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 partially 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. 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 C++ U{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 

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

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

47projections, Lambert I{conformal conic} projections and positions, functions to clip paths or polygons of C{LatLon} 

48points using the U{Cohen-Sutherland<https://WikiPedia.org/wiki/Cohen-Sutherland_algorithm>}, 

49U{Forster-Hormann-Popa<https://www.ScienceDirect.com/science/article/pii/S259014861930007X>}, 

50U{Greiner-Hormann<http://www.inf.USI.CH/hormann/papers/Greiner.1998.ECO.pdf>}, 

51U{Liang-Barsky<https://www.CS.Helsinki.FI/group/goa/viewing/leikkaus/intro.html>} and 

52U{Sutherland-Hodgman<https://WikiPedia.org/wiki/Sutherland-Hodgman_algorithm>} methods, 

53functions to U{simplify<https://Bost.Ocks.org/mike/simplify>} or linearize a path of C{LatLon} 

54points (or a U{NumPy array<https://docs.SciPy.org/doc/numpy/reference/generated/numpy.array.html>}), 

55including implementations of the U{Ramer-Douglas-Peucker<https://WikiPedia.org/wiki/ 

56Ramer-Douglas-Peucker_algorithm>}, the U{Visvalingam-Whyatt<https://hydra.Hull.ac.UK/ 

57resources/hull:8338>} and the U{Reumann-Witkam<https://psimpl.SourceForge.net/reumann-witkam.html>} 

58algorithms and modified versions of the former. Other classes provide I{boolean} operations between 

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

60the L{height<pygeodesy.heights>} of C{LatLon} points and L{Geoid<pygeodesy.geoids>} models, compute 

61various U{Fréchet<https://WikiPedia.org/wiki/Frechet_distance>} or U{Hausdorff<https://WikiPedia.org/ 

62wiki/Hausdorff_distance>} distances. 

63 

64Installation 

65============ 

66 

67To install PyGeodesy, type C{python[3] -m pip install PyGeodesy} or C{python[3] -m easy_install 

68PyGeodesy} in a terminal or command window. 

69 

70If the wheel C{PyGeodesy-yy.m.d-py2.py3-none-any.whl} is missing in U{PyPI Download files<https:// 

71PyPI.org/project/PyGeodesy/#files>}, download the file from U{GitHub/dist<https://GitHub.com/mrJean1/ 

72PyGeodesy/tree/master/dist>}. Install that with C{python[3] -m pip install <path-to-downloaded-wheel>} 

73and verify with C{python[3] -m pygeodesy}. 

74 

75Alternatively, download C{PyGeodesy-yy.m.d.tar.gz} from U{PyPI<https://PyPI.org/project/PyGeodesy>} 

76or U{GitHub<https://GitHub.com/mrJean1/PyGeodesy>}, C{unzip} the downloaded file, C{cd} to 

77directory C{Pygeodesy-yy.m.d} and type C{python[3] setup.py install}. 

78 

79To run all PyGeodesy tests, type C{python[3] test/run.py} or type C{python[3] test/unitTestSuite.py} 

80before or after installation. 

81 

82Dependencies 

83============ 

84 

85Installation of I{Karney}'s Python package U{geographiclib<https://PyPI.org/project/geographiclib>} 

86is optional, but required to use modules L{ellipsoidalKarney} and L{css}, L{azimuthal} classes 

87L{EquidistantKarney} and L{GnomonicKarney} and the L{HeightIDWkarney} interpolator. 

88 

89Both U{numpy<https://PyPI.org/project/numpy>} and U{scipy<https://PyPI.org/project/scipy>} must be 

90installed for most L{Geoid...<pygeodesy.geoids>} and L{Height...<pygeodesy.heights>} interpolators, 

91except L{GeoidKarney} and the L{HeightIDW...<pygeodesy.heights>} ones. 

92 

93Functions and C{LatLon} methods L{circin6}, L{circum3}, L{circum4_}, L{soddy4}, L{trilaterate3d2} do and 

94C{trilaterate5} and modules L{auxilats} and L{rhumb} may require U{numpy<https://PyPI.org/project/numpy>}. 

95 

96Modules L{ellipsoidalGeodSolve} and L{geodsolve} and L{azimuthal} classes L{EquidistantGeodSolve} 

97and L{GnomonicGeodSolve} depend on I{Karney}'s C++ utility U{GeodSolve 

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

99env variable C{PYGEODESY_GEODSOLVE} or with property L{Ellipsoid.geodsolve}. 

100 

101Class L{Intersectool} in module L{geodesici} needs I{Karney}'s C++ utility U{IntersectTool 

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

103env variable C{PYGEODESY_INTERSECTTOOL}. 

104 

105To compare C{MGRS} results from modules L{mgrs} and C{testMgrs} with I{Karney}'s C++ utility 

106U{GeoConvert<https://GeographicLib.SourceForge.io/C++/doc/GeoConvert.1.html>}, the latter must 

107be executable and set with env variable C{PYGEODESY_GEOCONVERT}. 

108 

109Module L{rhumb.solve} needs I{Karney}'s C++ utility U{RhumbSolve 

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

111env variable C{PYGEODESY_RHUMBSOLVE} or with property L{Ellipsoid.rhumbsolve}. 

112 

113Documentation 

114============= 

115 

116In addition to the C{pygeodesy} package, the U{PyGeodesy<https://PyPI.org/project/PyGeodesy>} 

117U{distribution files<https://GitHub.com/mrJean1/PyGeodesy/tree/master/dist>} contain the tests, 

118the test results (on macOS only) and the complete U{documentation<https://mrJean1.GitHub.io/PyGeodesy>} 

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

120C{epydoc --html --no-private --no-source --name=PyGeodesy --url=... -v pygeodesy}). 

121 

122Tests 

123===== 

124 

125The tests ran with Python 3.13.1 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0), 

126Python 3.12.7 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0, 

127U{numpy<https://PyPI.org/project/numpy>} 2.1.0, U{scipy<https://PyPI.org/project/scipy>} 1.14.1, 

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

129U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3 and 

130U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3), 

131Python 3.11.5 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0, 

132U{numpy<https://PyPI.org/project/numpy>} 1.24.2 and U{scipy<https://PyPI.org/project/scipy>} 1.10.1), 

133Python 3.10.8 (with U{geographiclib <https://PyPI.org/project/geographiclib>} 2.0, 

134U{numpy<https://PyPI.org/project/numpy>} 1.23.3, U{scipy<https://PyPI.org/project/scipy>} 1.9.1, 

135U{GeoConvert<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3, 

136U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3) and 

137Python 2.7.18 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 1.50, 

138U{numpy<https://PyPI.org/project/numpy>} 1.16.6, U{scipy<https://PyPI.org/project/scipy>} 1.2.2, 

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

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

141U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3 and 

142U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3), all in 64-bit on macOS 14.6.1 Sonoma. 

143 

144All tests ran with and without C{lazy import} for Python 3 and with command line option C{-W default} and 

145env variable C{PYGEODESY_WARNINGS=on} for all Python versions. The results of those tests are included in 

146the distribution files. 

147 

148Test coverage has been measured with U{coverage<https://PyPI.org/project/coverage>} 7.6.1 using Python 

1493.13.1, 3.12.7, 3.11.5 and 3.10.8. The complete coverage report in HTML and a PDF summary are included in 

150the distribution files. 

151 

152Python 3.13.1, 3.12.7, 3.11.5 and 3.10.8 run on Apple M1 Silicon (C{arm64}), I{natively}. Python 2.7.18 runs 

153on Intel (C{x86_64}) or Intel I{emulation} ("C{arm64_x86_64}", see function L{machine<pygeodesy.machine>}). 

154 

155The tests also ran with Python 3.13.1 (and U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0) on 

156U{Debian 12<https://Cirrus-CI.com/github/mrJean1/PyGeodesy/master>} in 64-bit only, with Python 3.12.5 (and 

157U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0) on U{Windows 2019Server 

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

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

160in 64- and 32-bit. 

161 

162A single-File and single-Directory application with C{pygeodesy} has been bundled using U{PyInstaller 

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

164 

165Previously, the tests were run with Python 3.13.0, 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, 

166U{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 

1672.7.13) (and U{geographiclib <https://PyPI.org/project/geographiclib>} 1.52, U{numpy<https://PyPI.org/project/numpy>} 

1681.16.3, 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, 

1691.5.2 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, 

1703.7.2-6, 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, 

1711.16.5, 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 

172<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) 

173and U{Intel-Python<https://software.Intel.com/en-us/distribution-for-python>} 3.5.3 (and U{numpy 

174<https://PyPI.org/project/numpy>} 1.11.3) on macOS 14.0-5 Sonoma, 13.0-5.2 Ventura, 12.1-6 Monterey, 11.0-5.2-6.1 

175Big 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 

17610.11 El Capitan and/or MacOS X 10.10 Yosemite, with U{Pythonista<https://OMZ-Software.com/pythonista>}3.2 (with 

177geographiclib 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 

178iPhone12, with U{Pythonista<https://OMZ-Software.com/pythonista>} 3.1 on iOS 10.3.3, 11.0.3, 11.1.2 and 11.3 

179on iPad4, all in 64-bit only and with 32-bit Python 2.7.14 on Windows Server 2012R2, Windows 10 Pro and with 

18032-bit Python 2.6.6 on Windows XP SP3. 

181 

182Notes 

183===== 

184 

185All Python source code has been statically U{checked<https://GitHub.com/ActiveState/code/tree/master/recipes/ 

186Python/546532_PyChecker_postprocessor>} with U{PyChecker<https://PyPI.org/project/pychecker>}, U{PyFlakes 

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

188U{McCabe<https://PyPI.org/project/mccabe>} using Python 2.7.18 and with U{Flake8<https://PyPI.org/project/flake8>} 

189using Python 3.11.5, both in 64-bit on macOS 14.6.1 Sonoma. 

190 

191For a summary of all I{Karney}-based functionality in C{pygeodesy}, see module U{karney 

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

193 

194In 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 

195characters and if so, I{not} C{unicode}. 

196 

197Env variables 

198============= 

199 

200The following environment variables are observed by C{PyGeodesy}: 

201 

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

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

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

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

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

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

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

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

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

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

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

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

214 

215and these to specify standard or I{named} C{repr}esentations: 

216 

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

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

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

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

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

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

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

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

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

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

227 

228plus during development: 

229 

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

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

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

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

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

235 

236and: 

237 

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

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

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

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

242 

243License 

244======= 

245 

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

247 

248C{Permission is hereby granted, free of charge, to any person obtaining a copy of this software 

249and associated documentation files (the "Software"), to deal in the Software without restriction, 

250including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, 

251and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, 

252subject to the following conditions:} 

253 

254C{The above copyright notice and this permission notice shall be included in all copies or substantial 

255portions of the Software.} 

256 

257C{THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT 

258NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. 

259IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, 

260WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE 

261SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.} 

262 

263@newfield example: Example, Examples 

264 

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

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

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

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

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

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

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

272 

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

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

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

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

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

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

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

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

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

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

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

284 

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

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

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

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

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

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

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

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

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

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

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

296 

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

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

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

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

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

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

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

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

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

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

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

308 

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

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

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

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

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

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

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

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

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

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

319 

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

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

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

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

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

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

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

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

328 

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

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

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

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

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

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

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

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

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

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

339 

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

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

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

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

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

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

346 

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

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

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

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

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

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

353 

354@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. 

355 

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

357 

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

359''' 

360 

361import os.path as _os_path 

362import sys as _sys 

363 

364_init__all__ = True 

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

366_isfrozen = getattr(_sys, 'frozen', False) 

367pygeodesy_abspath = _os_path.dirname(_os_path.abspath(__file__)) # _sys._MEIPASS + '/pygeodesy' 

368_pygeodesy_ = __package__ or _os_path.basename(pygeodesy_abspath) 

369 

370if _isfrozen: # avoid lazy import 

371 _lazy_import2 = None 

372else: 

373 # setting __path__ should ... 

374 __path__ = [pygeodesy_abspath] 

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

376 import pygeodesy.lazily as _ 

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

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

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

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

381 

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

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

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

385 

386 except (ImportError, NotImplementedError): # LazyImportError 

387 _lazy_import2 = None 

388 

389if _init__all__ and not _lazy_import2: # import and set __all__ 

390 

391 # import all public modules and export as such 

392 import pygeodesy.albers as albers # PYCHOK exported 

393 import pygeodesy.auxilats as auxilats # PYCHOK exported 

394 import pygeodesy.azimuthal as azimuthal # PYCHOK exported 

395 import pygeodesy.basics as basics # PYCHOK exported 

396 import pygeodesy.booleans as booleans # PYCHOK exported 

397 import pygeodesy.cartesianBase as cartesianBase # PYCHOK INTERNAL 

398 import pygeodesy.clipy as clipy # PYCHOK exported 

399 import pygeodesy.constants as constants # PYCHOK exported 

400 import pygeodesy.css as css # PYCHOK exported 

401 import pygeodesy.datums as datums # PYCHOK exported 

402 import pygeodesy.deprecated as deprecated # PYCHOK exported 

403 import pygeodesy.dms as dms # PYCHOK exported 

404 import pygeodesy.ecef as ecef # PYCHOK exported 

405 import pygeodesy.elevations as elevations # PYCHOK exported 

406 import pygeodesy.ellipsoidalBase as ellipsoidalBase # PYCHOK INTERNAL 

407 import pygeodesy.ellipsoidalBaseDI as ellipsoidalBaseDI # PYCHOK INTERNAL 

408 import pygeodesy.ellipsoidalExact as ellipsoidalExact # PYCHOK exported 

409 import pygeodesy.ellipsoidalGeodSolve as ellipsoidalGeodSolve # PYCHOK exported 

410 import pygeodesy.ellipsoidalKarney as ellipsoidalKarney # PYCHOK exported 

411 import pygeodesy.ellipsoidalNvector as ellipsoidalNvector # PYCHOK exported 

412 import pygeodesy.ellipsoidalVincenty as ellipsoidalVincenty # PYCHOK exported 

413 import pygeodesy.ellipsoids as ellipsoids # PYCHOK exported 

414 import pygeodesy.elliptic as elliptic # PYCHOK exported 

415 import pygeodesy.epsg as epsg # PYCHOK exported 

416 import pygeodesy.etm as etm # PYCHOK exported 

417 import pygeodesy.errors as errors # PYCHOK exported 

418 import pygeodesy.fmath as fmath # PYCHOK exported 

419 import pygeodesy.formy as formy # PYCHOK exported 

420 import pygeodesy.frechet as frechet # PYCHOK exported 

421 import pygeodesy.fstats as fstats # PYCHOK exported 

422 import pygeodesy.fsums as fsums # PYCHOK exported 

423 import pygeodesy.gars as gars # PYCHOK exported 

424 import pygeodesy.geodesici as geodesici # PYCHOK exported 

425 import pygeodesy.geodesicw as geodesicw # PYCHOK exported 

426 import pygeodesy.geodesicx as geodesicx # PYCHOK exported 

427 import pygeodesy.geodsolve as geodsolve # PYCHOK exported 

428 import pygeodesy.geohash as geohash # PYCHOK exported 

429 import pygeodesy.geoids as geoids # PYCHOK exported 

430 import pygeodesy.hausdorff as hausdorff # PYCHOK exported 

431 import pygeodesy.heights as heights # PYCHOK exported 

432 import pygeodesy.internals as internals # PYCHOK exported 

433 import pygeodesy.interns as interns # PYCHOK exported 

434 import pygeodesy.iters as iters # PYCHOK exported 

435 import pygeodesy.karney as karney # PYCHOK exported 

436 import pygeodesy.ktm as ktm # PYCHOK exported 

437 import pygeodesy.latlonBase as latlonBase # PYCHOK INTERNAL 

438 import pygeodesy.lazily as lazily # PYCHOK exported 

439 import pygeodesy.lcc as lcc # PYCHOK exported 

440 import pygeodesy.ltp as ltp # PYCHOK exported 

441 import pygeodesy.ltpTuples as ltpTuples # PYCHOK exported 

442 import pygeodesy.mgrs as mgrs # PYCHOK exported 

443 import pygeodesy.named as named # PYCHOK exported 

444 import pygeodesy.namedTuples as namedTuples # PYCHOK exported 

445 import pygeodesy.nvectorBase as nvectorBase # PYCHOK INTERNAL 

446 import pygeodesy.osgr as osgr # PYCHOK exported 

447 import pygeodesy.points as points # PYCHOK exported 

448 import pygeodesy.props as props # PYCHOK exported 

449 import pygeodesy.resections as resections # PYCHOK exported 

450 import pygeodesy.rhumb as rhumb # PYCHOK exported 

451 import pygeodesy.simplify as simplify # PYCHOK exported 

452 import pygeodesy.sphericalBase as sphericalBase # PYCHOK INTERNAL 

453 import pygeodesy.sphericalNvector as sphericalNvector # PYCHOK exported 

454 import pygeodesy.sphericalTrigonometry as sphericalTrigonometry # PYCHOK exported 

455 import pygeodesy.solveBase as solveBase # PYCHOK exported 

456 import pygeodesy.streprs as streprs # PYCHOK exported 

457 import pygeodesy.trf as trf # PYCHOK exported 

458 import pygeodesy.triaxials as triaxials # PYCHOK exported 

459 import pygeodesy.units as units # PYCHOK exported 

460 import pygeodesy.unitsBase as unitsBase # PYCHOK INTERNAL 

461 import pygeodesy.ups as ups # PYCHOK exported 

462 import pygeodesy.utily as utily # PYCHOK exported 

463 import pygeodesy.utm as utm # PYCHOK exported 

464 import pygeodesy.utmups as utmups # PYCHOK exported 

465 import pygeodesy.utmupsBase as utmupsBase # PYCHOK INTERNAL 

466 import pygeodesy.vector2d as vector2d # PYCHOK exported 

467 import pygeodesy.vector3d as vector3d # PYCHOK exported 

468 import pygeodesy.vector3dBase as vector3dBase # PYCHOK INTERNAL 

469 import pygeodesy.webmercator as webmercator # PYCHOK exported 

470 import pygeodesy.wgrs as wgrs # PYCHOK exported 

471 

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

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

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

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

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

477 from pygeodesy.albers import * # PYCHOK __all__ 

478 from pygeodesy.azimuthal import * # PYCHOK __all__ 

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

480 from pygeodesy.basics import * # PYCHOK __all__ 

481 from pygeodesy.booleans import * # PYCHOK __all__ 

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

483 from pygeodesy.clipy import * # PYCHOK __all__ 

484 from pygeodesy.constants import * # PYCHOK __all__ 

485 from pygeodesy.css import * # PYCHOK __all__ 

486 from pygeodesy.datums import * # PYCHOK __all__ 

487 from pygeodesy.deprecated import * # PYCHOK __all__ DEPRECATED 

488 from pygeodesy.dms import * # PYCHOK __all__ 

489 from pygeodesy.ecef import * # PYCHOK __all__ 

490 from pygeodesy.elevations import * # PYCHOK __all__ 

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

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

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

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

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

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

497 from pygeodesy.ellipsoidalVincenty import * # PYCHOK __(_)__ 

498 from pygeodesy.ellipsoids import * # PYCHOK __all__ 

499 from pygeodesy.elliptic import * # PYCHOK __all__ 

500 from pygeodesy.epsg import * # PYCHOK __all__ 

501 from pygeodesy.etm import * # PYCHOK __all__ 

502 from pygeodesy.errors import * # PYCHOK __all__ 

503 from pygeodesy.fmath import * # PYCHOK __all__ 

504 from pygeodesy.formy import * # PYCHOK __all__ 

505 from pygeodesy.frechet import * # PYCHOK __all__ 

506 from pygeodesy.fstats import * # PYCHOK __all__ 

507 from pygeodesy.fsums import * # PYCHOK __all__ 

508 from pygeodesy.gars import * # PYCHOK __all__ 

509 from pygeodesy.geodesici import * # PYCHOK __all__ 

510 from pygeodesy.geodesicw import * # PYCHOK __all__ 

511 from pygeodesy.geodesicx import * # PYCHOK __all__ 

512 from pygeodesy.geodsolve import * # PYCHOK __all__ 

513 from pygeodesy.geohash import * # PYCHOK __all__ 

514 from pygeodesy.geoids import * # PYCHOK __all__ 

515 from pygeodesy.hausdorff import * # PYCHOK __all__ 

516 from pygeodesy.heights import * # PYCHOK __all__ 

517 from pygeodesy.internals import * # PYCHOK __all__ 

518 from pygeodesy.interns import * # PYCHOK __all__ 

519 from pygeodesy.iters import * # PYCHOK __all__ 

520 from pygeodesy.karney import * # PYCHOK __all__ 

521 from pygeodesy.ktm import * # PYCHOK __all__ 

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

523 from pygeodesy.lazily import * # PYCHOK __all__ 

524 from pygeodesy.lcc import * # PYCHOK __all__ 

525 from pygeodesy.ltp import * # PYCHOK __all__ 

526 from pygeodesy.ltpTuples import * # PYCHOK __all__ 

527 from pygeodesy.mgrs import * # PYCHOK __all__ 

528 from pygeodesy.named import * # PYCHOK __all__ 

529 from pygeodesy.namedTuples import * # PYCHOK __all__ 

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

531 from pygeodesy.osgr import * # PYCHOK __all__ 

532 from pygeodesy.points import * # PYCHOK __all__ 

533 from pygeodesy.props import * # PYCHOK __all__ 

534 from pygeodesy.resections import * # PYCHOK __all__ 

535 from pygeodesy.rhumb import * # PYCHOK __all__ 

536 from pygeodesy.simplify import * # PYCHOK __all__ 

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

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

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

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

541 from pygeodesy.streprs import * # PYCHOK __all__ 

542 from pygeodesy.trf import * # PYCHOK __all__ 

543 from pygeodesy.triaxials import * # PYCHOK __all__ 

544 from pygeodesy.units import * # PYCHOK __all__ 

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

546 from pygeodesy.ups import * # PYCHOK __all__ 

547 from pygeodesy.utily import * # PYCHOK __all__ 

548 from pygeodesy.utm import * # PYCHOK __all__ 

549 from pygeodesy.utmups import * # PYCHOK __all__ 

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

551 from pygeodesy.vector2d import * # PYCHOK __all__ 

552 from pygeodesy.vector3d import * # PYCHOK __all__ 

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

554 from pygeodesy.webmercator import * # PYCHOK __all__ 

555 from pygeodesy.wgrs import * # PYCHOK __all__ 

556 

557 def _all(globalocals): 

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

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

560 _module_, _s_, _UNDER_ # PYCHOK expected 

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

562 # collect all public module and attribute names and check 

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

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

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

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

567 ns = list(lazily._ALL_INIT) 

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

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

570 mod = _headof(_headof(mod)) 

571 if mod not in globalocals: 

572 t = _DOT_(_pygeodesy_, mod) 

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

574 ns.append(mod) 

575 # check that all other public attrs do exist 

576 if attrs and isinstance(attrs, tuple): 

577 attrs = lazily._ALL_ATTRS(attrs) 

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

579 if t: 

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

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

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

583 ns.extend(attrs) 

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

585# XXX m = globalocals[mod] # assert(_DUNDER_nameof(m) == mod) 

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

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

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

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

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

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

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

593 

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

595else: 

596 __all__ = () 

597 _init__all__ = False 

598 

599from pygeodesy.internals import _version2, _DOT_ # PYCHOK import 

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

601__version__ = '25.01.05' 

602# see setup.py for similar logic 

603version = _DOT_(*_version2(__version__, n=3)) 

604 

605del _DOT_, _lazy_import2, _os_path, _sys, _version2 

606 

607# **) MIT License 

608# 

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

610# 

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

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

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

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

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

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

617# 

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

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

620# 

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

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

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

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

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

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

627# OTHER DEALINGS IN THE SOFTWARE.