Coverage for pygeodesy / __init__.py: 98%
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2# -*- coding: utf-8 -*-
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.
10Transcoded in part from U{JavaScript originals<https://GitHub.com/ChrisVeness/geodesy>} by I{Chris Veness (C)
112005-2025} and from several U{C++ classes<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>} by I{Charles
12F. F. Karney (C) 2008-2025} and published under the same U{MIT License<https://OpenSource.org/licenses/MIT>}**.
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), among other things.
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>}.
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.
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, to compute various U{Fréchet
55<https://WikiPedia.org/wiki/Frechet_distance>} or U{Hausdorff<https://WikiPedia.org/wiki/Hausdorff_distance>}
56distances or to perform I{boolean} operations between (composite) polygons of C{LatLon} points.
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>}.
66Installation
67============
69To install C{pygeodesy}, type C{python[3] -m pip install pygeodesy} in a terminal or command window.
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}.
76Alternatively, download C{pygeodesy-yy.m.d.tar.gz} 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}.
80To run all C{pygeodesy} tests, type C{python[3] -m test.run} or type C{python[3] -m test.unitTestSuite}
81before or after installation.
83Dependencies
84============
86Installation of I{Karney}'s Python package U{geographiclib<https://PyPI.org/project/geographiclib>}
87is optional, but required for module L{ellipsoidalKarney}, L{azimuthal} classes L{EquidistantKarney}
88and L{GnomonicKarney} and the L{HeightIDWkarney} interpolator.
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.
94Functions and C{LatLon} methods L{circin6}, L{circum3}, L{circum4_} and L{soddy4} and functions
95L{triaxum5} and L{trilaterate3d2} require U{numpy<https://PyPI.org/project/numpy>} to be installed,
96modules L{auxilats} and L{rhumb} may need U{numpy<https://PyPI.org/project/numpy>}.
98Modules L{ellipsoidalGeodSolve} and L{geodsolve} and L{azimuthal} classes L{EquidistantGeodSolve}
99and L{GnomonicGeodSolve} depend on I{Karney}'s C++ utility U{GeodSolve
100<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>} to be executable and set with
101env variable C{PYGEODESY_GEODSOLVE} or with property L{Ellipsoid.geodsolve}.
103Triaxial geodesic classes L{Geodesic3Solve} and L{GeodesicLine3Solve} in module L{geod3solve} need
104I{Karney}'s C++ utility U{Geod3Solve<https://GeographicLib.SourceForge.io/C++/doc/Geod3Solve.1.html>}
105to be executable and set with env variable C{PYGEODESY_GEOD3SOLVE} or with property
106L{Geodesic3Solve.Geod3Solve<geod3solve._Geodesic3SolveBase.Geod3Solve>}.
108Class L{Intersectool} in module L{geodesici} needs I{Karney}'s C++ utility U{IntersectTool
109<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>} to be executable and set with
110env variable C{PYGEODESY_INTERSECTTOOL} or with property L{Intersectool.IntersectTool
111<geodesici.Intersectool.IntersectTool>}.
113To compare C{MGRS} results from modules L{mgrs} and C{testMgrs} with I{Karney}'s C++ utility
114U{GeoConvert<https://GeographicLib.SourceForge.io/C++/doc/GeoConvert.1.html>}, the latter must
115be executable and set with env variable C{PYGEODESY_GEOCONVERT}.
117Module L{rhumb.solve} needs I{Karney}'s C++ utility U{RhumbSolve
118<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>} to be executable and set with
119env variable C{PYGEODESY_RHUMBSOLVE} or with property L{Ellipsoid.rhumbsolve}.
121Documentation
122=============
124In addition to the C{pygeodesy} package, the U{pygeodesy<https://PyPI.org/project/pygeodesy>}
125U{distribution file<https://GitHub.com/mrJean1/PyGeodesy/tree/master/dist>} contain the tests,
126the test results (on macOS only) and the complete U{documentation<https://mrJean1.GitHub.io/PyGeodesy>}
127(generated by U{Epydoc<https://PyPI.org/project/epydoc>} using command line:
128C{epydoc --html --no-private --no-source --name=pygeodesy --url=... -v pygeodesy}).
130Tests
131=====
133The tests ran with Python 3.14.7 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.1),
134Python 3.13.13 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.1),
135U{numpy<https://PyPI.org/project/numpy>} 2.5.0, U{scipy<https://PyPI.org/project/scipy>} 1.18.0,
136U{GeoConvert<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.7 and
137U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.7),
138Python 3.12.10 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0,
139U{numpy<https://PyPI.org/project/numpy>} 2.1.0, U{scipy<https://PyPI.org/project/scipy>} 1.14.1,
140U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.7,
141U{GeodS3olve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.7,
142U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.7 and
143U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.7),
144Python 3.11.9 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0,
145U{numpy<https://PyPI.org/project/numpy>} 1.24.2 and U{scipy<https://PyPI.org/project/scipy>} 1.10.1),
146and with Python 2.7.18 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 1.50,
147U{numpy<https://PyPI.org/project/numpy>} 1.16.6, U{scipy<https://PyPI.org/project/scipy>} 1.2.2,
148U{GeoConvert<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.7,
149U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.7,
150U{Geod3Solve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.7,
151U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.7 and
152U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.7), all in 64-bit on
153macOS 27.0.1 Golden Gate.
155All tests ran with and without C{lazy import} for Python 3 and with command line option C{-W default} and
156env variable C{PYGEODESY_WARNINGS=on} for all Python versions. The results of those tests are included in
157the distribution file.
159Test coverage has been measured with U{coverage<https://PyPI.org/project/coverage>} 7.14.0 using Python
1603.14.7, 3.13.13 and 3.12.10. The complete coverage report in HTML and a PDF summary are included in the
161distribution file.
163Python 3.14.7, 3.13.13, 3.12.10 and 3.11.9 run on Apple Si M4 (C{arm64}), I{natively}. Python 2.7.18 runs
164on Intel (C{x86_64}) or Intel I{emulation} ("C{arm64_x86_64}", see function L{machine<pygeodesy.machine>}).
166The tests also ran with Python 3.13.13 (and U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0)
167on U{Windows 2019Server<https://CI.AppVeyor.com/project/mrJean1/pygeodesy>} in 64-bit only and with Python
1682.7.18 (and U{geographiclib<https://PyPI.org/project/geographiclib>} 1.52) on U{Windows 10
169<https://CI.AppVeyor.com/project/mrJean1/pygeodesy>} in 64-bit.
171A single-File and single-Directory application with C{pygeodesy} has been bundled using U{PyInstaller
172<https://PyPI.org/project/pyinstaller>} 3.4 and 64-bit Python 3.7.3 on macOS 10.13.6 High Sierra.
174Previously, the tests were run with Python 3.14.0-6, 3.13.0-9, 3.12.0-7, 3.11.2-5, 3.10.1-7, 3.9.6, 3.9.1, 3.8.7, 3.7.1,
1752.7.15, U{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
176(Python 2.7.13) (and U{geographiclib <https://PyPI.org/project/geographiclib>} 1.52, U{numpy<https://PyPI.org/project/numpy>}
1771.16.3, 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, 1.5.2 or
1781.8.1) 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, 3.7.2-6,
1793.7.0, 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, 1.16.5, 1.16.2,
1801.15.2, 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<https://PyPy.org>}
1817.3.0 (Python 2.7.13 and 3.6.9), U{PyPy<https://PyPy.org>} 6.0.0 (Python 2.7.13 and 3.5.3) and
182U{Intel-Python<https://software.Intel.com/en-us/distribution-for-python>} 3.5.3 (and U{numpy<https://PyPI.org/project/numpy>}
1831.11.3) on macOS 26.6.0-2 Tahoe, 15.0-6 Sequoia, 14.0-6.1 Sonoma, 13.0-5.2 Ventura, 12.1-6 Monterey, 11.0-5.2-6.1 Big Sur
184(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 10.11 El Capitan
185and/or MacOS X 10.10 Yosemite, with U{Pythonista<https://OMZ-Software.com/pythonista>}3.2 (with geographiclib 1.50 or
1861.49 and numpy 1.8.0) on iOS 14.4.2, 11.4.1, 12.0-3 on iPad4, iPhone6, iPhone10 and/or iPhone12, with U{Pythonista
187<https://OMZ-Software.com/pythonista>} 3.1 on iOS 10.3.3, 11.0.3, 11.1.2 and 11.3 on iPad4, all in 64-bit only and with
18832-bit Python 2.7.14 on Windows Server 2012R2, Windows 10 Pro and with 32-bit Python 2.6.6 on Windows XP SP3.
190Notes
191=====
193All Python source code has been statically U{checked<https://GitHub.com/ActiveState/code/tree/master/recipes/Python/
194546532_PyChecker_postprocessor>} with U{Ruff<https://GitHub.com/astral-sh/ruff>}, U{PyLint<https://PyPI.org/project/pylint>},
195U{PyFlakes<https://PyPI.org/project/pyflakes>}, U{PyCodeStyle<https://PyPI.org/project/pycodestyle>} (formerly Pep8) and
196U{McCabe<https://PyPI.org/project/mccabe>} using Python 3.13.13 on macOS 27.0.1 Golden Gate.
198For a summary of all I{Karney}-based functionality in C{pygeodesy}, see module U{karney
199<https://mrJean1.GitHub.io/PyGeodesy/docs/pygeodesy.karney-module.html>}.
201In 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
202characters and if so, I{not} C{unicode}.
204Env variables
205=============
207The following environment variables are observed by C{pygeodesy}:
209 - C{PYGEODESY_EXCEPTION_CHAINING} - see module L{errors<pygeodesy.errors>}.
210 - C{PYGEODESY_FMT_FORM} - see module L{dms<pygeodesy.dms>}.
211 - C{PYGEODESY_FSUM_F2PRODUCT} - see module L{fsums<pygeodesy.fsums>} and method L{f2product<pygeodesy.Fsum.f2product>}.
212 - C{PYGEODESY_FSUM_NONFINITES} - see module L{fsums<pygeodesy.fsums>} and method L{nonfinites<pygeodesy.Fsum.nonfinites>}.
213 - C{PYGEODESY_FSUM_RESIDUAL} - see module L{fsums<pygeodesy.fsums>} and method L{RESIDUAL<pygeodesy.Fsum.RESIDUAL>}.
214 - C{PYGEODESY_GEOCONVERT} - see module L{mgrs<pygeodesy.mgrs>}.
215 - C{PYGEODESY_GEODSOLVE} - see module L{geodsolve<pygeodesy.geodsolve>}.
216 - C{PYGEODESY_GEOD3SOLVE} - see module L{geod3solve<pygeodesy.geod3solve>}.
217 - C{PYGEODESY_INTERSECTTOOL} - see module L{geodesici<pygeodesy.geodesici>}.
218 - C{PYGEODESY_LAZY_IMPORT} - see module L{lazily<pygeodesy.lazily>} and variable L{isLazy<pygeodesy.isLazy>}.
219 - C{PYGEODESY_NOTIMPLEMENTED} - C{__special__} methods return C{NotImplemented} if set to "std".
220 - C{PYGEODESY_RHUMBSOLVE} - see module L{rhumb.solve<pygeodesy.rhumb.solve>}.
221 - C{PYGEODESY_UPS_POLES} - see modules L{ups<pygeodesy.ups>} and L{mgrs<pygeodesy.mgrs>}.
223and these to specify standard or I{named} C{repr}esentations:
225 - C{PYGEODESY_AZIMUTH_STD_REPR} - see method L{Azimuth<pygeodesy.Azimuth>}C{.__repr__}.
226 - C{PYGEODESY_BEARING_STD_REPR} - see method L{Bearing<pygeodesy.Bearing>}C{.__repr__}.
227 - C{PYGEODESY_BOOL_STD_REPR} - see method L{Bool<pygeodesy.Bool>}C{.__repr__}.
228 - C{PYGEODESY_DEGREES_STD_REPR} - see method L{Degrees<pygeodesy.Degrees>}C{.__repr__}.
229 - C{PYGEODESY_EPOCH_STD_REPR} - see method L{Float<pygeodesy.Epoch>}C{.__repr__}.
230 - C{PYGEODESY_FLOAT_STD_REPR} - see method L{Float<pygeodesy.Float>}C{.__repr__}.
231 - C{PYGEODESY_INT_STD_REPR} - see method L{Int<pygeodesy.Int>}C{.__repr__}.
232 - C{PYGEODESY_METER_STD_REPR} - see method L{Meter<pygeodesy.Meter>}C{.__repr__}.
233 - C{PYGEODESY_RADIANS_STD_REPR} - see method L{Radians<pygeodesy.Radians>}C{.__repr__}.
234 - C{PYGEODESY_STR_STD_REPR} - see method L{Str<pygeodesy.Str>}C{.__repr__}.
236plus during development:
238 - C{PYGEODESY_FOR_DOCS} - for extended documentation by C{epydoc}.
239 - C{PYGEODESY_GEOGRAPHICLIB} - see module L{karney<pygeodesy.karney>}.
240 - C{PYGEODESY_WARNINGS} - see module L{props<pygeodesy.props>} and function L{DeprecationWarnings<pygeodesy.DeprecationWarnings>}.
241 - C{PYGEODESY_XPACKAGES} - see module L{basics<pygeodesy.basics>}.
242 - C{PYTHONDEVMODE} - see modules L{errors<pygeodesy.errors>} and L{props<pygeodesy.props>}.
244and:
246 - C{PYGEODESY_INIT__ALL__} - Set env variable C{PYGEODESY_INIT__ALL__} to anything other than C{"__all__"} to avoid
247 importing all C{pygeodesy} modules unnecessarily (in Python 2 or with C{PYGEODESY_LAZY_IMPORT} turned off in Python
248 3). However, to import a C{pygeodesy} item, the item name must be qualified with the C{module} name, for example
249 C{ from pygeodesy.ellipsoidalExact import LatLon } or C{ from pygeodesy.deprecated import collins }
251License
252=======
254**) U{Copyright (C) 2016-2026 -- mrJean1 at Gmail -- All Rights Reserved.<https://OpenSource.org/licenses/MIT>}
256C{Permission is hereby granted, free of charge, to any person obtaining a copy of this software
257and associated documentation files (the "Software"), to deal in the Software without restriction,
258including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense,
259and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so,
260subject to the following conditions:}
262C{The above copyright notice and this permission notice shall be included in all copies or substantial
263portions of the Software.}
265C{THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT
266NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
267IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
268WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
269SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.}
271@newfield example: Example, Examples
273@var EPS: System's M{epsilon} ≈ 2.22044604925e-16 (C{float}).
274@var EPS0: M{EPS**2} ≈ 4.9e-32 for near-zero comparison
275@var EPS02: M{EPS**4} ≈ 2.4e-63 for near-zero squared comparison
276@var EPS1: M{1 - EPS} ≈ 0.9999999999999998 (C{float}).
277@var EPS2: M{EPS * 2} ≈ 4.440892098501e-16 (C{float}).
278@var EPS_2: M{EPS / 2} ≈ 1.110223024625e-16 (C{float}).
279@var EPS4: M{EPS * 4} ≈ 8.881784197001e-16 (C{float}).
280@var EPS8: M{EPS * 8} ≈ 1.776356839400e-15 (C{float}).
282@var F_D: Format degrees as unsigned "deg°" with symbol, plus compass point suffix C{N, S, E} or C{W} (C{str}).
283@var F_DM: Format degrees as unsigned "deg°min′" with symbols, plus suffix (C{str}).
284@var F_DMS: Format degrees as unsigned "deg°min′sec″" with symbols, plus suffix (C{str}).
285@var F_DEG: Format degrees as unsigned "[D]DD" I{without} symbol, plus suffix (C{str}).
286@var F_MIN: Format degrees as unsigned "[D]DDMM" I{without} symbols, plus suffix (C{str}).
287@var F_SEC: Format degrees as unsigned "[D]DDMMSS" I{without} symbols, plus suffix (C{str}).
288@var F_D60: Format degrees as unsigned "[D]DD.MMSS" C{sexagecimal} I{without} symbols, plus suffix (C{str}).
289@var F__E: Format degrees as unsigned "%E" I{without} symbols, plus suffix (C{str}).
290@var F__F: Format degrees as unsigned "%F" I{without} symbols, plus suffix (C{str}).
291@var F__G: Format degrees as unsigned "%G" I{without} symbols, plus suffix (C{str}).
292@var F_RAD: Convert degrees to radians and format as unsigned "RR" with symbol, plus suffix (C{str}).
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, I{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}).
306@var F_D__: Format degrees as signed "-/+deg°" with symbol, I{without} suffix (C{str}).
307@var F_DM__: Format degrees as signed "-/+deg°min′" with symbols, I{without} suffix (C{str}).
308@var F_DMS__: Format degrees as signed "-/+deg°min′sec″" with symbols, I{without} suffix (C{str}).
309@var F_DEG__: Format degrees as signed "-/+[D]DD" I{without} symbol, I{without} suffix (C{str}).
310@var F_MIN__: Format degrees as signed "-/+[D]DDMM" I{without} symbols, without suffix (C{str}).
311@var F_SEC__: Format degrees as signed "-/+[D]DDMMSS" I{without} symbols, I{without} suffix (C{str}).
312@var F_D60__: Format degrees as signed "-/+[D]DD.MMSS" C{sexagecimal} I{without} symbols, I{without} suffix (C{str}).
313@var F__E__: Format degrees as signed "-/+%E" I{without} symbols, I{without} suffix (C{str}).
314@var F__F__: Format degrees as signed "-/+%F" I{without} symbols, I{without} suffix (C{str}).
315@var F__G__: Format degrees as signed "-/+%G" I{without} symbols, I{without} suffix (C{str}).
316@var F_RAD__: Convert degrees to radians and format as signed "-/+RR" I{without} symbol, I{without} suffix (C{str}).
318@var DIG: System's M{float decimal digits} = 15 (C{int}).
319@var INF: Infinity (C{float}), see functions L{isinf<pygeodesy.isinf>} and L{isfinite<pygeodesy.isfinite>} and C{NINF}.
320@var INT0: C{int(0)}, missing Z-components, C{if B{z}=B{INT0}}, see functions L{isint0<pygeodesy.isint0>}, L{meeus2<pygeodesy.meeus2>}
321@var MANT_DIG: System's M{float mantissa bits} = 53 (C{int}).
322@var MAX: System's M{float max} ≈ 1.798e+308 (C{float}).
323@var MIN: System's M{float min} ≈ 2.225e-308 (C{float}).
324@var NAN: Not-A-Number (C{float}), see function L{isnan<pygeodesy.isnan>}.
325@var NEG0: Negative 0.0 (C{float}), see function L{isneg0<pygeodesy.isneg0>}.
326@var NINF: Negative infinity (C{float}), see function L{isninf<pygeodesy.isninf>} and C{INF}.
327@var NN: Empty (C{str}), U{I{Nomen Nescio}<https://Wiktionary.org/wiki/N.N.>}.
329@var OVERFLOW: Object representing C{overflow} (1 / L{EPS0<pygeodesy.constants.EPS0>} = 4.9e+32).
331@var PI: Constant M{math.pi} (C{float}).
332@var PI2: Two PI, M{PI * 2}, aka I{Tau} (C{float}).
333@var PI_2: Half PI, M{PI / 2} (C{float}).
334@var PI3: Three PI, M{PI * 3} (C{float}).
335@var PI3_2: One and a half PI, M{PI * 3 / 2} (C{float}).
336@var PI_3: One third PI, M{PI / 3} (C{float}).
337@var PI4: Four PI, M{PI * 4} (C{float}).
338@var PI_4: Quarter PI, M{PI / 4} (C{float}).
339@var PI_6: One sixth PI, M{PI / 6} (C{float}).
341@var R_MA: Equatorial earth radius (C{meter}), WGS84, EPSG:3785.
342@var R_MB: Polar earth radius (C{meter}), WGS84, EPSG:3785.
343@var R_M: Mean (spherical) earth radius (C{meter}).
344@var R_KM: Mean (spherical) earth radius (C{Km}, kilometer).
345@var R_NM: Mean (spherical) earth radius (C{NM}, nautical miles).
346@var R_SM: Mean (spherical) earth radius (C{SM}, statute miles).
347@var R_FM: Former FAI-Sphere earth radius (C{meter}).
348@var R_GM: Average earth radius, distance to geoid surface (C{meter})
349@var R_QM: Earth' (triaxial) quadratic mean radius (C{meter})
350@var R_VM: Aviation/Navigation earth radius (C{meter}).
352@var S_DEG: Degrees symbol, default C{"°"}
353@var S_MIN: Minutes symbol, default C{"′"} aka I{PRIME}
354@var S_SEC: Seconds symbol, default C{"″"} aka I{DOUBLE_PRIME}
355@var S_RAD: Radians symbol, default C{""} aka L{NN<pygeodesy.NN>}
356@var S_DMS: If C{True}, include, otherwise cancel all DMS symbols, default C{True}.
357@var S_SEP: Separator between C{deg°|min′|sec″|suffix}, default C{""} aka L{NN<pygeodesy.NN>}
359@var Conics: Registered, predefined L{conics<pygeodesy.Conic>} (C{enum-like}).
360@var Datums: Registered, predefined L{datums<pygeodesy.Datum>} (C{enum-like}).
361@var Ellipsoids: Registered, predefined L{ellipsoids<pygeodesy.Ellipsoid>} (C{enum-like}).
362@var RefFrames: Registered, predefined L{reference frames<pygeodesy.RefFrame>} (C{enum-like}).
363@var Transforms: Registered, predefined L{transforms<pygeodesy.Transform>} (C{enum-like}).
364@var Triaxials: Registered, predefined L{triaxial ellipsoids<pygeodesy.Triaxial>} (C{enum-like}).
365@var Triaxial3s: Registered, predefined L{triaxial3 ellipsoids<pygeodesy.Triaxial3>} (C{enum-like}).
367@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.
369@var pygeodesy_abspath: Fully qualified C{pygeodesy} directory name (C{str}).
371@var version: Normalized C{pygeodesy} version (C{str}).
372'''
374import os.path as _os_path
375import sys as _sys
377_init__all__ = True
378# <https://PyInstaller.ReadTheDocs.io/en/stable/runtime-information.html>
379_isfrozen = getattr(_sys, 'frozen', False)
380pygeodesy_abspath = _os_path.dirname(_os_path.abspath(__file__)) # _sys._MEIPASS + '/pygeodesy'
381_pygeodesy_ = __package__ or _os_path.basename(pygeodesy_abspath)
383if _isfrozen: # avoid lazy import
384 _lazy_import2 = None
385else:
386 # setting __path__ should ...
387 __path__ = [pygeodesy_abspath]
388 try: # ... make this import work, ...
389 import pygeodesy.lazily as _
390 except ImportError: # ... if it doesn't, extend _sys.path to include
391 # this very directory such that all public and private sub-modules
392 # can be imported (by epydoc, checked by PyChecker, etc.)
393 _sys.path.insert(0, pygeodesy_abspath) # XXX __path__[0]
395 try: # lazily requires Python 3.7+, see lazily.__doc__
396 from pygeodesy.lazily import _init__all__, _lazy_import2 # PYCHOK expected
397 _, __getattr__ = _lazy_import2(_pygeodesy_) # PYCHOK expected
399 except (ImportError, NotImplementedError): # LazyImportError
400 _lazy_import2 = None
402if _init__all__ and not _lazy_import2: # import and set __all__
404 # import all public modules and export as such
405 import pygeodesy.albers as albers # noqa: F401
406 import pygeodesy.angles as angles # noqa: F401
407 import pygeodesy.auxilats as auxilats # noqa: F401
408 import pygeodesy.azimuthal as azimuthal # noqa: F401
409 import pygeodesy.basics as basics # noqa: F401
410 import pygeodesy.booleans as booleans # noqa: F401
411 import pygeodesy.cartesianBase as cartesianBase # noqa: F401 INTERNAL
412 import pygeodesy.clipy as clipy # noqa: F401
413 import pygeodesy.constants as constants # noqa: F401
414 import pygeodesy.css as css # noqa: F401
415 import pygeodesy.datums as datums # noqa: F401
416 import pygeodesy.deprecated as deprecated # noqa: F401
417 import pygeodesy.dms as dms # noqa: F401
418 import pygeodesy.ecef as ecef # noqa: F401
419 import pygeodesy.ecefLocals as ecefLocals # noqa: F401
420 import pygeodesy.elevations as elevations # noqa: F401
421 import pygeodesy.ellipses as ellipses # noqa: F401
422 import pygeodesy.ellipsoidalBase as ellipsoidalBase # noqa: F401 INTERNAL
423 import pygeodesy.ellipsoidalBaseDI as ellipsoidalBaseDI # noqa: F401 INTERNAL
424 import pygeodesy.ellipsoidalExact as ellipsoidalExact # noqa: F401
425 import pygeodesy.ellipsoidalGeodSolve as ellipsoidalGeodSolve # noqa: F401
426 import pygeodesy.ellipsoidalKarney as ellipsoidalKarney # noqa: F401
427 import pygeodesy.ellipsoidalNvector as ellipsoidalNvector # noqa: F401
428 import pygeodesy.ellipsoidalVincenty as ellipsoidalVincenty # noqa: F401
429 import pygeodesy.ellipsoids as ellipsoids # noqa: F401
430 import pygeodesy.elliptic as elliptic # noqa: F401
431 import pygeodesy.epsg as epsg # noqa: F401
432 import pygeodesy.etm as etm # noqa: F401
433 import pygeodesy.errors as errors # noqa: F401
434 import pygeodesy.fmath as fmath # noqa: F401
435 import pygeodesy.formy as formy # noqa: F401
436 import pygeodesy.frechet as frechet # noqa: F401
437 import pygeodesy.fstats as fstats # noqa: F401
438 import pygeodesy.fsums as fsums # noqa: F401
439 import pygeodesy.gars as gars # noqa: F401
440 import pygeodesy.geodesici as geodesici # noqa: F401
441 import pygeodesy.geodesicw as geodesicw # noqa: F401
442 import pygeodesy.geodesicx as geodesicx # noqa: F401
443 import pygeodesy.geodsolve as geodsolve # noqa: F401
444 import pygeodesy.geod3solve as geod3solve # noqa: F401
445 import pygeodesy.geohash as geohash # noqa: F401
446 import pygeodesy.geoids as geoids # noqa: F401
447 import pygeodesy.hausdorff as hausdorff # noqa: F401
448 import pygeodesy.heights as heights # noqa: F401
449 import pygeodesy.hom as hom # noqa: F401
450 import pygeodesy.internals as internals # noqa: F401
451 import pygeodesy.interns as interns # noqa: F401
452 import pygeodesy.iters as iters # noqa: F401
453 import pygeodesy.karney as karney # noqa: F401
454 import pygeodesy.ktm as ktm # noqa: F401
455 import pygeodesy.latlonBase as latlonBase # noqa: F401 INTERNAL
456 import pygeodesy.lazily as lazily # noqa: F401
457 import pygeodesy.lcc as lcc # noqa: F401
458 import pygeodesy.lom as lom # noqa: F401
459 import pygeodesy.ltp as ltp # noqa: F401
460 import pygeodesy.ltpTuples as ltpTuples # noqa: F401
461 import pygeodesy.mgrs as mgrs # noqa: F401
462 import pygeodesy.named as named # noqa: F401
463 import pygeodesy.namedTuples as namedTuples # noqa: F401
464 import pygeodesy.nvectorBase as nvectorBase # noqa: F401 INTERNAL
465 import pygeodesy.osgr as osgr # noqa: F401
466 import pygeodesy.points as points # noqa: F401
467 import pygeodesy.props as props # noqa: F401
468 import pygeodesy.resections as resections # noqa: F401
469 import pygeodesy.rhumb as rhumb # noqa: F401
470 import pygeodesy.simplify as simplify # noqa: F401
471 import pygeodesy.sphericalBase as sphericalBase # noqa: F401 INTERNAL
472 import pygeodesy.sphericalNvector as sphericalNvector # noqa: F401
473 import pygeodesy.sphericalTrigonometry as sphericalTrigonometry # noqa: F401
474 import pygeodesy.solveBase as solveBase # noqa: F401
475 import pygeodesy.streprs as streprs # noqa: F401
476 import pygeodesy.trf as trf # noqa: F401
477 import pygeodesy.triaxials as triaxials # noqa: F401
478 import pygeodesy.units as units # noqa: F401
479 import pygeodesy.unitsBase as unitsBase # noqa: F401 INTERNAL
480 import pygeodesy.ups as ups # noqa: F401
481 import pygeodesy.utily as utily # noqa: F401
482 import pygeodesy.utm as utm # noqa: F401
483 import pygeodesy.utmups as utmups # noqa: F401
484 import pygeodesy.utmupsBase as utmupsBase # noqa: F401 INTERNAL
485 import pygeodesy.vector2d as vector2d # noqa: F401
486 import pygeodesy.vector3d as vector3d # noqa: F401
487 import pygeodesy.vector3dBase as vector3dBase # noqa: F401 INTERNAL
488 import pygeodesy.webmercator as webmercator # noqa: F401
489 import pygeodesy.wgrs as wgrs # noqa: F401
491 # lift all public classes, constants, functions, etc. but ONLY
492 # from the following modules ... (see also David Beazley's
493 # talk <https://DaBeaz.com/modulepackage/index.html>) ... BUT
494 # NOT modules ellipsoidal*, epsg, gars, geohash, spherical*,
495 # vector and wgrs ... in order keep those as modules ONLY
496 from pygeodesy.albers import * # noqa: F403
497 from pygeodesy.angles import * # noqa: F403
498 from pygeodesy.azimuthal import * # noqa: F403
499# from pygeodesy.auxilats import * # noqa: F403
500 from pygeodesy.basics import * # noqa: F403
501 from pygeodesy.booleans import * # noqa: F403
502 from pygeodesy.cartesianBase import * # noqa: F403 INTERNAL
503 from pygeodesy.clipy import * # noqa: F403
504 from pygeodesy.constants import * # noqa: F403
505 from pygeodesy.css import * # noqa: F403
506 from pygeodesy.datums import * # noqa: F403
507 from pygeodesy.deprecated import * # noqa: F403 DEPRECATED
508 from pygeodesy.dms import * # noqa: F403
509 from pygeodesy.ecef import * # noqa: F403
510# from pygeodesy.ecefLocals import * # noqa: F403
511 from pygeodesy.elevations import * # noqa: F403
512 from pygeodesy.ellipses import * # noqa: F403
513# from pygeodesy.ellipsoidalBase import * # noqa: F403 INTERNAL
514# from pygeodesy.ellipsoidalBaseDI import * # noqa: F403 INTERNAL
515# from pygeodesy.ellipsoidalExact import * # noqa: F403
516# from pygeodesy.ellipsoidalGeodSolve import * # noqa: F403
517# from pygeodesy.ellipsoidalKarney import * # noqa: F403
518# from pygeodesy.ellipsoidalNvector import * # noqa: F403
519 from pygeodesy.ellipsoidalVincenty import * # noqa: F403
520 from pygeodesy.ellipsoids import * # noqa: F403
521 from pygeodesy.elliptic import * # noqa: F403
522 from pygeodesy.epsg import * # noqa: F403
523 from pygeodesy.etm import * # noqa: F403
524 from pygeodesy.errors import * # noqa: F403
525 from pygeodesy.fmath import * # noqa: F403
526 from pygeodesy.formy import * # noqa: F403
527 from pygeodesy.frechet import * # noqa: F403
528 from pygeodesy.fstats import * # noqa: F403
529 from pygeodesy.fsums import * # noqa: F403
530 from pygeodesy.gars import * # noqa: F403
531 from pygeodesy.geodesici import * # noqa: F403
532 from pygeodesy.geodesicw import * # noqa: F403
533 from pygeodesy.geodesicx import * # noqa: F403
534 from pygeodesy.geodsolve import * # noqa: F403
535 from pygeodesy.geod3solve import * # noqa: F403
536 from pygeodesy.geohash import * # noqa: F403
537 from pygeodesy.geoids import * # noqa: F403
538 from pygeodesy.hausdorff import * # noqa: F403
539 from pygeodesy.heights import * # noqa: F403
540 from pygeodesy.hom import * # noqa: F403
541 from pygeodesy.internals import * # noqa: F403
542 from pygeodesy.interns import * # noqa: F403
543 from pygeodesy.iters import * # noqa: F403
544 from pygeodesy.karney import * # noqa: F403
545 from pygeodesy.ktm import * # noqa: F403
546 from pygeodesy.latlonBase import * # noqa: F403 INTERNAL
547 from pygeodesy.lazily import * # noqa: F403
548 from pygeodesy.lcc import * # noqa: F403
549 from pygeodesy.lom import * # noqa: F403
550 from pygeodesy.ltp import * # noqa: F403
551 from pygeodesy.ltpTuples import * # noqa: F403
552 from pygeodesy.mgrs import * # noqa: F403
553 from pygeodesy.named import * # noqa: F403
554 from pygeodesy.namedTuples import * # noqa: F403
555 from pygeodesy.nvectorBase import * # noqa: F403 INTERNAL
556 from pygeodesy.osgr import * # noqa: F403
557 from pygeodesy.points import * # noqa: F403
558 from pygeodesy.props import * # noqa: F403
559 from pygeodesy.resections import * # noqa: F403
560 from pygeodesy.rhumb import * # noqa: F403
561 from pygeodesy.simplify import * # noqa: F403
562# from pygeodesy.sphericalBase import * # noqa: F403 INTERNAL
563# from pygeodesy.sphericalNvector import * # noqa: F403
564# from pygeodesy.sphericalTrigonometry import * # noqa: F403
565# from pygeodesy.solveBase import * # noqa: F403 INTERNAL
566 from pygeodesy.streprs import * # noqa: F403
567 from pygeodesy.trf import * # noqa: F403
568 from pygeodesy.triaxials import * # noqa: F403
569# from pygeodesy.triaxials.bases import * # noqa: F403
570# from pygeodesy.triaxials.conformals import * # noqa: F403
571# from pygeodesy.triaxials.spheres import * # noqa: F403
572# from pygeodesy.triaxials.triaxial3 import * # noqa: F403
573# from pygeodesy.triaxials.triaxial5 import * # noqa: F403
574 from pygeodesy.units import * # noqa: F403
575 from pygeodesy.unitsBase import * # noqa: F403 Float, ...
576 from pygeodesy.ups import * # noqa: F403
577 from pygeodesy.utily import * # noqa: F403
578 from pygeodesy.utm import * # noqa: F403
579 from pygeodesy.utmups import * # noqa: F403
580# from pygeodesy.utmupsBase import * # noqa: F403 INTERNAL
581 from pygeodesy.vector2d import * # noqa: F403
582 from pygeodesy.vector3d import * # noqa: F403
583 from pygeodesy.vector3dBase import * # noqa: F403 INTERNAL
584 from pygeodesy.webmercator import * # noqa: F403
585 from pygeodesy.wgrs import * # noqa: F403
587 def _all(globalocals):
588 from pygeodesy.internals import _headof, _DOT_ # PYCHOK expected
589 from pygeodesy.interns import NN as _NN, _attribute_, _COMMASPACE_, \
590 _module_, _s_ # PYCHOK expected
591 from pygeodesy.streprs import Fmt as _Fmt # PYCHOK expected
592 # collect all public module and attribute names and check
593 # that modules are imported from this package, 'pygeodesy'
594 # (but the latter only when not bundled with PyInstaller or
595 # Py2Exe, since the file-layout is different. Courtesy of
596 # GilderGeek<https://GitHub.com/mrJean1/PyGeodesy/issues/31>)
597 ns = list(lazily._ALL_INIT)
598# XXX ps = () if _isfrozen else set([_pygeodesy_] + __name__.split(_DOT_))
599 for mod, attrs in lazily._all_enums():
600 mod = _headof(_headof(mod))
601 if mod not in globalocals:
602 t = _DOT_(_pygeodesy_, mod)
603 raise ImportError('missing %s%s: %s' % (_module_, _NN, t))
604 ns.append(mod)
605 # check that all other public attrs do exist
606 if attrs and isinstance(attrs, tuple):
607 attrs = lazily._ALL_ATTRS(attrs)
608 t = tuple(a for a in attrs if a not in globalocals)
609 if t:
610 s = _Fmt.SQUARE(_s_, len(t)) if len(t) > 1 else _NN
611 t = _COMMASPACE_.join(_DOT_(_pygeodesy_, mod, a) for a in t)
612 raise ImportError('missing %s%s: %s' % (_attribute_, s, t))
613 ns.extend(attrs)
614# XXX if ps: # check that mod is a _pygeodesy_ module
615# XXX m = globalocals[mod] # assert(typename(m) == mod)
616# XXX f = getattr(m, _dunder_file_, _NN)
617# XXX d = _os_path.dirname(_os_path.abspath(f)) if f else pygeodesy_abspath
618# XXX p = getattr(m, _dunder_package_, _NN) or _pygeodesy_
619# XXX if p not in ps or d != pygeodesy_abspath:
620# XXX t = '%s from %r' % (_DOT_(p, mod), f or p)
621# XXX raise ImportError('foreign %s: %s' % (_module_, t))
622 return tuple(set(ns)) # remove duplicates
624 __all__ = _all(globals()) # or locals()
625else:
626 __all__ = ()
627 _init__all__ = False
629from pygeodesy.internals import _version2, _DOT_ # noqa: E402
630# from pygeodesy.interns import _DOT_ # from .internals
631__version__ = '26.10.20'
632# see setup.py for similar logic
633version = _DOT_(*_version2(__version__, n=3))
635del _DOT_, _lazy_import2, _os_path, _sys, _version2
637# **) MIT License
638#
639# Copyright (C) 2016-2026 -- mrJean1 at Gmail -- All Rights Reserved.
640#
641# Permission is hereby granted, free of charge, to any person obtaining a
642# copy of this software and associated documentation files (the "Software"),
643# to deal in the Software without restriction, including without limitation
644# the rights to use, copy, modify, merge, publish, distribute, sublicense,
645# and/or sell copies of the Software, and to permit persons to whom the
646# Software is furnished to do so, subject to the following conditions:
647#
648# The above copyright notice and this permission notice shall be included
649# in all copies or substantial portions of the Software.
650#
651# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
652# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
653# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
654# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
655# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
656# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
657# OTHER DEALINGS IN THE SOFTWARE.