def _callname(name, class_name, self_name, up=1): # imported by .points
'''(INTERNAL) Assemble the name for an invokation.
'''
n, c = class_name, callername(up=up + 1)
if c:
n = _dot_(n, _item_ps(c, name))
if self_name:
n = '%s %r' % (n, self_name)
return n
def toRepr(self, **kwds): # PYCHOK expected
'''(INTERNAL) I{Could be overloaded}.
@kwarg kwds: Optional, keyword arguments.
@return: C{toStr}() with keyword arguments (as C{str}).
'''
t = self.toStr(**kwds).lstrip('([{').rstrip('}])')
return _item_ps(self.classname, t) # XXX (self.named, t)
def _ll2datum(ll, datum, name):
'''(INTERNAL) Convert datum if needed.
'''
if datum not in (None, ll.datum):
try:
ll = ll.convertDatum(datum)
except AttributeError:
raise _TypeError(name,
ll,
txt=_item_ps(_no_convertDatum_, datum.name))
return ll
def unstr(name, *args, **kwds):
'''Return the string representation of an invokation.
@arg name: Function, method or class name (C{str}).
@arg args: Optional positional arguments.
@kwarg kwds: Optional keyword arguments.
@return: Representation (C{str}).
'''
t = reprs(args, fmt=_g) + pairs(sorted(kwds.items()))
return _item_ps(name, _COMMA_SPACE_.join(t))
def toRepr(self, prec=6, sep=_COMMA_SPACE_, **unused): # PYCHOK signature
'''Return the -Tuple items as C{name=value} string(s).
@kwarg prec: The C{float} precision, number of decimal digits (0..9).
Trailing zero decimals are stripped for B{C{prec}} values
of 1 and above, but kept for negative B{C{prec}} values.
@kwarg sep: Optional separator to join (C{str}).
@return: Tuple items (C{str}).
'''
return _item_ps(self.named, sep.join(pairs(self.items(), prec=prec)))
def _latlon3(self, LatLon, datum):
'''(INTERNAL) Convert cached LatLon
'''
ll = self._latlon
if LatLon is None:
if datum and datum != ll.datum:
raise _TypeError(latlon=ll,
txt=_item_ps(_no_convertDatum_, datum.name))
return _xnamed(LatLonDatum3Tuple(ll.lat, ll.lon, ll.datum),
ll.name)
else:
_xsubclassof(_LLEB, LatLon=LatLon)
ll = _xnamed(LatLon(ll.lat, ll.lon, datum=ll.datum), ll.name)
return _ll2datum(ll, datum, _LatLon_)
def toLatLon(self, LatLon=None, datum=Datums.WGS84):
'''Convert this OSGR coordinate to an (ellipsoidal) geodetic
point.
While OS grid references are based on the OSGB36 datum, the
I{Ordnance Survey} have deprecated the use of OSGB36 for
lat-/longitude coordinates (in favour of WGS84). Hence, this
method returns WGS84 by default with OSGB36 as an option,
U{see<https://www.OrdnanceSurvey.co.UK/blog/2014/12/2>}.
I{Note formulation implemented here due to Thomas, Redfearn,
etc. is as published by OS, but is inferior to Krüger as
used by e.g. Karney 2011.}
@kwarg LatLon: Optional ellipsoidal class to return the
geodetic point (C{LatLon}) or C{None}.
@kwarg datum: Optional datum to convert to (L{Datum},
L{Ellipsoid}, L{Ellipsoid2}, L{Ellipsoid2}
or L{a_f2Tuple}).
@return: The geodetic point (B{C{LatLon}}) or a
L{LatLonDatum3Tuple}C{(lat, lon, datum)}
if B{C{LatLon}} is C{None}.
@raise OSGRError: No convergence.
@raise TypeError: If B{C{LatLon}} is not ellipsoidal or
B{C{datum}} is invalid or conversion failed.
@example:
>>> from pygeodesy import ellipsoidalVincenty as eV
>>> g = Osgr(651409.903, 313177.270)
>>> p = g.toLatLon(eV.LatLon) # 52°39′28.723″N, 001°42′57.787″E
>>> # to obtain (historical) OSGB36 lat-/longitude point
>>> p = g.toLatLon(eV.LatLon, datum=Datums.OSGB36) # 52°39′27.253″N, 001°43′04.518″E
'''
if self._latlon:
return self._latlon3(LatLon, datum)
E = self.datum.ellipsoid # _Datums_OSGB36.ellipsoid, Airy130
a_F0 = E.a * _F0
b_F0 = E.b * _F0
e, n = self.easting, self.northing
n_N0 = n - _N0
a, m = _A0, n_N0
sa = Fsum(a)
for self._iteration in range(1, _TRIPS):
a = sa.fsum_(m / a_F0)
m = n_N0 - b_F0 * _M(E.Mabcd, a) # meridional arc
if abs(m) < _10um:
break
else:
t = _dot_(_item_ps(self.classname, self.toStr(prec=-3)),
self.toLatLon.__name__)
raise OSGRError(_no_convergence_, txt=t)
sa, ca = sincos2(a)
s = E.e2s2(sa) # r, v = E.roc2_(sa, _F0)
v = a_F0 / sqrt(s) # nu
r = v * E.e12 / s # rho = a_F0 * E.e12 / pow(s, 1.5) == a_F0 * E.e12 / (s * sqrt(s))
vr = v / r # == s / E.e12
x2 = vr - 1 # η2
ta = tan(a)
v3, v5, v7 = fpowers(v, 7, 3) # PYCHOK false!
ta2, ta4, ta6 = fpowers(ta**2, 3) # PYCHOK false!
tar = ta / r
V4 = (a, tar / (2 * v), tar / (24 * v3) * fdot(
(1, 3, -9), 5 + x2, ta2, ta2 * x2), tar / (720 * v5) * fdot(
(61, 90, 45), 1, ta2, ta4))
csa = 1.0 / ca
X5 = (_B0, csa / v, csa / (6 * v3) * fsum_(vr, ta2, ta2),
csa / (120 * v5) * fdot(
(5, 28, 24), 1, ta2, ta4), csa / (5040 * v7) * fdot(
(61, 662, 1320, 720), 1, ta2, ta4, ta6))
d, d2, d3, d4, d5, d6, d7 = fpowers(e - _E0, 7) # PYCHOK false!
a = fdot(V4, 1, -d2, d4, -d6)
b = fdot(X5, 1, d, -d3, d5, -d7)
r = _LLEB(degrees90(a),
degrees180(b),
datum=self.datum,
name=self.name)
r._iteration = self._iteration # only ellipsoidal LatLon
self._latlon = r
return self._latlon3(LatLon, datum)
def toRepr(self, prec=6, fmt=_Fmt): # PYCHOK _Named
'''Like C{repr(dict)} but with C{name} and C{floats} formatting by C{fstr}.
'''
t = pairs(self.items(), prec=prec, fmt=fmt, sep=_EQUAL_)
return _item_ps(self.name, _COMMA_SPACE_.join(sorted(t)))
def __repr__(self):
return _item_ps(self.named, int.__repr__(self))
def __str__(self):
from pygeodesy.named import classname
return _item_ps(classname(self, prefixed=True), NN)
def _error(fun, lat, lon, e):
'''(INTERNAL) Format an error
'''
return _item_cs(_item_ps(fun.__name__, fstr((lat, lon))), e)