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 

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

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

7cartesian) and certain U{triaxial ellipsoidal<https://GeographicLib.SourceForge.io/1.44/triaxial.html>} 

8coordinates. 

9 

10Transcoded from U{JavaScript originals<https://GitHub.com/ChrisVeness/geodesy>} by I{Chris Veness (C) 2005-2022} 

11and from several U{C++ classes<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>} by I{Charles F. F. 

12Karney (C) 2008-2023} 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 3d), conversions and unrolling, among other things. For more information and further details see 

21the U{documentation<https://mrJean1.GitHub.io/PyGeodesy>}, the descriptions of U{Latitude/Longitude 

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

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

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

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

26and I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>} and U{C++ GeographicLib 

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

28 

29Also included are modules for conversions to and from U{Cassini-Soldner 

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

31U{ECEF<https://WikiPedia.org/wiki/ECEF>} (Earth-Centered, Earth-Fixed cartesian), U{UTM 

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

33and U{Exact<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercatorExact.html>}), 

34U{UPS<https://WikiPedia.org/wiki/Universal_polar_stereographic_coordinate_system>} (Universal Polar 

35Stereographic) and U{Web Mercator<https://WikiPedia.org/wiki/Web_Mercator>} (Pseudo-Mercator) coordinates, 

36U{MGRS<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1MGRS.html>} (Military Grid Reference 

37System, UTM I{and} UPS) and U{OSGR<https://www.Movable-Type.co.UK/scripts/latlong-os-gridref.html>} (British 

38Ordinance Survery Grid Reference) grid references, U{TRF<http://ITRF.ENSG.IGN.Fr>} (Terrestrial Reference 

39Frames) and modules to encode and decode U{EPSG<https://EPSG.org>}, U{Geohashes 

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

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

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

43 

44Other modules provide U{Albers equal-area<https://GeographicLib.SourceForge.io/ 

45C++/doc/classGeographicLib_1_1AlbersEqualArea.html>} projections, U{equidistant 

46<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AzimuthalEquidistant.html>} 

47and other I{azimuthal} projections, Lambert I{conformal conic} projections and 

48positions, functions to clip paths or polygons of C{LatLon} points using the 

49U{Cohen-Sutherland<https://WikiPedia.org/wiki/Cohen-Sutherland_algorithm>}, 

50U{Forster-Hormann-Popa<https://www.ScienceDirect.com/science/article/pii/S259014861930007X>}, 

51U{Greiner-Hormann<http://www.inf.USI.CH/hormann/papers/Greiner.1998.ECO.pdf>}, 

52U{Liang-Barsky<https://www.CS.Helsinki.FI/group/goa/viewing/leikkaus/intro.html>} and 

53U{Sutherland-Hodgman<https://WikiPedia.org/wiki/Sutherland-Hodgman_algorithm>} methods, 

54functions to U{simplify<https://Bost.Ocks.org/mike/simplify>} or linearize a path of C{LatLon} 

55points (or a U{NumPy array<https://docs.SciPy.org/doc/numpy/reference/generated/numpy.array.html>}), 

56including implementations of the U{Ramer-Douglas-Peucker<https://WikiPedia.org/wiki/ 

57Ramer-Douglas-Peucker_algorithm>}, the U{Visvalingam-Whyatt<https://hydra.Hull.ac.UK/ 

58resources/hull:8338>} and the U{Reumann-Witkam<https://psimpl.SourceForge.net/reumann-witkam.html>} 

59algorithms and modified versions of the former. Other classes provide I{boolean} operations between 

60(composite) polygons or U{interpolate <https://docs.SciPy.org/doc/scipy/reference/interpolate.html>} 

61the L{height<pygeodesy.heights>} of C{LatLon} points and L{Geoid<pygeodesy.geoids>} models, compute 

62various U{Fréchet<https://WikiPedia.org/wiki/Frechet_distance>} or U{Hausdorff<https://WikiPedia.org/ 

63wiki/Hausdorff_distance>} distances. 

64 

65Installation 

66============ 

67 

68To install PyGeodesy, type C{python[3] -m pip install PyGeodesy} or C{python[3] -m easy_install 

69PyGeodesy} in a terminal or command window. 

70 

71If the wheel C{PyGeodesy-yy.m.d-py2.py3-none-any.whl} is missing in U{PyPI Download files<https:// 

72PyPI.org/project/PyGeodesy/#files>}, download the file from U{GitHub/dist<https://GitHub.com/mrJean1/ 

73PyGeodesy/tree/master/dist>}. Install that with C{python[3] -m pip install <path-to-downloaded-wheel>} 

74and verify with C{python[3] -m pygeodesy}. 

75 

76Alternatively, download C{PyGeodesy-yy.m.d.zip} from U{PyPI<https://PyPI.org/project/PyGeodesy>} 

77or U{GitHub<https://GitHub.com/mrJean1/PyGeodesy>}, C{unzip} the downloaded file, C{cd} to 

78directory C{Pygeodesy-yy.m.d} and type C{python[3] setup.py install}. 

79 

80To run all PyGeodesy tests, type C{python[3] test/run.py} or type C{python[3] test/unitTestSuite.py} 

81before or after installation. 

82 

83Dependencies 

84============ 

85 

86Installation of I{Karney}'s Python package U{geographiclib<https://PyPI.org/project/geographiclib>} 

87is optional, but required to use modules L{ellipsoidalKarney} and L{css}, L{azimuthal} classes 

88L{EquidistantKarney} and L{GnomonicKarney} and the L{HeightIDWkarney} interpolator. 

89 

90Both U{numpy<https://PyPI.org/project/numpy>} and U{scipy<https://PyPI.org/project/scipy>} must be 

91installed for most L{Geoid...<pygeodesy.geoids>} and L{Height...<pygeodesy.heights>} interpolators, 

92except L{GeoidKarney} and the L{HeightIDW...<pygeodesy.heights>} ones. 

93 

94Functions and C{LatLon} methods L{circin6}, L{circum3}, L{circum4_}, L{soddy4}, L{trilaterate3d2} do and 

95C{trilaterate5} and modules L{auxilats} and L{rhumb} may require U{numpy<https://PyPI.org/project/numpy>}. 

96 

97Modules L{ellipsoidalGeodSolve} and L{geodsolve} and L{azimuthal} classes L{EquidistantGeodSolve} 

98and L{GnomonicGeodSolve} depend on I{Karney}'s C++ utility U{GeodSolve 

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

100env variable C{PYGEODESY_GEODSOLVE} or with property L{Ellipsoid.geodsolve}. 

101 

102Class L{Intersectool} in module L{geodesici} needs I{Karney}'s C++ utility U{IntersectTool 

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

104env variable C{PYGEODESY_INTERSECTTOOL}. 

105 

106To compare C{MGRS} results from modules L{mgrs} and C{testMgrs} with I{Karney}'s C++ utility 

107U{GeoConvert<https://GeographicLib.SourceForge.io/C++/doc/GeoConvert.1.html>}, the latter must 

108be executable and set with env variable C{PYGEODESY_GEOCONVERT}. 

109 

110Module L{rhumb.solve} needs I{Karney}'s C++ utility U{RhumbSolve 

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

112env variable C{PYGEODESY_RHUMBSOLVE} or with property L{Ellipsoid.rhumbsolve}. 

113 

114Documentation 

115============= 

116 

117In addition to the C{pygeodesy} package, the U{PyGeodesy<https://PyPI.org/project/PyGeodesy>} 

118U{distribution files<https://GitHub.com/mrJean1/PyGeodesy/tree/master/dist>} contain the tests, 

119the test results (on macOS only) and the complete U{documentation<https://mrJean1.GitHub.io/PyGeodesy>} 

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

121C{epydoc --html --no-private --no-source --name=PyGeodesy --url=... -v pygeodesy}). 

122 

123Tests 

124===== 

125 

126The tests ran with Python 3.13.0b4, Python 3.12.4 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0, 

127U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3, 

128U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3 and 

129U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3), 

130Python 3.11.5 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0, 

131U{numpy<https://PyPI.org/project/numpy>} 1.24.2 and U{scipy<https://PyPI.org/project/scipy>} 1.10.1), 

132Python 3.10.8 (with U{geographiclib <https://PyPI.org/project/geographiclib>} 2.0, 

133U{numpy<https://PyPI.org/project/numpy>} 1.23.3, U{scipy<https://PyPI.org/project/scipy>} 1.9.1, 

134U{GeoConvert<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3, 

135U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3) and 

136Python 2.7.18 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 1.50, 

137U{numpy<https://PyPI.org/project/numpy>} 1.16.6, U{scipy<https://PyPI.org/project/scipy>} 1.2.2, 

138U{GeoConvert<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3, 

139U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3, 

140U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3 and 

141U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3), all in 64-bit on macOS 14.5 Sonoma. 

142 

143All tests ran with and without C{lazy import} for Python 3 and with command line option C{-W default} and 

144env variable C{PYGEODESY_WARNINGS=on} for all Python versions. The results of those tests are included in 

145the distribution files. 

146 

147Test coverage has been measured with U{coverage<https://PyPI.org/project/coverage>} 7.6.0 using Python 3.12.4, 

1483.11.5 and 3.10.8. The complete coverage report in HTML and a PDF summary are included in the distribution files. 

149 

150Python 3.13.0b4, 3.12.4, 3.11.5 and 3.10.8 run on Apple M1 Silicon (C{arm64}), I{natively}. Python 2.7.18 runs on 

151Intel (C{x86_64}) or Intel I{emulation} ("C{arm64_x86_64}", see function L{machine<pygeodesy.machine>}). 

152 

153The tests also ran with Python 3.12.4 (and U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0) on U{Debian 

15412<https://Cirrus-CI.com/github/mrJean1/PyGeodesy/master>} in 64-bit only, with Python 3.12.3 (and 

155U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0) on U{Windows 

1562019Server<https://CI.AppVeyor.com/project/mrJean1/pygeodesy>} in 64-bit only and with Python 2.7.18 (and 

157U{geographiclib<https://PyPI.org/project/geographiclib>} 1.52) on U{Windows 

15810<https://CI.AppVeyor.com/project/mrJean1/pygeodesy>} in 64- and 32-bit. 

159 

160A single-File and single-Directory application with C{pygeodesy} has been bundled using U{PyInstaller 

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

162 

163Previously, the tests were run with Python 3.12.0-3, 3.11.2-4, 3.10.1-7, 3.9.6, 3.9.1, 3.8.7, 3.7.1, 2.7.15, U{PyPy 

164<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 

1652.7.13) (and U{geographiclib <https://PyPI.org/project/geographiclib>} 1.52, U{numpy<https://PyPI.org/project/numpy>} 

1661.16.3, 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, 

1671.5.2 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, 

1683.7.2-6, 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, 

1691.16.5, 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 

170<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) 

171and U{Intel-Python<https://software.Intel.com/en-us/distribution-for-python>} 3.5.3 (and U{numpy 

172<https://PyPI.org/project/numpy>} 1.11.3) on macOS 14.0-4.1 Sonoma, 13.0-5.2 Ventura, 12.1-6 Monterey, 11.0-5.2-6.1 

173Big Sur (aka 10.16), 10.15.3, 10.15.5-7 Catalina, 10.14 Mojave, 10.13.6 High Sierra and 10.12 Sierra, MacOS X 

17410.11 El Capitan and/or MacOS X 10.10 Yosemite, with U{Pythonista<https://OMZ-Software.com/pythonista>}3.2 (with 

175geographiclib 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 

176iPhone12, with U{Pythonista<https://OMZ-Software.com/pythonista>} 3.1 on iOS 10.3.3, 11.0.3, 11.1.2 and 11.3 

177on iPad4, all in 64-bit only and with 32-bit Python 2.7.14 on Windows Server 2012R2, Windows 10 Pro and with 

17832-bit Python 2.6.6 on Windows XP SP3. 

179 

180Notes 

181===== 

182 

183All Python source code has been statically U{checked<https://GitHub.com/ActiveState/code/tree/master/recipes/ 

184Python/546532_PyChecker_postprocessor>} with U{PyChecker<https://PyPI.org/project/pychecker>}, U{PyFlakes 

185<https://PyPI.org/project/pyflakes>}, U{PyCodeStyle<https://PyPI.org/project/pycodestyle>} (formerly Pep8) and 

186U{McCabe<https://PyPI.org/project/mccabe>} using Python 2.7.18 and with U{Flake8<https://PyPI.org/project/flake8>} 

187using Python 3.11.5, both in 64-bit on macOS 14.5 Sonoma. 

188 

189For a summary of all I{Karney}-based functionality in C{pygeodesy}, see module U{karney 

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

191 

192In 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 

193characters and if so, I{not} C{unicode}. 

194 

195Env variables 

196============= 

197 

198The following environment variables are observed by C{PyGeodesy}: 

199 

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

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

202 - C{PYGEODESY_FSUM_RESIDUAL} - see module L{fsums<pygeodesy.fsums>} and class L{Fsum<pygeodesy.Fsum>}. 

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

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

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

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

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

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

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

210 

211and these to control standard or I{named} C{repr}esentations: 

212 

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

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

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

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

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

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

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

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

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

222 

223plus during development: 

224 

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

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

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

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

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

230 

231and: 

232 

233 - C{PYGEODESY_INIT__ALL__} - Set env variable C{PYGEODESY_INIT__ALL__} to anything 

234 other than C{"__all__"} to avoid importing all C{pygeodesy} modules unnecessarily 

235 (in Python 2 or with C{PYGEODESY_LAZY_IMPORT} turned off in Python 3). However, 

236 to import a C{pygeodesy} item, the item name must be qualified with the C{module} 

237 name, for example C{ from pygeodesy.ellipsoidalExact import LatLon } or C{ from 

238 pygeodesy.deprecated import collins } 

239 

240License 

241======= 

242 

243**) U{Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.<https://OpenSource.org/licenses/MIT>} 

244 

245C{Permission is hereby granted, free of charge, to any person obtaining a copy of this software 

246and associated documentation files (the "Software"), to deal in the Software without restriction, 

247including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, 

248and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, 

249subject to the following conditions:} 

250 

251C{The above copyright notice and this permission notice shall be included in all copies or substantial 

252portions of the Software.} 

253 

254C{THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT 

255NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. 

256IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, 

257WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE 

258SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.} 

259 

260@newfield example: Example, Examples 

261 

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

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

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

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

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

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

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

269 

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

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

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

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

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

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

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

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

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

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

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

281 

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

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

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

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

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

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

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

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

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

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

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

293 

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

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

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

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

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

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

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

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

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

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

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

305 

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

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

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

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

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

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

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

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

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

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

316 

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

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

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

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

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

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

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

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

325 

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

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

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

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

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

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

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

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

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

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

336 

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

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

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

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

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

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

343 

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

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

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

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

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

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

350 

351@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. 

352 

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

354 

355@var version: Normalized C{PyGeodesy} version (C{str}). 

356''' 

357 

358import os.path as _os_path 

359import sys as _sys 

360 

361_init__all__ = True 

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

363_isfrozen = getattr(_sys, 'frozen', False) 

364pygeodesy_abspath = _os_path.dirname(_os_path.abspath(__file__)) # _sys._MEIPASS + '/pygeodesy' 

365_pygeodesy_ = __package__ or _os_path.basename(pygeodesy_abspath) 

366 

367if _isfrozen: # avoid lazy import 

368 _lazy_import2 = None 

369else: 

370 # setting __path__ should ... 

371 __path__ = [pygeodesy_abspath] 

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

373 import pygeodesy.lazily as _ 

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

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

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

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

378 

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

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

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

382 

383 except (ImportError, NotImplementedError): # LazyImportError 

384 _lazy_import2 = None 

385 

386if _init__all__ and not _lazy_import2: # import and set __all__ 

387 

388 # import all public modules and export as such 

389 import pygeodesy.albers as albers # PYCHOK exported 

390 import pygeodesy.auxilats as auxilats # PYCHOK exported 

391 import pygeodesy.azimuthal as azimuthal # PYCHOK exported 

392 import pygeodesy.basics as basics # PYCHOK exported 

393 import pygeodesy.booleans as booleans # PYCHOK exported 

394 import pygeodesy.cartesianBase as cartesianBase # PYCHOK INTERNAL 

395 import pygeodesy.clipy as clipy # PYCHOK exported 

396 import pygeodesy.constants as constants # PYCHOK exported 

397 import pygeodesy.css as css # PYCHOK exported 

398 import pygeodesy.datums as datums # PYCHOK exported 

399 import pygeodesy.deprecated as deprecated # PYCHOK exported 

400 import pygeodesy.dms as dms # PYCHOK exported 

401 import pygeodesy.ecef as ecef # PYCHOK exported 

402 import pygeodesy.elevations as elevations # PYCHOK exported 

403 import pygeodesy.ellipsoidalBase as ellipsoidalBase # PYCHOK INTERNAL 

404 import pygeodesy.ellipsoidalBaseDI as ellipsoidalBaseDI # PYCHOK INTERNAL 

405 import pygeodesy.ellipsoidalExact as ellipsoidalExact # PYCHOK exported 

406 import pygeodesy.ellipsoidalGeodSolve as ellipsoidalGeodSolve # PYCHOK exported 

407 import pygeodesy.ellipsoidalKarney as ellipsoidalKarney # PYCHOK exported 

408 import pygeodesy.ellipsoidalNvector as ellipsoidalNvector # PYCHOK exported 

409 import pygeodesy.ellipsoidalVincenty as ellipsoidalVincenty # PYCHOK exported 

410 import pygeodesy.ellipsoids as ellipsoids # PYCHOK exported 

411 import pygeodesy.elliptic as elliptic # PYCHOK exported 

412 import pygeodesy.epsg as epsg # PYCHOK exported 

413 import pygeodesy.etm as etm # PYCHOK exported 

414 import pygeodesy.errors as errors # PYCHOK exported 

415 import pygeodesy.fmath as fmath # PYCHOK exported 

416 import pygeodesy.formy as formy # PYCHOK exported 

417 import pygeodesy.frechet as frechet # PYCHOK exported 

418 import pygeodesy.fstats as fstats # PYCHOK exported 

419 import pygeodesy.fsums as fsums # PYCHOK exported 

420 import pygeodesy.gars as gars # PYCHOK exported 

421 import pygeodesy.geodesici as geodesici # PYCHOK exported 

422 import pygeodesy.geodesicw as geodesicw # PYCHOK exported 

423 import pygeodesy.geodesicx as geodesicx # PYCHOK exported 

424 import pygeodesy.geodsolve as geodsolve # PYCHOK exported 

425 import pygeodesy.geohash as geohash # PYCHOK exported 

426 import pygeodesy.geoids as geoids # PYCHOK exported 

427 import pygeodesy.hausdorff as hausdorff # PYCHOK exported 

428 import pygeodesy.heights as heights # PYCHOK exported 

429 import pygeodesy.internals as internals # PYCHOK exported 

430 import pygeodesy.interns as interns # PYCHOK exported 

431 import pygeodesy.iters as iters # PYCHOK exported 

432 import pygeodesy.karney as karney # PYCHOK exported 

433 import pygeodesy.ktm as ktm # PYCHOK exported 

434 import pygeodesy.latlonBase as latlonBase # PYCHOK INTERNAL 

435 import pygeodesy.lazily as lazily # PYCHOK exported 

436 import pygeodesy.lcc as lcc # PYCHOK exported 

437 import pygeodesy.ltp as ltp # PYCHOK exported 

438 import pygeodesy.ltpTuples as ltpTuples # PYCHOK exported 

439 import pygeodesy.mgrs as mgrs # PYCHOK exported 

440 import pygeodesy.named as named # PYCHOK exported 

441 import pygeodesy.namedTuples as namedTuples # PYCHOK exported 

442 import pygeodesy.nvectorBase as nvectorBase # PYCHOK INTERNAL 

443 import pygeodesy.osgr as osgr # PYCHOK exported 

444 import pygeodesy.points as points # PYCHOK exported 

445 import pygeodesy.props as props # PYCHOK exported 

446 import pygeodesy.resections as resections # PYCHOK exported 

447 import pygeodesy.rhumb as rhumb # PYCHOK exported 

448 import pygeodesy.simplify as simplify # PYCHOK exported 

449 import pygeodesy.sphericalBase as sphericalBase # PYCHOK INTERNAL 

450 import pygeodesy.sphericalNvector as sphericalNvector # PYCHOK exported 

451 import pygeodesy.sphericalTrigonometry as sphericalTrigonometry # PYCHOK exported 

452 import pygeodesy.solveBase as solveBase # PYCHOK exported 

453 import pygeodesy.streprs as streprs # PYCHOK exported 

454 import pygeodesy.trf as trf # PYCHOK exported 

455 import pygeodesy.triaxials as triaxials # PYCHOK exported 

456 import pygeodesy.units as units # PYCHOK exported 

457 import pygeodesy.unitsBase as unitsBase # PYCHOK INTERNAL 

458 import pygeodesy.ups as ups # PYCHOK exported 

459 import pygeodesy.utily as utily # PYCHOK exported 

460 import pygeodesy.utm as utm # PYCHOK exported 

461 import pygeodesy.utmups as utmups # PYCHOK exported 

462 import pygeodesy.utmupsBase as utmupsBase # PYCHOK INTERNAL 

463 import pygeodesy.vector2d as vector2d # PYCHOK exported 

464 import pygeodesy.vector3d as vector3d # PYCHOK exported 

465 import pygeodesy.vector3dBase as vector3dBase # PYCHOK INTERNAL 

466 import pygeodesy.webmercator as webmercator # PYCHOK exported 

467 import pygeodesy.wgrs as wgrs # PYCHOK exported 

468 

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

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

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

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

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

474 from pygeodesy.albers import * # PYCHOK __all__ 

475 from pygeodesy.azimuthal import * # PYCHOK __all__ 

476# from pygeodesy.auxilats import * # PYCHOK __(_)__ 

477 from pygeodesy.basics import * # PYCHOK __all__ 

478 from pygeodesy.booleans import * # PYCHOK __all__ 

479 from pygeodesy.cartesianBase import * # PYCHOK __(_)__ INTERNAL 

480 from pygeodesy.clipy import * # PYCHOK __all__ 

481 from pygeodesy.constants import * # PYCHOK __all__ 

482 from pygeodesy.css import * # PYCHOK __all__ 

483 from pygeodesy.datums import * # PYCHOK __all__ 

484 from pygeodesy.deprecated import * # PYCHOK __all__ DEPRECATED 

485 from pygeodesy.dms import * # PYCHOK __all__ 

486 from pygeodesy.ecef import * # PYCHOK __all__ 

487 from pygeodesy.elevations import * # PYCHOK __all__ 

488# from pygeodesy.ellipsoidalBase import * # PYCHOK __(_)__ INTERNAL 

489# from pygeodesy.ellipsoidalBaseDI import * # PYCHOK __(_)__ INTERNAL 

490# from pygeodesy.ellipsoidalExact import * # PYCHOK __(_)__ 

491# from pygeodesy.ellipsoidalGeodSolve import * # PYCHOK __(_)__ 

492# from pygeodesy.ellipsoidalKarney import * # PYCHOK __(_)__ 

493# from pygeodesy.ellipsoidalNvector import * # PYCHOK __(_)__ 

494 from pygeodesy.ellipsoidalVincenty import VincentyError # PYCHOK lazily 

495 from pygeodesy.ellipsoids import * # PYCHOK __all__ 

496 from pygeodesy.elliptic import * # PYCHOK __all__ 

497 from pygeodesy.epsg import Epsg, EPSGError # PYCHOK lazily 

498 from pygeodesy.etm import * # PYCHOK __all__ 

499 from pygeodesy.errors import * # PYCHOK __all__ 

500 from pygeodesy.fmath import * # PYCHOK __all__ 

501 from pygeodesy.formy import * # PYCHOK __all__ 

502 from pygeodesy.frechet import * # PYCHOK __all__ 

503 from pygeodesy.fstats import * # PYCHOK __all__ 

504 from pygeodesy.fsums import * # PYCHOK __all__ 

505 from pygeodesy.gars import Garef, GARSError # PYCHOK lazily 

506 from pygeodesy.geodesici import * # PYCHOK __all__ 

507 from pygeodesy.geodesicw import * # PYCHOK __all__ 

508 from pygeodesy.geodesicx import * # PYCHOK __all__ 

509 from pygeodesy.geodsolve import * # PYCHOK __all__ 

510 from pygeodesy.geohash import * # PYCHOK __all__ 

511 from pygeodesy.geoids import * # PYCHOK __all__ 

512 from pygeodesy.hausdorff import * # PYCHOK __all__ 

513 from pygeodesy.heights import * # PYCHOK __all__ 

514 from pygeodesy.internals import * # PYCHOK __all__ 

515 from pygeodesy.interns import * # PYCHOK __all__ 

516 from pygeodesy.iters import * # PYCHOK __all__ 

517 from pygeodesy.karney import * # PYCHOK __all__ 

518 from pygeodesy.ktm import * # PYCHOK __all__ 

519 from pygeodesy.latlonBase import * # PYCHOK __(_)__ INTERNAL 

520 from pygeodesy.lazily import * # PYCHOK __all__ 

521 from pygeodesy.lcc import * # PYCHOK __all__ 

522 from pygeodesy.ltp import * # PYCHOK __all__ 

523 from pygeodesy.ltpTuples import * # PYCHOK __all__ 

524 from pygeodesy.mgrs import * # PYCHOK __all__ 

525 from pygeodesy.named import * # PYCHOK __all__ 

526 from pygeodesy.namedTuples import * # PYCHOK __all__ 

527# from pygeodesy.nvectorBase import * # PYCHOK __(_)__ INTERNAL 

528 from pygeodesy.osgr import * # PYCHOK __all__ 

529 from pygeodesy.points import * # PYCHOK __all__ 

530 from pygeodesy.props import * # PYCHOK __all__ 

531 from pygeodesy.resections import * # PYCHOK __all__ 

532 from pygeodesy.rhumb import * # PYCHOK __all__ 

533 from pygeodesy.simplify import * # PYCHOK __all__ 

534# from pygeodesy.sphericalBase import * # PYCHOK __(_)__ INTERNAL 

535# from pygeodesy.sphericalNvector import * # PYCHOK __(_)__ 

536# from pygeodesy.sphericalTrigonometry import * # PYCHOK __(_)__ 

537# from pygeodesy.solveBase import * # PYCHOK __(_)__ INTERNAL 

538 from pygeodesy.streprs import * # PYCHOK __all__ 

539 from pygeodesy.trf import * # PYCHOK __all__ 

540 from pygeodesy.triaxials import * # PYCHOK __all__ 

541 from pygeodesy.units import * # PYCHOK __all__ 

542 from pygeodesy.unitsBase import * # PYCHOK __all__ Float, ... 

543 from pygeodesy.ups import * # PYCHOK __all__ 

544 from pygeodesy.utily import * # PYCHOK __all__ 

545 from pygeodesy.utm import * # PYCHOK __all__ 

546 from pygeodesy.utmups import * # PYCHOK __all__ 

547# from pygeodesy.utmupsBase import * # PYCHOK __(_)__ INTERNAL 

548 from pygeodesy.vector2d import * # PYCHOK __all__ 

549 from pygeodesy.vector3d import * # PYCHOK __all__ 

550 from pygeodesy.vector3dBase import * # PYCHOK __(_)__ INTERNAL 

551 from pygeodesy.webmercator import * # PYCHOK __all__ 

552 from pygeodesy.wgrs import Georef, WGRSError # PYCHOK lazily 

553 

554 def _all(globalocals): 

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

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

557 _module_, _s_, _UNDER_ # PYCHOK expected 

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

559 # collect all public module and attribute names and check 

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

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

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

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

564 ns = list(lazily._ALL_INIT) 

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

566 for mod, attrs in lazily._ALL_LAZY.enums(): 

567 mod = _headof(_headof(mod)) 

568 if mod not in globalocals: 

569 t = _DOT_(_pygeodesy_, mod) 

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

571 ns.append(mod) 

572 # check that all other public attrs do exist 

573 if attrs and isinstance(attrs, tuple): 

574 attrs = lazily._ALL_ATTRS(attrs) 

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

576 if t: 

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

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

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

580 ns.extend(attrs) 

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

582# XXX m = globalocals[mod] # assert(_dunder_nameof(m) == mod) 

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

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

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

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

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

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

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

590 

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

592else: 

593 __all__ = () 

594 _init__all__ = False 

595 

596from pygeodesy.internals import _version2, _DOT_ # PYCHOK import 

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

598__version__ = '24.08.04' 

599# see setup.py for similar logic 

600version = _DOT_(*_version2(__version__, n=3)) 

601 

602del _DOT_, _lazy_import2, _os_path, _sys, _version2 

603 

604# **) MIT License 

605# 

606# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

607# 

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

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

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

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

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

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

614# 

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

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

617# 

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

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

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

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

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

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

624# OTHER DEALINGS IN THE SOFTWARE.