# Coverage for pygeodesy/latlonBase.py : 96%

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After I{(C) Chris Veness 2011-2015} published under the same MIT Licence**, see U{https://www.Movable-Type.co.UK/scripts/latlong.html}, U{<https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>} and U{https://www.Movable-Type.co.UK/scripts/latlong-vectors.html}. @newfield example: Example, Examples ''' from pygeodesy.basics import EPS, map1, R_M, property_doc_, property_RO, \ scalar, _TypeError from pygeodesy.dms import F_D, F_DMS, latDMS, lonDMS, parseDMS, parseDMS2 from pygeodesy.ecef import EcefKarney from pygeodesy.fmath import favg from pygeodesy.formy import antipode, compassAngle, equirectangular, euclidean, \ haversine, isantipode, latlon2n_xyz, points2, vincentys from pygeodesy.lazily import _ALL_DOCS from pygeodesy.named import Bounds2Tuple, LatLon2Tuple, _NamedBase, \ notOverloaded, PhiLam2Tuple, Vector3Tuple from pygeodesy.vector3d import Vector3d from math import asin, cos, degrees, radians # XXX the following classes are listed only to get # Epydoc to include class and method documentation __all__ = _ALL_DOCS('LatLonBase') __version__ = '20.03.15' class LatLonBase(_NamedBase): '''(INTERNAL) Base class for C{LatLon} points on spherical or ellipsoidal earth models. ''' _datum = None #: (INTERNAL) L{Datum}, to be overriden. _Ecef = EcefKarney #: (INTERNAL) Preferred C{Ecef...} class. _e9t = None #: (INTERNAL) Cached toEcef (L{Ecef9Tuple}). _height = 0 #: (INTERNAL) Height (C{meter}). _lat = 0 #: (INTERNAL) Latitude (C{degrees}). _latlon = None #: (INTERNAL) Cached (L{LatLon2Tuple}). _lon = 0 #: (INTERNAL) Longitude (C{degrees}). _name = '' #: (INTERNAL) name (C{str}). _philam = None #: (INTERNAL) Cached (L{PhiLam2Tuple}). _v3d = None #: (INTERNAL) Cached toVector3d (L{Vector3d}). _xyz = None #: (INTERNAL) Cached xyz (L{Vector3Tuple}). _xyzh = None #: (INTERNAL) Cached xyzh (L{Vector4Tuple}). def __init__(self, lat, lon, height=0, name=''): '''New C{LatLon}. @param lat: Latitude (C{degrees} or DMS C{str} with N or S suffix). @param lon: Longitude (C{degrees} or DMS C{str} with E or W suffix). @keyword height: Optional height (C{meter} above or below the earth surface). @keyword name: Optional name (C{str}). @return: New instance (C{LatLon}). @raise RangeError: Value of B{C{lat}} or B{C{lon}} outside the valid range and C{rangerrors} set to C{True}. @raise ValueError: Invalid B{C{lat}} or B{C{lon}}. @example: >>> p = LatLon(50.06632, -5.71475) >>> q = LatLon('50°03′59″N', """005°42'53"W""") ''' self._lat, self._lon = parseDMS2(lat, lon) # PYCHOK LatLon2Tuple if height: # elevation self._height = scalar(height, None, name='height') if name: self.name = name def __eq__(self, other): return self.isequalTo(other) def __ne__(self, other): return not self.isequalTo(other) def __str__(self): return self.toStr(form=F_D, prec=6) def _havg(self, other, f=0.5): '''(INTERNAL) Weighted, average height. @param other: An other point (C{LatLon}). @keyword f: Optional fraction (C{float}). @return: Average, fractional height (C{float}). ''' return favg(self.height, other.height, f=f) def _update(self, updated, *attrs): '''(INTERNAL) Zap cached attributes if updated. ''' if updated: _NamedBase._update(self, updated, '_e9t', '_latlon', '_philam', '_v3d', '_xyz', '_xyzh', *attrs) def antipode(self, height=None): '''Return the antipode, the point diametrically opposite to this point. @keyword height: Optional height of the antipode, height of this point otherwise (C{meter}). @return: The antipodal point (C{LatLon}). ''' a, b = antipode(self.lat, self.lon) # PYCHOK LatLon2Tuple h = self.height if height is None else height return self.classof(a, b, height=h) def bounds(self, wide, high, radius=R_M): '''DEPRECATED, use method C{boundsOf}. ''' return self.boundsOf(wide, high, radius=radius) # PYCHOK no cover def boundsOf(self, wide, high, radius=R_M): '''Return the SE and NW lat-/longitude of a great circle bounding box centered at this location. @param wide: Longitudinal box width (C{meter}, same units as B{C{radius}} or C{degrees} if B{C{radius}} is C{None}). @param high: Latitudinal box height (C{meter}, same units as B{C{radius}} or C{degrees} if B{C{radius}} is C{None}). @keyword radius: Mean earth radius (C{meter}). @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)}, the lower-left and upper-right corner (C{LatLon}). @see: U{https://www.Movable-Type.co.UK/scripts/latlong-db.html} ''' w = wide * 0.5 h = high * 0.5 if radius > EPS: ca = cos(self.phi) if ca > EPS: w = degrees(asin(w / radius) / ca) else: w = 0 # XXX h = degrees(h / radius) w, h = abs(w), abs(h) r = Bounds2Tuple(self.classof(self.lat - h, self.lon - w, height=self.height), self.classof(self.lat + h, self.lon + w, height=self.height)) return self._xnamed(r) def compassAngle(self, other): '''DEPRECATED, use method C{compassAngleTo}. ''' return self.compassAngleTo(other) # PYCHOK no cover def compassAngleTo(self, other, adjust=True, wrap=False): '''Return the angle from North for the direction vector between this and an other point. Suitable only for short, non-near-polar vectors up to a few hundred Km or Miles. Use method C{initialBearingTo} for larger distances. @param other: The other point (C{LatLon}). @keyword adjust: Adjust the longitudinal delta by the cosine of the mean latitude (C{bool}). @keyword wrap: Wrap and L{unroll180} longitudes and longitudinal delta (C{bool}). @return: Compass angle from North (C{degrees360}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @note: Courtesy Martin Schultz. @see: U{Local, flat earth approximation <https://www.EdWilliams.org/avform.htm#flat>}. ''' self.others(other) return compassAngle(self.lat, self.lon, other.lat, other.lon, adjust=adjust, wrap=wrap) @property_RO def datum(self): '''(INTERNAL) I{Must be overloaded}. ''' notOverloaded(self, self.datum.__name__) def _distanceTo(self, func, other, radius, **options): '''(INTERNAL) Helper for methods C{<func>To}. ''' self.others(other) if radius is None: radius = self._datum.ellipsoid.R1 if self._datum else R_M return func(self.lat, self.lon, other.lat, other.lon, radius=radius, **options) @property_RO def Ecef(self): '''Get the ECEF C{class} (L{EcefKarney} or L{EcefVeness}). ''' return self._Ecef def equals(self, other, eps=None): '''DEPRECATED, use method C{isequalTo}. ''' return self.isequalTo(other, eps=eps) # PYCHOK no cover def equals3(self, other, eps=None): '''DEPRECATED, use method C{isequalTo3}. ''' return self.isequalTo3(other, eps=eps) # PYCHOK no cover def equirectangularTo(self, other, radius=None, **options): '''Compute the distance between this and an other point using the U{Equirectangular Approximation / Projection <https://www.Movable-Type.co.UK/scripts/latlong.html>}. Suitable only for short, non-near-polar distances up to a few hundred Km or Miles. Use method C{haversineTo} or C{distanceTo*} for more accurate and/or larger distances. See function L{equirectangular_} for more details, the available B{C{options}} and errors raised. @param other: The other point (C{LatLon}). @keyword radius: Mean earth radius (C{meter}) or C{None} for the mean radius of this point's datum ellipsoid. @keyword options: Optional keyword arguments for function L{equirectangular}. @return: Distance (C{meter}, same units as B{C{radius}}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @see: Function L{equirectangular}, methods C{euclideanTo}, C{distanceTo*}, C{haversineTo} and C{vincentysTo}. ''' return self._distanceTo(equirectangular, other, radius, **options) def euclideanTo(self, other, radius=None, **options): '''Approximate the C{Euclidian} distance between this and an other point. See function L{euclidean} for the available B{C{options}}. @param other: The other point (C{LatLon}). @keyword radius: Mean earth radius (C{meter}) or C{None} for the mean radius of this point's datum ellipsoid. @keyword options: Optional keyword arguments for function L{euclidean}. @return: Distance (C{meter}, same units as B{C{radius}}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @see: Function L{euclidean}, methods C{equirectangularTo}, C{distanceTo*}, C{haversineTo} and C{vincentysTo}. ''' return self._distanceTo(euclidean, other, radius, **options) def haversineTo(self, other, radius=None, wrap=False): '''Compute the distance between this and an other point using the U{Haversine<https://www.Movable-Type.co.UK/scripts/latlong.html>} formula. @param other: The other point (C{LatLon}). @keyword radius: Mean earth radius (C{meter}) or C{None} for the mean radius of this point's datum ellipsoid. @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @return: Distance (C{meter}, same units as B{C{radius}}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @see: Function L{haversine}, methods C{equirectangularTo}, C{euclideanTo}, C{distanceTo*} and C{vincentysTo}. ''' return self._distanceTo(haversine, other, radius, wrap=wrap) @property_doc_(' the height (C{meter}).') def height(self): '''Get the height (C{meter}). ''' return self._height @height.setter # PYCHOK setter! def height(self, height): '''Set the height. @param height: New height (C{meter}). @raise TypeError: Invalid B{C{height}} C{type}. @raise ValueError: Invalid B{C{height}}. ''' h = scalar(height, None, name='height') self._update(h != self._height) self._height = h def isantipodeTo(self, other, eps=EPS): '''Check whether this and an other point are antipodal, on diametrically opposite sides of the earth. @param other: The other point (C{LatLon}). @keyword eps: Tolerance for near-equality (C{degrees}). @return: C{True} if points are antipodal within the given tolerance, C{False} otherwise. ''' return isantipode(self.lat, self.lon, other.lat, other.lon, eps=eps) def isantipode(self, other, eps=EPS): '''DEPRECATED, use method C{isantipodeTo}. ''' return self.isantipodeTo(other, eps=eps) # PYCHOK no cover @property_RO def isEllipsoidal(self): '''Check whether this point is ellipsoidal (C{bool} or C{None} if unknown). ''' return self.datum.isEllipsoidal if self._datum else None def isequalTo(self, other, eps=None): '''Compare this point with an other point. @param other: The other point (C{LatLon}). @keyword eps: Tolerance for equality (C{degrees}). @return: C{True} if both points are identical, I{ignoring} height, C{False} otherwise. @raise TypeError: The B{C{other}} point is not C{LatLon}. @see: Method L{isequalTo3}. @example: >>> p = LatLon(52.205, 0.119) >>> q = LatLon(52.205, 0.119) >>> e = p.isequalTo(q) # True ''' self.others(other) if eps and eps > 0: return max(map1(abs, self.lat - other.lat, self.lon - other.lon)) < eps else: return self.lat == other.lat and \ self.lon == other.lon def isequalTo3(self, other, eps=None): '''Compare this point with an other point. @param other: The other point (C{LatLon}). @keyword eps: Tolerance for equality (C{degrees}). @return: C{True} if both points are identical I{including} height, C{False} otherwise. @raise TypeError: The B{C{other}} point is not C{LatLon}. @see: Method L{isequalTo}. @example: >>> p = LatLon(52.205, 0.119, 42) >>> q = LatLon(52.205, 0.119) >>> e = p.isequalTo3(q) # False ''' return self.isequalTo(other, eps=eps) and self.height == other.height @property_RO def isSpherical(self): '''Check whether this point is spherical (C{bool} or C{None} if unknown). ''' return self.datum.isSpherical if self._datum else None @property_RO def lam(self): '''Get the longitude (B{C{radians}}). ''' return self.philam.lam if self._philam is None else self._philam.lam @property_doc_(' the latitude (C{degrees90}).') def lat(self): '''Get the latitude (C{degrees90}). ''' return self._lat @lat.setter # PYCHOK setter! def lat(self, lat): '''Set the latitude. @param lat: New latitude (C{str[N|S]} or C{degrees}). @raise ValueError: Invalid B{C{lat}}. ''' lat = parseDMS(lat, suffix='NS', clip=90) self._update(lat != self._lat) self._lat = lat @property_doc_(' the lat- and longitude, optionally height.') def latlon(self): '''Get the lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}). ''' if self._latlon is None: self._latlon = LatLon2Tuple(self._lat, self._lon) return self._xrenamed(self._latlon) @latlon.setter # PYCHOK setter! def latlon(self, latlonh): '''Set the lat- and longitude and optionally the height. @param latlonh: New lat-, longitude and height (2- or 3-tuple of C{degrees} and C{meter}). @raise TypeError: Height of B{C{latlonh}} not C{scalar} or B{C{latlonh}} not C{list} or C{tuple}. @raise ValueError: Invalid B{C{latlonh}} or M{len(latlonh)}. @see: Function L{parse3llh} to parse a B{C{latlonh}} string into a 3-tuple (lat, lon, h). ''' _TypeError(list, tuple, latlonh=latlonh) if len(latlonh) == 3: h = scalar(latlonh[2], None, name='latlonh') elif len(latlonh) != 2: raise ValueError('%s invalid: %r' % ('latlonh', latlonh)) else: h = self._height lat, lon = parseDMS2(latlonh[0], latlonh[1]) self._update(lat != self._lat or lon != self._lon or h != self._height) self._lat, self._lon, self._height = lat, lon, h def latlon_(self, ndigits=0): '''DEPRECATED, use method C{latlon2}. ''' return self.latlon2(ndigits) # PYCHOK no cover def latlon2(self, ndigits=0): '''Return this point's lat- and longitude in C{degrees}, rounded. @keyword ndigits: Number of decimal digits (C{int}). @return: A L{LatLon2Tuple}C{(lat, lon)}, both C{float} and rounded away from zero. @note: The C{round}ed values are always C{float}, also if B{C{ndigits}} is omitted. ''' r = LatLon2Tuple(round(self.lat, ndigits), round(self.lon, ndigits)) return self._xnamed(r) def latlon2round(self, ndigits=0): '''DEPRECATED, use method C{latlon2}. ''' return self.latlon2(ndigits) # PYCHOK no cover @property_RO def latlonheight(self): '''Get the lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}). ''' return self.latlon.to3Tuple(self.height) @property_doc_(' the longitude (C{degrees180}).') def lon(self): '''Get the longitude (C{degrees180}). ''' return self._lon @lon.setter # PYCHOK setter! def lon(self, lon): '''Set the longitude. @param lon: New longitude (C{str[E|W]} or C{degrees}). @raise ValueError: Invalid B{C{lon}}. ''' lon = parseDMS(lon, suffix='EW', clip=180) self._update(lon != self._lon) self._lon = lon @property_RO def _N_vector(self): '''(INTERNAL) Get the (C{nvectorBase._N_vector_}) ''' from pygeodesy.nvectorBase import _N_vector_ r = self._xyz or self._v3d or self.toVector() return _N_vector_(r.x, r.y, r.z, h=self.height) @property_RO def phi(self): '''Get the latitude (B{C{radians}}). ''' return self.philam.phi if self._philam is None else self._philam.phi @property_RO def philam(self): '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}). ''' if self._philam is None: self._philam = PhiLam2Tuple(radians(self.lat), radians(self.lon)) return self._xnamed(self._philam) def philam2(self, ndigits=0): '''Return this point's lat- and longitude in C{radians}, rounded. @keyword ndigits: Number of decimal digits (C{int}). @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float} and rounded away from zero. @note: The C{round}ed values are always C{float}, also if B{C{ndigits}} is omitted. ''' r = PhiLam2Tuple(round(self.phi, ndigits), round(self.lam, ndigits)) return self._xnamed(r) @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) def points(self, points, closed=True): # PYCHOK no cover '''DEPRECATED, use method C{points2}. ''' return self.points2(points, closed=closed) def points2(self, points, closed=True): '''Check a path or polygon represented by points. @param points: The path or polygon points (C{LatLon}[]) @keyword closed: Optionally, consider the polygon closed, ignoring any duplicate or closing final B{C{points}} (C{bool}). @return: A L{Points2Tuple}C{(number, points)}, C{int} and C{list} or C{tuple}. @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Insufficient number of B{C{points}}. ''' return points2(points, closed=closed, base=self) def to2ab(self): # PYCHOK no cover '''DEPRECATED, use property C{philam}. @return: A L{PhiLam2Tuple}C{(phi, lam)}. ''' return self.philam def to3llh(self, height=None): # PYCHOK no cover '''DEPRECATED, use property C{latlonheight} or C{latlon.to3Tuple(B{height})}. @return: A L{LatLon3Tuple}C{(lat, lon, height)}. ''' return self.latlonheight if height in (None, self.height) else \ self.latlon.to3Tuple(height) def to3xyz(self): # PYCHOK no cover '''DEPRECATED, use method C{toNvector}, C{toVector}, C{toVector3d} or property C{xyz} or perhaps (geocentric) C{toEcef}. @return: A L{Vector3Tuple}C{(x, y, z)}, see property C{xyz}. ''' return self.xyz # self.toVector() def toCartesian(self, Cartesian=None, **kwds): '''Convert this point to cartesian (ECEF) coordinates. @keyword Cartesian: Optional (sub-)class to return the geocentric coordinates (C{Cartesian}) or C{None}. @keyword kwds: Optional, additional B{C{Cartesian}} keyword arguments, ignored if C{B{Cartesian}=None}. @return: A B{C{Cartesian}} or if C{B{Cartesian}=None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C} 0 and C{M} if available. @raise TypeError: Invalid B{C{Cartesian}} or B{C{kwds}}. ''' r = self.toEcef() if Cartesian is not None: # class or .classof r = Cartesian(r, **kwds) r = self._xnamed(r) return r def toEcef(self): '''Convert this point to geocentric coordinates, also known as I{Earth-Centered, Earth-Fixed} (U{ECEF <https://WikiPedia.org/wiki/ECEF>}). @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C} 0 and C{M} if available. @raise EcefError: A C{.datum} or an ECEF issue. ''' if self._e9t is None: e = self.Ecef(self.datum).forward(self, M=True) self._e9t = self._xnamed(e) return self._e9t def toNvector(self, h=None, Nvector=None, **kwds): '''Convert this point to C{n-vector} (normal to the earth's surface) components, I{including height}. @keyword h: Optional height, overriding this point's height (C{meter}). @keyword Nvector: Optional (sub-)class to return the C{n-vector} components (C{Nvector}) or C{None}. @keyword kwds: Optional, additional B{C{Nvector}} keyword arguments, ignored if C{B{Nvector}=None}. @return: A B{C{Nvector}} or an L{Vector4Tuple}C{(x, y, z, h)} if C{B{Nvector}=None}. @raise TypeError: Invalid B{C{Nvector}} or B{C{kwds}}. ''' return self.toVector(Vector=Nvector, h=self.height if h is None else h, ll=self, **kwds) def toStr(self, form=F_DMS, prec=None, m='m', sep=', '): # PYCHOK expected '''Convert this point to a "lat, lon [+/-height]" string, formatted in the given form. @keyword form: Optional format, F_D, F_DM, F_DMS for deg°, deg°min′, deg°min′sec″ (C{str}). @keyword prec: Optional number of decimal digits (0..8 or C{None}). @keyword m: Optional unit of the height (C{str}), use C{None} to exclude height from the returned string. @keyword sep: Optional separator to join (C{str}). @return: Point in the specified form (C{str}). @example: >>> LatLon(51.4778, -0.0016).toStr() # 51°28′40″N, 000°00′06″W >>> LatLon(51.4778, -0.0016).toStr(F_D) # 51.4778°N, 000.0016°W >>> LatLon(51.4778, -0.0016, 42).toStr() # 51°28′40″N, 000°00′06″W, +42.00m ''' t = [latDMS(self.lat, form=form, prec=prec), lonDMS(self.lon, form=form, prec=prec)] if self.height and m is not None: t += ['%+.2f%s' % (self.height, m)] return sep.join(t) def toVector(self, Vector=None, **kwds): '''Convert this point to C{n-vector} (normal to the earth's surface) components, I{ignoring height}. @keyword Vector: Optional (sub-)class to return the C{n-vector} components (L{Vector3d}) or C{None}. @keyword kwds: Optional, additional B{C{Vector}} keyword arguments, ignored if C{B{Vector}=None}. @return: A B{C{Vector}} or an L{Vector3Tuple}C{(x, y, z)} if C{B{Vector}=None}. @raise TypeError: Invalid B{C{Vector}} or B{C{kwds}}. @note: These are C{n-vector} x, y and z components, I{NOT} (geocentric) ECEF x, y and z coordinates! ''' r = latlon2n_xyz(self.lat, self.lon) if Vector is not None: r = Vector(r.x, r.y, r.z, **kwds) return self._xnamed(r) def toVector3d(self): '''Convert this point to C{n-vector} (normal to the earth's surface) components, I{ignoring height}. @return: Unit vector (L{Vector3d}). @note: These are C{n-vector} x, y and z components, I{NOT} (geocentric) ECEF x, y and z coordinates! ''' if self._v3d is None: self._v3d = self.toVector(Vector=Vector3d) # XXX .unit() return self._xnamed(self._v3d) def vincentysTo(self, other, radius=None, wrap=False): '''Compute the distance between this and an other point using U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>} spherical formula. @param other: The other point (C{LatLon}). @keyword radius: Mean earth radius (C{meter}) or C{None} for the mean radius of this point's datum ellipsoid. @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @return: Distance (C{meter}, same units as B{C{radius}}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @see: Function L{vincentys}, methods C{equirectangularTo}, C{euclideanTo}, C{distanceTo*} and C{haversineTo}. ''' return self._distanceTo(vincentys, other, radius, wrap=wrap) @property_RO def xyz(self): '''Get the C{n-vector} X, Y and Z components (L{Vector3Tuple}C{(x, y, z)}) @note: These are C{n-vector} x, y and z components, I{NOT} (geocentric) ECEF x, y and z coordinates! ''' if self._xyz is None: self._xyz = self.toVector(Vector=Vector3Tuple) return self._xnamed(self._xyz) @property_RO def xyzh(self): '''Get the C{n-vector} X, Y, Z and H components (L{Vector4Tuple}C{(x, y, z, h)}) @note: These are C{n-vector} x, y and z components, I{NOT} (geocentric) ECEF x, y and z coordinates! ''' if self._xyzh is None: self._xyzh = self.xyz.to4Tuple(self.height) return self._xnamed(self._xyzh) # **) MIT License # # Copyright (C) 2016-2020 -- 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.