Coverage for pygeodesy/auxilats/auxDLat.py: 95%
151 statements
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« prev ^ index » next coverage.py v7.2.2, created at 2023-08-23 12:10 -0400
1# -*- coding: utf-8 -*-
3u'''Class L{AuxDLat} transcoded to Python from I{Karney}'s C++ class U{DAuxLatitude
4<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1DAuxLatitude.html>}
5in I{GeographicLib version 2.2+}.
7Copyright (C) U{Charles Karney<mailto:Karney@Alum.MIT.edu>} (2022-2023) and licensed
8under the MIT/X11 License. For more information, see the U{GeographicLib
9<https://GeographicLib.SourceForge.io>} documentation.
10'''
11# make sure int/int division yields float quotient, see .basics
12from __future__ import division as _; del _ # PYCHOK semicolon
14from pygeodesy.auxilats.auxily import Aux, _Datan, _Dasinh, _sc, _sn, AuxError
15from pygeodesy.auxilats.auxLat import AuxLat, _ALL_DOCS
16from pygeodesy.basics import map1, _reverange
17from pygeodesy.constants import INF, NAN, isfinite, isinf, isnan, _0_0, \
18 _0_5, _1_0, _2_0, _N_2_0, _3_0, _naninf, \
19 _over, _1_over
20from pygeodesy.elliptic import Elliptic as _Ef, Fsum
21# from pygeodesy.errors import AuxError # from .auxilats.auxily
22# from pygeodesy.fsums import Fsum # from .elliptic
23# from pygeodesy.lazily import _ALL_DOCS # from .auxilats.auxLat
25from math import atan, atan2, cos, sin, sqrt
27__all__ = ()
28__version__ = '23.08.19'
31class AuxDLat(AuxLat):
32 '''Class to compute C{Divided Differences} of I{Auxiliary}
33 latitudes and other C{Divided Differences} needed for
34 L{RhumbAux} and L{RhumbLineAux} calculations.
35 '''
37 def CParametric(self, Zeta1, Zeta2):
38 '''Short for C{.Dconvert(Aux.BETA, B{Zeta1}, B{Zeta2})}.
39 '''
40 return self.Dconvert(Aux.BETA, Zeta1, Zeta2)
42 def CRectifying(self, Zeta1, Zeta2):
43 '''Short for C{.Dconvert(Aux.MU, B{Zeta1}, B{Zeta2})}.
44 '''
45 return self.Dconvert(Aux.MU, Zeta1, Zeta2)
47 def _Datanhee(self, x, y):
48 # atan(e*sn(tphi))/e:
49 # Datan(e*sn(x),e*sn(y))*Dsn(x,y)/Datan(x,y)
50 # asinh(e1*sn(fm1*tphi)):
51 # Dasinh(e1*sn(fm1*x)), e1*sn(fm1*y)) *
52 # e1 * Dsn(fm1*x, fm1*y) *fm1 / (e * Datan(x,y))
53 # = Dasinh(e1*sn(fm1*x)), e1*sn(fm1*y)) *
54 # Dsn(fm1*x, fm1*y) / Datan(x,y)
55 if self.f < 0:
56 e = self._e
57 r = _Datan(e * _sn(x), e * _sn(y))
58 else:
59 x *= self._fm1
60 y *= self._fm1
61 e1 = self._e1
62 r = _Dasinh(e1 * _sn(x), e1 * _sn(y))
63 return _Dsn(x, y) * r
65 def Dconvert(self, auxout, Zeta1, Zeta2):
66 '''I{Divided Difference} of one auxiliary latitude wrt another.
67 '''
68 auxin = Zeta1._AUX
69 # assert Zeta2._AUX == auxin
70 try:
71 if auxout != auxin:
72 cs = self._coeffs(auxout, auxin)
73 # assert len(cs) == self.ALorder
74 r = _DClenshaw(True, Zeta1, Zeta2, cs, self.ALorder)
75 else:
76 r = _1_0
77 except AuxError: # no _coeffs
78 r = NAN
79 return r
81 def DE(self, X, Y):
82 # We assume that X and Y are in [-90d, 90d] and
83 # have the same sign. If not we would include
84 # if (Xn.y() * Yn.y() < 0)
85 # return d != 0 ? (E(X) - E(Y)) / d : 1
86 # The general formula fails for x = y = 0d and
87 # x = y = 90d. Probably this is fixable (the
88 # formula works for other x = y. But let's
89 # also stipulate that x != y.
91 # Make both y positive, so we can do the swap a <-> b trick
92 sx, cx, x = X._yxr_normalized(True)
93 sy, cy, y = Y._yxr_normalized(True)
94 k2, d = -self._e12, (y - x)
95 # Switch prolate to oblate, then use formulas for k2 < 0
96 if self.f < 0: # XXX and False?
97 sx, cx = cx, sx
98 sy, cy = cy, sy
99 d, k2 = -d, self._e2
100 # See DLMF: Eqs (19.11.2) and (19.11.4) letting
101 Dt = _Dsin(x, y) * (sx + sy)
102 if Dt:
103 t = _sxk2y(sx, sy, k2) + _sxk2y(sy, sx, k2)
104 Dt = _over(Dt, t * (cx + cy))
105 t = d * Dt
106 t2 = _1_0 + t**2
107 Dt *= _2_0 / t2
108 sk2 = (d * Dt)**2 * k2
109 d2 = _1_0 - sk2
110 c2 = ((_1_0 - t) * (_1_0 + t) / t2)**2 if t else _1_0
111 # E(z)/sin(z)
112 E_s = (_Ef.fRF(c2, d2, _1_0) -
113 _Ef.fRD(c2, d2, _1_0, _3_0) * sk2)
114 Dt *= E_s - k2 * sx * sy
115 return Dt
117 def DIsometric(self, Phi1, Phi2):
118 '''I{Divided Difference} of the isometric wrt the geographic latitude.
119 '''
120 tx, ty = Phi1.tan, Phi2.tan
121 if isnan(ty) or isnan(tx): # PYCHOK no cover
122 r = NAN
123 elif isinf(ty) or isinf(tx): # PYCHOK no cover
124 r = INF
125 else: # psi = asinh(tan(Phi)) - e^2 * atanhee(tan(Phi))
126 r = self._Datanhee(tx, ty) * self._e2
127 r = _over(_Dasinh(tx, ty) - r, _Datan(tx, ty))
128 return r
130 def DParametric(self, Phi1, Phi2):
131 '''I{Divided Difference} of the parametric wrt the geographic latitude.
132 '''
133 fm1, e2m1 = self._fm1, self._e2m1
134 tx, ty = Phi1.tan, Phi2.tan
135 # DbetaDphi = Datan(fm1*tx, fm1*ty) * fm1 / Datan(tx, ty)
136 # Datan(x, y) = 1 / (1 + x^2), if x == y
137 # = (atan(y) - atan(x)) / (y-x), if x*y < 0
138 # = atan((y-x) / (1 + x*y)) / (y-x), if x*y > 0
139 txy = tx * ty
140 if txy < 0 or (isinf(ty) and not tx):
141 _a = atan
142 r = _over(_a(fm1 * ty) - _a(fm1 * tx), _a(ty) - _a(tx))
143 elif tx == ty: # includes tx = ty = inf
144 if txy > 1: # == tx**2
145 txy = _1_over(txy)
146 r = txy + e2m1
147 else:
148 r = txy * e2m1 + _1_0
149 r = _over(fm1 * (txy + _1_0), r)
150 else:
151 if txy > 1:
152 tx = _1_over(tx)
153 ty = _1_over(ty)
154 txy = tx * ty
155 t = txy + e2m1
156 else:
157 t = txy * e2m1 + _1_0
158 r = ty - tx
159 r = _over(atan2(r * fm1, t), atan2(r, _1_0 + txy))
160 return r
162 def DRectifying(self, Phi1, Phi2):
163 '''I{Divided Difference} of the rectifying wrt the geographic latitude.
164 '''
165 # Stipulate that Phi1 and Phi2 are in [-90d, 90d]
166 x, y = Phi1.toRadians, Phi2.toRadians
167 if y == x: # isnear0
168 Mu1 = self.Rectifying(Phi1, diff=True)
169 tphi1, r = Phi1.tan, Mu1.diff
170 if isfinite(tphi1):
171 r *= _over(_sc(tphi1), _sc(Mu1.tan))**2
172 else: # PYCHOK no cover
173 r = _1_over(r)
174 elif (x * y) < 0:
175 r = _over(self.Rectifying(Phi2).toRadians -
176 self.Rectifying(Phi1).toRadians, y - x)
177 else:
178 r = _over(self.b, self.RectifyingRadius(True))
179 r *= self.DE(*map1(self.Parametric, Phi1, Phi2))
180 r *= self.DParametric(Phi1, Phi2)
181 return r # or INF or NAN
184def _DClenshaw(sinp, Zeta1, Zeta2, cs, K):
185 '''(INTERNAL) I{Divided Difference} of L{AuxLat._Clenshaw}.
187 @return: C{Fsum} if B{C{sinp}} otherwise a C{float}.
188 '''
189 s1, c1, r1 = Zeta1._yxr_normalized(False)
190 s2, c2, r2 = Zeta2._yxr_normalized(False)
191 Delta = r2 - r1
192 # Evaluate (Clenshaw(sinp, szeta2, czeta2, cs, K) -
193 # Clenshaw(sinp, szeta1, czeta1, cs, K)) / Delta
194 # or f = sin if sinp else cos
195 # sum(cs[k] * (f((2*k+2) * Zeta2) -
196 # f((2*k+2) * Zeta2))) / Delta
197 #
198 # Delta is EITHER 1, giving the plain difference OR (Zeta2 - Zeta1)
199 # in radians, giving the I{Divided Difference}. Other values will
200 # produce nonsense.
201 #
202 # Suffices a and b denote [1,1], [2,1] elements of matrix/vector
203 cp = cm = c2 * c1
204 t = s2 * s1
205 cp -= t # not +
206 cm += t # not -
208 sp = s2 * c1
209 t = c2 * s1
210 smd = ((sin(Delta) / Delta) if Delta != _1_0 else
211 (sp - t)) if Delta else _1_0
212 sp += t
214 xa = cp * cm * _2_0
215 xb = sp * smd * _N_2_0
216 xD = xb * Delta**2
218 if isfinite(xD) and isfinite(xb) and isfinite(xa):
219 U0a, U1a = Fsum(), Fsum()
220 U0b, U1b = Fsum(), Fsum()
221 for k in _reverange(K): # assert len(cs) == K
222 # t = x . U0 - U1 + cs[k] * I
223 U1a -= U0a * xa + U0b * xD + cs[k]
224 U1b -= U0a * xb + U0b * xa
225 U1a, U0a = U0a, -U1a
226 U1b, U0b = U0b, -U1b
227 # F0a = (sp if sinp else cp) * cm
228 # F0b = (cp if sinp else -sp) * smd
229 # Fm1a = 0 if sinp else 1 # Fm1b = 0
230 # return (U0b * F0a + U0a * F0b - U1b * Fm1a) * 2
231 if sinp:
232 U1b = _0_0
233 else:
234 sp, cp = cp, -sp
235 U0b *= sp * cm
236 U0a *= cp * smd
237 U0a += U0b
238 U0a -= U1b
239 U0a *= _2_0
240 r = float(U0a) if sinp else U0a # Fsum
241 else:
242 r = _naninf(xD, xb, xa)
243 return r
246def _Dsin(x, y): # see also .rhumbx._Dsin
247 r = cos((x + y) * _0_5)
248 d = (x - y) * _0_5
249 if d:
250 r *= sin(d) / d
251 return r
254def _Dsn(x, y):
255 # (sn(y) - sn(x)) / (y - x)
256 if x != y:
257 snx, sny = _sn(x), _sn(y)
258 if (x * y) > 0:
259 scx, scy = _sc(x), _sc(y)
260 r = _over((snx / scy) + (sny / scx),
261 (snx + sny) * scy * scx)
262 else:
263 r = (sny - snx) / (y - x)
264 elif x:
265 r = _1_over(_sc(x) * (x**2 + _1_0)) # == 1 / sqrt3(x**2 + 1)
266 else:
267 r = _1_0
268 return r
271def _sxk2y(sx, sy, k2):
272 # .DE helper
273 sy *= sy * k2
274 if sy:
275 try:
276 sx *= sqrt(_1_0 - sy)
277 except ValueError: # domain error
278 sx = NAN
279 return sx
282__all__ += _ALL_DOCS(AuxDLat)
284# **) MIT License
285#
286# Copyright (C) 2023-2023 -- mrJean1 at Gmail -- All Rights Reserved.
287#
288# Permission is hereby granted, free of charge, to any person obtaining a
289# copy of this software and associated documentation files (the "Software"),
290# to deal in the Software without restriction, including without limitation
291# the rights to use, copy, modify, merge, publish, distribute, sublicense,
292# and/or sell copies of the Software, and to permit persons to whom the
293# Software is furnished to do so, subject to the following conditions:
294#
295# The above copyright notice and this permission notice shall be included
296# in all copies or substantial portions of the Software.
297#
298# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
299# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
300# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
301# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
302# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
303# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
304# OTHER DEALINGS IN THE SOFTWARE.