# Coverage for pygeodesy/lcc.py : 96%

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See U{LCC<https://WikiPedia.org/wiki/Lambert_conformal_conic_projection>}, U{Lambert Conformal Conic to Geographic Transformation Formulae <https://www.Linz.govt.NZ/data/geodetic-system/coordinate-conversion/ projection-conversions/lambert-conformal-conic-geographic>}, U{Lambert Conformal Conic Projection <https://MathWorld.Wolfram.com/LambertConformalConicProjection.html>} and John P. Snyder U{'Map Projections - A Working Manual' <https://Pubs.USGS.gov/pp/1395/report.pdf>}, 1987, pp 107-109. @newfield example: Example, Examples @var Conics.Be08Lb: Conic(name='Be08Lb', lat0=50.797815, lon0=4.35921583, par1=49.8333339, par2=51.1666672, E0=649328, N0=665262, k0=1, SP=2, datum=Datum(name='GRS80', ellipsoid=Ellipsoids.GRS80, transform=Transforms.WGS84), @var Conics.Be72Lb: Conic(name='Be72Lb', lat0=90, lon0=4.3674867, par1=49.8333339, par2=51.1666672, E0=150000.013, N0=5400088.438, k0=1, SP=2, datum=Datum(name='NAD83', ellipsoid=Ellipsoids.GRS80, transform=Transforms.NAD83), @var Conics.Fr93Lb: Conic(name='Fr93Lb', lat0=46.5, lon0=3, par1=49, par2=44, E0=700000, N0=6600000, k0=1, SP=2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84), @var Conics.MaNLb: Conic(name='MaNLb', lat0=33.3, lon0=-5.4, par1=31.73, par2=34.87, E0=500000, N0=300000, k0=1, SP=2, datum=Datum(name='NTF', ellipsoid=Ellipsoids.Clarke1880IGN, transform=Transforms.NTF), @var Conics.MxLb: Conic(name='MxLb', lat0=12, lon0=-102, par1=17.5, par2=29.5, E0=2500000, N0=0, k0=1, SP=2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84), @var Conics.PyT_Lb: Conic(name='PyT_Lb', lat0=46.8, lon0=2.33722917, par1=45.8989389, par2=47.6960144, E0=600000, N0=200000, k0=1, SP=2, datum=Datum(name='NTF', ellipsoid=Ellipsoids.Clarke1880IGN, transform=Transforms.NTF), @var Conics.USA_Lb: Conic(name='USA_Lb', lat0=23, lon0=-96, par1=33, par2=45, E0=0, N0=0, k0=1, SP=2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84), @var Conics.WRF_Lb: Conic(name='WRF_Lb', lat0=40, lon0=-97, par1=33, par2=45, E0=0, N0=0, k0=1, SP=2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84) ''' # make sure int/int division yields float quotient, see .basics from __future__ import division from pygeodesy.basics import copysign, _xinstanceof, _xsubclassof from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB from pygeodesy.datums import Datums, _ellipsoidal_datum from pygeodesy.errors import _IsnotError, _ValueError from pygeodesy.interns import EPS, NN, PI_2, _COMMASPACE_, _ellipsoidal_, \ _EPS0__2, _float as _F, _GRS80_, _k0_, _lat0_, \ _lon0_, _m_, _NAD83_, _NTF_, _SPACE_, _WGS84_, \ _0_0, _0_5, _1_0, _90_0 from pygeodesy.interns import _C_ # PYCHOK used! from pygeodesy.lazily import _ALL_LAZY from pygeodesy.named import _lazyNamedEnumItem as _lazy, _NamedBase, \ _NamedEnum, _NamedEnumItem, nameof, _xnamed from pygeodesy.namedTuples import EasNor3Tuple, LatLonDatum3Tuple, \ LatLon2Tuple, _LL4Tuple, PhiLam2Tuple from pygeodesy.props import Property_RO, _update_all from pygeodesy.streprs import Fmt, _fstrENH2, _xzipairs from pygeodesy.units import Easting, Height, Lam_, Northing, Phi_, Scalar_ from pygeodesy.utily import degrees90, degrees180, sincos2, tanPI_2_2 from math import atan, hypot, log, radians, sin, sqrt __all__ = _ALL_LAZY.lcc __version__ = '21.01.24' _E0_ = 'E0' _N0_ = 'N0' _par1_ = 'par1' _par2_ = 'par2' _SP_ = 'SP' class Conic(_NamedEnumItem): '''Lambert conformal conic projection (1- or 2-SP). ''' _auth = NN # authorization (C{str}) _datum = None # datum (L{Datum}) _name = NN # conic (L{Conic}) _e = _0_0 # ellipsoid excentricity (C{float}) _E0 = _0_0 # false easting (C{float}) _k0 = _1_0 # scale factor (C{float}) _N0 = _0_0 # false northing (C{float}) _SP = 0 # 1- or 2-SP (C{int}) _opt3 = _0_0 # optional, longitude (C{radians}) _par1 = _0_0 # 1st std parallel (C{radians}) _par2 = _0_0 # 2nd std parallel (C{radians}) _phi0 = _0_0 # origin lat (C{radians}) _lam0 = _0_0 # origin lon (C{radians}) _aF = _0_0 # precomputed F (C{float}) _n = _0_0 # precomputed n (C{float}) _n_ = _0_0 # precomputed 1 / n (C{float}) _r0 = _0_0 # precomputed rho0 (C{float}) def __init__(self, latlon0, par1, par2=None, E0=0, N0=0, k0=1, opt3=0, name=NN, auth=NN): '''New Lambert conformal conic projection. @arg latlon0: Origin with (ellipsoidal) datum (C{LatLon}). @arg par1: First standard parallel (C{degrees90}). @kwarg par2: Optional, second standard parallel (C{degrees90}). @kwarg E0: Optional, false easting (C{meter}). @kwarg N0: Optional, false northing (C{meter}). @kwarg k0: Optional scale factor (C{scalar}). @kwarg opt3: Optional meridian (C{degrees180}). @kwarg name: Optional name of the conic (C{str}). @kwarg auth: Optional authentication authority (C{str}). @return: A Lambert projection (L{Conic}). @raise TypeError: Non-ellipsoidal B{C{latlon0}}. @raise ValueError: Invalid B{C{par1}}, B{C{par2}}, B{C{E0}}, B{C{N0}}, B{C{k0}} or B{C{opt3}}. @example: >>> from pygeodesy import Conic, Datums, ellipsoidalNvector >>> ll0 = ellipsoidalNvector.LatLon(23, -96, datum=Datums.NAD27) >>> Snyder = Conic(ll0, 33, 45, E0=0, N0=0, name='Snyder') ''' if latlon0 is not None: _xinstanceof(_LLEB, latlon0=latlon0) self._phi0, self._lam0 = latlon0.philam self._par1 = Phi_(par1=par1) self._par2 = self._par1 if par2 is None else Phi_(par2=par2) if k0 != 1: self._k0 = Scalar_(k0=k0) if E0: self._E0 = Northing(E0=E0, falsed=True) if N0: self._N0 = Easting(N0=N0, falsed=True) if opt3: self._opt3 = Lam_(opt3=opt3) self.toDatum(latlon0.datum)._dup2(self) self._register(Conics, name) elif name: self.name = name if auth: self._auth = str(auth) @Property_RO def auth(self): '''Get the authentication authority (C{str}). ''' return self._auth @Property_RO def datum(self): '''Get the datum (L{Datum}). ''' return self._datum @Property_RO def E0(self): '''Get the false easting (C{meter}). ''' return self._E0 @Property_RO def k0(self): '''Get scale factor (C{float}). ''' return self._k0 @Property_RO def lat0(self): '''Get the origin latitude (C{degrees90}). ''' return degrees90(self._phi0) @Property_RO def latlon0(self): '''Get the central origin (L{LatLon2Tuple}C{(lat, lon)}). ''' return LatLon2Tuple(self.lat0, self.lon0, name=self.name) @Property_RO def lam0(self): '''Get the central meridian (C{radians}). ''' return self._lam0 @Property_RO def lon0(self): '''Get the central meridian (C{degrees180}). ''' return degrees180(self._lam0) @Property_RO def N0(self): '''Get the false northing (C{meter}). ''' return self._N0 @Property_RO def name2(self): '''Get the conic and datum names as "conic.datum" (C{str}). ''' return self._DOT_(self.datum.name) @Property_RO def opt3(self): '''Get the optional meridian (C{degrees180}). ''' return degrees180(self._opt3) @Property_RO def par1(self): '''Get the 1st standard parallel (C{degrees90}). ''' return degrees90(self._par1) @Property_RO def par2(self): '''Get the 2nd standard parallel (C{degrees90}). ''' return degrees90(self._par2) @Property_RO def phi0(self): '''Get the origin latitude (C{radians}). ''' return self._phi0 @Property_RO def philam0(self): '''Get the central origin (L{PhiLam2Tuple}C{(phi, lam)}). ''' return PhiLam2Tuple(self.phi0, self.lam0, name=self.name) @Property_RO def SP(self): '''Get the number of standard parallels (C{int}). ''' return self._SP def toDatum(self, datum): '''Convert this conic to the given datum. @arg datum: Ellipsoidal datum to use (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @return: Converted conic, unregistered (L{Conic}). @raise TypeError: Non-ellipsoidal B{C{datum}}. ''' d = _ellipsoidal_datum(datum, name=self.name) E = d.ellipsoid if not E.isEllipsoidal: raise _IsnotError(_ellipsoidal_, datum=datum) c = self if c._e != E.e or c._datum != d: c = Conic(None, 0, name=self._name) self._dup2(c) c._datum = d c._e = E.e if abs(c._par1 - c._par2) < EPS: m1 = c._mdef(c._phi0) t1 = c._tdef(c._phi0) t0 = t1 k = 1 # _1_0 n = sin(c._phi0) sp = 1 else: m1 = c._mdef(c._par1) m2 = c._mdef(c._par2) t1 = c._tdef(c._par1) t2 = c._tdef(c._par2) t0 = c._tdef(c._phi0) k = c._k0 n = (log(m1) - log(m2)) \ / (log(t1) - log(t2)) sp = 2 F = m1 / (n * pow(t1, n)) c._aF = k * E.a * F c._n = n c._n_ = _1_0 / n c._r0 = c._rdef(t0) c._SP = sp return c convertDatum = toDatum # synonymous def toStr(self, prec=8): # PYCHOK expected '''Return this conic as a string. @kwarg prec: Optional number of decimals, unstripped (C{int}). @return: Conic attributes (C{str}). ''' if self._SP == 1: return self._instr(prec, _lat0_, _lon0_, _par1_, _E0_, _N0_, _k0_, _SP_, datum=self.datum) else: return self._instr(prec, _lat0_, _lon0_, _par1_, _par2_, _E0_, _N0_, _k0_, _SP_, datum=self.datum) def _dup2(self, c): '''(INTERNAL) Copy this conic to C{c}. @arg c: Duplicate (L{Conic}). ''' _update_all(c) c._auth = self._auth c._datum = self._datum c._e = self._e c._E0 = self._E0 c._k0 = self._k0 c._N0 = self._N0 c._SP = self._SP c._par1 = self._par1 c._par2 = self._par2 c._phi0 = self._phi0 c._lam0 = self._lam0 c._opt3 = self._opt3 c._aF = self._aF c._n = self._n c._n_ = self._n_ c._r0 = self._r0 def _mdef(self, a): '''(INTERNAL) Compute m(a). ''' s, c = sincos2(a) s = _1_0 - (s * self._e)**2 return (c / sqrt(s)) if s > _EPS0__2 else _0_0 def _pdef(self, a): '''(INTERNAL) Compute p(a). ''' s = self._e * sin(a) return pow((_1_0 - s) / (_1_0 + s), self._e * _0_5) def _rdef(self, t): '''(INTERNAL) Compute r(t). ''' return self._aF * pow(t, self._n) def _tdef(self, a): '''(INTERNAL) Compute t(lat). ''' return max(_0_0, tanPI_2_2(-a) / self._pdef(a)) def _xdef(self, t_x): '''(INTERNAL) Compute x(t_x). ''' return PI_2 - 2 * atan(t_x) # XXX + self._phi0 Conic._name = Conic.__name__ class Conics(_NamedEnum): '''(INTERNAL) L{Conic} registry, I{must} be a sub-class to accommodate the L{_LazyNamedEnumItem} properties. ''' def _Lazy(self, lat, lon, datum_name, *args, **kwds): '''(INTERNAL) Instantiate the L{Conic}. ''' return Conic(_LLEB(lat, lon, datum=Datums.get(datum_name)), *args, **kwds) Conics = Conics(Conic) # PYCHOK singleton '''Some pre-defined L{Conic}s, all I{lazily} instantiated.''' Conics._assert( # <https://SpatialReference.org/ref/sr-org/...> # AsLb = _lazy('AsLb', -14.2666667, 170, _NAD27_, _0_0, _0_0, # E0=_F(500000), N0=_0_0, auth='EPSG:2155'), # American Samoa ... SP=1 ! Be08Lb = _lazy('Be08Lb', 50.7978150, 4.359215833, _GRS80_, _F(49.8333339), _F(51.1666672), E0=_F(649328.0), N0=_F(665262.0), auth='EPSG:9802'), # Belgium Be72Lb = _lazy('Be72Lb', _90_0, 4.3674867, _NAD83_, _F(49.8333339), _F(51.1666672), E0=_F(150000.013), N0=_F(5400088.438), auth='EPSG:31370'), # Belgium Fr93Lb = _lazy('Fr93Lb', 46.5, 3, _WGS84_, _F(49), _F(44), E0=_F(700000), N0=_F(6600000), auth='EPSG:2154'), # RFG93, France MaNLb = _lazy('MaNLb', 33.3, -5.4, _NTF_, _F(31.73), _F(34.87), E0=_F(500000), N0=_F(300000)), # Marocco MxLb = _lazy('MxLb', 12, -102, _WGS84_, _F(17.5), _F(29.5), E0=_F(2500000), N0=_0_0, auth='EPSG:2155'), # Mexico PyT_Lb = _lazy('PyT_Lb', 46.8, 2.33722917, _NTF_, _F(45.89893890000052), _F(47.69601440000037), E0=_F(600000), N0=_F(200000), auth='Test'), # France? USA_Lb = _lazy('USA_Lb', 23, -96, _WGS84_, _F(33), _F(45), E0=_0_0, N0=_0_0), # Conterminous, contiguous USA? WRF_Lb = _lazy('WRF_Lb', 40, -97, _WGS84_, _F(33), _F(45), E0=_0_0, N0=_0_0, auth='EPSG:4326') # World ) class LCCError(_ValueError): '''Lambert Conformal Conic C{LCC} or other L{Lcc} issue. ''' pass class Lcc(_NamedBase): '''Lambert conformal conic East-/Northing location. ''' _conic = None # Lambert projection (L{Conic}) _easting = _0_0 # Easting (C{float}) _height = 0 # height (C{meter}) _northing = _0_0 # Northing (C{float}) def __init__(self, e, n, h=0, conic=Conics.WRF_Lb, name=NN): '''New L{Lcc} Lamber conformal conic position. @arg e: Easting (C{meter}). @arg n: Northing (C{meter}). @kwarg h: Optional height (C{meter}). @kwarg conic: Optional, the conic projection (L{Conic}). @kwarg name: Optional name (C{str}). @return: The Lambert location (L{Lcc}). @raise LCCError: Invalid B{C{h}} or invalid or negative B{C{e}} or B{C{n}}. @raise TypeError: If B{C{conic}} is not L{Conic}. @example: >>> lb = Lcc(448251, 5411932.0001) ''' _xinstanceof(Conic, conic=conic) self._conic = conic self._easting = Easting(e, falsed=conic.E0 > 0, Error=LCCError) self._northing = Northing(n, falsed=conic.N0 > 0, Error=LCCError) if h: self._height = Height(h=h, Error=LCCError) if name: self.name = name @Property_RO def conic(self): '''Get the conic projection (L{Conic}). ''' return self._conic @Property_RO def easting(self): '''Get the easting (C{meter}). ''' return self._easting @Property_RO def height(self): '''Get the height (C{meter}). ''' return self._height @Property_RO def latlon(self): '''Get the lat- and longitude in C{degrees} (L{LatLon2Tuple}). ''' ll = self.toLatLon(LatLon=None, datum=None) return LatLon2Tuple(ll.lat, ll.lon, name=self.name) @Property_RO def latlonheight(self): '''Get the lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}). ''' return self.latlon.to3Tuple(self.height) @Property_RO def latlonheightdatum(self): '''Get the lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}). ''' return self.latlonheight.to4Tuple(self.conic.datum) @Property_RO def northing(self): '''Get the northing (C{meter}). ''' return self._northing @Property_RO def philam(self): '''Get the lat- and longitude in C{radians} (L{PhiLam2Tuple}). ''' return PhiLam2Tuple(radians(self.latlon.lat), radians(self.latlon.lon), name=self.name) @Property_RO def philamheight(self): '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}). ''' return self.philam.to3Tuple(self.height) @Property_RO def philamheightdatum(self): '''Get the lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}). ''' return self.philamheight.to4Tuple(self.datum) def to3lld(self, datum=None): # PYCHOK no cover '''DEPRECATED, use method C{toLatLon}. @kwarg datum: Optional datum to use, otherwise use this B{C{Lcc}}'s conic.datum (C{Datum}). @return: A L{LatLonDatum3Tuple}C{(lat, lon, datum)}. @raise TypeError: If B{C{datum}} is not ellipsoidal. ''' if datum in (None, self.conic.datum): r = LatLonDatum3Tuple(self.latlon.lat, self.latlon.lon, self.conic.datum, name=self.name) else: r = self.toLatLon(LatLon=None, datum=datum) r = LatLonDatum3Tuple(r.lat, r.lon, r.datum, name=r.name) return r def toLatLon(self, LatLon=None, datum=None, height=None, **LatLon_kwds): '''Convert this L{Lcc} to an (ellipsoidal) geodetic point. @kwarg LatLon: Optional, ellipsoidal class to return the geodetic point (C{LatLon}) or C{None}. @kwarg datum: Optional datum to use, otherwise use this B{C{Lcc}}'s conic.datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg height: Optional height for the point, overriding the default height (C{meter}). @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, unused if C{B{LatLon}=None}. @return: The point (B{C{LatLon}}) or a L{LatLon4Tuple}C{(lat, lon, height, datum)} if B{C{LatLon}} is C{None}. @raise TypeError: If B{C{LatLon}} or B{C{datum}} is not ellipsoidal or not valid. ''' if LatLon: _xsubclassof(_LLEB, LatLon=LatLon) c = self.conic if datum not in (None, self.conic.datum): c = c.toDatum(datum) e = self.easting - c._E0 n = c._r0 - self.northing + c._N0 r_ = copysign(hypot(e, n), c._n) t_ = pow(r_ / c._aF, c._n_) x = c._xdef(t_) # XXX c._lam0 while True: p, x = x, c._xdef(t_ * c._pdef(x)) if abs(x - p) < 1e-9: # XXX EPS too small? break lat = degrees90(x) lon = degrees180((atan(e / n) + c._opt3) * c._n_ + c._lam0) h = self.height if height is None else Height(height) return _LL4Tuple(lat, lon, h, c.datum, LatLon, LatLon_kwds, name=self.name) def toRepr(self, prec=0, fmt=Fmt.SQUARE, sep=_COMMASPACE_, m=_m_, C=False, **unused): # PYCHOK expected '''Return a string representation of this L{Lcc} position. @kwarg prec: Optional number of decimals, unstripped (C{int}). @kwarg fmt: Optional, enclosing backets format (C{str}). @kwarg sep: Optional separator between name:values (C{str}). @kwarg m: Optional unit of the height, default meter (C{str}). @kwarg C: Optionally, include name of conic and datum (C{bool}). @return: This Lcc as "[E:meter, N:meter, H:m, C:Conic.Datum]" (C{str}). ''' t, T = _fstrENH2(self, prec, m) if C: t += self.conic.name2, T += _C_, return _xzipairs(T, t, sep=sep, fmt=fmt) def toStr(self, prec=0, sep=_SPACE_, m=_m_): # PYCHOK expected '''Return a string representation of this L{Lcc} position. @kwarg prec: Optional number of decimal, unstripped (C{int}). @kwarg sep: Optional separator to join (C{str}) or C{None} to return an unjoined C{tuple} of C{str}s. @kwarg m: Optional height units, default C{meter} (C{str}). @return: This Lcc as "easting nothing" C{str} in C{meter} plus " height" and 'm' if heigth is non-zero (C{str}). @example: >>> lb = Lcc(448251, 5411932.0001) >>> lb.toStr(4) # 448251.0 5411932.0001 >>> lb.toStr(sep=', ') # 448251, 5411932 ''' t, _ = _fstrENH2(self, prec, m) return t if sep is None else sep.join(t) def toLcc(latlon, conic=Conics.WRF_Lb, height=None, Lcc=Lcc, name=NN, **Lcc_kwds): '''Convert an (ellipsoidal) geodetic point to a I{Lambert} location. @arg latlon: Ellipsoidal point (C{LatLon}). @kwarg conic: Optional Lambert projection to use (L{Conic}). @kwarg height: Optional height for the point, overriding the default height (C{meter}). @kwarg Lcc: Optional class to return the I{Lambert} location (L{Lcc}). @kwarg name: Optional B{C{Lcc}} name (C{str}). @kwarg Lcc_kwds: Optional, additional B{C{Lcc}} keyword arguments, ignored if B{C{Lcc=None}}. @return: The I{Lambert} location (L{Lcc}) or an L{EasNor3Tuple}C{(easting, northing, height)} if B{C{Lcc}} is C{None}. @raise TypeError: If B{C{latlon}} is not ellipsoidal. ''' _xinstanceof(_LLEB, latlon=latlon) a, b = latlon.philam c = conic.toDatum(latlon.datum) t = c._n * (b - c._lam0) - c._opt3 st, ct = sincos2(t) r = c._rdef(c._tdef(a)) e = c._E0 + r * st n = c._N0 + c._r0 - r * ct h = latlon.height if height is None else height r = EasNor3Tuple(e, n, h) if Lcc is None else \ Lcc(e, n, h=h, conic=c, **Lcc_kwds) return _xnamed(r, name or nameof(latlon)) if __name__ == '__main__': from pygeodesy.interns import _NL_, _NL_var_ # __doc__ of this file, force all into registery t = _NL_ + Conics.toRepr(all=True) print(_NL_var_.join(t.split(_NL_))) # **) MIT License # # Copyright (C) 2016-2021 -- 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.