
# -*- coding: utf-8 -*-

u'''I{Veness}' Terrestrial Reference Frames (TRF), classes L{RefFrame}, registry L{RefFrames} and L{TRFError}.

Transcoded from I{Chris Veness'} (C) 2006-2024 JavaScript originals U{latlon-ellipsoidal-referenceframe.js
<https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe.js>} and
U{latlon-ellipsoidal-referenceframe-txparams.js
<https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe-txparams.js>}.

Following is a copy of the comments in I{Veness}' U{latlon-ellipsoidal-referenceframe.js
<https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe.js>}.

Modern geodetic reference frames: a latitude/longitude point defines a geographic location on,
above or below the earth’s surface, measured in degrees from the equator and the U{International
Reference Meridian<https://WikiPedia.org/wiki/IERS_Reference_Meridian>} (IRM) and metres above
the ellipsoid within a given I{Terrestrial Reference Frame} at a given I{epoch}.

This is scratching the surface of complexities involved in high precision geodesy, but may
be of interest and/or value to those with less demanding requirements.  More information U{here
<https://www.Movable-Type.co.UK/scripts/geodesy-library.html>} and U{here
<https://www.Movable-Type.co.UK/scripts/geodesy-library.html#latlon-ellipsoidal-referenceframe>}.

Note that I{ITRF solutions} do not directly use an ellipsoid, but are specified by Cartesian
coordinates.  The GRS80 ellipsoid is recommended for transformations to geographical coordinates.

Note WGS84(G730/G873/G1150) are coincident with ITRF at 10-centimetre level, see also U{here
<ftp://ITRF.ENSG.IGN.Fr/pub/itrf/WGS84.TXT>}.  WGS84(G1674) and ITRF20014 / ITRF2008 I{"are likely
to agree at the centimeter level"}, see also U{QPS/Qinsy<https://Confluence.QPS.NL/qinsy/
en/how-to-deal-with-etrs89-datum-and-time-dependent-transformation-parameters-45353274.html>}.

@var RefFrames.ETRF2000: RefFrame(name='ETRF2000', epoch=2005, datum=Datums.GRS80) .Xforms=(0, -14)
@var RefFrames.ETRF2005: RefFrame(name='ETRF2005', epoch=2005, datum=Datums.GRS80) .Xforms=(0, -1)
@var RefFrames.ETRF2008: RefFrame(name='ETRF2008', epoch=2008, datum=Datums.GRS80) .Xforms=(0, 0)
@var RefFrames.ETRF2014: RefFrame(name='ETRF2014', epoch=2014, datum=Datums.GRS80) .Xforms=(0, -14)
@var RefFrames.ETRF2020: RefFrame(name='ETRF2020', epoch=2020, datum=Datums.GRS80) .Xforms=(0, -14)
@var RefFrames.ETRF88: RefFrame(name='ETRF88', epoch=1988, datum=Datums.GRS80) .Xforms=(0, 0)
@var RefFrames.ETRF89: RefFrame(name='ETRF89', epoch=1989, datum=Datums.GRS80) .Xforms=(0, -1)
@var RefFrames.ETRF90: RefFrame(name='ETRF90', epoch=1990, datum=Datums.GRS80) .Xforms=(0, -1)
@var RefFrames.ETRF91: RefFrame(name='ETRF91', epoch=1991, datum=Datums.GRS80) .Xforms=(0, -1)
@var RefFrames.ETRF92: RefFrame(name='ETRF92', epoch=1992, datum=Datums.GRS80) .Xforms=(0, -1)
@var RefFrames.ETRF93: RefFrame(name='ETRF93', epoch=1993, datum=Datums.GRS80) .Xforms=(0, -1)
@var RefFrames.ETRF94: RefFrame(name='ETRF94', epoch=1994, datum=Datums.GRS80) .Xforms=(0, -1)
@var RefFrames.ETRF96: RefFrame(name='ETRF96', epoch=1996, datum=Datums.GRS80) .Xforms=(0, -1)
@var RefFrames.ETRF97: RefFrame(name='ETRF97', epoch=1997, datum=Datums.GRS80) .Xforms=(0, -1)
@var RefFrames.GDA2020: RefFrame(name='GDA2020', epoch=2020, datum=Datums.GRS80) .Xforms=(0, -4)
@var RefFrames.GDA94: RefFrame(name='GDA94', epoch=1994, datum=Datums.GRS80) .Xforms=(0, -3)
@var RefFrames.ITRF2000: RefFrame(name='ITRF2000', epoch=1997, datum=Datums.GRS80) .Xforms=(15, -5)
@var RefFrames.ITRF2005: RefFrame(name='ITRF2005', epoch=2000, datum=Datums.GRS80) .Xforms=(8, -3)
@var RefFrames.ITRF2008: RefFrame(name='ITRF2008', epoch=2005, datum=Datums.GRS80) .Xforms=(17, -2)
@var RefFrames.ITRF2014: RefFrame(name='ITRF2014', epoch=2010, datum=Datums.GRS80) .Xforms=(16, -1)
@var RefFrames.ITRF2020: RefFrame(name='ITRF2020', epoch=2015, datum=Datums.GRS80) .Xforms=(16, 0)
@var RefFrames.ITRF88: RefFrame(name='ITRF88', epoch=1988, datum=Datums.GRS80) .Xforms=(3, -4)
@var RefFrames.ITRF89: RefFrame(name='ITRF89', epoch=1989, datum=Datums.GRS80) .Xforms=(4, -4)
@var RefFrames.ITRF90: RefFrame(name='ITRF90', epoch=1988, datum=Datums.GRS80) .Xforms=(6, -4)
@var RefFrames.ITRF91: RefFrame(name='ITRF91', epoch=1988, datum=Datums.GRS80) .Xforms=(4, -4)
@var RefFrames.ITRF92: RefFrame(name='ITRF92', epoch=1988, datum=Datums.GRS80) .Xforms=(4, -4)
@var RefFrames.ITRF93: RefFrame(name='ITRF93', epoch=1988, datum=Datums.GRS80) .Xforms=(4, -4)
@var RefFrames.ITRF94: RefFrame(name='ITRF94', epoch=1993, datum=Datums.GRS80) .Xforms=(4, -4)
@var RefFrames.ITRF96: RefFrame(name='ITRF96', epoch=1997, datum=Datums.GRS80) .Xforms=(5, -5)
@var RefFrames.ITRF97: RefFrame(name='ITRF97', epoch=1997, datum=Datums.GRS80) .Xforms=(5, -4)
@var RefFrames.NAD83: RefFrame(name='NAD83', epoch=1997, datum=Datums.GRS80) .Xforms=(0, -6)
@var RefFrames.NAD83cors96: RefFrame(name='NAD83cors96', epoch=1997, datum=Datums.GRS80) .Xforms=(1, 0)
@var RefFrames.WGS84: RefFrame(name='WGS84', epoch=1984, datum=Datums.GRS80) .Xforms=(0, -1)
@var RefFrames.WGS84g1150: RefFrame(name='WGS84g1150', epoch=2001, datum=Datums.GRS80) .Xforms=(1, 0)
@var RefFrames.WGS84g1674: RefFrame(name='WGS84g1674', epoch=2005, datum=Datums.GRS80) .Xforms=(0, 0)
@var RefFrames.WGS84g1762: RefFrame(name='WGS84g1762', epoch=2005, datum=Datums.GRS80) .Xforms=(0, 0)
'''

from pygeodesy.basics import _isin, map1, neg, isidentifier, isstr, _xinstanceof, \
                             _xscalar,  typename
from pygeodesy.constants import _float as _F, _0_0s, _0_0, _0_001, _0_5, _0_75, _1_0
from pygeodesy.datums import Datums, _earth_datum, _equall, _GDA2020_, _Names7, \
                            _negastr, Transform, _WGS84,  _EWGS84, _operator
# from pygeodesy.ellipsoids import _EWGS84  # from .datums
from pygeodesy.errors import TRFError, _xattr, _xellipsoidall, _xkwds, _xkwds_item2
# from pygeodesy.internals import typename  # from .basics
from pygeodesy.interns import MISSING, NN, _AT_, _COMMASPACE_, _conversion_, \
                             _datum_, _DMAIN_, _DOT_, _exists_, _invalid_, _MINUS_, \
                             _NAD83_, _no_, _PLUS_, _reframe_, _s_, _SPACE_, _to_, \
                             _STAR_, _vs_, _WGS84_, _x_, _intern as _i
# from pygeodesy.lazily import _ALL_LAZY  # from .units
from pygeodesy.named import ADict, classname, _lazyNamedEnumItem as _lazy, _name2__, \
                           _Named, _NamedEnum, _NamedEnumItem, _NamedTuple,  Fmt, unstr
from pygeodesy.props import deprecated_method, property_doc_, Property_RO, property_RO
# from pygeodesy.streprs import Fmt, unstr  # from .named
from pygeodesy.units import Epoch, Float,  _ALL_LAZY
# from pygeodesy.utily import sincos2d_

from math import ceil as _ceil, fabs
# import operator as _operator  # from .datums

__all__ = _ALL_LAZY.trf
__version__ = '25.09.11'

_EP0CH    =  Epoch(0, low=0)
_Es       = {_EP0CH: _EP0CH}  # L{Epoch}s, deleted below
_GRS80    =  Datums.GRS80
_inverse_ = 'inverse'
_MAS      = _MM = _PPB = Float  # Units
_MM2M     = _0_001  # scale mm2m, ppB2ppM, mas2as
_mDays    = (0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 0)
_366_0    = _F(sum(_mDays))
_rates_   = 'rates'  # PYCHOK used!
_Rs       = {}  # L{TRFXform7Tuple}s de-dup, deleted below
_xform_   = 'xform'  # PYCHOK used!
_Xs       = {}  # L{TRFXform7Tuple}s de-dup, deleted below

_ETRF88_      = _i('ETRF88')
_ETRF89_      = _i('ETRF89')
_ETRF90_      = _i('ETRF90')
_ETRF91_      = _i('ETRF91')
_ETRF92_      = _i('ETRF92')
_ETRF93_      = _i('ETRF93')
_ETRF94_      = _i('ETRF94')
_ETRF96_      = _i('ETRF96')
_ETRF97_      = _i('ETRF97')
_ETRF2000_    = _i('ETRF2000')
_ETRF2005_    = _i('ETRF2005')
_ETRF2008_    = _i('ETRF2008')
_ETRF2014_    = _i('ETRF2014')
_ETRF2020_    = _i('ETRF2020')
_GDA94_       = _i('GDA94')
_ITRF_        = _i('ITRF')
_ITRF88_      = _i('ITRF88')
_ITRF89_      = _i('ITRF89')
_ITRF90_      = _i('ITRF90')
_ITRF91_      = _i('ITRF91')
_ITRF92_      = _i('ITRF92')
_ITRF93_      = _i('ITRF93')
_ITRF94_      = _i('ITRF94')
_ITRF96_      = _i('ITRF96')
_ITRF97_      = _i('ITRF97')
_ITRF2000_    = _i('ITRF2000')
_ITRF2005_    = _i('ITRF2005')
_ITRF2008_    = _i('ITRF2008')
_ITRF2014_    = _i('ITRF2014')
_ITRF2020_    = _i('ITRF2020')
_NAD83cors96_ = _i('NAD83cors96')
_WGS84g1150_  = _i('WGS84g1150')
_WGS84g1674_  = _i('WGS84g1674')
_WGS84g1762_  = _i('WGS84g1762')


def _E(epoch):  # deleted below
    '''(INTERNAL) De-dup L{Epochs}s.
    '''
    e = Epoch(_F(epoch))
    return _Es.setdefault(e, e)  # noqa: F821 del


def _P(ps, name, _Ps):  # deleted below
    '''(INTERNAL) De-dup L{TRFXform7Tuple}s.
    '''
    t = TRFXform7Tuple(map(_F, ps), name=name)
    return _Ps.setdefault(t, t)


class RefFrame(_NamedEnumItem):
    '''Terrestrial Reference Frame (TRF) parameters.
    '''
    _datum = _GRS80  # Datums.GRS80 or .WGS84 (L{Datum})
    _epoch = _EP0CH  # epoch, fractional year (L{Epoch})

    def __init__(self, epoch, datum=_GRS80, name=NN):
        '''New L{RefFrame}.

           @arg epoch: Epoch, a fractional calendar year (C{scalar} or C{str}).
           @arg datum: Datum or ellipsoid (L{Datum}, {Ellipsoid}, L{Ellipsoid2}
                       or L{a_f2Tuple}).
           @kwarg name: Unique, non-empty name (C{str}).

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

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

           @raise TypeError: Invalid B{C{datum}}.
        '''
        if _isin(datum, None, _GRS80):
            pass
        elif _isin(datum, _WGS84, _EWGS84):
            self._datum = _WGS84
        else:
            _earth_datum(self, datum, raiser=_datum_)
        self._epoch = _Epoch(epoch)
        self._Xto = {}  # dict of Xforms
        if name:
            self._register(RefFrames, _stref(name=name))

    def __eq__(self, other):
        return isinstance(other, RefFrame) and other.epoch == self.epoch \
                                           and other.datum == self.datum \
                                           and other.name  == self.name

    def __lt__(self, other):  # for sorting
        return isinstance(other, RefFrame) and (self.name  < other.name
                                             or self.epoch < other.epoch)

    @deprecated_method  # PYCHOK Python 3.5+
    def __matmul__(self, point):
        '''DEPRECATED on 2024.02.16, use method C{B{point}.toRefFrame}.'''
        return _toRefFrame(point, self)

    @property_RO
    def datum(self):
        '''Get this reference frame's datum (L{Datum}).
        '''
        return self._datum

    @property_RO
    def ellipsoid(self):
        '''Get this reference frame's ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
        '''
        return self._datum.ellipsoid

    @Property_RO
    def epoch(self):
        '''Get this reference frame's epoch (C{Epoch}).
        '''
        return self._epoch

    def toRefFrame(self, point, reframe2, **epoch_epoch2_name):
        '''Convert an ellipsoidal point from this reframe and from C{epoch} to
           an other C{reframe2} and C{epoch2 or epoch}.

           @arg point: The point to convert (C{LatLon} or C{Cartesian}).
           @arg reframe2: Reference frame to convert I{to} (L{RefFrame}).
           @kwarg epoch_epoch2_name: Optional keyword arguments C{B{epoch}=None},
                        C{B{epoch2}=None} and C{B{name}=B{reframe2}.name}.

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

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

           @note: The C{B{point}.reframe} is overridden by this reframe and
                  C{B{point}.epoch} by C{B{epoch}} or this reframe.C{epoch}.

           @see: Methods L{LatLon.toRefFrame<ellipsoidalBase.LatLonEllipsoidalBase.toRefFrame>}
                 and L{Cartesian.toRefFrame<ellipsoidalBase.CartesianEllipsoidalBase.toRefFrame>}
                 for more details.
        '''
        return _toRefFrame(point, reframe2, reframe=self, **_xkwds(epoch_epoch2_name,
                                               name=_xattr(reframe2, name=self.name)))

    def toStr(self, epoch=None, name=NN, **unused):  # PYCHOK signature
        '''Return this reference frame as a string.

           @kwarg epoch: Override this reframe's epoch (C{scalar} or C{str}).
           @kwarg name: Override name (C{str}) or C{None} to exclude the
                        reframe's name.

           @return: This L{RefFrame}'s attributes (C{str}).
        '''
        D = self.datum
        e = self.epoch if epoch is None else _Epoch(epoch)
        t = (Fmt.EQUAL(name=repr(self._name__(name))),
             Fmt.EQUAL(epoch=e),
             Fmt.EQUAL(datum=_DOT_(classname(D) + _s_, D.name)))
        return _COMMASPACE_.join(t[int(name is None):])

    def Xform(self, reframe2):
        '''Get the converter Xform I{from} this reference frame I{to} C{reframe2}.

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

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

           @raise TypeError: Invalid B{C{reframe2}}.
        '''
        _xinstanceof(RefFrame, str, reframe2=reframe2)
        n2 = reframe2 if isstr(reframe2) else reframe2.name
        return self._Xto.get(n2, None)

    def Xforms(self, inverse=False):
        '''Return all Xforms converting I{from} or I{to} this reference frame or both.

           @kwarg inverse: If C{True}, get all I{from} otherwise I{to} Xforms
                           I{un-inverted} (C{bool}) or if C{B{inverse}=2} (C{int})
                           get all I{to} Xforms I{inverted} plus all I{from}s.

           @return: An L{ADict} of C{name=}L{TRFXform}s I{from} this reframe or if
                    C{B{inverse}=True} I{to} this reframe or both if C{B{inverse}=2}.
        '''
        return ADict(self._Xitems(inverse, RefFrames))

    def _Xfrom(self, RFs, inverted):
        '''(INTERNAL) Yield all 2-tuples C{(name, I{from} Xform)} converting I{to}
           this reframe, inverted if C{inverted is True}.
        '''
        n2 = self.name
        for n1, r in RFs.items():
            X = r._Xto.get(n2, None)
            if X:
                yield n1, (X.inverse() if inverted else X)

    def _Xitems(self, inverse, RFs):  # in _eXhaustives, .Xforms
        '''(INTERNAL) Yield all C{._Xfrom} and C{._Xto}'s as 2-tuple items.
        '''
        i = inverse == 2
        if i or inverse:
            for item in self._Xfrom(RFs, i):
                yield item
        if i or not inverse:
            for item in self._Xto.items():
                yield item


class RefFrames(_NamedEnum):
    '''(INTERNAL) L{RefFrame} registry, I{must} be a sub-class
       to accommodate the L{_LazyNamedEnumItem} properties.
    '''
    def _Lazy(self, epoch, datum=_GRS80, name=NN):
        '''(INTERNAL) Instantiate the L{RefFrame}.
        '''
        return RefFrame(epoch, datum, name=name)

RefFrames = RefFrames(RefFrame)  # PYCHOK singleton
'''Some pre-defined L{RefFrame}s, all I{lazily} instantiated.'''
# <https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-ellipsoidal-referenceframe.js>
RefFrames._assert(
    ETRF88      = _lazy(_ETRF88_,      _E(1988)),  # epoch, datum?
    ETRF89      = _lazy(_ETRF89_,      _E(1989)),  # epoch, datum?
    ETRF90      = _lazy(_ETRF90_,      _E(1990)),  # epoch, datum?
    ETRF91      = _lazy(_ETRF91_,      _E(1991)),  # epoch, datum?
    ETRF92      = _lazy(_ETRF92_,      _E(1992)),  # epoch, datum?
    ETRF93      = _lazy(_ETRF93_,      _E(1993)),  # epoch, datum?
    ETRF94      = _lazy(_ETRF94_,      _E(1994)),  # epoch, datum?
    ETRF96      = _lazy(_ETRF96_,      _E(1996)),  # epoch, datum?
    ETRF97      = _lazy(_ETRF97_,      _E(1997)),  # epoch, datum?
    ETRF2000    = _lazy(_ETRF2000_,    _E(2005)),
    ETRF2005    = _lazy(_ETRF2005_,    _E(2005)),  # epoch, datum?
    ETRF2008    = _lazy(_ETRF2008_,    _E(2008)),  # epoch, datum?
    ETRF2014    = _lazy(_ETRF2014_,    _E(2014)),  # epoch, datum?
    ETRF2020    = _lazy(_ETRF2020_,    _E(2020)),  # epoch, datum?
    GDA94       = _lazy(_GDA94_,       _E(1994)),  # Australia
    GDA2020     = _lazy(_GDA2020_,     _E(2020)),  # Australia
    ITRF88      = _lazy(_ITRF88_,      _E(1988)),
    ITRF89      = _lazy(_ITRF89_,      _E(1989)),
    ITRF90      = _lazy(_ITRF90_,      _E(1988)),
    ITRF91      = _lazy(_ITRF91_,      _E(1988)),
    ITRF92      = _lazy(_ITRF92_,      _E(1988)),
    ITRF93      = _lazy(_ITRF93_,      _E(1988)),
    ITRF94      = _lazy(_ITRF94_,      _E(1993)),
    ITRF96      = _lazy(_ITRF96_,      _E(1997)),
    ITRF97      = _lazy(_ITRF97_,      _E(1997)),
    ITRF2000    = _lazy(_ITRF2000_,    _E(1997)),  # aka ITRF00
    ITRF2005    = _lazy(_ITRF2005_,    _E(2000)),
    ITRF2008    = _lazy(_ITRF2008_,    _E(2005)),  # aka ITRF08
    ITRF2014    = _lazy(_ITRF2014_,    _E(2010)),
    ITRF2020    = _lazy(_ITRF2020_,    _E(2015)),
    NAD83       = _lazy(_NAD83_,       _E(1997)),
    NAD83cors96 = _lazy(_NAD83cors96_, _E(1997)),
    WGS84       = _lazy(_WGS84_,       _E(1984), _WGS84),
    WGS84g1150  = _lazy(_WGS84g1150_,  _E(2001), _WGS84),
    WGS84g1674  = _lazy(_WGS84g1674_,  _E(2005), _WGS84),
    WGS84g1762  = _lazy(_WGS84g1762_,  _E(2005), _WGS84))  # same epoch


class TransformXform(Transform):
    '''Helmert transformation, extended with an C{Xform} TRF converter.

       @see: L{Transform<datums.Transform>} and L{Xform<TRFXform>}.
    '''
    _Xform = None

    def __init__(self, name=NN, **tx_ty_tz_s_sx_sy_sz):  # PYCHOK signature
        '''New L{TransformXform}.

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

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

           @note: This L{TransformXform}'s name starts with C{"-"} iff
                  I{inversed}.
        '''
        Transform.__init__(self, **tx_ty_tz_s_sx_sy_sz)
        if name:
            self.name = name  # unregistered

    def __eq__(self, other):
        return isinstance(other, TransformXform) and _equall(other, self)

    def __hash__(self):
        return Transform.__hash__(self)

    def inverse(self, **name):
        '''Return the inverse of this transform.

           @kwarg name: Optional, unique C{B{name}=NN} (C{str}).

           @return: Inverse (L{TransformXform}), unregistered.
        '''
        r = Transform.inverse(self, **name)
        X = self.Xform
        if X:  # unregistered
            r._Xform = X.inverse()
        return r

    def rename(self, name=NN):
        '''Change this transform's name.

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

           @return: The previous name (C{str}).
        '''
        X = self.Xform
        n = name or (X.toStr() if X else NN)
        return Transform.rename(self, n)

    def toRefFrame(self, point, **name):  # PYCHOK signature
        '''Convert an ellipsoidal point using this transform and Xform.

           @arg point: The point to convert (C{Cartesian} or C{LatLon}).
           @kwarg name: Optional C{B{name}=NN} (C{str}).

           @return: A copy of the B{C{point}}, converted I{directly} to
                    this transform's Xform's C{refName2} and C{epoch}.

           @note: The B{C{point}}'s original C{reframe} and C{epoch} are
                  I{ignored}, its C{datum} and C{height} are preserved
                  but I{not} taken into account.
        '''
        _ = _xellipsoidall(point)
        p =  point.dup() if self.isunity else point.toTransform(self)
        X =  self.Xform
        if X:  # see _toRefFrame below
            p._reframe = X.reframe2
            p._epoch   = X.epoch
        p.rename(self._name__(name))
        return p

    def toTransform(self, epoch1, **epoch2_inverse):
        '''Return this transform observed at B{C{epoch1}} as a Helmert
           L{TransformXform}, optionally at B{C{epoch2 or epoch1}}.

           @arg epoch1: Epoch to observe I{from} (C{scalar}).
           @kwarg epoch2_inverse: Optional C{B{epoch2}=None} to observe
                         I{to} and C{B{inverse}=False}, see method
                         L{toTransform<TRFXform.toTransform>} from
                         L{TRFXform}.

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

           @raise TRFError: Invalid B{C{epoch1}}, B{C{epoch2}} or
                            missing Xform.
        '''
        X = self.Xform
        if X is None:
            raise TRFError(Xform=X, txt=MISSING)
        return X.toTransform(epoch1, **epoch2_inverse)

    def transform2(self, x, y, z, vx=0, vy=0, vz=0, inverse=False, factor=_MM2M,
                                                  **Vector_and_kwds):
        '''Transform a (cartesian) position I{with} velocities, forward or inverse.

           @arg x: X coordinate (C{meter}).
           @arg y: Y coordinate (C{meter}).
           @arg z: Z coordinate (C{meter}).
           @kwarg vx: X velocity (C{meter-per-year}).
           @kwarg vy: Y velocity (C{meter-per-year}).
           @kwarg vz: Z velocity (C{meter-per-year}).
           @kwarg inverse: If C{True}, apply the inverse transform (C{bool}).
           @kwarg factor: Factor to scale this Xform's C{rates} (C{scalar}),
                          default from C{milli-meter-} to C{meter-per-year},
                          from C{milli-arc-} to C{arc-seconds-per-year} and
                          from C{ppB-} to C{ppM-per-year}.
           @kwarg Vector_and_kwds: An optional, (3-D) C{B{Vector}=None} or cartesian
                         class and additional C{B{Vector}} keyword arguments to
                         return the transformed position and the I{velocities}.

           @return: 2-Tuple C{(position, velocities)}, the tranformed C{position}
                    and C{velocities}, each a L{Vector3Tuple}C{(x, y, z)} unless
                    some B{C{Vector_and_kwds}} are specified.

           @note: If this transform's Xform is missing, the returned C{velocities}
                  are the given ones, I{un-transformed}.

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

           @see: Soler, T. & Snay, R.A. "Transforming Positions and Velocities ...", U{equations
                 (4) and (5)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>}
                 and HTDP functions C{VTRANF} and C{VTRANF_IERS} in file U{HTDP/hdtp.f
                 <https://Geodesy.NOAA.gov/TOOLS/Htdp/Htdp.shtml>}.
        '''
        p = self.transform(x, y, z, inverse=inverse, **Vector_and_kwds)
        X = self.Xform
        if X is not None:
            r = X.rates * factor  # equ (4) ...
            # vx', vy', vz' = (.tx + x * .s  + y * .rz - z * .ry,
            #                  .ty - x * .rz + y * .s  + z * .rx,
            #                  .tz + x * .ry - y * .rx + z * .s)
            # using counter-/clockwise .rx, .ry, and .rz
            V = Transform(**dict(r.items()))  # unregistered
            _ = V._s_s1(0)  # XXX r.s?
            v = V.transform(p.x, p.y, p.z, inverse=inverse)
            # + (vx, vy, vz) like HTDP
            vx += v.x
            vy += v.y
            vz += v.z
        v = p.dup(x=vx, y=vy, z=vz, name=NN(p.name, _vs_))
        return p, v

    def velocities(self, factor=_MM2M, **Vector_and_kwds):
        '''Compute the X, Y and Z I{velocities} of this transform.

           @kwarg factor: Factor to scale this Xform's C{rates} (C{scalar}),
                          default from C{milli-meter-} to C{meter-per-year},
                          from C{milli-arc-} to C{arc-seconds-per-year} and
                          from C{ppB-} to C{ppM-per-year}.
           @kwarg Vector_and_kwds: An optional, (3-D) C{B{Vector}=None} or
                         cartesian class and additional C{B{Vector}} keyword
                         arguments to return the I{velocities}.

           @return: A L{Vector3Tuple}C{(x, y, z)} unless some B{C{Vector_and_kwds}}
                    are specified or C{None} if this transform's Xform is missing.

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

           @see: Altamimi, Z. "EUREF-TN-1-Jan-31-2024", U{Appendix A, equation (3)
                 <http://ETRS89.ENSG.IGN.FR/pub/EUREF-TN-1-Jan-31-2024.pdf>} and
                 method L{transform2<TransformXform.transform2>}.
        '''
        v = X = self.Xform
        if X is not None:
            r = X.rates * factor  # equ (3) ...
            V = self.dup(tx=r.sx, ty=r.sy, tz=r.sz, _Xform=None,  # Xyy-dot
                         name=NN(self.name, _vs_))  # unregistered
            _ = V._s_s1(0)
            v = V.transform(r.tx, r.ty, r.tz, inverse=False,  # Xyy
                                            **Vector_and_kwds)
        return v

    @property_doc_(''' the Xform (L{TRFXform}).''')
    def Xform(self):
        '''Get this Helmert transform's Xform (L{TRFXform} or C{None}).
        '''
        return self._Xform

    @Xform.setter  # PYCHOK setter!
    def Xform(self, Xform):
        '''Set this Helmert transform's Xform (L{TRFXform}).

           @raise TypeError: Invalid B{C{Xform}}.
        '''
        _xinstanceof(TRFXform, Xform=Xform)
        self._Xform = Xform


class TRFXform7Tuple(_NamedTuple):
    '''7-Tuple C{(tx, ty, tz, s, sx, sy, sz)} of conversion parameters with
       translations C{tx}, C{ty} and C{tz} in C{milli-meter}, scale C{s} in
       C{ppB} and rotations C{sx}, C{sy} and C{sz} in C{milli-arc-seconds}.
       For C{rates} all are C{units-per-year}.

       @note: The parameters are also named as C{(Tx, Ty, Tz, D, Rx, Ry, Rz)}
              or C{(T1, T2, T3, D, R1, R2, R3)}.

       @see: Class L{TransformXform}'s matching keyword argument names.
    '''
    _Names_ = _Names7  # ('tx', 'ty', 'tz', _s_,  'sx', 'sy', 'sz') == TransformXform.__init__
    _Units_ =            (_MM,  _MM,  _MM,  _PPB, _MAS, _MAS, _MAS)

    def __add__(self, other):
        return self._add_sub(other, True)

    def __eq__(self, other):
        return isinstance(other, TRFXform7Tuple) and _equall(other, self)
                                       # PYCHOK  and self.name == other.name

    def __hash__(self):
        return _NamedTuple.__hash__(self)

    def __mul__(self, factor):
        _xscalar(factor=factor)
        return type(self)((x * factor for x in self), name=_STAR_)  # .fsums._mul_op

    def __neg__(self):
        return self.inverse()

    def __sub__(self, other):
        return self._add_sub(other, False)

    def _add_sub(self, other, p_):
        '''(INTERNAL) Return C{this +/- other} L{TRFXform7Tuple}.
        '''
        _xinstanceof(TRFXform7Tuple, other=other)
        op = _operator.add if p_ else _operator.sub
        return type(self)(map(op, self, other), name=_PLUS_ if p_ else _MINUS_)

    def inverse(self, name=NN):
        '''Return the inverse of this transform.

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

           @return: Inverse (L{TransformXform}).
        '''
        n = name or _negastr(self.name)
        return type(self)(map(neg, self), name=n)

    @Property_RO
    def isunity(self):
        '''Is this a C{unity, identity} transform (C{bool}).
        '''
        return not any(self)


class TRFXform(_Named):
    '''A Terrestrial Reference Frame (TRF) converter between two
       reference frames observed at an C{epoch}.
    '''
    _epoch   = _EP0CH
    _epoch_d = _0_0
    _indir_d =  NN  # refName
    _inver_d =  False
    refName1 =  \
    refName2 =  NN
    rates    =  \
    xform    =  None

    def __init__(self, refName1, refName2, epoch=None, xform=None,
                                           rates=None, name=NN):
        '''New L{TRFXform} TRF converter.

           @arg refName1: Source reframe (C{str}), converting I{from}.
           @arg refName2: Destination reframe (C{str}), converting I{to}.
           @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str}).
           @kwarg xform: I{Transform} parameters at B{C{epoch}} (L{TRFXform7Tuple}).
           @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), like B{C{xform}},
                         but in C{units-per-year}.
           @kwarg name: Optional name (C{str}), overriding the default from method
                        L{toStr<TRFXform.toStr>}.

           @raise TRFError: Invalid B{C{refName1}}, B{C{refName2}} or B{C{epoch}}.

           @raise TypeError: Invalid B{C{xform}} or B{C{rates}}.

           @see: Functions L{trfXform}, L{trfTransform0} and L{trfTransforms}.
        '''
        self.refName1 = _stref(refName1=refName1)
        self.refName2 = _stref(refName2=refName2)
        _xinstanceof(TRFXform7Tuple, xform=xform, rates=rates)
        self.epoch = epoch
        self.xform = xform
        self.rates = rates
        self.rename(name or self.toStr())

    def __add__(self, other):
        return self._add_sub(other, True)

    def __eq__(self, other):
        return isinstance(other, TRFXform) and other.epoch == self.epoch \
                                           and other.xform == self.xform \
                                           and other.rates == self.rates

#   def __hash__(self):
#       return hash((self.epoch, self.xform, self.rates))

    def __lt__(self, other):  # for sorting
        return isinstance(other, TRFXform) and (self.refName1 < other.refName1
                                             or self.refName2 < other.refName2
                                             or self.epoch    < other.epoch)

    def __neg__(self):
        return self.inverse()

    def __repr__(self):
        return self.toRepr()

    def __str__(self):
        return self.toStr()

    def __sub__(self, other):
        return self._add_sub(other, False)

    def _add_sub(self, other, p_, *n1_n2_n):  # in _indirects below
        '''(INTERNAL) Summate C{this +/- other} Xform at C{this.epoch}.

           @see: U{Appendix, Table 7, last column "Sum of the previous ..."
                 <https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf">}
        '''
        _xinstanceof(TRFXform, other=other)
        X1 = self
        e1 = X1.epoch
        X2 = other.toEpoch(e1)  # if other.epoch != e1 else other

        n1, n2, n = n1_n2_n or _n1_n2_n3(X1, X2)

        X = type(X1)(n1, n2, epoch=e1, xform=X1.xform._add_sub(X2.xform, p_),
                                       rates=X1.rates._add_sub(X2.rates, p_),
                                       name=_sumstr(X1.name,   X2.name,  p_))
        X._epoch_d = X1.epoched + X2.epoched
        X._indir_d = n  # reframe?
        X._inver_d = X1.inversed and X2.inversed
        return X

    def _at(self, epoch):
        '''(INTERNAL) Return C{"self.nameB{@}epoch"}.
        '''
        n = self.name
        if epoch != self.epoch:
            _e = _AT_(NN, epoch)
            if not n.endswith(_e):
                n = NN(n, _e)
        return n

    @property_doc_(''' the epoch, fractional year (L{Epoch}).''')
    def epoch(self):
        '''Get the epoch (L{Epoch}).
        '''
        return self._epoch

    @epoch.setter  # PYCHOK setter!
    def epoch(self, epoch):
        '''Set the epoch (L{Epoch}, C{scalar} or C{str}).

           @raise TRFError: Invalid B{C{epoch}}.
        '''
        e = _Epoch(epoch)
        if self._epoch != e:
            self.rename(self._at(e))
            self._epoch = e

    @property_RO
    def epoched(self):
        '''Get this Xform's aggregate I{epoch} deltas (C{float}).
        '''
        return self._epoch_d

    @property_RO
    def indirected(self):
        '''Is this an I{indirected} Xform? (C{str} of space-separated
           refNames) or C{NN}.
        '''
        return self._indir_d

    def inverse(self, name=NN):
        '''Return this Xform {inversed}, C{refName1} and C{-2} swapped.

           @return: The inverse (L{TRFXform}).
        '''
        n = name or _negastr(self.name)
        X = self.dup(refName1=self.refName2, xform=-self.xform,
                     refName2=self.refName1, rates=-self.rates,
                     name=n, _inver_d=not self.inversed)
#       X = type(self)(self.refName2, self.refName1, epoch= self.epoch,
#                                                    xform=-self.xform,
#                                                    rates=-self.rates, name=n)
#       if self.epoched:
#           X._epoch_d = self.epoched
#       if self.indirected:
#           X._indir_d = self.indirected
#       if not self.inversed:
#           X._inver_d = True
        return X

    @property_RO
    def inversed(self):
        '''Is this an I{inversed} Xform? (C{bool}).
        '''
        return self._inver_d

    def _reframe(self, name, datum=_GRS80):
        '''(INTERNAL) Get an un-/registered frame.
        '''
        r = RefFrames.get(name)
        if r is None or r.datum != datum:
            r = RefFrame(self.epoch, datum)
            r.name = name  # unregistered
        return r

    @property_RO
    def reframe1(self):
        '''Get the un-/registered I{from} frame (C{RefFrame}).
        '''
        return self._reframe(self.refName1)

    @property_RO
    def reframe2(self):
        '''Get the un-/registered I{to} frame (C{RefFrame}).
        '''
        return self._reframe(self.refName2)

    def rename(self, name=NN):
        '''Change this Xform's name.

           @arg name: New name (C{str}), overriding the base
                      name C{"refName1B{@}epochB{x}refName2"}.

           @return: The old name (C{str}).
        '''
        return _Named.rename(self, name or self.toStr())

    def toEpoch(self, epoch):
        '''Convert this Xform to B{C{epoch}}, if needed.

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

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

           @raise TRFError: Invalid B{C{epoch}}.
        '''
        e    = _Epoch(epoch)
        X, d =  self, e - self.epoch
        if d:
            t = X.xform + X.rates * d
            X = X.dup(epoch=e, xform=t, name=X._at(e))
            X._epoch_d += fabs(d)
        return X

    def toHelmert(self, factor=_MM2M):
        '''Return the Helmert transform from this Xform scaled accordingly.

           @kwarg factor: Factor to scale this Xform's C{xform} (C{scalar}),
                          default from C{milli-meter-} to C{meter-}, from
                          C{milli-arc-} to C{arc-seconds} and from C{ppB}
                          to C{ppM}.

           @return: The Helmert transform (L{TransformXform}).
        '''
        h = self.xform * factor
        H = TransformXform(**dict(h.items()))
        H.name  = self.name  # unregistered
        H.Xform = self
        return H

    def toRefFrame(self, point, datum=_GRS80, **epoch_epoch2_name):
        '''Convert an ellipsoidal point from this Xform's C{refName1} and
           C{epoch} to this Xform's C{refName2} and C{epoch2 or epoch}.

           @arg point: The point to convert (C{Cartesian} or C{LatLon}).
           @kwarg datum: Optional datum to define a temporary L{RefFrame} from
                         this Xform's C{refName1} or C{refName2} (C{datum}).
           @kwarg epoch_epoch2_name: Optional keyword arguments C{B{epoch}=None},
                        B{C{epoch2}=None} and C{B{name}=refName1}.

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

           @see: Method L{RefFrame.toRefFrame} for more details.
        '''
        r1 = self._reframe(self.refName1, datum=datum)
        r2 = self._reframe(self.refName2, datum=datum)
        return _toRefFrame(point, r2, reframe=r1,
                        **_xkwds(epoch_epoch2_name, name=r1.name))

    def toRepr(self, **unused):  # PYCHOK signature
        '''Return the represention of this Xform (C{str}).
        '''
        return unstr(self.classname, name=self.name, epoch=self.epoch)

    def toStr(self, epoch=None, **unused):  # PYCHOK signature
        '''Return this Xform as C{"refName1B{@}epochB{x}refName2"} (C{str}).

           @kwarg epoch: Epoch (C{Epoch}, C{scalar} or C{str}), overriding
                         this Xform's epoch.
        '''
        e = self.epoch if epoch is None else _Epoch(epoch)
        return NN(_AT_(self.refName1, e), _x_, self.refName2)

    def toTransform(self, epoch=None, epoch2=None, inverse=False):
        '''Combine this Xform observed at B{C{epoch}} into a Helmert
           L{TransformXform}, optionally at B{C{epoch2 or epoch}}.

           @kwarg epoch: Epoch to observe I{from} (C{scalar}),
                         overriding this converter's epoch.
           @kwarg epoch2: Optional epoch to observe I{to} (C{scalar}),
                          overriding B{C{epoch}}.
           @kwarg inverse: Use the Xform's inverse (C{bool}).

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

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

           @see: Method L{toHelmert}.
        '''
        if epoch2 is None:
            e = self.epoch if epoch is None else epoch
        elif isinstance(epoch2, Epoch):
            e = epoch2
        else:
            e = Epoch(epoch2=epoch2)
        X = self.toEpoch(e)
        if inverse:
            X = X.inverse()
        return X.toHelmert()


def date2epoch(year, month, day):
    '''Return the C{epoch} for a calendar day.

       @arg year: Year of the date (C{scalar}).
       @arg month: Month in the B{C{year}} (C{scalar}, 1..12).
       @arg day: Day in the B{C{month}} (C{scalar}, 1..31).

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

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

       @note: Any B{C{year}} is considered a leap year, i.e. having
              29 days in February.
    '''
    try:
        y, m, d = map1(int, year, month, day)
        if y > 0 and 1 <= m <= 12 and 1 <= d <= _mDays[m]:
            e = y + float(sum(_mDays[:m]) + d) / _366_0
            return Epoch(e, low=0)

        raise ValueError()  # _invalid_
    except (TRFError, TypeError, ValueError) as x:
        raise TRFError(year=year, month=month, day=day, cause=x)


def _direct(n1, n2):
    '''(INTERNAL) Get the C{n1} to C{n2} Xform or C{None}.
    '''
    r = RefFrames.get(n1)
    return r._Xto.get(n2, None) if r else None


def _Epoch(e, **kwds):
    '''(INTERNAL) Get the C{Epoch(B{e})}.
    '''
    return e if isinstance(e, Epoch) and not kwds else Epoch(e, **kwds)


def epoch2date(epoch):
    '''Return the date for a reference frame C{epoch}.

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

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

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

       @note: Any B{C{year}} is considered a leap year, i.e. having
              29 days in February.
    '''
    e = Epoch(epoch, low=0)
    y = int(e)
    d = int(_ceil((e - y) * _366_0))
    for m, n in enumerate(_mDays[1:]):
        if d > n:
            d -= n
        else:
            break
    return y, (m + 1), max(1, d)


def _eXhaustives(n1, n2):
    '''(INTERNAL) Yield all I{coalesced} Xforms from C{n1} to {n2}
       via I{any number of} intermediate reframe conversions.
    '''
    def _k2(item):
        return -item[1].epoch  # most recent first

    R = dict(RefFrames)
    r = R.pop(n1, None)
    if r:
        Xs = list(sorted(tuple(r._Xitems(2, R)), key=_k2))
        while Xs:
            n, X = Xs.pop(0)
            if n == n2:
                yield _n_pop(X)
            else:
                r = R.pop(n, None)
                if r:
                    for n, x in r._Xitems(2, R):
                        Xs.append((n, X + x))


def _indirects(n1, n2):
    '''(INTERNAL) Yield all Xforms between C{n1} and C{n2} via
       I{one} intermediate reframe C{n} conversion.
    '''
    def _X4(_Xto, n2):
        _d = _direct
        for n, X1 in _Xto.items():
            X2 = _d(n, n2)
            if X2:
                yield X1, X2, n, True   # X1 + X2
            X2 = _d(n2, n)
            if X2:
                yield X1, X2, n, False  # X1 - X2

    r1 = RefFrames.get(n1)
    if r1:
        for X1, X2, n, p_ in _X4(r1._Xto, n2):
            e1, e2 = X1.epoch, X2.epoch
            if e1 < e2:  # X1 to e2
                X1 = X1.toEpoch(e2)
#           elif e1 > e2:  # X2 to e1
#               X2 = X2.toEpoch(e1)
            yield X1._add_sub(X2, p_, n1, n2, n)


def _n1_n2_n3(X1, X2):
    '''(INTERNAL) L{TRFXform._add_sub} helper.
    '''
    n =  X1.indirected
    n = _SPACE_(n, X1.refName2) if n else X1.refName2
    return X1.refName1, X2.refName2, n


def _n_pop(X):
    '''(INTERNAL) Pop L{TRFXform.indirected}'s ends.
    '''
    p, n = None, X.indirected.split()
    if n and n[-1] == X.refName2:
        p = n.pop()
    if n and n[ 0] == X.refName1:
        p = n.pop(0)
    if p:
        X._indir_d = _SPACE_.join(n) if n else NN
    return X


def _reframe(**name_reframe):
    '''(INTERNAL) Get a C{reframe}.
    '''
    _, r = _xkwds_item2(name_reframe)
    if isstr(r) and r:  # not NN
        r = RefFrames.get(r)
    if r and isinstance(r, RefFrame):
        return r
    raise TRFError(**name_reframe)  # _invalid_


def _stref(**name_refname):
    '''(INTERNAL) Check a reference frame name.
    '''
    _, n = _xkwds_item2(name_refname)
    if isstr(n) and isidentifier(n):
        return str(n)
    raise TRFError(**name_refname)  # _invalid_


def _sumstr(name1, name2, p_):
    '''(INTERNAL) "Sum" of C{name1 + ('+' if p_ else '-') + name2}.
    '''
    if name2:
        n = name2 if p_ else _negastr(name2)
        p = NN if n.startswith(_MINUS_) or \
                  n.startswith(_PLUS_) else _PLUS_
        name1 = NN(name1, p, n)
    return name1


def _toRefFrame(point, reframe2, reframe=None, epoch=None,
                       epoch2=None, **name_LatLon_kwds):
    '''(INTERNAL) Convert an ellipsoidal point to C{reframe2}
       and C{epoch2 or epoch or pont.epoch or reframe.epoch}.
    '''
    ll = _xellipsoidall(point)
    r1 =  reframe or point.reframe
    if not r1:
        t = _SPACE_(_DOT_(repr(point), _reframe_), MISSING)
        raise TRFError(_no_(_conversion_), txt=t)

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

    e1 = _Epoch(epoch or point.epoch or r1.epoch)
    e2 =  e1 if epoch2 is None else Epoch(epoch2=epoch2)
    t0 = _toTransform0(r1.name, e1, reframe2.name, e2)
    if t0 is None:
        t = _SPACE_(typename(RefFrame), _AT_(r1.name, e1),
                            _to_, _AT_(reframe2.name, e2))
        raise TRFError(_no_(_conversion_), txt=t)

    name, LatLon_kwds = _name2__(name_LatLon_kwds)
    if t0:  # is not ()
        if t0.isunity:
            p = point.dup()
        elif point.datum:
            p = point.toCartesian() if ll else point
            p = p.toDatum(      r1.datum).toTransform(t0) \
                 .toDatum(reframe2.datum).toDatum(point.datum)
            if ll:
                p = p.toLatLon(LatLon=point.classof, **LatLon_kwds)
        elif ll:  # and LatLon_kwds
            p = point.toTransform(t0, **LatLon_kwds)
        else:
            p = point.toTransform(t0)
        p._reframe =  reframe2  # see TRFXform.toRefFrame above
        p._epoch   = _xattr(t0.Xform, epoch=e2)
        p.rename(reframe2._name__(name))
    else:
        p = point.dup(_reframe=reframe2,  # ditto
                      _epoch=e2, name=name) if name else point
    return p


def _toTransform0(n1, e1, n2, e2, **indirect_inverse):
    '''(INTERNAL) Return a L{TransformXform}, 0-tuple or C{None}.
    '''
    if n1 == n2 and e1 == e2:
        return ()  # unity?

    for X in _toTransforms(n1, e1, n2, e2, **indirect_inverse):
        return X  # first OK?

    if (n1.startswith(_ITRF_) and n2.startswith(_WGS84_)) or \
       (n2.startswith(_ITRF_) and n1.startswith(_WGS84_)):  # and e1 == e2?
        return ()  # unity?

    return None


def _toTransforms(n1, e1, n2, e2, indirect=True, inverse=True, exhaust=False):  # MCCABE 16
    '''(INTERNAL) Yield all possible Helmert transforms, if any.
    '''
    class Ts(list):  # L{TransformXform}s de-dup
        def __call__(self, Xs, e1=e1, e2=e2, **inverse):
            for X in Xs:
                if X:
                    T = X.toTransform(e1, epoch2=e2, **inverse)
                    if T not in self:
                        self.append(T)
                        yield T

#       def __contains__(self, T):
#           _xinstanceof(TransformXform, T=T)
#           return any(t == T for t in self)

    def _k(X):
        return -X.epoch  # most recent first

    _Ts = Ts()

    for T in _Ts((_direct(n1, n2),), inverse=False):
        yield T
    if inverse:
        for T in _Ts((_direct(n2, n1),), inverse=True):
            yield T

    if indirect:
        for T in _Ts(sorted(_indirects(n1, n2), key=_k), inverse=False):
            yield T
        if inverse:
            for T in _Ts(sorted(_indirects(n2, n1), key=_k), inverse=True):
                yield T

    if exhaust:
        for T in _Ts(_eXhaustives(n1, n2), inverse=False):
            yield T
        for T in _Ts(_eXhaustives(n2, n1), inverse=True):
            yield T


def trfTransform0(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True, exhaust=False):
    '''Get a Helmert transform to convert one C{reframe} observed at C{epoch}
       to an other C{reframe2} at observed at C{epoch2 or epoch}.

       @return: A L{TransformXform} instance, a C{0-tuple} for I{unity, identity} or
                C{None} if no conversion exists.

       @see: Function L{trfTransforms} for futher details.
    '''
    return _trfT0s(_toTransform0, reframe, reframe2, epoch, epoch2,
                                  indirect=indirect, inverse=inverse, exhaust=exhaust)


def trfTransforms(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True, exhaust=False):
    '''Yield all Helmert transform to convert one C{reframe} observed at C{epoch}
       to an other C{reframe2} at observed at C{epoch2 or epoch}.

       @arg reframe: The frame to convert I{from} (L{RefFrame} or C{str}).
       @arg reframe2: The frame to convert I{to} (L{RefFrame} or C{str}).
       @arg epoch: Epoch to observe I{from} (L{Epoch}, C{scalar} or C{str}),
                   otherwise C{B{reframe}}'s C{epoch}.
       @kwarg epoch2: Optional epoch to observe I{to} (L{Epoch}, C{scalar} or C{str}),
                      otherwise B{C{epoch}}.
       @kwarg indirect: If C{True}, include transforms via I{one} intermediate reframe,
                        otherwise only I{direct} B{C{reframe}} to B{C{reframe2}}
                        transforms (C{bool}).
       @kwarg inverse: If C{True}, include inverse, otherwise only forward transforms
                       (C{bool}).
       @kwarg exhaust: If C{True}, exhaustively generate all transforms, forward and
                       inverse and via any number of intermediate reframes (C{bool}).

       @return: A L{TransformXform} instance for each available conversion, without
                duplicates.

       @raise TRFError: Invalid B{C{reframe}}, B{C{reframe2}}, B{C{epoch}} or B{C{epoch2}}.

       @raise TypeError: Invalid B{C{reframe}} or B{C{reframe2}}.
    '''
    return _trfT0s(_toTransforms, reframe, reframe2, epoch, epoch2,
                                  indirect=indirect, inverse=inverse, exhaust=exhaust)


def _trfT0s(_toT0s, reframe, reframe2, epoch, epoch2, **indirect_inverse_exhaust):
    '''(INTERNAL) Handle C{trfTransforms0} and C{trfTransforms} calls.
    '''
    r1 = _reframe(reframe=reframe)
    e1 =  r1.epoch if epoch is None else _Epoch(epoch)
    r2 = _reframe(reframe2=reframe2)
    e2 =  e1 if epoch2 is None else Epoch(epoch2=epoch2)
    return _toT0s(r1.name, e1, r2.name, e2, **indirect_inverse_exhaust)


def trfXform(reframe1, reframe2, epoch=None, xform=None, rates=None, raiser=True):
    '''Define a new Terrestrial Reference Frame (TRF) converter or get an
       existing one.

       @arg reframe1: Source frame (L{RefFrame} or C{str}), converting I{from}.
       @arg reframe2: Destination frame (L{RefFrame} or C{str}), converting I{to}.
       @kwarg epoch: Epoch, a fractional year (L{Epoch}, C{scalar} or C{str})
                     or C{None} for C{B{reframe2}}'s epoch.
       @kwarg xform: I{Transform} parameters (L{TRFXform7Tuple}).
       @kwarg rates: I{Rate} parameters (L{TRFXform7Tuple}), as B{C{xform}},
                     but in C{units-per-year}.
       @kwarg raiser: If C{False}, do not raise an error if the converter
                      exists, replace it (C{bool}).

       @return: The new TRF converter (L{TRFXform}) or if no B{C{epoch}},
                B{C{xform}} and B{C{rates}} are given, return the existing
                one (L{TRFXform}) or C{None} if not available.

       @raise TRFError: Invalid B{C{reframe1}}, B{C{reframe2}}, B{C{epoch}},
                        B{C{xform}} or B{C{rates}} or the TRF converter
                        already exists.
    '''
    try:
        r1 = _reframe(reframe1=reframe1)
        r2 = _reframe(reframe2=reframe2)
        if epoch is None:
            if xform is rates is None:
                return r1._Xto.get(r2.name, None)
            e =  r2.epoch
        else:
            e = _Epoch(epoch)
        return _trfX(r1.name, r2.name, raiser=raiser, epoch=e,
                                       xform=xform, rates=rates)
    except (TypeError, ValueError) as x:
        t = unstr(trfXform, reframe1, reframe2, epoch=epoch)
        raise TRFError(t, cause=x)


def _trfX(n1, n2, raiser=True, **epoch_xform_rates):
    '''(INTERNAL) New, I{unique} L{TRFXform} converter.
    '''
    r1 = RefFrames.get(n1)
    if r1 is None:
        raise ValueError(_invalid_)
    r2 = RefFrames.get(n2)
    if r2 is None:
        raise ValueError(_invalid_)
    if raiser:
        if n2 in r1._Xto:
            raise ValueError(_exists_)
        if n1 in r2._Xto:
            raise ValueError(_SPACE_(_inverse_, _exists_))
    r1._Xto[n2] = X = TRFXform(n1, n2, **epoch_xform_rates)
    return X


# def velocities2neu(vx, vy, vz, lat=0, lon=0):
#     '''Convert X, Y, and Z I{velocities} to North, East, Up.
#
#        @arg vx: X velocity (C{meter-per-time}).
#        @arg vx: Y velocity (C{meter-per-time}).
#        @arg vx: Z velocity (C{meter-per-time}).
#        @kwarg lat: Latitude (C{degrees}).
#        @kwarg lon: Longitude (C{degrees}).
#
#        @return: 3-Tuple C{(vnorth, veast, vup)} with the
#                 North, East and Up velocities, same units
#                 as B{C{vx}, B{C{vy}} and B{C{vx}}.
#     '''
#     sa, ca, sb, cb = sincos2d_(lat, lon)
#     ve  = cb * vy - sb * vx
#     v   = cb * vx + sb * vy
#     vn  = ca * vz - sa * v
#     vu  = sa * vz + ca * v
#     return vn, ve, vu


# def velocities2xyz(vn, ve, vu, lat=0, lon=0):
#     '''Convert North, East and Up I{velocities} to X, Y, Z.
#
#        @arg vn: North velocity (C{meter-per-time}).
#        @arg ve: East velocity (C{meter-per-time}).
#        @arg vu: Up velocity (C{meter-per-time}).
#        @kwarg lat: Latitude (C{degrees}).
#        @kwarg lon: Longitude (C{degrees}).
#
#        @return: 3-Tuple C{(vx, vy, vz)} with the X, Y
#                 and Z velocities, same units as B{C{vn},
#                 B{C{ve}} and B{C{vu}}.
#     '''
#     sa, ca, sb, cb = sincos2d_(lat, lon)
#     vz = ca * vn + sa * vu
#     v  = ca * vu - sa * vn
#     vx = cb * v  - sb * ve
#     vy = sb * v  + cb * ve
#     return vx, vy, vz


def _X(*ps):  # deleted below
    return _P(ps, _xform_, _Xs)  # noqa: F821 del


def _R(*ps):  # deleted below
    return _P(ps, _rates_, _Rs)  # noqa: F821 del


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

# TRF conversions specified as an epoch and 2 sets of 7 parameters.  Most from Altamimi, Z. U{"EUREF Technical
# Note 1: Relationship and Transformation between the International and the European Terrestrial Reference
# Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Appendix A, more at U{Quinsy QPS <https://
# confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/ITRF_Transformation_Parameters.xlsx>}.
# See also U{Quinsy International Terrestrial Reference Frame 2014 (ITRF2014)<https://confluence.QPS.NL/qinsy/latest/
# en/international-terrestrial-reference-frame-2014-itrf2014-182618383.html>}.
_trfX(_ITRF2020_, _ITRF2014_, epoch=_E(2015),  # <https://ITRF.IGN.Fr/docs/solutions/itrf2020/Transfo-ITRF2020_TRFs.txt>
                              xform=_X(  -1.4,     -0.9,     1.4,   -0.42,     _0_0,      _0_0,     _0_0),
                              rates=_R(  _0_0,     -0.1,     0.2,    _0_0,     _0_0,      _0_0,     _0_0))
_trfX(_ITRF2020_, _ITRF2008_, epoch=_E(2015),
                              xform=_X(   0.2,      1.0,     3.3,   -0.29,     _0_0,      _0_0,     _0_0),
                              rates=_R(  _0_0,     -0.1,     0.1,    0.03,     _0_0,      _0_0,     _0_0))
_trfX(_ITRF2020_, _ITRF2005_, epoch=_E(2015),
                              xform=_X(   2.7,      0.1,    -1.4,    0.65,     _0_0,      _0_0,     _0_0),
                              rates=_R(   0.3,     -0.1,     0.1,    0.03,     _0_0,      _0_0,     _0_0))
_trfX(_ITRF2020_, _ITRF2000_, epoch=_E(2015),
                              xform=_X(  -0.2,      0.8,   -34.2,    2.25,     _0_0,      _0_0,     _0_0),
                              rates=_R(   0.1,     _0_0,    -1.7,    0.11,     _0_0,      _0_0,     _0_0))
_trfX(_ITRF2020_, _ITRF97_,   epoch=_E(2015),
                              xform=_X(   6.5,     -3.9,   -77.9,    3.98,     _0_0,      _0_0,      0.36),
                              rates=_R(   0.1,     -0.6,    -3.1,    0.12,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2020_, _ITRF96_,   epoch=_E(2015),
                              xform=_X(   6.5,     -3.9,   -77.9,    3.98,     _0_0,      _0_0,      0.36),
                              rates=_R(   0.1,     -0.6,    -3.1,    0.12,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2020_, _ITRF94_,   epoch=_E(2015),
                              xform=_X(   6.5,     -3.9,   -77.9,    3.98,     _0_0,      _0_0,      0.36),
                              rates=_R(   0.1,     -0.6,    -3.1,    0.12,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2020_, _ITRF93_,   epoch=_E(2015),
                              xform=_X( -65.8,      1.9,   -71.3,    4.47,     -3.36,     -4.33,    _0_75),
                              rates=_R(  -2.8,     -0.2,    -2.3,    0.12,     -0.11,     -0.19,     0.07))
_trfX(_ITRF2020_, _ITRF92_,   epoch=_E(2015),
                              xform=_X(  14.5,     -1.9,   -85.9,    3.27,     _0_0,      _0_0,      0.36),
                              rates=_R(   0.1,     -0.6,    -3.1,    0.12,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2020_, _ITRF91_,   epoch=_E(2015),
                              xform=_X(  26.5,     12.1,   -91.9,    4.67,     _0_0,      _0_0,      0.36),
                              rates=_R(   0.1,     -0.6,    -3.1,    0.12,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2020_, _ITRF90_,   epoch=_E(2015),
                              xform=_X(  24.5,      8.1,  -107.9,    4.97,     _0_0,      _0_0,      0.36),
                              rates=_R(   0.1,     -0.6,    -3.1,    0.12,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2020_, _ITRF89_,   epoch=_E(2015),
                              xform=_X(  29.5,     32.1,  -145.9,    8.37,     _0_0,      _0_0,      0.36),
                              rates=_R(   0.1,     -0.6,    -3.1,    0.12,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2020_, _ITRF88_,   epoch=_E(2015),
                              xform=_X(  24.5,     -3.9,  -169.9,   11.47,      0.1,      _0_0,      0.36),
                              rates=_R(   0.1,     -0.6,    -3.1,    0.12,     _0_0,      _0_0,      0.02))

# see U{Transformation Parameters ITRF2014<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2014_ITRFs.txt>} and
# Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1.pdf>} Appendix A.
_trfX(_ITRF2014_, _ITRF2008_, epoch=(2010),  # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2014/tp_14-08.php>
                              xform=_X(   1.6,      1.9,     2.4,   -0.02,     _0_0,      _0_0,     _0_0),
                              rates=_R(  _0_0,     _0_0,    -0.1,    0.03,     _0_0,      _0_0,     _0_0))
_trfX(_ITRF2014_, _ITRF2005_, epoch=_E(2010),
                              xform=_X(   2.6,     _1_0,    -2.3,    0.92,     _0_0,      _0_0,     _0_0),
                              rates=_R(   0.3,     _0_0,    -0.1,    0.03,     _0_0,      _0_0,     _0_0))
_trfX(_ITRF2014_, _ITRF2000_, epoch=_E(2010),
                              xform=_X(   0.7,      1.2,   -26.1,    2.12,     _0_0,      _0_0,     _0_0),
                              rates=_R(   0.1,      0.1,    -1.9,    0.11,     _0_0,      _0_0,     _0_0))
_trfX(_ITRF2014_, _ITRF97_,   epoch=_E(2010),
                              xform=_X(   7.4,     -0.5,   -62.8,    3.8,      _0_0,      _0_0,      0.26),
                              rates=_R(   0.1,     -0.5,    -3.3,    0.12,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2014_, _ITRF96_,   epoch=_E(2010),
                              xform=_X(   7.4,     -0.5,   -62.8,    3.8,      _0_0,      _0_0,      0.26),
                              rates=_R(   0.1,     -0.5,    -3.3,    0.12,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2014_, _ITRF94_,   epoch=_E(2010),
                              xform=_X(   7.4,     -0.5,   -62.8,    3.8,      _0_0,      _0_0,      0.26),
                              rates=_R(   0.1,     -0.5,    -3.3,    0.12,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2014_, _ITRF93_,   epoch=_E(2010),
                              xform=_X( -50.4,      3.3,   -60.2,    4.29,     -2.81,     -3.38,     0.4),
                              rates=_R(  -2.8,     -0.1,    -2.5,    0.12,     -0.11,     -0.19,     0.07))
_trfX(_ITRF2014_, _ITRF92_,   epoch=_E(2010),
                              xform=_X(  15.4,      1.5,   -70.8,    3.09,     _0_0,      _0_0,      0.26),
                              rates=_R(   0.1,     -0.5,    -3.3,    0.12,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2014_, _ITRF91_,   epoch=_E(2010),
                              xform=_X(  27.4,     15.5,   -76.8,    4.49,     _0_0,      _0_0,      0.26),
                              rates=_R(   0.1,     -0.5,    -3.3,    0.12,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2014_, _ITRF90_,   epoch=_E(2010),
                              xform=_X(  25.4,     11.5,   -92.8,    4.79,     _0_0,      _0_0,      0.26),
                              rates=_R(   0.1,     -0.5,    -3.3,    0.12,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2014_, _ITRF89_,   epoch=_E(2010),
                              xform=_X(  30.4,     35.5,  -130.8,    8.19,     _0_0,      _0_0,      0.26),
                              rates=_R(   0.1,     -0.5,    -3.3,    0.12,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2014_, _ITRF88_,   epoch=_E(2010),
                              xform=_X(  25.4,     -0.5,  -154.8,   11.29,      0.1,      _0_0,      0.26),
                              rates=_R(   0.1,     -0.5,    -3.3,    0.12,     _0_0,      _0_0,      0.02))

# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 1st and 2nd column
_trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2005),
                              xform=_X(  -0.5,     -0.9,    -4.7,    0.94,     _0_0,      _0_0,     _0_0),
                              rates=_R(   0.3,     _0_0,    _0_0,   _0_0,      _0_0,      _0_0,     _0_0))
# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(1997),
#                             xform=_X(  -2.9,     -0.9,    -4.7,    0.94,     _0_0,      _0_0,     _0_0),
#                             rates=_R(   0.3,     _0_0,    _0_0,   _0_0,      _0_0,      _0_0,     _0_0))
# see U{Transformation Parameters ITRF2008<http://ITRF.IGN.Fr/doc_ITRF/Transfo-ITRF2008_ITRFs.txt>}
# _trfX(_ITRF2008_, _ITRF2005_, epoch=_E(2000),  # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2008/tp_08-05.php>
#                             xform=_X(  -2.0,     -0.9,    -4.7,    0.94,     _0_0,      _0_0,     _0_0),
#                             rates=_R(   0.3,     _0_0,    _0_0,   _0_0,      _0_0,      _0_0,     _0_0))
_trfX(_ITRF2008_, _ITRF2000_, epoch=_E(2000),
                              xform=_X(  -1.9,     -1.7,   -10.5,    1.34,     _0_0,      _0_0,     _0_0),
                              rates=_R(   0.1,      0.1,    -1.8,    0.08,     _0_0,      _0_0,     _0_0))
_trfX(_ITRF2008_, _ITRF97_,   epoch=_E(2000),
                              xform=_X(   4.8,      2.6,   -33.2,    2.92,     _0_0,      _0_0,      0.06),
                              rates=_R(   0.1,     -0.5,    -3.2,    0.09,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2008_, _ITRF96_,   epoch=_E(2000),
                              xform=_X(   4.8,      2.6,   -33.2,    2.92,     _0_0,      _0_0,      0.06),
                              rates=_R(   0.1,     -0.5,    -3.2,    0.09,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2008_, _ITRF94_,   epoch=_E(2000),
                              xform=_X(   4.8,      2.6,   -33.2,    2.92,     _0_0,      _0_0,      0.06),
                              rates=_R(   0.1,     -0.5,    -3.2,    0.09,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2008_, _ITRF93_,   epoch=_E(2000),
                              xform=_X( -24.0,      2.4,   -38.6,    3.41,     -1.71,     -1.48,    -0.3),
                              rates=_R(  -2.8,     -0.1,    -2.4,    0.09,     -0.11,     -0.19,     0.07))
_trfX(_ITRF2008_, _ITRF92_,   epoch=_E(2000),
                              xform=_X(  12.8,      4.6,   -41.2,    2.21,     _0_0,      _0_0,      0.06),
                              rates=_R(   0.1,     -0.5,    -3.2,    0.09,     _0_0,      _0_0,      0.02))
_trfX(_ITRF2008_, _ITRF91_,   epoch=_E(2000),
                              xform=_X(  24.8,     18.6,   -47.2,    3.61,     _0_0,     _0_0,       0.06),
                              rates=_R(   0.1,     -0.5,    -3.2,    0.09,     _0_0,     _0_0,       0.02))
_trfX(_ITRF2008_, _ITRF90_,   epoch=_E(2000),
                              xform=_X(  22.8,     14.6,   -63.2,    3.91,     _0_0,     _0_0,       0.06),
                              rates=_R(   0.1,     -0.5,    -3.2,    0.09,     _0_0,     _0_0,       0.02))
_trfX(_ITRF2008_, _ITRF89_,   epoch=_E(2000),
                              xform=_X(  27.8,     38.6,  -101.2,    7.31,     _0_0,     _0_0,       0.06),
                              rates=_R(   0.1,     -0.5,    -3.2,    0.09,     _0_0,     _0_0,       0.02))
_trfX(_ITRF2008_, _ITRF88_,   epoch=_E(2000),
                              xform=_X(  22.8,      2.6,  -125.2,   10.41,      0.1,     _0_0,       0.06),
                              rates=_R(   0.1,     -0.5,    -3.2,    0.09,     _0_0,     _0_0,       0.02))

# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 3rd column
# _trfX(_ITRF2005_, _ITRF2000_, epoch=_E(1997),
#                             xform=_X(   0.7,     -1.1,    -0.4,    0.16,     -0.2,      0.1       -1.8),
#                             rates=_R(  -0.2,      0.1,    -1.8,    0.08,     _0_0,     _0_0,      _0_0))
_trfX(_ITRF2005_, _ITRF2000_, epoch=_E(2000),  # <http://ITRF.ENSG.IGN.Fr/ITRF_solutions/2005/tp_05-00.php>
                              xform=_X(   0.1,     -0.8,    -5.8,    0.4,      _0_0,     _0_0,      _0_0),
                              rates=_R(  -0.2,      0.1,    -1.8,    0.08,     _0_0,     _0_0,      _0_0))

_trfX(_ITRF2000_, _ITRF97_,   epoch=_E(1997),
                              xform=_X(   0.67,     0.61,   -1.85,   1.55,     _0_0,     _0_0,      _0_0),
                              rates=_R(  _0_0,     -0.06,   -0.14,   0.01,     _0_0,     _0_0,      -0.02))  # 0.02?
_trfX(_ITRF2000_, _ITRF96_,   epoch=_E(1997),
                              xform=_X(   0.67,     0.61,   -1.85,   1.55,     _0_0,     _0_0,      _0_0),
                              rates=_R(  _0_0,     -0.06,   -0.14,   0.01,     _0_0,     _0_0,       0.02))
_trfX(_ITRF2000_, _ITRF94_,   epoch=_E(1997),
                              xform=_X(   0.67,     0.61,   -1.85,   1.55,     _0_0,     _0_0,      _0_0),
                              rates=_R(  _0_0,     -0.06,   -0.14,   0.01,     _0_0,     _0_0,       0.02))
_trfX(_ITRF2000_, _ITRF93_,   epoch=_E(1988),
                              xform=_X(  12.7,      6.5,   -20.9,    1.95,     -0.39,     0.8,      -1.14),
                              rates=_R(  -2.9,     -0.2,    -0.6,    0.01,     -0.11,    -0.19,      0.07))
_trfX(_ITRF2000_, _ITRF92_,   epoch=_E(1988),
                              xform=_X(   1.47,     1.35,   -1.39,  _0_75,     _0_0,     _0_0,      -0.18),
                              rates=_R(  _0_0,     -0.06,   -0.14,   0.01,     _0_0,     _0_0,       0.02))
_trfX(_ITRF2000_, _ITRF91_,   epoch=_E(1988),
                              xform=_X(   26.7,    27.5,   -19.9,    2.15,     _0_0,     _0_0,      -0.18),
                              rates=_R(   _0_0,    -0.6,    -1.4,    0.01,     _0_0,     _0_0,       0.02))
_trfX(_ITRF2000_, _ITRF90_,   epoch=_E(1988),
                              xform=_X(   2.47,     2.35,   -3.59,   2.45,     _0_0,     _0_0,      -0.18),
                              rates=_R(  _0_0,     -0.06,   -0.14,   0.01,     _0_0,     _0_0,       0.02))
_trfX(_ITRF2000_, _ITRF89_,   epoch=_E(1988),
                              xform=_X(   2.97,     4.75,   -7.39,   5.85,     _0_0,     _0_0,      -0.18),
                              rates=_R(  _0_0,     -0.06,   -0.14,   0.01,     _0_0,     _0_0,       0.02))
_trfX(_ITRF2000_, _ITRF88_,   epoch=_E(1988),
                              xform=_X(   2.47,     1.15,   -9.79,   8.95,      0.1,     _0_0,      -0.18),
                              rates=_R(  _0_0,     -0.06,   -0.14,   0.01,     _0_0,     _0_0,       0.02))

# Soler, T .& Snay R.A. U{"Transforming Positions and Velocities between the International Terrestrial
# Reference Frame of 2000 and North American Datum of 1983"<https://www.ResearchGate.net/publication/245291390>},
# Pearson, C. & Snay, R. U{"Introducing HTDP 3.1 to transform coordinates across time and spatial reference
# frames"<https://Geodesy.NOAA.gov/TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 5th and 6th column
_trfX(_ITRF97_,   _ITRF96_,   epoch=_E(1997),
                              xform=_X(  -2.07,    -0.21,    9.95,  -0.93496,   0.1267,   -0.22355,  -0.06065,),
                              rates=_R(   0.69,    -0.1,     1.86,  -0.19201,   0.01347,  -0.01514,   0.00027))
_trfX(_ITRF96_,   _NAD83_,    epoch=_E(1997),
                              xform=_X( 991.0,   -190.72, -512.9,   _0_0,      25.79,      9.65,     11.66,),
                              rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.0532,   -0.7423,   -0.0316,))

# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 1.
# _trfX(_ITRF2020_, _ETRF2020_, epoch=_E(1989),  # see Table 2 below
#                             xform=_P_0_0s,
#                             rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.086,     0.519,    -0.753))
# _trfX(_ITRF2014_, _ETRF2014_, epoch=_E(1989),  # see Table 3 below
#                             xform=_P_0_0s,
#                             rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.085,     0.531,    -0.77))
_trfX(_ITRF2005_, _ETRF2005_, epoch=_E(1989),
                              xform=_X(  56.0,     48.0,   -37.0,   _0_0,      _0_0,      _0_0,      _0_0),
                              rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.054,     0.518,    -0.781))
# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(1989),  # see Table 4 below
#                             xform=_X(  54.0,     51.0,   -48.0,   _0_0,      _0_0,      _0_0,      _0_0),
#                             rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.081,     0.49,     -0.792))
_trfX(_ITRF97_,   _ETRF97_,   epoch=_E(1989),
                              xform=_X(  41.0,     41.0,   -49.0,   _0_0,      _0_0,      _0_0,      _0_0),
                              rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.2,       0.5,      -0.65))
_trfX(_ITRF96_,   _ETRF96_,   epoch=_E(1989),
                              xform=_X(  41.0,     41.0,   -49.0,   _0_0,      _0_0,      _0_0,      _0_0),
                              rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.2,       0.5,      -0.65))
_trfX(_ITRF94_,   _ETRF94_,   epoch=_E(1989),
                              xform=_X(  41.0,     41.0,   -49.0,   _0_0,      _0_0,      _0_0,      _0_0),
                              rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.2,       0.5,      -0.65))
_trfX(_ITRF93_,   _ETRF93_,   epoch=_E(1989),
                              xform=_X(  19.0,     53.0,   -21.0,   _0_0,      _0_0,      _0_0,      _0_0),
                              rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.32,      0.78,     -0.67))
_trfX(_ITRF92_,   _ETRF92_,   epoch=_E(1989),
                              xform=_X(  38.0,     40.0,   -37.0,    0.0,       0.0,       0.0,       0.0),
                              rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.21,      0.52,     -0.68))
_trfX(_ITRF91_,   _ETRF91_,   epoch=_E(1989),
                              xform=_X(  21.0,     25.0,   -37.0,   _0_0,      _0_0,      _0_0,      _0_0),
                              rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.21,      0.52,     -0.68))
_trfX(_ITRF90_,   _ETRF90_,   epoch=_E(1989),
                              xform=_X(  19.0,     28.0,   -23.0,   _0_0,      _0_0,      _0_0,      _0_0),
                              rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.11,      0.57,     -0.71))
_trfX(_ITRF89_,   _ETRF89_,   epoch=_E(1989),
                              xform=_P_0_0s,
                              rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.11,      0.57,     -0.71))

# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 2.
_trfX(_ITRF2020_, _ETRF2020_, epoch=_E(2015),
                              xform=_X(  _0_0,     _0_0,    _0_0,   _0_0,       2.236,    13.494,   -19.578),
                              rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.086,     0.519,    -0.753))
_trfX(_ITRF2014_, _ETRF2020_, epoch=_E(2015),
                              xform=_X(   1.4,      0.9,    -1.4,    0.42,      2.236,    13.494,   -19.578),
                              rates=_R(  _0_0,      0.1,    -0.2,   _0_0,       0.086,     0.519,    -0.753))
_trfX(_ITRF2008_, _ETRF2020_, epoch=_E(2015),
                              xform=_X(   3.0,      2.8,     0.5,    0.55,      2.236,    13.494,   -19.578),
                              rates=_R(  _0_0,      0.1,    -0.3,    0.03,      0.086,     0.519,    -0.753))
_trfX(_ITRF2005_, _ETRF2020_, epoch=_E(2015),
                              xform=_X(   5.5,      1.9,    -4.2,    1.49,      2.236,    13.494,   -19.578),
                              rates=_R(   0.3,      0.1,    -0.3,    0.03,      0.086,     0.519,    -0.753))
_trfX(_ITRF2000_, _ETRF2020_, epoch=_E(2015),
                              xform=_X(   2.6,      2.6,   -37.0,    3.09,      2.236,    13.494,   -19.578),
                              rates=_R(   0.1,      0.2,    -2.1,    0.11,      0.086,     0.519,    -0.753))
_trfX(_ITRF97_,   _ETRF2020_, epoch=_E(2015),
                              xform=_X(   9.3,     -2.1,   -80.7,    4.82,      2.236,    13.494,   -19.218),
                              rates=_R(   0.1,     -0.4,    -3.5,    0.12,      0.086,     0.519,    -0.733))
_trfX(_ITRF96_,   _ETRF2020_, epoch=_E(2015),
                              xform=_X(   9.3,     -2.1,   -80.7,    4.82,      2.236,    13.494,   -19.218),
                              rates=_R(   0.1,     -0.4,    -3.5,    0.12,      0.086,     0.519,    -0.733))
_trfX(_ITRF94_,   _ETRF2020_, epoch=_E(2015),
                              xform=_X(   9.3,     -2.1,   -80.7,    4.82,      2.236,    13.494,   -19.218),
                              rates=_R(   0.1,     -0.4,    -3.5,    0.12,      0.086,     0.519,    -0.733))
_trfX(_ITRF93_,   _ETRF2020_, epoch=_E(2015),
                              xform=_X( -63.0,      3.7,   -74.1,    5.31,     -1.124,     9.164,   -18.828),
                              rates=_R(  -2.8,     _0_0,    -2.7,    0.12,     -0.024,     0.329,    -0.683))
_trfX(_ITRF92_,   _ETRF2020_, epoch=_E(2015),
                              xform=_X(  17.3,     -0.1,   -88.7,    4.11,      2.236,    13.494,   -19.218),
                              rates=_R(   0.1,     -0.4,    -3.5,    0.12,      0.086,     0.519,    -0.733))
_trfX(_ITRF91_,   _ETRF2020_, epoch=_E(2015),
                              xform=_X(  29.3,     13.9,   -94.7,    5.51,      2.236,    13.494,   -19.218),
                              rates=_R(   0.1,     -0.4,    -3.5,    0.12,      0.086,     0.519,    -0.733))
_trfX(_ITRF90_,   _ETRF2020_, epoch=_E(2015),
                              xform=_X(  27.3,      9.9,  -110.7,    5.81,      2.236,    13.494,   -19.218),
                              rates=_R(   0.1,     -0.4,    -3.5,    0.12,      0.086,     0.519,    -0.733))
_trfX(_ITRF89_,   _ETRF2020_, epoch=_E(2015),
                              xform=_X(  32.3,     33.9,  -148.7,    9.21,      2.236,    13.494,   -19.218),
                              rates=_R(   0.1,     -0.4,    -3.5,    0.12,      0.086,     0.519,    -0.733))
_trfX(_ITRF88_,   _ETRF2020_, epoch=_E(2015),
                              xform=_X(  27.3,     -2.1,  -172.7,   12.31,      2.336,    13.494,   -19.218),
                              rates=_R(   0.1,     -0.4,    -3.5,    0.12,      0.086,     0.519,    -0.733))

# see Altamimi, Z. U{"EUREF Technical Note 1: Relationship and Transformation between the International and
# the European Terrestrial Reference Systems"<https://ERTS89.ENSG.IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 3.
_trfX(_ITRF2020_, _ETRF2014_, epoch=_E(2015),
                              xform=_X(  -1.4,     -0.9,     1.4,    0.42,      2.21,     13.806,   -20.02),
                              rates=_R(  _0_0,     -0.1,     0.2,   _0_0,       0.085,     0.531,    -0.77))
_trfX(_ITRF2014_, _ETRF2014_, epoch=_E(2015),
                              xform=_X(  _0_0,     _0_0,    _0_0,   _0_0,       2.21,     13.806,   -20.02),
                              rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.085,     0.531,    -0.77))
_trfX(_ITRF2008_, _ETRF2014_, epoch=_E(2015),
                              xform=_X(  -1.6,     -1.9,    -1.9,   -0.13,      2.21,     13.806,   -20.02),
                              rates=_R(  _0_0,     _0_0,     0.1,   -0.03,      0.085,     0.531,    -0.77))
_trfX(_ITRF2005_, _ETRF2014_, epoch=_E(2015),
                              xform=_X(  -4.1,     -1.0,     2.8,   -1.07,      2.21,     13.806,   -20.02),
                              rates=_R(  -0.3,     _0_0,     0.1,   -0.03,      0.085,     0.531,    -0.77))
_trfX(_ITRF2000_, _ETRF2014_, epoch=_E(2015),
                              xform=_X(  -1.2,     -1.7,    35.6,   -2.67,      2.21,     13.806,   -20.02),
                              rates=_R(  -0.1,     -0.1,     1.9,   -0.11,      0.085,     0.531,    -0.77))
_trfX(_ITRF97_,   _ETRF2014_, epoch=_E(2015),
                              xform=_X(  -7.9,      3.0,    79.3,   -4.40,      2.210,    13.806,   -20.38),
                              rates=_R(  -0.1,      0.5,     3.3,   -0.12,      0.085,     0.531,    -0.79))
_trfX(_ITRF96_,   _ETRF2014_, epoch=_E(2015),
                              xform=_X(  -7.9,      3.0,    79.3,   -4.40,      2.210,    13.806,   -20.38),
                              rates=_R(  -0.1,      0.5,     3.3,   -0.12,      0.085,     0.531,    -0.79))
_trfX(_ITRF94_,   _ETRF2014_, epoch=_E(2015),
                              xform=_X(  -7.9,      3.0,    79.3,   -4.40,      2.210,    13.806,   -20.38),
                              rates=_R(  -0.1,      0.5,     3.3,   -0.12,      0.085,     0.531,    -0.79))
_trfX(_ITRF93_,   _ETRF2014_, epoch=_E(2015),
                              xform=_X(  64.4,     -2.8,    72.7,   -4.89,      5.570,    18.136,   -20.77),
                              rates=_R(   2.8,      0.1,     2.5,   -0.12,      0.195,     0.721,    -0.84))
_trfX(_ITRF92_,   _ETRF2014_, epoch=_E(2015),
                              xform=_X( -15.9,      1.0,    87.3,   -3.69,      2.21,     13.806,   -20.38),
                              rates=_R(  -0.1,      0.5,     3.3,   -0.12,      0.085,     0.531,    -0.79))
_trfX(_ITRF91_,   _ETRF2014_, epoch=_E(2015),
                              xform=_X( -27.9,    -13.0,    93.3,   -5.09,      2.21,     13.806,   -20.38),
                              rates=_R(  -0.1,      0.5,     3.3,   -0.12,      0.085,     0.531,    -0.79))
_trfX(_ITRF90_,   _ETRF2014_, epoch=_E(2015),
                              xform=_X( -25.9,     -9.0,   109.3,   -5.39,      2.21,     13.806,   -20.38),
                              rates=_R(  -0.1,      0.5,     3.3,   -0.12,      0.085,     0.531,    -0.79))
_trfX(_ITRF89_,   _ETRF2014_, epoch=_E(2015),
                              xform=_X( -30.9,    -33.0,   147.3,   -8.79,      2.21,     13.806,   -20.38),
                              rates=_R(  -0.1,      0.5,     3.3,   -0.12,      0.085,     0.531,    -0.79))
_trfX(_ITRF88_,   _ETRF2014_, epoch=_E(2015),
                              xform=_X( -25.9,      3.0,   171.3,  -11.89,      2.11,     13.806,   -20.38),
                              rates=_R(  -0.1,      0.5,     3.3,   -0.12,      0.085,     0.531,    -0.79))

# see U{Altamimi, Z. "EUREF Technical Note 1: Relationship and Transformation between the International and
# the European Terrestrial Reference Systems"<https://ERTS89.ENSG,IFN.Fr/pub/EUREF-TN-1-Jan-31-2024.pdf>} Table 4,
# U{Boucher, C. & Altamimi, Z. "Memo: Specifications for reference frame fixing in the analysis of a EUREF GPS
# campaign" (2011) <https://ETRS89.ENSG.IGN.Fr/memo-V8.pdf>} and U{Altamimi, Z. "Key results of ITRF2014 and
# implication to ETRS89 realization", EUREF2016<https://www.EUREF.EU/symposia/2016SanSebastian/01-02-Altamimi.pdf>}.
_trfX(_ITRF2020_, _ETRF2000_, epoch=_E(2015),
                              xform=_X(  53.8,     51.8,   -82.2,    2.25,      2.106,   12.74,    -20.592),
                              rates=_R(   0.1,     _0_0,    -1.7,    0.11,      0.081,    0.49,     -0.792))
# _trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2000),
#                             xform=_X(  53.7,     51.2,   -55.1,    1.02,      0.891,    5.39,     -8.712),
#                             rates=_R(   0.1,      0.1,    -1.9,    0.11,      0.081,    0.49,     -0.792))
_trfX(_ITRF2014_, _ETRF2000_, epoch=_E(2015),
                              xform=_X(  55.2,     52.7,   -83.6,    2.67,      2.106,   12.74,    -20.592),
                              rates=_R(   0.1,      0.1,    -1.9,    0.11,      0.081,    0.49,     -0.792))
# _trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2000),
#                             xform=_X(  52.1,     49.3,   -58.5,    1.34,      0.891,    5.39,     -8.712),
#                             rates=_R(   0.1,      0.1,    -1.8,    0.08,      0.081,    0.49,     -0.792))
_trfX(_ITRF2008_, _ETRF2000_, epoch=_E(2015),
                              xform=_X(  53.6,     50.8,   -85.5,    2.54,      2.106,   12.74,    -20.592),
                              rates=_R(   0.1,      0.1,    -1.8,    0.08,      0.081,    0.49,     -0.792))
# _trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2000),
#                             xform=_X(  54.1,     50.2,   -53.8,    0.4,       0.891,    5.39,     -8.712),
#                             rates=_R(  -0.2,      0.1,    -1.8,    0.08,      0.081,    0.49,     -0.792))
_trfX(_ITRF2005_, _ETRF2000_, epoch=_E(2015),
                              xform=_X(  51.1,     51.7,   -80.8,    1.6,       2.106,   12.74,    -20.592),
                              rates=_R(  -0.2,      0.1,    -1.8,    0.08,      0.081,    0.49,     -0.792))
# _trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2000),
#                             xform=_X(  54.0,     51.0,   -48.0,   _0_0,       0.891,    5.39,     -8.712),
#                             rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.081,    0.49,     -0.792))
_trfX(_ITRF2000_, _ETRF2000_, epoch=_E(2015),
                              xform=_X(  54.0,     51.0,   -48.0,   _0_0,       2.106,   12.74,    -20.592),
                              rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       0.081,    0.49,     -0.792))
_trfX(_ITRF97_,   _ETRF2000_, epoch=_E(2015),
                              xform=_X(  47.3,     55.7,    -4.3,   -1.73,      2.106,   12.74,    -20.952),
                              rates=_R(  _0_0,      0.6,     1.4,   -0.01,      0.081,    0.49,     -0.812))
_trfX(_ITRF96_,   _ETRF2000_, epoch=_E(2015),
                              xform=_X(  47.3,     55.7,    -4.3,   -1.73,      2.106,   12.74,    -20.952),
                              rates=_R(  _0_0,      0.6,     1.4,   -0.01,      0.081,    0.49,     -0.812))
_trfX(_ITRF94_,   _ETRF2000_, epoch=_E(2015),
                              xform=_X(  47.3,     55.7,    -4.3,   -1.73,      2.106,   12.74,    -20.952),
                              rates=_R(  _0_0,      0.6,     1.4,   -0.01,      0.081,    0.49,     -0.812))
_trfX(_ITRF93_,   _ETRF2000_, epoch=_E(2015),
                              xform=_X( 119.6,     49.9,   -10.9,   -2.22,      5.466,   17.07,    -21.342),
                              rates=_R(   2.9,      0.2,     0.6,   -0.01,      0.191,    0.68,     -0.862))
_trfX(_ITRF92_,   _ETRF2000_, epoch=_E(2015),
                              xform=_X(  39.3,     53.7,     3.7,   -1.02,      2.106,   12.74,    -20.952),
                              rates=_R(  _0_0,      0.6,     1.4,   -0.01,      0.081,    0.49,     -0.812))
_trfX(_ITRF91_,   _ETRF2000_, epoch=_E(2015),
                              xform=_X(  27.3,     39.7,     9.7,   -2.42,      2.106,   12.74,    -20.952),
                              rates=_R(  _0_0,      0.6,     1.4,   -0.01,      0.081,    0.49,     -0.812))
_trfX(_ITRF90_,   _ETRF2000_, epoch=_E(2015),
                              xform=_X(  29.3,     43.7,    25.7,   -2.72,      2.106,   12.74,    -20.952),
                              rates=_R(  _0_0,      0.6,     1.4,   -0.01,      0.081,    0.49,     -0.812))
_trfX(_ITRF89_,   _ETRF2000_, epoch=_E(2015),
                              xform=_X(  24.3,     19.7,    63.7,   -6.12,      2.106,   12.74,    -20.952),
                              rates=_R(  _0_0,      0.6,     1.4,   -0.01,      0.081,    0.49,     -0.812))
_trfX(_ITRF88_,   _ETRF2000_, epoch=_E(2015),
                              xform=_X(  29.3,     55.7,    87.7,   -9.22,      2.006,   12.74,    -20.952),
                              rates=_R(  _0_0,      0.6,     1.4,   -0.01,      0.081,    0.49,     -0.812))

# GDA2020 "Geocentric Datum of Australia 2020 Technical Manual", v1.5, 2020-12-09, Table 3.3 and 3.4
# <https://www.ICSM.gov.AU/sites/default/files/2020-12/GDA2020%20Technical%20Manual%20V1.5_4.pdf>
# (the GDA2020 xforms are different but the rates are the same as GDA94, further below)
_trfX(_ITRF2014_, _GDA2020_,  epoch=_E(2020),
                              xform=_P_0_0s,
                              rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,       1.50379,  1.18346,   1.20716))
_trfX(_ITRF2008_, _GDA2020_,  epoch=_E(2020),
                              xform=_X(  13.79,     4.55,   15.22,   2.5,       0.2808,   0.2677,   -0.4638),
                              rates=_R(   1.42,     1.34,    0.9,    0.109,     1.5461,   1.182,     1.1551))
_trfX(_ITRF2005_, _GDA2020_,  epoch=_E(2020),
                              xform=_X(  40.32,   -33.85,  -16.72,   4.286,    -1.2893,  -0.8492,   -0.3342),
                              rates=_R(   2.25,    -0.62,   -0.56,   0.294,    -1.4707,  -1.1443,   -1.1701))
_trfX(_ITRF2000_, _GDA2020_,  epoch=_E(2020),
                              xform=_X(-105.52,    51.58,  231.68,   3.55,      4.2175,   6.3941,    0.8617),
                              rates=_R(  -4.66,     3.55,   11.24,   0.249,     1.7454,   1.4868,    1.224))

# see Table 2 in U{Dawson, J. & Woods, A. "ITRF to GDA94 coordinate transformations", Journal of Applied
# Geodesy 4 (2010), 189-199<https://www.ResearchGate.net/publication/258401581_ITRF_to_GDA94_coordinate_transformations>}
# (note, sign of rotations for GDA94 reversed as "Australia assumes rotation to be of coordinate axes",
# rather than the more conventional "position around the coordinate axes")
_trfX(_ITRF2008_, _GDA94_,    epoch=_E(1994),
                              xform=_X( -84.68,   -19.42,   32.01,   9.71,     -0.4254,   2.2578,    2.4015),
                              rates=_R(   1.42,     1.34,    0.9,    0.109,     1.5461,   1.182,     1.1551))
_trfX(_ITRF2005_, _GDA94_,    epoch=_E(1994),
                              xform=_X( -79.73,    -6.86,   38.03,   6.636,     0.0351,  -2.1211,   -2.1411),
                              rates=_R(   2.25,    -0.62,   -0.56,   0.294,    -1.4707,  -1.1443,   -1.1701))
_trfX(_ITRF2000_, _GDA94_,    epoch=_E(1994),
                              xform=_X( -45.91,   -29.85,  -20.37,   7.07,     -1.6705,   0.4594,    1.9356),
                              rates=_R(  -4.66,     3.55,   11.24,   0.249,     1.7454,   1.4868,    1.224))

# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/
# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83 and Pearson, C. & Snay, R. U{"Introducing
# HTDP 3.1 to transform coordinates across time and spatial reference frames"<https://Geodesy.NOAA.gov/
# TOOLS/Htdp/Pearson_Snay_2012.pdf> Table 7, 7th column
_trfX(_ITRF2008_, _NAD83_,    epoch=_E(1997),
                              xform=_X( 993.43, -1903.31, -526.55,   1.71504, -25.91467, -9.42645, -11.59935),
                              rates=_R(   0.79,    -0.6,    -1.34,  -0.10201,  -0.06667,  0.75744,   0.05133))
# see U{Quinsy QPS<https://confluence.QPS.NL/qinsy/files/latest/en/182618383/182618384/1/1579182881000/
# ITRF_Transformation_Parameters.xlsx>}, sheets ITRF and NAD83
_trfX(_ITRF2005_, _NAD83_,    epoch=_E(1997),
                              xform=_X( 996.3,  -1902.4,  -521.9,    0.775,   -25.915,   -9.426,   -11.599),
                              rates=_R(   0.5,     -0.6,    -1.3,   -0.10201,  -0.06667,  0.75744,   0.05133))
# see U{Solar, T. & Snay, R.A. "Transforming Positions and Velocities between the International Terrestrial Reference
# Frame of 2000 and North American Datum of 1983" (2004)<https://www.NGS.NOAA.gov/CORS/Articles/SolerSnayASCE.pdf>}
_trfX(_ITRF2000_, _NAD83_,    epoch=_E(1997),  # note NAD83(CORS96)
                              xform=_X( 995.6,  -1901.3,  -521.5,    0.615,   -25.915,   -9.426,   -11.599),
                              rates=_R(   0.7,     -0.7,    _0_5,   -0.182,    -0.06667,  0.75744,   0.05133))
_trfX(_ITRF90_,   _NAD83_,    epoch=_E(1997),
                              xform=_X( 973.0,  -1919.2,  -482.9,   -0.9,     -25.79,    -9.65,    -11.66),
                              rates=_R(  _0_0,     _0_0,    _0_0,   _0_0,      -0.053,    0.742,     0.032))
_trfX(_ITRF90_,   _WGS84_,    epoch=_E(1984),  # coverage
                              xform=_X(  60.0,   -517.0,  -223.0,  -11.0,      18.3,     -0.3,       7.0),
                              rates=_P_0_0s)

# equivalents U{"Transformations Between NAD83 and WGS84"<https://www.NGS.NOAA.gov/CORS/Articles/WGS84NAD83.pdf>}
trfXform(_NAD83cors96_, _NAD83_,    epoch=_E(1997), xform=_P_0_0s, rates=_P_0_0s)
trfXform(_WGS84g1150_,  _ITRF2000_, epoch=_E(2004), xform=_P_0_0s, rates=_P_0_0s)

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

if __name__ == _DMAIN_:

    def _main():
        from pygeodesy.basics import _args_kwds_names
        from pygeodesy.interns import _COLONSPACE_,_COMMA_, _NL_, _NLATvar_, _vs_
        from pygeodesy import printf
        from time import localtime

        D = typename(date2epoch)
        E = typename(epoch2date)
        y = localtime()[0]
        for m in range(1, 13):
            for d in (1, 15, _mDays[m] - 1, _mDays[m]):
                f = '%s(%d,%3d,%3d)' % (D, y, m, d)
                e = date2epoch(y, m, d)
                t = epoch2date(e)
                x = NN if t == (y, m, d) else _STAR_
                e = '%.3f' % (e,)
                e = '%s, %s(%s)' % (e, E, e)
                t = '%d,%3d,%3d' % t
                printf('# %s = %s = %s %s', f, e, t, x)

        # __doc__ of this file, force all into registry
        def _RFs():
            yield NN
            for t in RefFrames.toRepr(all=True).split(_NL_):
                t = t.strip(_COMMA_)
                n = t.split(_COLONSPACE_)[0].split(_DOT_)[1]
                r = RefFrames.get(n)
                x = len(r.Xforms()), -len(r.Xforms(inverse=True))
                yield '%s .Xforms=%s' % (t, x)

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

        X, t = (), 0  # all  form
        for r in RefFrames.values():
            X += tuple(r._Xto.values())
        for X in sorted(X):
            t += 1
            printf('#%4d %-24s xform=%r', t, X.name, X.xform)
            printf('#%29s rates=%r', _SPACE_, X.rates)

        t = _args_kwds_names(Transform.__init__)
        for n in TRFXform7Tuple._Names_:
            if n not in t:
                raise AssertionError(_SPACE_(n, _vs_, t))

    _main()
#   del _main

# **) MIT License
#
# Copyright (C) 2016-2026 -- mrJean1 at Gmail -- All Rights Reserved.
#
# Permission is hereby granted, free of charge, to any person obtaining a
# copy of this software and associated documentation files (the "Software"),
# to deal in the Software without restriction, including without limitation
# the rights to use, copy, modify, merge, publish, distribute, sublicense,
# and/or sell copies of the Software, and to permit persons to whom the
# Software is furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included
# in all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
# OTHER DEALINGS IN THE SOFTWARE.

# % python -m pygeodesy.trf
#
# date2epoch(2024,  1,  1) = 2024.003, epoch2date(2024.003) = 2024,  1,  1
# date2epoch(2024,  1, 15) = 2024.041, epoch2date(2024.041) = 2024,  1, 15
# date2epoch(2024,  1, 30) = 2024.082, epoch2date(2024.082) = 2024,  1, 30
# date2epoch(2024,  1, 31) = 2024.085, epoch2date(2024.085) = 2024,  1, 31
# date2epoch(2024,  2,  1) = 2024.087, epoch2date(2024.087) = 2024,  2,  2 *
# date2epoch(2024,  2, 15) = 2024.126, epoch2date(2024.126) = 2024,  2, 16 *
# date2epoch(2024,  2, 28) = 2024.161, epoch2date(2024.161) = 2024,  2, 28
# date2epoch(2024,  2, 29) = 2024.164, epoch2date(2024.164) = 2024,  3,  1 *
# date2epoch(2024,  3,  1) = 2024.167, epoch2date(2024.167) = 2024,  3,  2 *
# date2epoch(2024,  3, 15) = 2024.205, epoch2date(2024.205) = 2024,  3, 16 *
# date2epoch(2024,  3, 30) = 2024.246, epoch2date(2024.246) = 2024,  3, 31 *
# date2epoch(2024,  3, 31) = 2024.249, epoch2date(2024.249) = 2024,  4,  1 *
# date2epoch(2024,  4,  1) = 2024.251, epoch2date(2024.251) = 2024,  4,  1
# date2epoch(2024,  4, 15) = 2024.290, epoch2date(2024.290) = 2024,  4, 15
# date2epoch(2024,  4, 29) = 2024.328, epoch2date(2024.328) = 2024,  4, 29
# date2epoch(2024,  4, 30) = 2024.331, epoch2date(2024.331) = 2024,  4, 30
# date2epoch(2024,  5,  1) = 2024.333, epoch2date(2024.333) = 2024,  5,  1
# date2epoch(2024,  5, 15) = 2024.372, epoch2date(2024.372) = 2024,  5, 15
# date2epoch(2024,  5, 30) = 2024.413, epoch2date(2024.413) = 2024,  5, 30
# date2epoch(2024,  5, 31) = 2024.415, epoch2date(2024.415) = 2024,  6,  1 *
# date2epoch(2024,  6,  1) = 2024.418, epoch2date(2024.418) = 2024,  6,  2 *
# date2epoch(2024,  6, 15) = 2024.456, epoch2date(2024.456) = 2024,  6, 16 *
# date2epoch(2024,  6, 29) = 2024.495, epoch2date(2024.495) = 2024,  6, 30 *
# date2epoch(2024,  6, 30) = 2024.497, epoch2date(2024.497) = 2024,  7,  1 *
# date2epoch(2024,  7,  1) = 2024.500, epoch2date(2024.500) = 2024,  7,  1
# date2epoch(2024,  7, 15) = 2024.538, epoch2date(2024.538) = 2024,  7, 16 *
# date2epoch(2024,  7, 30) = 2024.579, epoch2date(2024.579) = 2024,  7, 30
# date2epoch(2024,  7, 31) = 2024.582, epoch2date(2024.582) = 2024,  7, 31
# date2epoch(2024,  8,  1) = 2024.585, epoch2date(2024.585) = 2024,  8,  1
# date2epoch(2024,  8, 15) = 2024.623, epoch2date(2024.623) = 2024,  8, 15
# date2epoch(2024,  8, 30) = 2024.664, epoch2date(2024.664) = 2024,  8, 31 *
# date2epoch(2024,  8, 31) = 2024.667, epoch2date(2024.667) = 2024,  9,  1 *
# date2epoch(2024,  9,  1) = 2024.669, epoch2date(2024.669) = 2024,  9,  2 *
# date2epoch(2024,  9, 15) = 2024.708, epoch2date(2024.708) = 2024,  9, 16 *
# date2epoch(2024,  9, 29) = 2024.746, epoch2date(2024.746) = 2024,  9, 30 *
# date2epoch(2024,  9, 30) = 2024.749, epoch2date(2024.749) = 2024, 10,  1 *
# date2epoch(2024, 10,  1) = 2024.751, epoch2date(2024.751) = 2024, 10,  1
# date2epoch(2024, 10, 15) = 2024.790, epoch2date(2024.790) = 2024, 10, 15
# date2epoch(2024, 10, 30) = 2024.831, epoch2date(2024.831) = 2024, 10, 30
# date2epoch(2024, 10, 31) = 2024.833, epoch2date(2024.833) = 2024, 10, 31
# date2epoch(2024, 11,  1) = 2024.836, epoch2date(2024.836) = 2024, 11,  1
# date2epoch(2024, 11, 15) = 2024.874, epoch2date(2024.874) = 2024, 11, 15
# date2epoch(2024, 11, 29) = 2024.913, epoch2date(2024.913) = 2024, 11, 29
# date2epoch(2024, 11, 30) = 2024.915, epoch2date(2024.915) = 2024, 12,  1 *
# date2epoch(2024, 12,  1) = 2024.918, epoch2date(2024.918) = 2024, 12,  2 *
# date2epoch(2024, 12, 15) = 2024.956, epoch2date(2024.956) = 2024, 12, 16 *
# date2epoch(2024, 12, 30) = 2024.997, epoch2date(2024.997) = 2024, 12, 31 *
# date2epoch(2024, 12, 31) = 2025.000, epoch2date(2025.000) = 2025,  1,  1 *

#   1 WGS84g1150@2004xITRF2000 xform=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
#                              rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
#   2 NAD83cors96@1997xNAD83   xform=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
#                              rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
#   3 ITRF88@2015xETRF2014     xform=xform(tx=-25.9, ty=3.0, tz=171.3, s=-11.89, sx=2.11, sy=13.806, sz=-20.38)
#                              rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
#   4 ITRF89@2015xETRF2000     xform=xform(tx=24.3, ty=19.7, tz=63.7, s=-6.12, sx=2.106, sy=12.74, sz=-20.952)
#                              rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
#   5 ITRF89@2015xETRF2014     xform=xform(tx=-30.9, ty=-33.0, tz=147.3, s=-8.79, sx=2.21, sy=13.806, sz=-20.38)
#                              rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
#   6 ITRF89@2015xETRF2020     xform=xform(tx=32.3, ty=33.9, tz=-148.7, s=9.21, sx=2.236, sy=13.494, sz=-19.218)
#                              rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
#   7 ITRF89@1989xETRF89       xform=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71)
#   8 ITRF90@1984xWGS84        xform=xform(tx=60.0, ty=-517.0, tz=-223.0, s=-11.0, sx=18.3, sy=-0.3, sz=7.0)
#                              rates=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
#   9 ITRF90@2015xETRF2000     xform=xform(tx=29.3, ty=43.7, tz=25.7, s=-2.72, sx=2.106, sy=12.74, sz=-20.952)
#                              rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
#  10 ITRF90@1989xETRF90       xform=xform(tx=19.0, ty=28.0, tz=-23.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.11, sy=0.57, sz=-0.71)
#  11 ITRF90@1997xNAD83        xform=xform(tx=973.0, ty=-1919.2, tz=-482.9, s=-0.9, sx=-25.79, sy=-9.65, sz=-11.66)
#                              rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=-0.053, sy=0.742, sz=0.032)
#  12 ITRF91@2015xETRF2000     xform=xform(tx=27.3, ty=39.7, tz=9.7, s=-2.42, sx=2.106, sy=12.74, sz=-20.952)
#                              rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
#  13 ITRF91@1989xETRF91       xform=xform(tx=21.0, ty=25.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68)
#  14 ITRF92@2015xETRF2000     xform=xform(tx=39.3, ty=53.7, tz=3.7, s=-1.02, sx=2.106, sy=12.74, sz=-20.952)
#                              rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
#  15 ITRF92@2015xETRF2014     xform=xform(tx=-15.9, ty=1.0, tz=87.3, s=-3.69, sx=2.21, sy=13.806, sz=-20.38)
#                              rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
#  16 ITRF92@2015xETRF2020     xform=xform(tx=17.3, ty=-0.1, tz=-88.7, s=4.11, sx=2.236, sy=13.494, sz=-19.218)
#                              rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
#  17 ITRF92@1989xETRF92       xform=xform(tx=38.0, ty=40.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.21, sy=0.52, sz=-0.68)
#  18 ITRF93@2015xETRF2000     xform=xform(tx=119.6, ty=49.9, tz=-10.9, s=-2.22, sx=5.466, sy=17.07, sz=-21.342)
#                              rates=rates(tx=2.9, ty=0.2, tz=0.6, s=-0.01, sx=0.191, sy=0.68, sz=-0.862)
#  19 ITRF93@2015xETRF2014     xform=xform(tx=64.4, ty=-2.8, tz=72.7, s=-4.89, sx=5.57, sy=18.136, sz=-20.77)
#                              rates=rates(tx=2.8, ty=0.1, tz=2.5, s=-0.12, sx=0.195, sy=0.721, sz=-0.84)
#  20 ITRF93@2015xETRF2020     xform=xform(tx=-63.0, ty=3.7, tz=-74.1, s=5.31, sx=-1.124, sy=9.164, sz=-18.828)
#                              rates=rates(tx=-2.8, ty=0.0, tz=-2.7, s=0.12, sx=-0.024, sy=0.329, sz=-0.683)
#  21 ITRF93@1989xETRF93       xform=xform(tx=19.0, ty=53.0, tz=-21.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.32, sy=0.78, sz=-0.67)
#  22 ITRF94@2015xETRF2000     xform=xform(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
#                              rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
#  23 ITRF94@2015xETRF2014     xform=xform(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
#                              rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
#  24 ITRF94@2015xETRF2020     xform=xform(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
#                              rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
#  25 ITRF94@1989xETRF94       xform=xform(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
#  26 ITRF96@1989xETRF96       xform=xform(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
#  27 ITRF97@1989xETRF97       xform=xform(tx=41.0, ty=41.0, tz=-49.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.2, sy=0.5, sz=-0.65)
#  28 ITRF2000@1994xGDA94      xform=xform(tx=-45.91, ty=-29.85, tz=-20.37, s=7.07, sx=-1.6705, sy=0.4594, sz=1.9356)
#                              rates=rates(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224)
#  29 ITRF2000@2015xETRF2000   xform=xform(tx=54.0, ty=51.0, tz=-48.0, s=0.0, sx=2.106, sy=12.74, sz=-20.592)
#                              rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.081, sy=0.49, sz=-0.792)
#  30 ITRF88@2015xETRF2000     xform=xform(tx=29.3, ty=55.7, tz=87.7, s=-9.22, sx=2.006, sy=12.74, sz=-20.952)
#                              rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
#  31 ITRF88@2015xETRF2020     xform=xform(tx=27.3, ty=-2.1, tz=-172.7, s=12.31, sx=2.336, sy=13.494, sz=-19.218)
#                              rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
#  32 ITRF96@2015xETRF2000     xform=xform(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
#                              rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
#  33 ITRF97@2015xETRF2000     xform=xform(tx=47.3, ty=55.7, tz=-4.3, s=-1.73, sx=2.106, sy=12.74, sz=-20.952)
#                              rates=rates(tx=0.0, ty=0.6, tz=1.4, s=-0.01, sx=0.081, sy=0.49, sz=-0.812)
#  34 ITRF2000@2015xETRF2014   xform=xform(tx=-1.2, ty=-1.7, tz=35.6, s=-2.67, sx=2.21, sy=13.806, sz=-20.02)
#                              rates=rates(tx=-0.1, ty=-0.1, tz=1.9, s=-0.11, sx=0.085, sy=0.531, sz=-0.77)
#  35 ITRF90@2015xETRF2014     xform=xform(tx=-25.9, ty=-9.0, tz=109.3, s=-5.39, sx=2.21, sy=13.806, sz=-20.38)
#                              rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
#  36 ITRF90@2015xETRF2020     xform=xform(tx=27.3, ty=9.9, tz=-110.7, s=5.81, sx=2.236, sy=13.494, sz=-19.218)
#                              rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
#  37 ITRF91@2015xETRF2014     xform=xform(tx=-27.9, ty=-13.0, tz=93.3, s=-5.09, sx=2.21, sy=13.806, sz=-20.38)
#                              rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
#  38 ITRF96@2015xETRF2014     xform=xform(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
#                              rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
#  39 ITRF97@2015xETRF2014     xform=xform(tx=-7.9, ty=3.0, tz=79.3, s=-4.4, sx=2.21, sy=13.806, sz=-20.38)
#                              rates=rates(tx=-0.1, ty=0.5, tz=3.3, s=-0.12, sx=0.085, sy=0.531, sz=-0.79)
#  40 ITRF2000@2015xETRF2020   xform=xform(tx=2.6, ty=2.6, tz=-37.0, s=3.09, sx=2.236, sy=13.494, sz=-19.578)
#                              rates=rates(tx=0.1, ty=0.2, tz=-2.1, s=0.11, sx=0.086, sy=0.519, sz=-0.753)
#  41 ITRF91@2015xETRF2020     xform=xform(tx=29.3, ty=13.9, tz=-94.7, s=5.51, sx=2.236, sy=13.494, sz=-19.218)
#                              rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
#  42 ITRF96@2015xETRF2020     xform=xform(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
#                              rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
#  43 ITRF97@2015xETRF2020     xform=xform(tx=9.3, ty=-2.1, tz=-80.7, s=4.82, sx=2.236, sy=13.494, sz=-19.218)
#                              rates=rates(tx=0.1, ty=-0.4, tz=-3.5, s=0.12, sx=0.086, sy=0.519, sz=-0.733)
#  44 ITRF2000@2020xGDA2020    xform=xform(tx=-105.52, ty=51.58, tz=231.68, s=3.55, sx=4.2175, sy=6.3941, sz=0.8617)
#                              rates=rates(tx=-4.66, ty=3.55, tz=11.24, s=0.249, sx=1.7454, sy=1.4868, sz=1.224)
#  45 ITRF2000@1988xITRF88     xform=xform(tx=2.47, ty=1.15, tz=-9.79, s=8.95, sx=0.1, sy=0.0, sz=-0.18)
#                              rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
#  46 ITRF2000@1988xITRF89     xform=xform(tx=2.97, ty=4.75, tz=-7.39, s=5.85, sx=0.0, sy=0.0, sz=-0.18)
#                              rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
#  47 ITRF2000@1988xITRF90     xform=xform(tx=2.47, ty=2.35, tz=-3.59, s=2.45, sx=0.0, sy=0.0, sz=-0.18)
#                              rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
#  48 ITRF2000@1988xITRF91     xform=xform(tx=26.7, ty=27.5, tz=-19.9, s=2.15, sx=0.0, sy=0.0, sz=-0.18)
#                              rates=rates(tx=0.0, ty=-0.6, tz=-1.4, s=0.01, sx=0.0, sy=0.0, sz=0.02)
#  49 ITRF2000@1988xITRF92     xform=xform(tx=1.47, ty=1.35, tz=-1.39, s=0.75, sx=0.0, sy=0.0, sz=-0.18)
#                              rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
#  50 ITRF2000@1988xITRF93     xform=xform(tx=12.7, ty=6.5, tz=-20.9, s=1.95, sx=-0.39, sy=0.8, sz=-1.14)
#                              rates=rates(tx=-2.9, ty=-0.2, tz=-0.6, s=0.01, sx=-0.11, sy=-0.19, sz=0.07)
#  51 ITRF2000@1997xITRF94     xform=xform(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
#  52 ITRF2000@1997xITRF96     xform=xform(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=0.02)
#  53 ITRF97@1997xITRF96       xform=xform(tx=-2.07, ty=-0.21, tz=9.95, s=-0.93496, sx=0.1267, sy=-0.22355, sz=-0.06065)
#                              rates=rates(tx=0.69, ty=-0.1, tz=1.86, s=-0.19201, sx=0.01347, sy=-0.01514, sz=0.00027)
#  54 ITRF2000@1997xITRF97     xform=xform(tx=0.67, ty=0.61, tz=-1.85, s=1.55, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.0, ty=-0.06, tz=-0.14, s=0.01, sx=0.0, sy=0.0, sz=-0.02)
#  55 ITRF2000@1997xNAD83      xform=xform(tx=995.6, ty=-1901.3, tz=-521.5, s=0.615, sx=-25.915, sy=-9.426, sz=-11.599)
#                              rates=rates(tx=0.7, ty=-0.7, tz=0.5, s=-0.182, sx=-0.06667, sy=0.75744, sz=0.05133)
#  56 ITRF2005@2015xETRF2000   xform=xform(tx=51.1, ty=51.7, tz=-80.8, s=1.6, sx=2.106, sy=12.74, sz=-20.592)
#                              rates=rates(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792)
#  57 ITRF2005@1989xETRF2005   xform=xform(tx=56.0, ty=48.0, tz=-37.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.054, sy=0.518, sz=-0.781)
#  58 ITRF2005@1994xGDA94      xform=xform(tx=-79.73, ty=-6.86, tz=38.03, s=6.636, sx=0.0351, sy=-2.1211, sz=-2.1411)
#                              rates=rates(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701)
#  59 ITRF2005@1997xNAD83      xform=xform(tx=996.3, ty=-1902.4, tz=-521.9, s=0.775, sx=-25.915, sy=-9.426, sz=-11.599)
#                              rates=rates(tx=0.5, ty=-0.6, tz=-1.3, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133)
#  60 ITRF2005@2015xETRF2014   xform=xform(tx=-4.1, ty=-1.0, tz=2.8, s=-1.07, sx=2.21, sy=13.806, sz=-20.02)
#                              rates=rates(tx=-0.3, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77)
#  61 ITRF2005@2015xETRF2020   xform=xform(tx=5.5, ty=1.9, tz=-4.2, s=1.49, sx=2.236, sy=13.494, sz=-19.578)
#                              rates=rates(tx=0.3, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753)
#  62 ITRF2005@2020xGDA2020    xform=xform(tx=40.32, ty=-33.85, tz=-16.72, s=4.286, sx=-1.2893, sy=-0.8492, sz=-0.3342)
#                              rates=rates(tx=2.25, ty=-0.62, tz=-0.56, s=0.294, sx=-1.4707, sy=-1.1443, sz=-1.1701)
#  63 ITRF2005@2000xITRF2000   xform=xform(tx=0.1, ty=-0.8, tz=-5.8, s=0.4, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=-0.2, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0)
#  64 ITRF2008@1994xGDA94      xform=xform(tx=-84.68, ty=-19.42, tz=32.01, s=9.71, sx=-0.4254, sy=2.2578, sz=2.4015)
#                              rates=rates(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551)
#  65 ITRF2008@1997xNAD83      xform=xform(tx=993.43, ty=-1903.31, tz=-526.55, s=1.71504, sx=-25.91467, sy=-9.42645, sz=-11.59935)
#                              rates=rates(tx=0.79, ty=-0.6, tz=-1.34, s=-0.10201, sx=-0.06667, sy=0.75744, sz=0.05133)
#  66 ITRF96@1997xNAD83        xform=xform(tx=991.0, ty=-190.72, tz=-512.9, s=0.0, sx=25.79, sy=9.65, sz=11.66)
#                              rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0532, sy=-0.7423, sz=-0.0316)
#  67 ITRF2008@2015xETRF2000   xform=xform(tx=53.6, ty=50.8, tz=-85.5, s=2.54, sx=2.106, sy=12.74, sz=-20.592)
#                              rates=rates(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.081, sy=0.49, sz=-0.792)
#  68 ITRF2008@2015xETRF2014   xform=xform(tx=-1.6, ty=-1.9, tz=-1.9, s=-0.13, sx=2.21, sy=13.806, sz=-20.02)
#                              rates=rates(tx=0.0, ty=0.0, tz=0.1, s=-0.03, sx=0.085, sy=0.531, sz=-0.77)
#  69 ITRF2008@2015xETRF2020   xform=xform(tx=3.0, ty=2.8, tz=0.5, s=0.55, sx=2.236, sy=13.494, sz=-19.578)
#                              rates=rates(tx=0.0, ty=0.1, tz=-0.3, s=0.03, sx=0.086, sy=0.519, sz=-0.753)
#  70 ITRF2008@2020xGDA2020    xform=xform(tx=13.79, ty=4.55, tz=15.22, s=2.5, sx=0.2808, sy=0.2677, sz=-0.4638)
#                              rates=rates(tx=1.42, ty=1.34, tz=0.9, s=0.109, sx=1.5461, sy=1.182, sz=1.1551)
#  71 ITRF2008@2000xITRF2000   xform=xform(tx=-1.9, ty=-1.7, tz=-10.5, s=1.34, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.1, ty=0.1, tz=-1.8, s=0.08, sx=0.0, sy=0.0, sz=0.0)
#  72 ITRF2008@2000xITRF88     xform=xform(tx=22.8, ty=2.6, tz=-125.2, s=10.41, sx=0.1, sy=0.0, sz=0.06)
#                              rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
#  73 ITRF2008@2000xITRF89     xform=xform(tx=27.8, ty=38.6, tz=-101.2, s=7.31, sx=0.0, sy=0.0, sz=0.06)
#                              rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
#  74 ITRF2008@2000xITRF90     xform=xform(tx=22.8, ty=14.6, tz=-63.2, s=3.91, sx=0.0, sy=0.0, sz=0.06)
#                              rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
#  75 ITRF2008@2000xITRF91     xform=xform(tx=24.8, ty=18.6, tz=-47.2, s=3.61, sx=0.0, sy=0.0, sz=0.06)
#                              rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
#  76 ITRF2008@2000xITRF92     xform=xform(tx=12.8, ty=4.6, tz=-41.2, s=2.21, sx=0.0, sy=0.0, sz=0.06)
#                              rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
#  77 ITRF2008@2000xITRF93     xform=xform(tx=-24.0, ty=2.4, tz=-38.6, s=3.41, sx=-1.71, sy=-1.48, sz=-0.3)
#                              rates=rates(tx=-2.8, ty=-0.1, tz=-2.4, s=0.09, sx=-0.11, sy=-0.19, sz=0.07)
#  78 ITRF2008@2000xITRF94     xform=xform(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
#                              rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
#  79 ITRF2008@2000xITRF96     xform=xform(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
#                              rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
#  80 ITRF2008@2000xITRF97     xform=xform(tx=4.8, ty=2.6, tz=-33.2, s=2.92, sx=0.0, sy=0.0, sz=0.06)
#                              rates=rates(tx=0.1, ty=-0.5, tz=-3.2, s=0.09, sx=0.0, sy=0.0, sz=0.02)
#  81 ITRF2008@2005xITRF2005   xform=xform(tx=-0.5, ty=-0.9, tz=-4.7, s=0.94, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.3, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
#  82 ITRF2014@2015xETRF2000   xform=xform(tx=55.2, ty=52.7, tz=-83.6, s=2.67, sx=2.106, sy=12.74, sz=-20.592)
#                              rates=rates(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.081, sy=0.49, sz=-0.792)
#  83 ITRF2014@2015xETRF2014   xform=xform(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=2.21, sy=13.806, sz=-20.02)
#                              rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.085, sy=0.531, sz=-0.77)
#  84 ITRF2014@2015xETRF2020   xform=xform(tx=1.4, ty=0.9, tz=-1.4, s=0.42, sx=2.236, sy=13.494, sz=-19.578)
#                              rates=rates(tx=0.0, ty=0.1, tz=-0.2, s=0.0, sx=0.086, sy=0.519, sz=-0.753)
#  85 ITRF2014@2020xGDA2020    xform=unity(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=1.50379, sy=1.18346, sz=1.20716)
#  86 ITRF2014@2010xITRF2000   xform=xform(tx=0.7, ty=1.2, tz=-26.1, s=2.12, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.1, ty=0.1, tz=-1.9, s=0.11, sx=0.0, sy=0.0, sz=0.0)
#  87 ITRF2014@2010xITRF2005   xform=xform(tx=2.6, ty=1.0, tz=-2.3, s=0.92, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.3, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
#  88 ITRF2014@2010xITRF2008   xform=xform(tx=1.6, ty=1.9, tz=2.4, s=-0.02, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.0, ty=0.0, tz=-0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
#  89 ITRF2014@2010xITRF88     xform=xform(tx=25.4, ty=-0.5, tz=-154.8, s=11.29, sx=0.1, sy=0.0, sz=0.26)
#                              rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
#  90 ITRF2014@2010xITRF89     xform=xform(tx=30.4, ty=35.5, tz=-130.8, s=8.19, sx=0.0, sy=0.0, sz=0.26)
#                              rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
#  91 ITRF2014@2010xITRF90     xform=xform(tx=25.4, ty=11.5, tz=-92.8, s=4.79, sx=0.0, sy=0.0, sz=0.26)
#                              rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
#  92 ITRF2014@2010xITRF91     xform=xform(tx=27.4, ty=15.5, tz=-76.8, s=4.49, sx=0.0, sy=0.0, sz=0.26)
#                              rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
#  93 ITRF2014@2010xITRF92     xform=xform(tx=15.4, ty=1.5, tz=-70.8, s=3.09, sx=0.0, sy=0.0, sz=0.26)
#                              rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
#  94 ITRF2014@2010xITRF93     xform=xform(tx=-50.4, ty=3.3, tz=-60.2, s=4.29, sx=-2.81, sy=-3.38, sz=0.4)
#                              rates=rates(tx=-2.8, ty=-0.1, tz=-2.5, s=0.12, sx=-0.11, sy=-0.19, sz=0.07)
#  95 ITRF2014@2010xITRF94     xform=xform(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
#                              rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
#  96 ITRF2014@2010xITRF96     xform=xform(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
#                              rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
#  97 ITRF2014@2010xITRF97     xform=xform(tx=7.4, ty=-0.5, tz=-62.8, s=3.8, sx=0.0, sy=0.0, sz=0.26)
#                              rates=rates(tx=0.1, ty=-0.5, tz=-3.3, s=0.12, sx=0.0, sy=0.0, sz=0.02)
#  98 ITRF2020@2015xETRF2000   xform=xform(tx=53.8, ty=51.8, tz=-82.2, s=2.25, sx=2.106, sy=12.74, sz=-20.592)
#                              rates=rates(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.081, sy=0.49, sz=-0.792)
#  99 ITRF2020@2015xETRF2014   xform=xform(tx=-1.4, ty=-0.9, tz=1.4, s=0.42, sx=2.21, sy=13.806, sz=-20.02)
#                              rates=rates(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.085, sy=0.531, sz=-0.77)
# 100 ITRF2020@2015xETRF2020   xform=xform(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=2.236, sy=13.494, sz=-19.578)
#                              rates=rates(tx=0.0, ty=0.0, tz=0.0, s=0.0, sx=0.086, sy=0.519, sz=-0.753)
# 101 ITRF2020@2015xITRF2000   xform=xform(tx=-0.2, ty=0.8, tz=-34.2, s=2.25, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.1, ty=0.0, tz=-1.7, s=0.11, sx=0.0, sy=0.0, sz=0.0)
# 102 ITRF2020@2015xITRF2005   xform=xform(tx=2.7, ty=0.1, tz=-1.4, s=0.65, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.3, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
# 103 ITRF2020@2015xITRF2008   xform=xform(tx=0.2, ty=1.0, tz=3.3, s=-0.29, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.0, ty=-0.1, tz=0.1, s=0.03, sx=0.0, sy=0.0, sz=0.0)
# 104 ITRF2020@2015xITRF2014   xform=xform(tx=-1.4, ty=-0.9, tz=1.4, s=-0.42, sx=0.0, sy=0.0, sz=0.0)
#                              rates=rates(tx=0.0, ty=-0.1, tz=0.2, s=0.0, sx=0.0, sy=0.0, sz=0.0)
# 105 ITRF2020@2015xITRF88     xform=xform(tx=24.5, ty=-3.9, tz=-169.9, s=11.47, sx=0.1, sy=0.0, sz=0.36)
#                              rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
# 106 ITRF2020@2015xITRF89     xform=xform(tx=29.5, ty=32.1, tz=-145.9, s=8.37, sx=0.0, sy=0.0, sz=0.36)
#                              rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
# 107 ITRF2020@2015xITRF90     xform=xform(tx=24.5, ty=8.1, tz=-107.9, s=4.97, sx=0.0, sy=0.0, sz=0.36)
#                              rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
# 108 ITRF2020@2015xITRF91     xform=xform(tx=26.5, ty=12.1, tz=-91.9, s=4.67, sx=0.0, sy=0.0, sz=0.36)
#                              rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
# 109 ITRF2020@2015xITRF92     xform=xform(tx=14.5, ty=-1.9, tz=-85.9, s=3.27, sx=0.0, sy=0.0, sz=0.36)
#                              rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
# 110 ITRF2020@2015xITRF93     xform=xform(tx=-65.8, ty=1.9, tz=-71.3, s=4.47, sx=-3.36, sy=-4.33, sz=0.75)
#                              rates=rates(tx=-2.8, ty=-0.2, tz=-2.3, s=0.12, sx=-0.11, sy=-0.19, sz=0.07)
# 111 ITRF2020@2015xITRF94     xform=xform(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
#                              rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
# 112 ITRF2020@2015xITRF96     xform=xform(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
#                              rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
# 113 ITRF2020@2015xITRF97     xform=xform(tx=6.5, ty=-3.9, tz=-77.9, s=3.98, sx=0.0, sy=0.0, sz=0.36)
#                              rates=rates(tx=0.1, ty=-0.6, tz=-3.1, s=0.12, sx=0.0, sy=0.0, sz=0.02)
