Coverage for pygeodesy/constants.py: 100%
174 statements
« prev ^ index » next coverage.py v7.2.2, created at 2023-07-12 13:40 -0400
« prev ^ index » next coverage.py v7.2.2, created at 2023-07-12 13:40 -0400
1# -*- coding: utf-8 -*-
3u'''Single-instance C{float} and C{int} constants across C{pygeodesy}
4modules and related functions L{pygeodesy.float_}, L{pygeodesy.isclose},
5L{pygeodesy.isfinite}, L{pygeodesy.isinf}, L{pygeodesy.isint0},
6L{pygeodesy.isnan}, L{pygeodesy.isnear0}, L{pygeodesy.isnear1},
7L{pygeodesy.isnear90}, L{pygeodesy.isneg0}, L{pygeodesy.isninf},
8L{pygeodesy.isnon0} and L{pygeodesy.remainder}.
9'''
10# make sure int/int division yields float quotient, see .basics
11from __future__ import division as _; del _ # PYCHOK semicolon
13from pygeodesy.basics import _0_0, _copysign, isbool, iscomplex, isint
14from pygeodesy.errors import _xError, _xError2, _xkwds_get, _ALL_LAZY
15from pygeodesy.interns import _INF_, _NAN_, _UNDER_
16# from pygeodesy.lazily import _ALL_LAZY # from .errors
17# from pygeodesy.streprs import Fmt # from .unitsBase
18from pygeodesy.unitsBase import Float, Int, Radius, Fmt
20from math import fabs, isinf, isnan, pi as _pi, sqrt
21try:
22 from math import inf as _inf, nan as _nan # PYCHOK Python 3+
23except ImportError: # Python 2-
24 _inf, _nan = float(_INF_), float(_NAN_)
26__all__ = _ALL_LAZY.constants
27__version__ = '23.05.31'
30def _Float(**name_arg):
31 '''(INTERNAL) New named, cached C{Float}.
32 '''
33 n, arg = name_arg.popitem()
34 return Float(_float(arg), name=n)
37def _Radius(**name_arg):
38 '''(INTERNAL) New named, cached C{Radius}.
39 '''
40 n, arg = name_arg.popitem()
41 return Radius(_float(arg), name=n)
44def float_(*fs, **sets): # sets=False
45 '''Get scalars as C{float} or I{intern}'ed C{float}.
47 @arg fs: One more values (C{scalar}), all positional.
48 @kwarg sets: Use C{B{sets}=True} to C{intern} each
49 B{C{fs}}, otherwise don't C{intern}.
51 @return: A single C{float} if only one B{C{fs}} is
52 given, otherwise a tuple of C{float}s.
54 @raise TypeError: Some B{C{fs}} is not C{scalar}.
55 '''
56 fl = []
57 _f = _floats.setdefault if _xkwds_get(sets, sets=False) else \
58 _floats.get
59 try:
60 for i, f in enumerate(fs):
61 f = float(f)
62 fl.append(_f(f, f))
63 except Exception as x:
64 E, t = _xError2(x)
65 fs_i = Fmt.SQUARE(fs=i)
66 raise E(fs_i, f, txt=t)
67 return fl[0] if len(fl) == 1 else tuple(fl)
70def _float(f): # in .datums, .ellipsoids, ...
71 '''(INTERNAL) Cache initial C{float}s.
72 '''
73 f = float(f)
74 return _floats.setdefault(f, f) # PYCHOK del _floats
77def float0_(*xs):
78 '''Yield C{B{x}s} as a non-NEG0 C{float}.
79 '''
80 for x in xs:
81 yield float(x) if x else _0_0
84def _float0(f): # in .resections, .vector3dBase, ...
85 '''(INTERNAL) Return C{float(B{f})} or C{INT0}.
86 '''
87 if f:
88 f = float(f)
89 f = _floats.get(f, f)
90 elif f is not INT0:
91 f = _0_0
92 return f
95def _floatuple(*fs):
96 '''(INTERNAL) Cache a tuple of C{float}s.
97 '''
98 return tuple(map(_float, fs))
101def _1_over(x):
102 '''(INTERNAL) Return reciprocal C{1 / B{x}}.
103 '''
104 return _float(_1_0 / float(x))
107_floats = {} # PYCHOK floats cache, in .__main__
108# _float = float # PYCHOK expected
109# del _floats # XXX zap floats cache never
111_0_0 = _float( _0_0) # PYCHOK expected
112_0_0_1T = _0_0, # PYCHOK 1-tuple
113_0_0_9T = _0_0_1T * 9 # PYCHOK 9-tuple
114_0_0001 = _float( 0.0001) # PYCHOK expected
115_0_001 = _float( 0.001) # PYCHOK expected
116_0_01 = _float( 0.01) # PYCHOK expected
117_0_1 = _float( 0.1) # PYCHOK expected
118_0_125 = _float( 0.125) # PYCHOK expected
119_0_25 = _float( 0.25) # PYCHOK expected
120_0_26 = _float( 0.26) # PYCHOK expected
121_0_5 = _float( 0.5) # PYCHOK expected
122_1_0 = _float( 1) # PYCHOK expected
123_1_0_1T = _1_0, # PYCHOK 1-tuple
124_1_5 = _float( 1.5) # PYCHOK expected
125_1_75 = _float( 1.75) # PYCHOK expected
126_2_0 = _float( 2) # PYCHOK expected
127_3_0 = _float( 3) # PYCHOK expected
128_4_0 = _float( 4) # PYCHOK expected
129_5_0 = _float( 5) # PYCHOK expected
130_6_0 = _float( 6) # PYCHOK expected
131_8_0 = _float( 8) # PYCHOK expected
132_9_0 = _float( 9) # PYCHOK expected
133_10_0 = _float( 10) # PYCHOK expected
134_16_0 = _float( 16) # PYCHOK expected
135_32_0 = _float( 32) # PYCHOK expected
136_60_0 = _float( 60) # PYCHOK expected
137_90_0 = _float( 90) # PYCHOK expected
138_100_0 = _float( 100) # PYCHOK expected
139_180_0 = _float( 180) # PYCHOK expected
140_270_0 = _float( 270) # PYCHOK expected
141_360_0 = _float( 360) # PYCHOK expected
142_400_0 = _float( 400) # PYCHOK expected
143_720_0 = _float( 720) # PYCHOK expected
144_1000_0 = _float(1000) # PYCHOK expected
145_3600_0 = _float(3600) # PYCHOK expected
147_N_0_0 = float( '-0.0') # PYCHOK NOT _float!
148_N_0_5 = _float( -_0_5) # PYCHOK expected
149_N_1_0 = _float( -_1_0) # PYCHOK expected
150_N_2_0 = _float( -_2_0) # PYCHOK expected
151_N_90_0 = _float( -_90_0) # PYCHOK expected
152_N_180_0 = _float(-_180_0) # PYCHOK expected
154_M_KM = _1000_0 # meter per Kilo meter, see .utily
155_M_NM = _float(1852.0) # meter per Nautical Mile
156_M_SM = _float(1609.344) # meter per Statute Mile
158try:
159 from sys import float_info as _f_i
160 # @see: <https://NumPy.org/doc/stable/reference/generated/numpy.finfo.html>
161 DIG = Int( DIG =_f_i.dig) # PYCHOK system's float decimal digits
162 EPS = _Float(EPS =_f_i.epsilon) # PYCHOK system's EPSilon
163 MANT_DIG = Int( MANT_DIG=_f_i.mant_dig) # PYCHOK system's float mantissa bits
164 MAX = _Float(MAX =_f_i.max) # PYCHOK system's MAX float 1.7976931348623157e+308
165# MAX_EXP = Int( MAX_EXP =_f_i.max_exp) # PYTHON system's max base 2 exponent
166 MIN = _Float(MIN =_f_i.min) # PYCHOK system's MIN float 2.2250738585072014e-308
167# MIN_EXP = Int( MIN_EXP =_f_i.min_exp) # PYTHON system's min base 2 exponent
168# RADIX = Int( RADIX =_f_i.radix) # PYTHON system's float base
169 del _f_i
170except ImportError: # PYCHOK no cover
171 DIG = Int( DIG =15) # PYCHOK system's 64-bit float decimal digits
172 EPS = _Float(EPS =2.220446049250313e-16) # PYCHOK EPSilon 2**-52, M{EPS +/- 1 != 1}
173 MANT_DIG = Int( MANT_DIG=53) # PYCHOK float mantissa bits ≈ 53 (C{int})
174 MAX = _Float(MAX =pow(_2_0, 1023) * (_2_0 - EPS)) # PYCHOK ≈ 10**308
175# MAX_EXP = Int( MAX_ESP =1024) # 308 base 10
176 MIN = _Float(MIN =pow(_2_0, -1021)) # PYCHOK ≈ 10**-308
177# MIN_EXP = Int(MIN_EXP =-1021) # -307 base 10
178# RADIX = Int(Radix =2) # base
180EPS0 = _Float( EPS0 = EPS**2) # PYCHOK near-/non-zero comparison 4.930381e-32, or EPS or EPS_2
181EPS02 = _Float( EPS02 = EPS**4) # PYCHOK near-zero-squared comparison 2.430865e-63
182EPS_2 = _Float( EPS_2 = EPS / _2_0) # PYCHOK ≈ 1.110223024625e-16
183EPS1 = _Float( EPS1 =_1_0 - EPS) # PYCHOK ≈ 0.9999999999999998
184EPS2 = _Float( EPS2 = EPS * _2_0) # PYCHOK ≈ 4.440892098501e-16
185EPS4 = _Float( EPS4 = EPS * _4_0) # PYCHOK ≈ 8.881784197001e-16
186# _1EPS = _Float(_1EPS =_1_0 + EPS) # PYCHOK ≈ 1.0000000000000002
187_1_EPS = _Float(_1_EPS =_1_0 / EPS) # PYCHOK = 4503599627370496.0
188# _2_EPS = _Float(_2_EPS =_2_0 / EPS) # PYCHOK = 9007199254740992.0
189_EPS2e4 = _Float(_EPS2e4 = EPS2 * 1.e4) # PYCHOK ≈ 4.440892098501e-12
190_EPS4e8 = _Float(_EPS4e8 = EPS4 * 1.e8) # PYCHOK ≈ 8.881784197001e-08
191_EPSmin = _Float(_EPSmin = sqrt(MIN)) # PYCHOK = 1.49166814624e-154
192_EPSqrt = _Float(_EPSqrt = sqrt(EPS)) # PYCHOK = 1.49011611938e5-08
193_EPStol = _Float(_EPStol =_EPSqrt * _0_1) # PYCHOK = 1.49011611938e5-09 == sqrt(EPS * _0_01)
195_89_999_ = _Float(_89_999_= EPS1 * _90_0) # just below 90.0
196# <https://Numbers.Computation.Free.FR/Constants/Miscellaneous/digits.html>
197_1__90 = _Float(_1__90 =_1_0 / _90_0) # PYCHOK = 0.011_111_111_111_111_111_111_111_111_111_111_111_111_111_111_11111
198_2__PI = _Float(_2__PI =_2_0 / _pi) # PYCHOK = 0.636_619_772_367_581_343_075_535_053_490_057_448_137_838_582_96182
200_1_16th = _Float(_1_16th =_1_0 / _16_0) # PYCHOK in .ellipsoids, .karney
201_1_64th = _Float(_1_64th =_1_0 / 64) # PYCHOK in .elliptic, pow(2.0, -6)
202_1_3rd = _Float(_1_3rd =_1_0 / _3_0) # PYCHOK in .fmath
203_2_3rd = _Float(_2_3rd =_2_0 / _3_0) # PYCHOK in .fmath
205_K0_UTM = _Float(_K0_UTM = 0.9996) # PYCHOK in .etm, .ktm, .utm, UTM scale at central meridian
206# sqrt(2) <https://WikiPedia.org/wiki/Square_root_of_2>
207# 1.414213562373095_048_801_688_724_209_698_078_569_671_875_376_948_073_176_679_737_99
208# _1SQRT2= _Float(_1SQRT2 =sqrt(_2_0) + 1)
209_SQRT2_2 = _Float(_SQRT2_2=sqrt(_0_5)) # PYCHOK = 0.707106781186547_6 == sqrt(2) / 2
211INF = Float(INF =_inf) # PYCHOK INFinity, see function L{isinf}, L{isfinite}, NOT _Float!
212INT0 = Int( INT0= 0) # PYCHOK unique int(0) instance, see .fsums, useZ=False
213NAN = Float(NAN =_nan) # PYCHOK Not-A-Number, see function L{isnan}, NOT _Float!
214NEG0 = Float(NEG0=_N_0_0) # PYCHOK NEGative 0.0, see function L{isneg0}, NOT _Float!
215NINF = Float(NINF=-INF) # PYCHOK Negative INFinity, NOT _Float!
217PI = _Float(PI =_pi)
218PI2 = _Float(PI2 =_pi * _2_0) # PYCHOK Two PI, M{PI * 2} aka I{Tau}
219PI_2 = _Float(PI_2 =_pi / _2_0) # PYCHOK Half PI, M{PI / 2}
220PI3 = _Float(PI3 =_pi * _3_0) # PYCHOK Three PI, M{PI * 3}
221PI3_2 = _Float(PI3_2=_pi * _1_5) # PYCHOK PI and a half, M{PI * 3 / 2}
222PI_3 = _Float(PI_3 =_pi / _3_0) # PYCHOK One third PI, M{PI / 3}
223PI4 = _Float(PI4 =_pi * _4_0) # PYCHOK Four PI, M{PI * 4}
224PI_4 = _Float(PI_4 =_pi / _4_0) # PYCHOK Quarter PI, M{PI / 4}
226R_MA = _Radius(R_MA=6378137.0) # PYCHOK equatorial earth radius (C{meter}), WGS84, EPSG:3785
227R_MB = _Radius(R_MB=6356752.3) # PYCHOK polar earth radius (C{meter}), WGS84, EPSG:3785
228R_M = _Radius(R_M =6371008.771415) # PYCHOK mean, spherical earth radius (C{meter})
229R_KM = _Radius(R_KM=R_M / _M_KM) # PYCHOK mean, spherical earth radius (C{KM}, Kilo meter)
230R_NM = _Radius(R_NM=R_M / _M_NM) # PYCHOK mean, spherical earth radius (C{NM}, nautical miles)
231R_SM = _Radius(R_SM=R_M / _M_SM) # PYCHOK mean, spherical earth radius (C{SM}, statute miles)
232# See <https://www.EdWilliams.org/avform.htm>, <https://www.DTIC.mil/dtic/tr/fulltext/u2/a216843.pdf>
233# and <https://GitHub.com/NASA/MultiDop/blob/master/src/share/man/man3/geog_lib.3> based on the
234# International Standard Nautical Mile of 1,852 meter (1' latitude)
235R_FM = _Radius(R_FM=6371000.0) # PYCHOK former FAI Sphere earth radius (C{meter})
236R_GM = _Radius(R_GM=6371230.0) # PYCHOK avg. radius, distance to geoid surface (C{meter})
237# <http://Wiki.GIS.com/wiki/index.php/Ellipsoidal_quadratic_mean_radius>
238R_QM = _Radius(R_QM=6372797.560856) # PYCHOK earth' quadratic mean radius (C{meter})
239# Rtri= _Radius(Rtri=6372797.5559594) # PYCHOK Rtriaxial quadratic mean radius (C{meter}), WGS84
240# Rbi = _Radius(Rbi =6367453.6345163) # PYCHOK Rbiaxial quadratic mean radius (C{meter}), WGS84
241R_VM = _Radius(R_VM=6366707.0194937) # PYCHOK aViation/naVigation earth radius (C{meter})
242# R_AU= Meter( R_AU=149597870700.0) # PYCHOK <https://WikiPedia.org/wiki/Astronomical_unit>
244_INF_NAN_NINF = INF, NAN, NINF
245_pos_self = _1_0.__pos__() is _1_0 # PYCHOK in .fsums, .vector3dBase
248def _0_0s(n):
249 '''(INTERNAL) Return an C{B{n}-tuple} of C{_0_0} zeros.
250 '''
251 return _0_0_9T[:n] if 0 <= n <= len(_0_0_9T) else (_0_0_1T * n)
254try:
255 from math import isclose as _isclose
256except ImportError: # Python 3.4-
258 def _isclose(a, b, rel_tol=1e-9, abs_tol=0):
259 '''Mimick Python 3.5+ C{math.isclose}.
260 '''
261 t, d = abs_tol, fabs(a - b)
262 if d > t:
263 r = max(fabs(a), fabs(b)) * rel_tol
264 t = max(r, t)
265 return d <= t
268def isclose(a, b, rel_tol=1e-12, abs_tol=EPS0):
269 '''Like C{math.isclose}, but with defaults such
270 that C{isclose(0, EPS0)} is C{True} by default.
271 '''
272 return _isclose(a, b, rel_tol=rel_tol, abs_tol=abs_tol)
275try:
276 from math import isfinite as _isfinite # in .ellipsoids, .fsums, .karney
277except ImportError: # Python 3.1-
279 def _isfinite(x):
280 '''Mimick Python 3.2+ C{math.isfinite}.
281 '''
282 return not (isinf(x) or isnan(x))
285def isfinite(obj):
286 '''Check a finite C{scalar} or C{complex} value.
288 @arg obj: Value (C{scalar} or C{complex}).
290 @return: C{False} if B{C{obj}} is C{INF}, C{NINF}
291 or C{NAN}, C{True} otherwise.
293 @raise TypeError: Non-scalar and non-complex B{C{obj}}.
294 '''
295 try:
296 return (obj not in _INF_NAN_NINF) and _isfinite(obj)
297 except Exception as x:
298 if iscomplex(obj): # _isfinite(complex) thows TypeError
299 return isfinite(obj.real) and isfinite(obj.imag)
300 raise _xError(x, Fmt.PAREN(isfinite.__name__, obj))
303def isint0(obj, both=False):
304 '''Check for L{INT0} or C{int(0)} value.
306 @arg obj: The object (any C{type}).
307 @kwarg both: If C{true}, also check C{float(0)} (C{bool}).
309 @return: C{True} if B{C{obj}} is L{INT0}, C{int(0)} or
310 C{float(0)}, C{False} otherwise.
311 '''
312 return (obj is INT0 or obj is int(0) or bool(both and
313 (not obj) and isint(obj, both=True))) and not isbool(obj)
316def isnear0(x, eps0=EPS0):
317 '''Is B{C{x}} near I{zero} within a tolerance?
319 @arg x: Value (C{scalar}).
320 @kwarg eps0: Near-I{zero} tolerance (C{EPS0}).
322 @return: C{True} if C{abs(B{x}) < B{eps0}},
323 C{False} otherwise.
325 @see: Function L{isnon0}.
326 '''
327 return bool(eps0 > x > -eps0)
330def isnear1(x, eps1=EPS0):
331 '''Is B{C{x}} near I{one} within a tolerance?
333 @arg x: Value (C{scalar}).
334 @kwarg eps1: Near-I{one} tolerance (C{EPS0}).
336 @return: C{isnear0(B{x} - 1, eps0=B{eps1})}.
338 @see: Function L{isnear0}.
339 '''
340 return bool(eps1 > (x - _1_0) > -eps1)
343def isnear90(x, eps90=EPS0):
344 '''Is B{C{x}} near I{90} within a tolerance?
346 @arg x: Value (C{scalar}).
347 @kwarg eps90: Near-I{90} tolerance (C{EPS0}).
349 @return: C{isnear0(B{x} - 90)}.
351 @see: Function L{isnear0}.
352 '''
353 return bool(eps90 > (x - _90_0) > -eps90)
356def isneg0(x):
357 '''Check for L{NEG0}, negative C{0.0}.
359 @arg x: Value (C{scalar}).
361 @return: C{True} if B{C{x}} is C{NEG0} or C{-0.0},
362 C{False} otherwise.
363 '''
364 return x in (_0_0, NEG0) and _copysign(1, x) < 0
365# and str(x).startswith(_MINUS_)
368def isninf(x):
369 '''Check for L{NINF}, negative C{INF}.
371 @arg x: Value (C{scalar}).
373 @return: C{True} if B{C{x}} is C{NINF} or C{-inf},
374 C{False} otherwise.
375 '''
376 return x is NINF or (x < 0 and not isfinite(x))
379def isnon0(x, eps0=EPS0):
380 '''Is B{C{x}} non-zero with a tolerance?
382 @arg x: Value (C{scalar}).
383 @kwarg eps0: Non-zero tolerance (C{EPS0}).
385 @return: C{True} if C{abs(B{x}) > B{eps0}},
386 C{False} otherwise.
388 @see: Function L{isnear0}.
389 '''
390 return not bool(eps0 > x > -eps0) # not isnear0
393def _off90(lat):
394 '''(INTERNAL) Off 90.0 for .gars and .wgrs.
395 '''
396 return max(min(lat, _89_999_), -_89_999_)
399try:
400 from math import remainder
401except ImportError: # Python 3.6-
402 from math import fmod as _fmod
404 def remainder(x, y):
405 '''Mimick Python 3.7+ C{math.remainder}.
406 '''
407 if isnan(y):
408 x = NAN
409 elif x and not isnan(x):
410 y = fabs(y)
411 x = _fmod(x, y)
412 h = _0_5 * y
413 if x >= h:
414 x -= y
415 elif x < -h:
416 x += y
417 return x # keep signed 0.0
420def _umod_360(deg):
421 '''(INTERNAL) Non-negative C{deg} modulo 360, basic C{.utily.wrap360}.
422 '''
423 return (deg % _360_0) or _0_0
426def _umod_PI2(rad):
427 '''(INTERNAL) Non-negative C{rad} modulo PI2, basic C{.utily.wrapPI2}.
428 '''
429 return (rad % PI2) or _0_0
432if __name__ == '__main__':
434 from pygeodesy.errors import itemsorted
435 from pygeodesy.lazily import printf
437 t = n = v = []
438 for n, v in itemsorted(locals()):
439 if isinstance(v, (Float, Int, Radius)):
440 printf('%9s: %r', n, v.toRepr(std=False))
441 if v.name != n:
442 raise AssertionError('%r != %r' % (n, v))
443 if v.name is not n:
444 raise AssertionError('%r is not %r' % (n, v))
445 if not n.startswith(_UNDER_):
446 t.append(n)
447 t.append(float_.__name__)
448 printf('__all__ = %r', tuple(t))
450# **) MIT License
451#
452# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
453#
454# Permission is hereby granted, free of charge, to any person obtaining a
455# copy of this software and associated documentation files (the "Software"),
456# to deal in the Software without restriction, including without limitation
457# the rights to use, copy, modify, merge, publish, distribute, sublicense,
458# and/or sell copies of the Software, and to permit persons to whom the
459# Software is furnished to do so, subject to the following conditions:
460#
461# The above copyright notice and this permission notice shall be included
462# in all copies or substantial portions of the Software.
463#
464# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
465# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
466# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
467# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
468# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
469# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
470# OTHER DEALINGS IN THE SOFTWARE.