRF2000@2015 xform=(tx=53.6, ty=50.8, tz=-85.5, s=2.54, sx=2.106, sy=12.74, sz=-20.592)
1444# rates=(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792)
1445# 38 ITRF2008@2015xETRF2014@2015 xform=(tx=-1.6, ty=-1.9, tz=-1.9, s=-0.13, sx=2.21, sy=13.806, sz=-20.02)
1446# rates=(tx=0.0, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77)
1447# 39 ITRF2008@2015xETRF2020@2015 xform=(tx=3.0, ty=2.8, tz=0.5, s=0.55, sx=2.236, sy=13.494, sz=-19.578)
1448# rates=(tx=0.0, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753)
1449# 40 ITRF2008@2020xGDA2020@2020 xform=(tx=13.79, ty=4.55, tz=15.22, s=2.5, sx=0.2808, sy=0.2677, sz=-0.4638)
1450# rates=(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551)
1451# 41 ITRF2014@2010xITRF2000@2010 xform=(tx=0.7, ty=1.2, tz=-26.1, s=2.12, sx=0.0, sy=0.0, sz=0.0)
1452# rates=(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.0, sy=0.0, sz=0.0)
1453# 42 ITRF2014@2010xITRF2005@2010 xform=(tx=2.6, ty=1.0, tz=-2.3, s=0.92, sx=0.0, sy=0.0, sz=0.0)
1454# rates=(tx=0.3, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1455# 43 ITRF2014@2010xITRF2008@2010 xform=(tx=1.6, ty=1.9, tz=2.4, s=-0.02, sx=0.0, sy=0.0, sz=0.0)
1456# rates=(tx=0.0, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1457# 44 ITRF2014@2010xITRF88@2010 xform=(tx=25.4, ty=-0.5, tz=-154.8, s=11.29, sx=0.1, sy=0.0, sz=0.26)
1458# rates=(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1459# 45 ITRF2014@2010xITRF89@2010 xform=(tx=30.4, ty=35.5, tz=-130.8, s=8.19, sx=0.0, sy=0.0, sz=0.26)
1460# rates=(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1461# 46 ITRF2014@2010xITRF90@2010 xform=(tx=25.4, ty=11.5, tz=-92.8, s=4.79, sx=0.0, sy=0.0, sz=0.26)
1462# rates=(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1463# 47 ITRF2014@2010xITRF91@2010 xform=(tx=27.4, ty=15.5, tz=-76.8, s=4.49, sx=0.0, sy=0.0, sz=0.26)
1464# rates=(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1465# 48 ITRF2014@2010xITRF92@2010 xform=(tx=15.4, ty=1.5, tz=-70.8, s=3.09, sx=0.0, sy=0.0, sz=0.26)
1466# rates=(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1467# 49 ITRF2014@2010xITRF93@2010 xform=(tx=-50.4, ty=3.3, tz=-60.2, s=4.29, sx=-2.81, sy=-3.38, sz=0.4)
1468# rates=(tx=-2.8, ty=-0.1, tz=-2.5, s=0.12, sx=-0.11, sy=-0.19, sz=0.07)
1469# 50 ITRF2014@2010xITRF94@2010 xform=(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
1470# rates=(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1471# 51 ITRF2014@2010xITRF96@2010 xform=(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
1472# rates=(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1473# 52 ITRF2014@2010xITRF97@2010 xform=(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
1474# rates=(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1475# 53 ITRF2014@2015xETRF2000@2015 xform=(tx=55.2, ty=52.7, tz=-83.6, s=2.67, sx=2.106, sy=12.74, sz=-20.592)
1476# rates=(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.081, sy=0.49, sz=-0.792)
1477# 54 ITRF2014@2015xETRF2014@2015 xform=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=2.21, sy=13.806, sz=-20.02)
1478# rates=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.085, sy=0.531, sz=-0.77)
1479# 55 ITRF2014@2015xETRF2020@2015 xform=(tx=1.4, ty=0.9, tz=-1.4, s=0.42, sx=2.236, sy=13.494, sz=-19.578)
1480# rates=(tx=0.0, ty=0.1, tz=-0.2, s=0.0, sx=0.086, sy=0.519, sz=-0.753)
1481# 56 ITRF2014@2020xGDA2020@2020 xform=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1482# rates=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=1.50379, sy=1.18346, sz=1.20716)
1483# 57 ITRF2020@2015xETRF2000@2015 xform=(tx=53.8, ty=51.8, tz=-82.2, s=2.25, sx=2.106, sy=12.74, sz=-20.592)
1484# rates=(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.081, sy=0.49, sz=-0.792)
1485# 58 ITRF2020@2015xETRF2014@2015 xform=(tx=-1.4, ty=-0.9, tz=1.4, s=0.42, sx=2.21, sy=13.806, sz=-20.02)
1486# rates=(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.085, sy=0.531, sz=-0.77)
1487# 59 ITRF2020@2015xETRF2020@2015 xform=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=2.236, sy=13.494, sz=-19.578)
1488# rates=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.086, sy=0.519, sz=-0.753)
1489# 60 ITRF2020@2015xITRF2000@2015 xform=(tx=-0.2, ty=0.8, tz=-34.2, s=2.25, sx=0.0, sy=0.0, sz=0.0)
1490# rates=(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.0, sy=0.0, sz=0.0)
1491# 61 ITRF2020@2015xITRF2005@2015 xform=(tx=2.7, ty=0.1, tz=-1.4, s=0.65, sx=0.0, sy=0.0, sz=0.0)
1492# rates=(tx=0.3, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1493# 62 ITRF2020@2015xITRF2008@2015 xform=(tx=0.2, ty=1.0, tz=3.3, s=-0.29, sx=0.0, sy=0.0, sz=0.0)
1494# rates=(tx=0.0, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
1495# 63 ITRF2020@2015xITRF2014@2015 xform=(tx=-1.4, ty=-0.9, tz=1.4, s=-0.42, sx=0.0, sy=0.0, sz=0.0)
1496# rates=(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1497# 64 ITRF2020@2015xITRF88@2015 xform=(tx=24.5, ty=-3.9, tz=-169.9, s=11.47, sx=0.1, sy=0.0, sz=0.36)
1498# rates=(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1499# 65 ITRF2020@2015xITRF89@2015 xform=(tx=29.5, ty=32.1, tz=-145.9, s=8.37, sx=0.0, sy=0.0, sz=0.36)
1500# rates=(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1501# 66 ITRF2020@2015xITRF90@2015 xform=(tx=24.5, ty=8.1, tz=-107.9, s=4.97, sx=0.0, sy=0.0, sz=0.36)
1502# rates=(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1503# 67 ITRF2020@2015xITRF91@2015 xform=(tx=26.5, ty=12.1, tz=-91.9, s=4.67, sx=0.0, sy=0.0, sz=0.36)
1504# rates=(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1505# 68 ITRF2020@2015xITRF92@2015 xform=(tx=14.5, ty=-1.9, tz=-85.9, s=3.27, sx=0.0, sy=0.0, sz=0.36)
1506# rates=(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1507# 69 ITRF2020@2015xITRF93@2015 xform=(tx=-65.8, ty=1.9, tz=-71.3, s=4.47, sx=-3.36, sy=-4.33, sz=0.75)
1508# rates=(tx=-2.8, ty=-0.2, tz=-2.3, s=0.12, sx=-0.11, sy=-0.19, sz=0.07)
1509# 70 ITRF2020@2015xITRF94@2015 xform=(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
1510# rates=(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1511# 71 ITRF2020@2015xITRF96@2015 xform=(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
1512# rates=(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1513# 72 ITRF2020@2015xITRF97@2015 xform=(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
1514# rates=(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
1515# 73 ITRF88@2015xETRF2000@2015 xform=(tx=29.3, ty=55.7, tz=87.7, s=-9.22, sx=2.006, sy=12.74, sz=-20.952)
1516# rates=(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1517# 74 ITRF88@2015xETRF2014@2015 xform=(tx=-25.9, ty=3.0, tz=171.3, s=-11.89, sx=2.11, sy=13.806, sz=-20.38)
1518# rates=(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1519# 75 ITRF88@2015xETRF2020@2015 xform=(tx=27.3, ty=-2.1, tz=-172.7, s=12.31, sx=2.336, sy=13.494, sz=-19.218)
1520# rates=(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1521# 76 ITRF89@1989xETRF89@1989 xform=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1522# rates=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71)
1523# 77 ITRF89@2015xETRF2000@2015 xform=(tx=24.3, ty=19.7, tz=63.7, s=-6.12, sx=2.106, sy=12.74, sz=-20.952)
1524# rates=(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1525# 78 ITRF89@2015xETRF2014@2015 xform=(tx=-30.9, ty=-33.0, tz=147.3, s=-8.79, sx=2.21, sy=13.806, sz=-20.38)
1526# rates=(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1527# 79 ITRF89@2015xETRF2020@2015 xform=(tx=32.3, ty=33.9, tz=-148.7, s=9.21, sx=2.236, sy=13.494, sz=-19.218)
1528# rates=(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1529# 80 ITRF90@1984xWGS84@1984 xform=(tx=60.0, ty=-517.0, tz=-223.0, s=-11.0, sx=18.3, sy=-0.3, sz=7.0)
1530# rates=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1531# 81 ITRF90@1989xETRF90@1989 xform=(tx=19.0, ty=28.0, tz=-23.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1532# rates=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71)
1533# 82 ITRF90@1997xNAD83@1997 xform=(tx=973.0, ty=-1919.2, tz=-482.9, s=-0.9, sx=-25.79, sy=-9.65, sz=-11.66)
1534# rates=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=-0.053, sy=0.742, sz=0.032)
1535# 83 ITRF90@2015xETRF2000@2015 xform=(tx=29.3, ty=43.7, tz=25.7, s=-2.72, sx=2.106, sy=12.74, sz=-20.952)
1536# rates=(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1537# 84 ITRF90@2015xETRF2014@2015 xform=(tx=-25.9, ty=-9.0, tz=109.3, s=-5.39, sx=2.21, sy=13.806, sz=-20.38)
1538# rates=(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1539# 85 ITRF90@2015xETRF2020@2015 xform=(tx=27.3, ty=9.9, tz=-110.7, s=5.81, sx=2.236, sy=13.494, sz=-19.218)
1540# rates=(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1541# 86 ITRF91@1989xETRF91@1989 xform=(tx=21.0, ty=25.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1542# rates=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68)
1543# 87 ITRF91@2015xETRF2000@2015 xform=(tx=27.3, ty=39.7, tz=9.7, s=-2.42, sx=2.106, sy=12.74, sz=-20.952)
1544# rates=(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1545# 88 ITRF91@2015xETRF2014@2015 xform=(tx=-27.9, ty=-13.0, tz=93.3, s=-5.09, sx=2.21, sy=13.806, sz=-20.38)
1546# rates=(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1547# 89 ITRF91@2015xETRF2020@2015 xform=(tx=29.3, ty=13.9, tz=-94.7, s=5.51, sx=2.236, sy=13.494, sz=-19.218)
1548# rates=(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1549# 90 ITRF92@1989xETRF92@1989 xform=(tx=38.0, ty=40.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1550# rates=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68)
1551# 91 ITRF92@2015xETRF2000@2015 xform=(tx=39.3, ty=53.7, tz=3.7, s=-1.02, sx=2.106, sy=12.74, sz=-20.952)
1552# rates=(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1553# 92 ITRF92@2015xETRF2014@2015 xform=(tx=-15.9, ty=1.0, tz=87.3, s=-3.69, sx=2.21, sy=13.806, sz=-20.38)
1554# rates=(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1555# 93 ITRF92@2015xETRF2020@2015 xform=(tx=17.3, ty=-0.1, tz=-88.7, s=4.11, sx=2.236, sy=13.494, sz=-19.218)
1556# rates=(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1557# 94 ITRF93@1989xETRF93@1989 xform=(tx=19.0, ty=53.0, tz=-21.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1558# rates=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.32, sy=0.78, sz=-0.67)
1559# 95 ITRF93@2015xETRF2000@2015 xform=(tx=119.6, ty=49.9, tz=-10.9, s=-2.22, sx=5.466, sy=17.07, sz=-21.342)
1560# rates=(tx=2.9, ty=0.2, tz=0.6, s=-0.01, sx=0.191, sy=0.68, sz=-0.862)
1561# 96 ITRF93@2015xETRF2014@2015 xform=(tx=64.4, ty=-2.8, tz=72.7, s=-4.89, sx=5.57, sy=18.136, sz=-20.77)
1562# rates=(tx=2.8, ty=0.1, tz=2.5, s=-0.12, sx=0.195, sy=0.721, sz=-0.84)
1563# 97 ITRF93@2015xETRF2020@2015 xform=(tx=-63.0, ty=3.7, tz=-74.1, s=5.31, sx=-1.124, sy=9.164, sz=-18.828)
1564# rates=(tx=-2.8, ty=0.0, tz=-2.7, s=0.12, sx=-0.024, sy=0.329, sz=-0.683)
1565# 98 ITRF94@1989xETRF94@1989 xform=(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1566# rates=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1567# 99 ITRF94@2015xETRF2000@2015 xform=(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
1568# rates=(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1569# 100 ITRF94@2015xETRF2014@2015 xform=(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
1570# rates=(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1571# 101 ITRF94@2015xETRF2020@2015 xform=(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
1572# rates=(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1573# 102 ITRF96@1989xETRF96@1989 xform=(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1574# rates=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1575# 103 ITRF96@1997xNAD83@1997 xform=(tx=991.0, ty=-190.72, tz=-512.9, s=0.0, sx=25.79, sy=9.65, sz=11.66)
1576# rates=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0532, sy=-0.7423, sz=-0.0316)
1577# 104 ITRF96@2015xETRF2000@2015 xform=(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
1578# rates=(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1579# 105 ITRF96@2015xETRF2014@2015 xform=(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
1580# rates=(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1581# 106 ITRF96@2015xETRF2020@2015 xform=(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
1582# rates=(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
1583# 107 ITRF97@1989xETRF97@1989 xform=(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
1584# rates=(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
1585# 108 ITRF97@1997xITRF96@1997 xform=(tx=-2.07, ty=-0.21, tz=9.95, s=-0.93496, sx=0.1267, sy=-0.22355, sz=-0.06065)
1586# rates=(tx=0.69, ty=-0.1, tz=1.86, s=-0.19201, sx=0.01347, sy=-0.01514, sz=0.00027)
1587# 109 ITRF97@2015xETRF2000@2015 xform=(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
1588# rates=(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
1589# 110 ITRF97@2015xETRF2014@2015 xform=(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
1590# rates=(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
1591# 111 ITRF97@2015xETRF2020@2015 xform=(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
1592# rates=(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)