Coverage for pygeodesy/__init__.py: 98%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''A pure Python implementation of geodesy tools for various ellipsoidal and spherical earth models 

5using precision exact, elliptic, trigonometric, vector-based, iterative and approximate methods for 

6geodetic (lat-/longitude), geocentric (U{ECEF<https://WikiPedia.org/wiki/ECEF>} cartesian), local (U{LTP 

7<https://WikiPedia.org/wiki/Local_tangent_plane_coordinates>}) and certain U{triaxial ellipsoidal 

8<https://GeographicLib.SourceForge.io/1.44/triaxial.html>} coordinates. 

9 

10Transcoded in part from U{JavaScript originals<https://GitHub.com/ChrisVeness/geodesy>} by I{Chris Veness (C) 

112005-2024} and from several U{C++ classes<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>} by I{Charles 

12F. F. Karney (C) 2008-2024} and published under the same U{MIT License<https://OpenSource.org/licenses/MIT>}**. 

13 

14There are four modules for ellipsoidal earth models, C{ellipsoidalExact}, C{-Karney}, C{-Vincenty} and C{-Nvector} 

15and two for spherical ones, C{sphericalTrigonometry} and C{-Nvector}. Each module provides a geodetic B{C{LatLon}} 

16and a geocentric B{C{Cartesian}} class with methods and functions to compute distance, surface area, perimeter, 

17forward and reverse azimuth, initial and final bearing, intermediate and nearest points, intersections of geodesic, 

18great circle and rhumb lines, circle intersections and secants, U{3-point resections 

19<https://WikiPedia.org/wiki/Position_resection_and_intersection>}, triangulation, trilateration (by intersection, 

20by overlap and in 3-D), conversions and unrolling, among other things. 

21 

22Also included are modules for conversions to and from U{Cassini-Soldner 

23<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1CassiniSoldner.html>}, 

24U{ECEF<https://WikiPedia.org/wiki/ECEF>} (Earth-Centered, Earth-Fixed cartesian), U{UTM 

25<https://www.Movable-Type.co.UK/scripts/latlong-utm-mgrs.html>} (Universal Transverse Mercator 

26and U{Exact<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercatorExact.html>}), 

27U{UPS<https://WikiPedia.org/wiki/Universal_polar_stereographic_coordinate_system>} (Universal Polar 

28Stereographic) and U{Web Mercator<https://WikiPedia.org/wiki/Web_Mercator>} (Pseudo-Mercator) coordinates, 

29U{MGRS<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1MGRS.html>} (Military Grid Reference 

30System, UTM I{and} UPS) and U{OSGR<https://www.Movable-Type.co.UK/scripts/latlong-os-gridref.html>} (British 

31Ordinance Survery Grid Reference) grid references, U{TRF<http://ITRF.ENSG.IGN.Fr>} (Terrestrial Reference 

32Frames) and modules to encode and decode U{EPSG<https://EPSG.org>}, U{Geohashes 

33<https://www.Movable-Type.co.UK/scripts/geohash.html>}, U{Georefs (WGRS) 

34<https://WikiPedia.org/wiki/World_Geographic_Reference_System>} and U{Garefs (GARS) 

35<https://WikiPedia.org/wiki/Global_Area_Reference_System>}. 

36 

37Other modules provide U{Albers equal-area 

38<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AlbersEqualArea.html>} projections, U{equidistant 

39<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AzimuthalEquidistant.html>} and other I{azimuthal} 

40projections, Lambert I{conformal conic} projections and positions, functions to clip paths or polygons of C{LatLon} 

41points using the U{Cohen-Sutherland<https://WikiPedia.org/wiki/Cohen-Sutherland_algorithm>}, 

42U{Forster-Hormann-Popa<https://www.ScienceDirect.com/science/article/pii/S259014861930007X>}, 

43U{Greiner-Hormann<http://www.inf.USI.CH/hormann/papers/Greiner.1998.ECO.pdf>}, 

44U{Liang-Barsky<https://www.CS.Helsinki.FI/group/goa/viewing/leikkaus/intro.html>} and 

45U{Sutherland-Hodgman<https://WikiPedia.org/wiki/Sutherland-Hodgman_algorithm>} methods, 

46functions to U{simplify<https://Bost.Ocks.org/mike/simplify>} or linearize a path of C{LatLon} 

47points (or a U{NumPy array<https://docs.SciPy.org/doc/numpy/reference/generated/numpy.array.html>}), 

48including implementations of the U{Ramer-Douglas-Peucker<https://WikiPedia.org/wiki/ 

49Ramer-Douglas-Peucker_algorithm>}, the U{Visvalingam-Whyatt<https://hydra.Hull.ac.UK/ 

50resources/hull:8338>} and the U{Reumann-Witkam<https://psimpl.SourceForge.net/reumann-witkam.html>} 

51algorithms and modified versions of the former. 

52 

53Plus modules and classes to U{interpolate<https://docs.SciPy.org/doc/scipy/reference/interpolate.html>} the 

54L{height<pygeodesy.heights>} of C{LatLon} points and L{Geoid<pygeodesy.geoids>} models, compute various U{Fréchet 

55<https://WikiPedia.org/wiki/Frechet_distance>} or U{Hausdorff<https://WikiPedia.org/wiki/Hausdorff_distance>} 

56distances or perform I{boolean} operations between (composite) polygons. 

57 

58For further details see the U{documentation<https://mrJean1.GitHub.io/PyGeodesy>}, the descriptions of 

59U{Latitude/Longitude<https://www.Movable-Type.co.UK/scripts/latlong.html>}, U{Vincenty 

60<https://www.Movable-Type.co.UK/scripts/latlong-vincenty.html>} and U{Vector-based 

61<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>} geodesy, the original U{JavaScript source 

62<https://GitHub.com/ChrisVeness/geodesy>} or U{docs<https://www.Movable-Type.co.UK/scripts/geodesy/docs>} 

63and I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>} and C++ U{GeographicLib 

64<https://GeographicLib.SourceForge.io/C++/doc/index.html>}. 

65 

66Installation 

67============ 

68 

69To install C{pygeodesy}, type C{python[3] -m pip install pygeodesy} or C{python[3] -m easy_install 

70pygeodesy} in a terminal or command window. 

71 

72If the wheel C{pygeodesy-yy.m.d-py2.py3-none-any.whl} is missing in U{PyPI Download files<https:// 

73PyPI.org/project/pygeodesy/#files>}, download the file from U{GitHub/dist<https://GitHub.com/mrJean1/ 

74PyGeodesy/tree/master/dist>}. Install that with C{python[3] -m pip install <path-to-downloaded-wheel>} 

75and verify with C{python[3] -m pygeodesy}. 

76 

77Alternatively, download C{pygeodesy-yy.m.d.tar.gz} from U{PyPI<https://PyPI.org/project/pygeodesy>} 

78or U{GitHub<https://GitHub.com/mrJean1/PyGeodesy>}, C{unzip} the downloaded file, C{cd} to 

79directory C{pygeodesy-yy.m.d} and type C{python[3] setup.py install}. 

80 

81To run all C{pygeodesy} tests, type C{python[3] test/run.py} or type C{python[3] test/unitTestSuite.py} 

82before or after installation. 

83 

84Dependencies 

85============ 

86 

87Installation of I{Karney}'s Python package U{geographiclib<https://PyPI.org/project/geographiclib>} 

88is optional, but required for module L{ellipsoidalKarney}, L{azimuthal} classes L{EquidistantKarney} 

89and L{GnomonicKarney} and the L{HeightIDWkarney} interpolator. 

90 

91Both U{numpy<https://PyPI.org/project/numpy>} and U{scipy<https://PyPI.org/project/scipy>} must be 

92installed for most L{Geoid...<pygeodesy.geoids>} and L{Height...<pygeodesy.heights>} interpolators, 

93except L{GeoidKarney} and the L{HeightIDW...<pygeodesy.heights>} ones. 

94 

95Functions and C{LatLon} methods L{circin6}, L{circum3}, L{circum4_} and L{soddy4} and functions 

96L{triaxum5} and L{trilaterate3d2} require U{numpy<https://PyPI.org/project/numpy>} to be installed, 

97modules L{auxilats} and L{rhumb} may need U{numpy<https://PyPI.org/project/numpy>}. 

98 

99Modules L{ellipsoidalGeodSolve} and L{geodsolve} and L{azimuthal} classes L{EquidistantGeodSolve} 

100and L{GnomonicGeodSolve} depend on I{Karney}'s C++ utility U{GeodSolve 

101<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>} to be executable and set with 

102env variable C{PYGEODESY_GEODSOLVE} or with property L{Ellipsoid.geodsolve}. 

103 

104Class L{Intersectool} in module L{geodesici} needs I{Karney}'s C++ utility U{IntersectTool 

105<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>} to be executable and set with 

106env variable C{PYGEODESY_INTERSECTTOOL}. 

107 

108To compare C{MGRS} results from modules L{mgrs} and C{testMgrs} with I{Karney}'s C++ utility 

109U{GeoConvert<https://GeographicLib.SourceForge.io/C++/doc/GeoConvert.1.html>}, the latter must 

110be executable and set with env variable C{PYGEODESY_GEOCONVERT}. 

111 

112Module L{rhumb.solve} needs I{Karney}'s C++ utility U{RhumbSolve 

113<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>} to be executable and set with 

114env variable C{PYGEODESY_RHUMBSOLVE} or with property L{Ellipsoid.rhumbsolve}. 

115 

116Documentation 

117============= 

118 

119In addition to the C{pygeodesy} package, the U{pygeodesy<https://PyPI.org/project/pygeodesy>} 

120U{distribution files<https://GitHub.com/mrJean1/PyGeodesy/tree/master/dist>} contain the tests, 

121the test results (on macOS only) and the complete U{documentation<https://mrJean1.GitHub.io/PyGeodesy>} 

122(generated by U{Epydoc<https://PyPI.org/project/epydoc>} using command line: 

123C{epydoc --html --no-private --no-source --name=pygeodesy --url=... -v pygeodesy}). 

124 

125Tests 

126===== 

127 

128The tests ran with Python 3.13.3 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0), 

129Python 3.12.7 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0, 

130U{numpy<https://PyPI.org/project/numpy>} 2.1.0, U{scipy<https://PyPI.org/project/scipy>} 1.14.1, 

131U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.5, 

132U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.5 and 

133U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.5), 

134Python 3.11.5 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0, 

135U{numpy<https://PyPI.org/project/numpy>} 1.24.2 and U{scipy<https://PyPI.org/project/scipy>} 1.10.1), 

136Python 3.10.8 (with U{geographiclib <https://PyPI.org/project/geographiclib>} 2.0, 

137U{numpy<https://PyPI.org/project/numpy>} 1.23.3, U{scipy<https://PyPI.org/project/scipy>} 1.9.1, 

138U{GeoConvert<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.5, 

139U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.5) and 

140Python 2.7.18 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 1.50, 

141U{numpy<https://PyPI.org/project/numpy>} 1.16.6, U{scipy<https://PyPI.org/project/scipy>} 1.2.2, 

142U{GeoConvert<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.5, 

143U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.5, 

144U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.5 and 

145U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.5), all in 64-bit on 

146macOS 15.5 Sequoia. 

147 

148All tests ran with and without C{lazy import} for Python 3 and with command line option C{-W default} and 

149env variable C{PYGEODESY_WARNINGS=on} for all Python versions. The results of those tests are included in 

150the distribution files. 

151 

152Test coverage has been measured with U{coverage<https://PyPI.org/project/coverage>} 7.6.1 using Python 

1533.13.3, 3.12.7, 3.11.5 and 3.10.8. The complete coverage report in HTML and a PDF summary are included in 

154the distribution files. 

155 

156Python 3.13.3, 3.12.7, 3.11.5 and 3.10.8 run on Apple M4 Si (C{arm64}), I{natively}. Python 2.7.18 runs 

157on Intel (C{x86_64}) or Intel I{emulation} ("C{arm64_x86_64}", see function L{machine<pygeodesy.machine>}). 

158 

159The tests also ran with Python 3.13.3 (and U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0) on 

160U{Debian 12<https://Cirrus-CI.com/github/mrJean1/PyGeodesy/master>} in 64-bit only, with Python 3.12.8 (and 

161U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0) on U{Windows 2019Server 

162<https://CI.AppVeyor.com/project/mrJean1/pygeodesy>} in 64-bit only and with Python 2.7.18 (and U{geographiclib 

163<https://PyPI.org/project/geographiclib>} 1.52) on U{Windows 10<https://CI.AppVeyor.com/project/mrJean1/pygeodesy>} 

164in 64- and 32-bit. 

165 

166A single-File and single-Directory application with C{pygeodesy} has been bundled using U{PyInstaller 

167<https://PyPI.org/project/pyinstaller>} 3.4 and 64-bit Python 3.7.3 on macOS 10.13.6 High Sierra. 

168 

169Previously, the tests were run with Python 3.13.0-2, 3.12.0-6, 3.11.2-4, 3.10.1-7, 3.9.6, 3.9.1, 3.8.7, 3.7.1, 2.7.15, 

170U{PyPy<https://PyPy.org>} 7.3.12 (Python 3.10.12), 7.3.1 (Python 3.6.9) and U{PyPy<https://PyPy.org>} 7.1.1 (Python 

1712.7.13) (and U{geographiclib <https://PyPI.org/project/geographiclib>} 1.52, U{numpy<https://PyPI.org/project/numpy>} 

1721.16.3, 1.16.4, 1.16.6, 1.19.0, 1.19.4, 1.19.5 or 1.22.4 and U{scipy<https://PyPI.org/project/scipy>} 1.2.1, 1.4.1, 

1731.5.2 or 1.8.1) on U{Ubuntu 16.04<https://Travis-CI.com/mrJean1/PyGeodesy>}, with Python 3.10.0-1, 3.9.0-5, 3.8.0-6, 

1743.7.2-6, 3.7.0, 3.6.2-5, 3.5.3, 2.7.13-17, 2.7.10 and 2.6.9 (and U{numpy<https://PyPI.org/project/numpy>} 1.19.0, 

1751.16.5, 1.16.2, 1.15.2, 1.14.0, 1.13.1, 1.8.0rc1 or 1.6.2 and U{scipy<https://PyPI.org/project/scipy>} 1.5.0), U{PyPy 

176<https://PyPy.org>} 7.3.0 (Python 2.7.13 and 3.6.9), U{PyPy<https://PyPy.org>} 6.0.0 (Python 2.7.13 and 3.5.3) 

177and U{Intel-Python<https://software.Intel.com/en-us/distribution-for-python>} 3.5.3 (and U{numpy 

178<https://PyPI.org/project/numpy>} 1.11.3) on macOS 15.0-4 Sequoia, 14.0-6.1 Sonoma, 13.0-5.2 Ventura, 12.1-6 Monterey, 

17911.0-5.2-6.1 Big Sur (aka 10.16), 10.15.3, 10.15.5-7 Catalina, 10.14 Mojave, 10.13.6 High Sierra and 10.12 Sierra, 

180MacOS X 10.11 El Capitan and/or MacOS X 10.10 Yosemite, with U{Pythonista<https://OMZ-Software.com/pythonista>}3.2 

181(with geographiclib 1.50 or 1.49 and numpy 1.8.0) on iOS 14.4.2, 11.4.1, 12.0-3 on iPad4, iPhone6, iPhone10 and/or 

182iPhone12, with U{Pythonista<https://OMZ-Software.com/pythonista>} 3.1 on iOS 10.3.3, 11.0.3, 11.1.2 and 11.3 on iPad4, 

183all in 64-bit only and with 32-bit Python 2.7.14 on Windows Server 2012R2, Windows 10 Pro and with 32-bit Python 2.6.6 

184on Windows XP SP3. 

185 

186Notes 

187===== 

188 

189All Python source code has been statically U{checked<https://GitHub.com/ActiveState/code/tree/master/recipes/Python/ 

190546532_PyChecker_postprocessor>} with U{Ruff<https://GitHub.com/astral-sh/ruff>} using Python 3.13.3 and with 

191U{PyChecker<https://PyPI.org/project/pychecker>}, U{PyFlakes<https://PyPI.org/project/pyflakes>}, U{PyCodeStyle 

192<https://PyPI.org/project/pycodestyle>} (formerly Pep8) and U{McCabe<https://PyPI.org/project/mccabe>} using Python 

1932.7.18, both in 64-bit on macOS 15.5 Sequoia only. 

194 

195For a summary of all I{Karney}-based functionality in C{pygeodesy}, see module U{karney 

196<https://mrJean1.GitHub.io/PyGeodesy/docs/pygeodesy.karney-module.html>}. 

197 

198In Python 2, symbols L{S_DEG}, L{S_MIN}, L{S_SEC}, L{S_RAD} and L{S_SEP} may be multi-byte, non-ascii 

199characters and if so, I{not} C{unicode}. 

200 

201Env variables 

202============= 

203 

204The following environment variables are observed by C{pygeodesy}: 

205 

206 - C{PYGEODESY_EXCEPTION_CHAINING} - see module L{errors<pygeodesy.errors>}. 

207 - C{PYGEODESY_FMT_FORM} - see module L{dms<pygeodesy.dms>}. 

208 - C{PYGEODESY_FSUM_F2PRODUCT} - see module L{fsums<pygeodesy.fsums>} and method L{f2product<pygeodesy.Fsum.f2product>}. 

209 - C{PYGEODESY_FSUM_NONFINITES} - see module L{fsums<pygeodesy.fsums>} and method L{nonfinites<pygeodesy.Fsum.nonfinites>}. 

210 - C{PYGEODESY_FSUM_RESIDUAL} - see module L{fsums<pygeodesy.fsums>} and method L{RESIDUAL<pygeodesy.Fsum.RESIDUAL>}. 

211 - C{PYGEODESY_GEOCONVERT} - see module L{mgrs<pygeodesy.mgrs>}. 

212 - C{PYGEODESY_GEODSOLVE} - see module L{geodsolve<pygeodesy.geodsolve>}. 

213 - C{PYGEODESY_INTERSECTTOOL} - see module L{geodesici<pygeodesy.geodesici>}. 

214 - C{PYGEODESY_LAZY_IMPORT} - see module L{lazily<pygeodesy.lazily>} and variable L{isLazy<pygeodesy.isLazy>}. 

215 - C{PYGEODESY_NOTIMPLEMENTED} - C{__special__} methods return C{NotImplemented} if set to "std". 

216 - C{PYGEODESY_RHUMBSOLVE} - see module L{rhumb.solve<pygeodesy.rhumb.solve>}. 

217 - C{PYGEODESY_UPS_POLES} - see modules L{ups<pygeodesy.ups>} and L{mgrs<pygeodesy.mgrs>}. 

218 

219and these to specify standard or I{named} C{repr}esentations: 

220 

221 - C{PYGEODESY_AZIMUTH_STD_REPR} - see method L{Azimuth<pygeodesy.Azimuth>}C{.__repr__}. 

222 - C{PYGEODESY_BEARING_STD_REPR} - see method L{Bearing<pygeodesy.Bearing>}C{.__repr__}. 

223 - C{PYGEODESY_BOOL_STD_REPR} - see method L{Bool<pygeodesy.Bool>}C{.__repr__}. 

224 - C{PYGEODESY_DEGREES_STD_REPR} - see method L{Degrees<pygeodesy.Degrees>}C{.__repr__}. 

225 - C{PYGEODESY_EPOCH_STD_REPR} - see method L{Float<pygeodesy.Epoch>}C{.__repr__}. 

226 - C{PYGEODESY_FLOAT_STD_REPR} - see method L{Float<pygeodesy.Float>}C{.__repr__}. 

227 - C{PYGEODESY_INT_STD_REPR} - see method L{Int<pygeodesy.Int>}C{.__repr__}. 

228 - C{PYGEODESY_METER_STD_REPR} - see method L{Meter<pygeodesy.Meter>}C{.__repr__}. 

229 - C{PYGEODESY_RADIANS_STD_REPR} - see method L{Radians<pygeodesy.Radians>}C{.__repr__}. 

230 - C{PYGEODESY_STR_STD_REPR} - see method L{Str<pygeodesy.Str>}C{.__repr__}. 

231 

232plus during development: 

233 

234 - C{PYGEODESY_FOR_DOCS} - for extended documentation by C{epydoc}. 

235 - C{PYGEODESY_GEOGRAPHICLIB} - see module L{karney<pygeodesy.karney>}. 

236 - C{PYGEODESY_WARNINGS} - see module L{props<pygeodesy.props>} and function L{DeprecationWarnings<pygeodesy.DeprecationWarnings>}. 

237 - C{PYGEODESY_XPACKAGES} - see module L{basics<pygeodesy.basics>}. 

238 - C{PYTHONDEVMODE} - see modules L{errors<pygeodesy.errors>} and L{props<pygeodesy.props>}. 

239 

240and: 

241 

242 - C{PYGEODESY_INIT__ALL__} - Set env variable C{PYGEODESY_INIT__ALL__} to anything other than C{"__all__"} to avoid 

243 importing all C{pygeodesy} modules unnecessarily (in Python 2 or with C{PYGEODESY_LAZY_IMPORT} turned off in Python 

244 3). However, to import a C{pygeodesy} item, the item name must be qualified with the C{module} name, for example 

245 C{ from pygeodesy.ellipsoidalExact import LatLon } or C{ from pygeodesy.deprecated import collins } 

246 

247License 

248======= 

249 

250**) U{Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.<https://OpenSource.org/licenses/MIT>} 

251 

252C{Permission is hereby granted, free of charge, to any person obtaining a copy of this software 

253and associated documentation files (the "Software"), to deal in the Software without restriction, 

254including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, 

255and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, 

256subject to the following conditions:} 

257 

258C{The above copyright notice and this permission notice shall be included in all copies or substantial 

259portions of the Software.} 

260 

261C{THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT 

262NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. 

263IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, 

264WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE 

265SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.} 

266 

267@newfield example: Example, Examples 

268 

269@var EPS: System's M{epsilon} ≈ 2.22044604925e-16 (C{float}). 

270@var EPS0: M{EPS**2} ≈ 4.9e-32 for near-zero comparison 

271@var EPS02: M{EPS**4} ≈ 2.4e-63 for near-zero squared comparison 

272@var EPS1: M{1 - EPS} ≈ 0.9999999999999998 (C{float}). 

273@var EPS2: M{EPS * 2} ≈ 4.440892098501e-16 (C{float}). 

274@var EPS_2: M{EPS / 2} ≈ 1.110223024625e-16 (C{float}). 

275@var EPS4: M{EPS * 4} ≈ 8.881784197001e-16 (C{float}). 

276 

277@var F_D: Format degrees as unsigned "deg°" with symbol, plus compass point suffix C{N, S, E} or C{W} (C{str}). 

278@var F_DM: Format degrees as unsigned "deg°min′" with symbols, plus suffix (C{str}). 

279@var F_DMS: Format degrees as unsigned "deg°min′sec″" with symbols, plus suffix (C{str}). 

280@var F_DEG: Format degrees as unsigned "[D]DD" I{without} symbol, plus suffix (C{str}). 

281@var F_MIN: Format degrees as unsigned "[D]DDMM" I{without} symbols, plus suffix (C{str}). 

282@var F_SEC: Format degrees as unsigned "[D]DDMMSS" I{without} symbols, plus suffix (C{str}). 

283@var F_D60: Format degrees as unsigned "[D]DD.MMSS" C{sexagecimal} I{without} symbols, plus suffix (C{str}). 

284@var F__E: Format degrees as unsigned "%E" I{without} symbols, plus suffix (C{str}). 

285@var F__F: Format degrees as unsigned "%F" I{without} symbols, plus suffix (C{str}). 

286@var F__G: Format degrees as unsigned "%G" I{without} symbols, plus suffix (C{str}). 

287@var F_RAD: Convert degrees to radians and format as unsigned "RR" with symbol, plus suffix (C{str}). 

288 

289@var F_D_: Format degrees as signed "-/deg°" with symbol, I{without} suffix (C{str}). 

290@var F_DM_: Format degrees as signed "-/deg°min′" with symbols, I{without} suffix (C{str}). 

291@var F_DMS_: Format degrees as signed "-/deg°min′sec″" with symbols, I{without} suffix (C{str}). 

292@var F_DEG_: Format degrees as signed "-/[D]DD" I{without} symbol, I{without} suffix (C{str}). 

293@var F_MIN_: Format degrees as signed "-/[D]DDMM" I{without} symbols, I{without} suffix (C{str}). 

294@var F_SEC_: Format degrees as signed "-/[D]DDMMSS" I{without} symbols, I{without} suffix (C{str}). 

295@var F_D60_: Format degrees as signed "-/[D]DD.MMSS" C{sexagecimal} I{without} symbols, I{without} suffix (C{str}). 

296@var F__E_: Format degrees as signed "-/%E" I{without} symbols, I{without} suffix (C{str}). 

297@var F__F_: Format degrees as signed "-/%F" I{without} symbols, I{without} suffix (C{str}). 

298@var F__G_: Format degrees as signed "-/%G" I{without} symbols, I{without} suffix (C{str}). 

299@var F_RAD_: Convert degrees to radians and format as signed "-/RR" I{without} symbol, I{without} suffix (C{str}). 

300 

301@var F_D__: Format degrees as signed "-/+deg°" with symbol, I{without} suffix (C{str}). 

302@var F_DM__: Format degrees as signed "-/+deg°min′" with symbols, I{without} suffix (C{str}). 

303@var F_DMS__: Format degrees as signed "-/+deg°min′sec″" with symbols, I{without} suffix (C{str}). 

304@var F_DEG__: Format degrees as signed "-/+[D]DD" I{without} symbol, I{without} suffix (C{str}). 

305@var F_MIN__: Format degrees as signed "-/+[D]DDMM" I{without} symbols, without suffix (C{str}). 

306@var F_SEC__: Format degrees as signed "-/+[D]DDMMSS" I{without} symbols, I{without} suffix (C{str}). 

307@var F_D60__: Format degrees as signed "-/+[D]DD.MMSS" C{sexagecimal} I{without} symbols, I{without} suffix (C{str}). 

308@var F__E__: Format degrees as signed "-/+%E" I{without} symbols, I{without} suffix (C{str}). 

309@var F__F__: Format degrees as signed "-/+%F" I{without} symbols, I{without} suffix (C{str}). 

310@var F__G__: Format degrees as signed "-/+%G" I{without} symbols, I{without} suffix (C{str}). 

311@var F_RAD__: Convert degrees to radians and format as signed "-/+RR" I{without} symbol, I{without} suffix (C{str}). 

312 

313@var DIG: System's M{float decimal digits} = 15 (C{int}). 

314@var INF: Infinity (C{float}), see functions L{isinf<pygeodesy.isinf>} and L{isfinite<pygeodesy.isfinite>} and C{NINF}. 

315@var INT0: C{int(0)}, missing Z-components, C{if B{z}=B{INT0}}, see functions L{isint0<pygeodesy.isint0>}, L{meeus2<pygeodesy.meeus2>} 

316@var MANT_DIG: System's M{float mantissa bits} = 53 (C{int}). 

317@var MAX: System's M{float max} ≈ 1.798e+308 (C{float}). 

318@var MIN: System's M{float min} ≈ 2.225e-308 (C{float}). 

319@var NAN: Not-A-Number (C{float}), see function L{isnan<pygeodesy.isnan>}. 

320@var NEG0: Negative 0.0 (C{float}), see function L{isneg0<pygeodesy.isneg0>}. 

321@var NINF: Negative infinity (C{float}), see function L{isninf<pygeodesy.isninf>} and C{INF}. 

322@var NN: Empty (C{str}), U{I{Nomen Nescio}<https://Wiktionary.org/wiki/N.N.>}. 

323 

324@var PI: Constant M{math.pi} (C{float}). 

325@var PI2: Two PI, M{PI * 2}, aka I{Tau} (C{float}). 

326@var PI_2: Half PI, M{PI / 2} (C{float}). 

327@var PI3: Three PI, M{PI * 3} (C{float}). 

328@var PI3_2: One and a half PI, M{PI * 3 / 2} (C{float}). 

329@var PI_3: One third PI, M{PI / 3} (C{float}). 

330@var PI4: Four PI, M{PI * 4} (C{float}). 

331@var PI_4: Quarter PI, M{PI / 4} (C{float}). 

332 

333@var R_MA: Equatorial earth radius (C{meter}), WGS84, EPSG:3785. 

334@var R_MB: Polar earth radius (C{meter}), WGS84, EPSG:3785. 

335@var R_M: Mean (spherical) earth radius (C{meter}). 

336@var R_KM: Mean (spherical) earth radius (C{Km}, kilometer). 

337@var R_NM: Mean (spherical) earth radius (C{NM}, nautical miles). 

338@var R_SM: Mean (spherical) earth radius (C{SM}, statute miles). 

339@var R_FM: Former FAI-Sphere earth radius (C{meter}). 

340@var R_GM: Average earth radius, distance to geoid surface (C{meter}) 

341@var R_QM: Earth' (triaxial) quadratic mean radius (C{meter}) 

342@var R_VM: Aviation/Navigation earth radius (C{meter}). 

343 

344@var S_DEG: Degrees symbol, default C{"°"} 

345@var S_MIN: Minutes symbol, default C{"′"} aka I{PRIME} 

346@var S_SEC: Seconds symbol, default C{"″"} aka I{DOUBLE_PRIME} 

347@var S_RAD: Radians symbol, default C{""} aka L{NN<pygeodesy.NN>} 

348@var S_DMS: If C{True}, include, otherwise cancel all DMS symbols, default C{True}. 

349@var S_SEP: Separator between C{deg°|min′|sec″|suffix}, default C{""} aka L{NN<pygeodesy.NN>} 

350 

351@var Conics: Registered, predefined conics (C{enum-like}). 

352@var Datums: Registered, predefined datums (C{enum-like}). 

353@var Ellipsoids: Registered, predefined ellipsoids (C{enum-like}). 

354@var RefFrames: Registered, predefined reference frames (C{enum-like}). 

355@var Transforms: Registered, predefined transforms (C{enum-like}). 

356@var Triaxials: Registered, predefined triaxial ellipsoids (C{enum-like}). 

357 

358@var isLazy: Lazy import setting (C{int} 0, 1, 2 or 3+) from C{env} variable C{PYGEODESY_LAZY_IMPORT}, or C{None} if C{lazy import} is not supported or not enabled, or C{False} if initializing C{lazy import} failed. 

359 

360@var pygeodesy_abspath: Fully qualified C{pygeodesy} directory name (C{str}). 

361 

362@var version: Normalized C{pygeodesy} version (C{str}). 

363''' 

364 

365import os.path as _os_path 

366import sys as _sys 

367 

368_init__all__ = True 

369# <https://PyInstaller.ReadTheDocs.io/en/stable/runtime-information.html> 

370_isfrozen = getattr(_sys, 'frozen', False) 

371pygeodesy_abspath = _os_path.dirname(_os_path.abspath(__file__)) # _sys._MEIPASS + '/pygeodesy' 

372_pygeodesy_ = __package__ or _os_path.basename(pygeodesy_abspath) 

373 

374if _isfrozen: # avoid lazy import 

375 _lazy_import2 = None 

376else: 

377 # setting __path__ should ... 

378 __path__ = [pygeodesy_abspath] 

379 try: # ... make this import work, ... 

380 import pygeodesy.lazily as _ 

381 except ImportError: # ... if it doesn't, extend _sys.path to include 

382 # this very directory such that all public and private sub-modules 

383 # can be imported (by epydoc, checked by PyChecker, etc.) 

384 _sys.path.insert(0, pygeodesy_abspath) # XXX __path__[0] 

385 

386 try: # lazily requires Python 3.7+, see lazily.__doc__ 

387 from pygeodesy.lazily import _init__all__, _lazy_import2 # PYCHOK expected 

388 _, __getattr__ = _lazy_import2(_pygeodesy_) # PYCHOK expected 

389 

390 except (ImportError, NotImplementedError): # LazyImportError 

391 _lazy_import2 = None 

392 

393if _init__all__ and not _lazy_import2: # import and set __all__ 

394 

395 # import all public modules and export as such 

396 import pygeodesy.albers as albers # noqa: F401 

397 import pygeodesy.auxilats as auxilats # noqa: F401 

398 import pygeodesy.azimuthal as azimuthal # noqa: F401 

399 import pygeodesy.basics as basics # noqa: F401 

400 import pygeodesy.booleans as booleans # noqa: F401 

401 import pygeodesy.cartesianBase as cartesianBase # noqa: F401 INTERNAL 

402 import pygeodesy.clipy as clipy # noqa: F401 

403 import pygeodesy.constants as constants # noqa: F401 

404 import pygeodesy.css as css # noqa: F401 

405 import pygeodesy.datums as datums # noqa: F401 

406 import pygeodesy.deprecated as deprecated # noqa: F401 

407 import pygeodesy.dms as dms # noqa: F401 

408 import pygeodesy.ecef as ecef # noqa: F401 

409 import pygeodesy.ecefLocals as ecefLocals # noqa: F401 

410 import pygeodesy.elevations as elevations # noqa: F401 

411 import pygeodesy.ellipsoidalBase as ellipsoidalBase # noqa: F401 INTERNAL 

412 import pygeodesy.ellipsoidalBaseDI as ellipsoidalBaseDI # noqa: F401 INTERNAL 

413 import pygeodesy.ellipsoidalExact as ellipsoidalExact # noqa: F401 

414 import pygeodesy.ellipsoidalGeodSolve as ellipsoidalGeodSolve # noqa: F401 

415 import pygeodesy.ellipsoidalKarney as ellipsoidalKarney # noqa: F401 

416 import pygeodesy.ellipsoidalNvector as ellipsoidalNvector # noqa: F401 

417 import pygeodesy.ellipsoidalVincenty as ellipsoidalVincenty # noqa: F401 

418 import pygeodesy.ellipsoids as ellipsoids # noqa: F401 

419 import pygeodesy.elliptic as elliptic # noqa: F401 

420 import pygeodesy.epsg as epsg # noqa: F401 

421 import pygeodesy.etm as etm # noqa: F401 

422 import pygeodesy.errors as errors # noqa: F401 

423 import pygeodesy.fmath as fmath # noqa: F401 

424 import pygeodesy.formy as formy # noqa: F401 

425 import pygeodesy.frechet as frechet # noqa: F401 

426 import pygeodesy.fstats as fstats # noqa: F401 

427 import pygeodesy.fsums as fsums # noqa: F401 

428 import pygeodesy.gars as gars # noqa: F401 

429 import pygeodesy.geodesici as geodesici # noqa: F401 

430 import pygeodesy.geodesicw as geodesicw # noqa: F401 

431 import pygeodesy.geodesicx as geodesicx # noqa: F401 

432 import pygeodesy.geodsolve as geodsolve # noqa: F401 

433 import pygeodesy.geohash as geohash # noqa: F401 

434 import pygeodesy.geoids as geoids # noqa: F401 

435 import pygeodesy.hausdorff as hausdorff # noqa: F401 

436 import pygeodesy.heights as heights # noqa: F401 

437 import pygeodesy.internals as internals # noqa: F401 

438 import pygeodesy.interns as interns # noqa: F401 

439 import pygeodesy.iters as iters # noqa: F401 

440 import pygeodesy.karney as karney # noqa: F401 

441 import pygeodesy.ktm as ktm # noqa: F401 

442 import pygeodesy.latlonBase as latlonBase # noqa: F401 INTERNAL 

443 import pygeodesy.lazily as lazily # noqa: F401 

444 import pygeodesy.lcc as lcc # noqa: F401 

445 import pygeodesy.ltp as ltp # noqa: F401 

446 import pygeodesy.ltpTuples as ltpTuples # noqa: F401 

447 import pygeodesy.mgrs as mgrs # noqa: F401 

448 import pygeodesy.named as named # noqa: F401 

449 import pygeodesy.namedTuples as namedTuples # noqa: F401 

450 import pygeodesy.nvectorBase as nvectorBase # noqa: F401 INTERNAL 

451 import pygeodesy.osgr as osgr # noqa: F401 

452 import pygeodesy.points as points # noqa: F401 

453 import pygeodesy.props as props # noqa: F401 

454 import pygeodesy.resections as resections # noqa: F401 

455 import pygeodesy.rhumb as rhumb # noqa: F401 

456 import pygeodesy.simplify as simplify # noqa: F401 

457 import pygeodesy.sphericalBase as sphericalBase # noqa: F401 INTERNAL 

458 import pygeodesy.sphericalNvector as sphericalNvector # noqa: F401 

459 import pygeodesy.sphericalTrigonometry as sphericalTrigonometry # noqa: F401 

460 import pygeodesy.solveBase as solveBase # noqa: F401 

461 import pygeodesy.streprs as streprs # noqa: F401 

462 import pygeodesy.trf as trf # noqa: F401 

463 import pygeodesy.triaxials as triaxials # noqa: F401 

464 import pygeodesy.units as units # noqa: F401 

465 import pygeodesy.unitsBase as unitsBase # noqa: F401 INTERNAL 

466 import pygeodesy.ups as ups # noqa: F401 

467 import pygeodesy.utily as utily # noqa: F401 

468 import pygeodesy.utm as utm # noqa: F401 

469 import pygeodesy.utmups as utmups # noqa: F401 

470 import pygeodesy.utmupsBase as utmupsBase # noqa: F401 INTERNAL 

471 import pygeodesy.vector2d as vector2d # noqa: F401 

472 import pygeodesy.vector3d as vector3d # noqa: F401 

473 import pygeodesy.vector3dBase as vector3dBase # noqa: F401 INTERNAL 

474 import pygeodesy.webmercator as webmercator # noqa: F401 

475 import pygeodesy.wgrs as wgrs # noqa: F401 

476 

477 # lift all public classes, constants, functions, etc. but ONLY 

478 # from the following modules ... (see also David Beazley's 

479 # talk <https://DaBeaz.com/modulepackage/index.html>) ... BUT 

480 # NOT modules ellipsoidal*, epsg, gars, geohash, spherical*, 

481 # vector and wgrs ... in order keep those as modules ONLY 

482 from pygeodesy.albers import * # noqa: F403 

483 from pygeodesy.azimuthal import * # noqa: F403 

484# from pygeodesy.auxilats import * # noqa: F403 

485 from pygeodesy.basics import * # noqa: F403 

486 from pygeodesy.booleans import * # noqa: F403 

487 from pygeodesy.cartesianBase import * # noqa: F403 INTERNAL 

488 from pygeodesy.clipy import * # noqa: F403 

489 from pygeodesy.constants import * # noqa: F403 

490 from pygeodesy.css import * # noqa: F403 

491 from pygeodesy.datums import * # noqa: F403 

492 from pygeodesy.deprecated import * # noqa: F403 DEPRECATED 

493 from pygeodesy.dms import * # noqa: F403 

494 from pygeodesy.ecef import * # noqa: F403 

495# from pygeodesy.ecefLocals import * # noqa: F403 

496 from pygeodesy.elevations import * # noqa: F403 

497# from pygeodesy.ellipsoidalBase import * # noqa: F403 INTERNAL 

498# from pygeodesy.ellipsoidalBaseDI import * # noqa: F403 INTERNAL 

499# from pygeodesy.ellipsoidalExact import * # noqa: F403 

500# from pygeodesy.ellipsoidalGeodSolve import * # noqa: F403 

501# from pygeodesy.ellipsoidalKarney import * # noqa: F403 

502# from pygeodesy.ellipsoidalNvector import * # noqa: F403 

503 from pygeodesy.ellipsoidalVincenty import * # noqa: F403 

504 from pygeodesy.ellipsoids import * # noqa: F403 

505 from pygeodesy.elliptic import * # noqa: F403 

506 from pygeodesy.epsg import * # noqa: F403 

507 from pygeodesy.etm import * # noqa: F403 

508 from pygeodesy.errors import * # noqa: F403 

509 from pygeodesy.fmath import * # noqa: F403 

510 from pygeodesy.formy import * # noqa: F403 

511 from pygeodesy.frechet import * # noqa: F403 

512 from pygeodesy.fstats import * # noqa: F403 

513 from pygeodesy.fsums import * # noqa: F403 

514 from pygeodesy.gars import * # noqa: F403 

515 from pygeodesy.geodesici import * # noqa: F403 

516 from pygeodesy.geodesicw import * # noqa: F403 

517 from pygeodesy.geodesicx import * # noqa: F403 

518 from pygeodesy.geodsolve import * # noqa: F403 

519 from pygeodesy.geohash import * # noqa: F403 

520 from pygeodesy.geoids import * # noqa: F403 

521 from pygeodesy.hausdorff import * # noqa: F403 

522 from pygeodesy.heights import * # noqa: F403 

523 from pygeodesy.internals import * # noqa: F403 

524 from pygeodesy.interns import * # noqa: F403 

525 from pygeodesy.iters import * # noqa: F403 

526 from pygeodesy.karney import * # noqa: F403 

527 from pygeodesy.ktm import * # noqa: F403 

528 from pygeodesy.latlonBase import * # noqa: F403 INTERNAL 

529 from pygeodesy.lazily import * # noqa: F403 

530 from pygeodesy.lcc import * # noqa: F403 

531 from pygeodesy.ltp import * # noqa: F403 

532 from pygeodesy.ltpTuples import * # noqa: F403 

533 from pygeodesy.mgrs import * # noqa: F403 

534 from pygeodesy.named import * # noqa: F403 

535 from pygeodesy.namedTuples import * # noqa: F403 

536 from pygeodesy.nvectorBase import * # noqa: F403 INTERNAL 

537 from pygeodesy.osgr import * # noqa: F403 

538 from pygeodesy.points import * # noqa: F403 

539 from pygeodesy.props import * # noqa: F403 

540 from pygeodesy.resections import * # noqa: F403 

541 from pygeodesy.rhumb import * # noqa: F403 

542 from pygeodesy.simplify import * # noqa: F403 

543# from pygeodesy.sphericalBase import * # noqa: F403 INTERNAL 

544# from pygeodesy.sphericalNvector import * # noqa: F403 

545# from pygeodesy.sphericalTrigonometry import * # noqa: F403 

546# from pygeodesy.solveBase import * # noqa: F403 INTERNAL 

547 from pygeodesy.streprs import * # noqa: F403 

548 from pygeodesy.trf import * # noqa: F403 

549 from pygeodesy.triaxials import * # noqa: F403 

550 from pygeodesy.units import * # noqa: F403 

551 from pygeodesy.unitsBase import * # noqa: F403 Float, ... 

552 from pygeodesy.ups import * # noqa: F403 

553 from pygeodesy.utily import * # noqa: F403 

554 from pygeodesy.utm import * # noqa: F403 

555 from pygeodesy.utmups import * # noqa: F403 

556# from pygeodesy.utmupsBase import * # noqa: F403 INTERNAL 

557 from pygeodesy.vector2d import * # noqa: F403 

558 from pygeodesy.vector3d import * # noqa: F403 

559 from pygeodesy.vector3dBase import * # noqa: F403 INTERNAL 

560 from pygeodesy.webmercator import * # noqa: F403 

561 from pygeodesy.wgrs import * # noqa: F403 

562 

563 def _all(globalocals): 

564 from pygeodesy.internals import _headof, _DOT_ # PYCHOK expected 

565 from pygeodesy.interns import NN as _NN, _attribute_, _COMMASPACE_, \ 

566 _module_, _s_ # PYCHOK expected 

567 from pygeodesy.streprs import Fmt as _Fmt # PYCHOK expected 

568 # collect all public module and attribute names and check 

569 # that modules are imported from this package, 'pygeodesy' 

570 # (but the latter only when not bundled with PyInstaller or 

571 # Py2Exe, since the file-layout is different. Courtesy of 

572 # GilderGeek<https://GitHub.com/mrJean1/PyGeodesy/issues/31>) 

573 ns = list(lazily._ALL_INIT) 

574# XXX ps = () if _isfrozen else set([_pygeodesy_] + __name__.split(_DOT_)) 

575 for mod, attrs in lazily._all_enums(): 

576 mod = _headof(_headof(mod)) 

577 if mod not in globalocals: 

578 t = _DOT_(_pygeodesy_, mod) 

579 raise ImportError('missing %s%s: %s' % (_module_, _NN, t)) 

580 ns.append(mod) 

581 # check that all other public attrs do exist 

582 if attrs and isinstance(attrs, tuple): 

583 attrs = lazily._ALL_ATTRS(attrs) 

584 t = tuple(a for a in attrs if a not in globalocals) 

585 if t: 

586 s = _Fmt.SQUARE(_s_, len(t)) if len(t) > 1 else _NN 

587 t = _COMMASPACE_.join(_DOT_(_pygeodesy_, mod, a) for a in t) 

588 raise ImportError('missing %s%s: %s' % (_attribute_, s, t)) 

589 ns.extend(attrs) 

590# XXX if ps: # check that mod is a _pygeodesy_ module 

591# XXX m = globalocals[mod] # assert(typename(m) == mod) 

592# XXX f = getattr(m, _dunder_file_, _NN) 

593# XXX d = _os_path.dirname(_os_path.abspath(f)) if f else pygeodesy_abspath 

594# XXX p = getattr(m, _dunder_package_, _NN) or _pygeodesy_ 

595# XXX if p not in ps or d != pygeodesy_abspath: 

596# XXX t = '%s from %r' % (_DOT_(p, mod), f or p) 

597# XXX raise ImportError('foreign %s: %s' % (_module_, t)) 

598 return tuple(set(ns)) # remove duplicates 

599 

600 __all__ = _all(globals()) # or locals() 

601else: 

602 __all__ = () 

603 _init__all__ = False 

604 

605from pygeodesy.internals import _version2, _DOT_ # noqa: E402 

606# from pygeodesy.interns import _DOT_ # from .internals 

607__version__ = '25.05.28' 

608# see setup.py for similar logic 

609version = _DOT_(*_version2(__version__, n=3)) 

610 

611del _DOT_, _lazy_import2, _os_path, _sys, _version2 

612 

613# **) MIT License 

614# 

615# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

616# 

617# Permission is hereby granted, free of charge, to any person obtaining a 

618# copy of this software and associated documentation files (the "Software"), 

619# to deal in the Software without restriction, including without limitation 

620# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

621# and/or sell copies of the Software, and to permit persons to whom the 

622# Software is furnished to do so, subject to the following conditions: 

623# 

624# The above copyright notice and this permission notice shall be included 

625# in all copies or substantial portions of the Software. 

626# 

627# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

628# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

629# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

630# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

631# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

632# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

633# OTHER DEALINGS IN THE SOFTWARE.