# Coverage for pygeodesy/geodesicx/gxline.py : 96%

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 | # -*- coding: utf-8 -*- u'''A Python version of I{Karney}'s C++ class U{GeodesicLineExact <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1GeodesicLineExact.html>}. Copyright (C) Charles Karney (2012-2021) <Charles@Karney.com> and licensed under the MIT/X11 License. For more information, see U{GeographicLib<https://GeographicLib.SourceForge.io>}. ''' # make sure int/int division yields float quotient from __future__ import division # A copy of comments from Karney's C{GeodesicLineExact.cpp}: # # This is a reformulation of the geodesic problem. The # notation is as follows: # - at a general point (no suffix or 1 or 2 as suffix) # - phi = latitude # - beta = latitude on auxiliary sphere # - omega = longitude on auxiliary sphere # - lambda = longitude # - alpha = azimuth of great circle # - sigma = arc length along great circle # - s = distance # - tau = scaled distance (= sigma at multiples of PI/2) # - at northwards equator crossing # - beta = phi = 0 # - omega = lambda = 0 # - alpha = alpha0 # - sigma = s = 0 # - a 12 suffix means a difference, e.g., s12 = s2 - s1. # - s and c prefixes mean sin and cos # from pygeodesy.basics import copysign0 # from .fmath from pygeodesy.fmath import copysign0, fsum_, hypot, norm2 from pygeodesy.geodesicx.gxbases import _all_caps, _ALL_DOCS, Caps, \ _coSeries, _GeodesicBase, \ _sincos12, _TINY from pygeodesy.interns import NAN, NN, PI_2, _COMMASPACE_, \ _name_, _0_0, _1_0, _90_0, _180_0 # from pygeodesy.lazily import _ALL_DOCS # from .geodesicx.bases from pygeodesy.karney import _around, _fix90, GDict, _norm180 from pygeodesy.props import Property_RO, _update_all from pygeodesy.streprs import pairs from pygeodesy.utily import atan2d, sincos2, sincos2d from math import atan2, degrees, floor, radians __all__ = () __version__ = '21.06.30' _glXs = [] # instances of C{[_]GeodesicLineExact} def _update_glXs(gX_glX): # see .C4Order, ._ef_reset, .GdistDirect '''(INTERNAL) Zap cached/memoized C{Property}s or remove. ''' if _glXs: # can become empty, even None if isinstance(gX_glX, _GeodesicLineExact): _glXs.remove(gX_glX) # most recent else: # PYCHOK no cover for glX in _glXs: # XXX use weakref glX._update(glX._gX is gX_glX) class _GeodesicLineExact(_GeodesicBase): '''(INTERNAL) Base class for L{GeodesicLineExact}. ''' _a13 = _s13 = NAN _azi1 = _0_0 _caps = 0 # not initilized _cchi1 = NAN _dn1 = NAN _gX = None # Exact only _k2 = NAN _lat1 = _lon1 = _0_0 _salp0 = _calp0 = NAN _salp1 = _calp1 = NAN _somg1 = _comg1 = NAN _ssig1 = _csig1 = NAN def __init__(self, gX, lat1, lon1, azi1, caps, _debug, *salp1_calp1, **name): '''(INTERNAL) New C{[_]GeodesicLineExact} instance. ''' if salp1_calp1: salp1, calp1 = salp1_calp1 else: azi1 = _norm180(azi1) # guard against salp0 underflow, # also -0 is converted to +0 salp1, calp1 = sincos2d(_around(azi1)) self._gX = gX # Exact only self._lat1 = lat1 = _fix90(lat1) self._lon1 = lon1 self._azi1 = azi1 self._salp1 = salp1 self._calp1 = calp1 if _debug: # PYCHOK no cover caps |= Caps._DEBUG_LINE & _debug # allow lat, azimuth and unrolling of lon self._caps = caps | Caps._LINE self._caps_DISTANCE_IN = caps & (Caps._OUTMASK & Caps.DISTANCE_IN) name = name.get(_name_, NN) or gX.name if name: self.name = name sbet1, cbet1 = sincos2d(_around(lat1)) sbet1 *= gX.f1 # Ensure cbet1 = +epsilon at poles sbet1, cbet1 = norm2(sbet1, cbet1) cbet1 = max(_TINY, cbet1) self._dn1 = gX._dn(sbet1, cbet1) # Evaluate alp0 from sin(alp1) * cos(bet1) = sin(alp0), self._salp0 = cbet1 * salp1 # alp0 in [0, pi/2 - |bet1|] # Alt: calp0 = hypot(sbet1, calp1 * cbet1). The following # is slightly better (consider the case salp1 = 0). self._calp0 = hypot(calp1, salp1 * sbet1) self._k2 = gX._eF_reset_k2(self._calp0) # Evaluate sig with tan(bet1) = tan(sig1) * cos(alp1). # sig = 0 is nearest northward crossing of equator. # With bet1 = 0, alp1 = pi/2, we have sig1 = 0 (equatorial line). # With bet1 = pi/2, alp1 = -pi, sig1 = pi/2 # With bet1 = -pi/2, alp1 = 0 , sig1 = -pi/2 # Evaluate omg1 with tan(omg1) = sin(alp0) * tan(sig1). # With alp0 in (0, pi/2], quadrants for sig and omg coincide. # No atan2(0,0) ambiguity at poles since cbet1 = +epsilon. # With alp0 = 0, omg1 = 0 for alp1 = 0, omg1 = pi for alp1 = pi. self._somg1 = sbet1 * self._salp0 self._comg1 = c = (cbet1 * calp1) if (sbet1 or calp1) else _1_0 # Without normalization we have schi1 = somg1. self._cchi1 = gX.f1 * self._dn1 * c self._ssig1, self._csig1 = norm2(sbet1, c) # sig1 in (-pi, pi] # norm2(somg1, comg1) # no need to normalize! # norm2(schi1?, cchi1) # no need to normalize! _glXs.append(self) # no need to pre-compute other attrs based on _Caps.X. All are # Property_RO's, computed once and cached/memoized until reset # when C4Order is changed or Elliptic function reset. def __del__(self): # XXX use weakref? while _glXs: # may be None try: # PYCHOK no cover _glXs.remove(self) except ValueError: break _update_all(self) self._gX = None def _update(self, updated, *attrs): if updated: _update_all(self, *attrs) @Property_RO def a13(self): '''Get (spherical) arc length from the first to the reference point (C{degrees}). @see: Method L{SetArc}. ''' return self._a13 @Property_RO def _A4_e2a2(self): '''(INTERNAL) Cached/memoized. ''' return self._calp0 * self._salp0 * self._gX._e2a2 def ArcPosition(self, a12, outmask=Caps.STANDARD): '''Find the position on the line given B{C{a12}}. @arg a12: Spherical arc length from the first point to the second point (C{degrees}). @kwarg outmask: Bit-or'ed combination of L{Caps} values specifying the quantities to be returned. @return: A C{dict} with up to 12 items C{lat1, lon1, azi1, lat2, lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1}, C{lon1}, C{azi1} and arc length C{a12} always included, except when C{a12=NAN}. @note: By default, C{B{outmask}=STANDARD}, meaning thc C{lat1}, C{lon1}, C{azi1}, C{lat2}, C{lon2}, C{azi2}, C{s12} and C{a12} entries are returned, except when C{a12=NAN}. ''' return self._GDictPosition(True, a12, outmask) @Property_RO def azi0(self): '''Get the I{equatorial azimuth}, the azimuth of this geodesic line as it crosses the equator in a northward direction (C{degrees90}). ''' t = self.azi0_sincos2 return NAN if NAN in t else atan2d(*t) @Property_RO def azi0_sincos2(self): '''Get the sine and cosine of the I{equatorial azimuth} (2-tuple C{(sin, cos)}). ''' return self._salp0, self._calp0 @Property_RO def azi1(self): '''Get the azimuth at the first point (compass C{degrees}). ''' return self._azi1 @Property_RO def azi1_sincos2(self): '''Get the sine and cosine of the first point's azimuth (2-tuple C{(sin, cos)}). ''' return self._salp1, self._calp1 @Property_RO def _B41(self): '''(INTERNAL) Cached/memoized. ''' return _coSeries(self._C4a, self._ssig1, self._csig1) @Property_RO def _C4a(self): '''(INTERNAL) Cached/memoized. ''' return self._gX._C4f_k2(self._k2) @Property_RO def caps(self): '''Get the capabilities (bit-or'ed C{Caps}). ''' return self._caps def caps_(self, caps): '''Check the available capabilities. @arg caps: Bit-or'ed combination of L{Caps} values for all capabilities to be checked. @return: C{True} if I{all} B{C{caps}} are available, C{False} otherwise (C{bool}). ''' return _all_caps(self.caps, caps) @Property_RO def _D0_k2(self): '''(INTERNAL) Cached/memoized. ''' return self._eF.cD / PI_2 * self._k2 @Property_RO def _D1(self): '''(INTERNAL) Cached/memoized. ''' return self._eF.deltaD(self._ssig1, self._csig1, self._dn1) @Property_RO def _E0_b(self): '''(INTERNAL) Cached/memoized. ''' return self._eF.cE / PI_2 * self._gX.b @Property_RO def _E1(self): '''(INTERNAL) Cached/memoized. ''' return self._eF.deltaE(self._ssig1, self._csig1, self._dn1) @Property_RO def _eF(self): '''(INTERNAL) Cached/memoized. ''' return self._gX._eF # .geodesic._eF def _GDictPosition(self, arcmode, s12_a12, outmask): # MCCABE 17 '''(INTERNAL) Generate a new position along the geodesic. @return: A C{dict} with up to 12 items C{lat1, lon1, azi1, lat2, lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1}, C{lon1}, C{azi1} and arc length C{a12} always included, except when C{a12=NAN}. ''' r = GDict(a12=NAN, s12=NAN) # note both a12 and s12, always if not (arcmode or self._caps_DISTANCE_IN): # PYCHOK no cover return r # Uninitialized or impossible distance requested if self.debug: # PYCHOK no cover outmask |= Caps._DEBUG_LINE & self._debug outmask &= self._caps & Caps._OUTMASK gX = self._gX eF = self._eF if arcmode: # PYCHOK no cover # s12_a12 is spherical arc length E2 = _0_0 sig12 = radians(s12_a12) ssig12, csig12 = sincos2(sig12) a = abs(s12_a12) a -= floor(a / _180_0) * _180_0 if a == _0_0: ssig12 = _0_0 elif a == _90_0: csig12 = _0_0 else: # s12_a12 is distance t = s12_a12 / self._E0_b s, c = sincos2(t) # tau12 # tau2 = tau1 + tau12 E2 = -eF.deltaEinv(*_sincos12(-s, c, *self._stau1_ctau1)) sig12 = fsum_(self._E1, -E2, t) ssig12, csig12 = sincos2(sig12) salp0, calp0 = self._salp0, self._calp0 ssig1, csig1 = self._ssig1, self._csig1 # sig2 = sig1 + sig12 ssig2, csig2 = _sincos12(-ssig12, csig12, ssig1, csig1) dn2 = eF.fDelta(ssig2, csig2) # sin(bet2) = cos(alp0) * sin(sig2) sbet2 = calp0 * ssig2 # Alt: cbet2 = hypot(csig2, salp0 * ssig2); cbet2 = hypot(salp0, calp0 * csig2) if not cbet2: # salp0 = 0, csig2 = 0, break degeneracy cbet2 = csig2 = _TINY # tan(alp0) = cos(sig2) * tan(alp2) salp2 = salp0 calp2 = calp0 * csig2 # no need to normalize if (outmask & Caps.DISTANCE): if arcmode: E2 = eF.deltaE(ssig2, csig2, dn2) # AB1 = _E0 * (E2 - _E1) # s12 = _b * (_E0 * sig12 + AB1) # = _b * _E0 * (sig12 + (E2 - _E1)) # = _b * _E0 * (E2 - _E1 + sig12) s12 = self._E0_b * fsum_(E2, -self._E1, sig12) else: s12 = s12_a12 r.set_(s12=s12) if (outmask & Caps._DEBUG_LINE): # PYCHOK no cover r.set_(sig12=sig12, dn2=dn2, E0_b=self._E0_b, E1=self._E1, E2=E2, e2=gX.e2, f1=gX.f1, eFk2=eF.k2, eFa2=eF.alpha2) if (outmask & Caps.LONGITUDE): schi1 = self._somg1 cchi1 = self._cchi1 schi2 = ssig2 * salp0 cchi2 = gX.f1 * dn2 * csig2 # schi2 = somg2 without normalization lam12 = salp0 * self._H0_e2_f1 * fsum_(eF.deltaH(ssig2, csig2, dn2), -self._H1, sig12) if (outmask & Caps.LONG_UNROLL): E = copysign0(_1_0, salp0) # east-going? tchi1 = E * schi1 tchi2 = E * schi2 chi12 = E * fsum_(atan2(ssig1, csig1), -atan2(ssig2, csig2), atan2(tchi2, cchi2), -atan2(tchi1, cchi1), sig12) lon2 = self.lon1 + degrees(chi12 - lam12) else: chi12 = atan2(*_sincos12(schi1, cchi1, schi2, cchi2)) lon2 = _norm180(self._lon1_norm180 + _norm180(degrees(chi12 - lam12))) r.set_(lon2=lon2) if (outmask & Caps._DEBUG_LINE): # PYCHOK no cover r.set_(chi12=chi12, lam12=lam12, H0_e2_f1=self._H0_e2_f1, H1=self._H1, ssig2=ssig2, csig2=csig2) if (outmask & Caps.LATITUDE): r.set_(lat2=atan2d(sbet2, gX.f1 * cbet2)) if (outmask & Caps.AZIMUTH): r.set_(azi2=atan2d(salp2, calp2, reverse=outmask & Caps.REVERSE2)) if (outmask & Caps._REDUCEDLENGTH_GEODESICSCALE): dn1 = self._dn1 J12 = self._D0_k2 * fsum_(eF.deltaD(ssig2, csig2, dn2), -self._D1, sig12) if (outmask & Caps._DEBUG_LINE): # PYCHOK no cover r.set_(dn1=dn1, D0_k2=self._D0_k2, D1=self._D1, J12=J12, ssig1=ssig1, csig1=csig1, b=gX.b) if (outmask & Caps.REDUCEDLENGTH): # Add parens around (_csig1 * ssig2) and (_ssig1 * csig2) to ensure # accurate cancellation in the case of coincident points. r.set_(m12=gX.b * fsum_(dn2 * (csig1 * ssig2), -dn1 * (ssig1 * csig2), -J12 * (csig1 * csig2))) if (outmask & Caps.GEODESICSCALE): t = self._k2 * (ssig2 - ssig1) * (ssig2 + ssig1) / (dn2 + dn1) r.set_(M12=csig12 + (t * ssig2 - csig2 * J12) * ssig1 / dn1, M21=csig12 - (t * ssig1 - csig1 * J12) * ssig2 / dn2) if (outmask & Caps.AREA): B42 = _coSeries(self._C4a, ssig2, csig2) if calp0 and salp0: # tan(alp) = tan(alp0) * sec(sig) # tan(alp2-alp1) = (tan(alp2) - tan(alp1)) / (tan(alp2) * tan(alp1) + 1) # = calp0 * salp0 * (csig1 - csig2) / (salp0^2 + calp0^2 * csig1 * csig2) # If csig12 > 0, write # csig1 - csig2 = ssig12 * (csig1 * ssig12 / (1 + csig12) + ssig1) # else # csig1 - csig2 = csig1 * (1 - csig12) + ssig12 * ssig1 # No need to normalize salp12 = (((ssig12 * csig1 / (_1_0 + csig12) + ssig1) * ssig12) if csig12 > 0 else (csig1 * (_1_0 - csig12) + ssig1 * ssig12)) * salp0 * calp0 calp12 = salp0**2 + calp0**2 * csig1 * csig2 else: # alp12 = alp2 - alp1, used in atan2 so no need to normalize salp12, calp12 = _sincos12(self._salp1, self._calp1, salp2, calp2) # We used to include some patch up code that purported to deal # with nearly meridional geodesics properly. However, this turned # out to be wrong once salp1 = -0 was allowed (via InverseLine). # In fact, the calculation of {s,c}alp12 was already correct # (following the IEEE rules for handling signed zeros). So, # the patch up code was unnecessary (as well as dangerous). A4_e2a2 = self._A4_e2a2 r.set_(S12=fsum_(A4_e2a2 * B42, -A4_e2a2 * self._B41, gX.c2 * atan2(salp12, calp12))) if (outmask & Caps._DEBUG_LINE): # PYCHOK no cover r.set_(salp12=salp12, calp12=calp12, B42=B42, A4_e2a2=A4_e2a2, salp0=salp0, calp0=calp0, B41=self._B41, c2=gX.c2) r.set_(a12=s12_a12 if arcmode else degrees(sig12), lat1=self.lat1, # == _fix90(lat1) lon1=self.lon1 if (outmask & Caps.LONG_UNROLL) else self._lon1_norm180, azi1=_norm180(self.azi1)) return r def _GenPosition(self, arcmode, s12_a12, outmask): '''(INTERNAL) Generate a new position along the geodesic. @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)}. ''' r = self._GDictPosition(arcmode, s12_a12, outmask) return r.toDirect9Tuple() def _GenSet(self, arcmode, s13_a13): '''(INTERNAL) Aka C++ C{GenSetDistance}. ''' if arcmode: self.SetArc(s13_a13) else: self.SetDistance(s13_a13) return self # for gx.GeodesicExact.InverseLine and ._GenDirectLine @Property_RO def geodesic(self): '''Get the I{exact} geodesic (L{GeodesicExact}). ''' return self._gX @Property_RO def _H0_e2_f1(self): '''(INTERNAL) Cached/memoized. ''' return self._eF.cH / PI_2 * self._gX._e2_f1 @Property_RO def _H1(self): '''(INTERNAL) Cached/memoized. ''' return self._eF.deltaH(self._ssig1, self._csig1, self._dn1) @Property_RO def lat1(self): '''Get the latitude of the first point (C{degrees}). ''' return self._lat1 @Property_RO def lon1(self): '''Get the longitude of the first point (C{degrees}). ''' return self._lon1 @Property_RO def _lon1_norm180(self): '''(INTERNAL) Cached/memoized. ''' return _norm180(self._lon1) def Position(self, s12, outmask=Caps.STANDARD): '''Find the position on the line given B{C{s12}}. @arg s12: Distance from the first point to the second C({meter}). @kwarg outmask: Bit-or'ed combination of L{Caps} values specifying the quantities to be returned. @return: A C{dict} with up to 12 items C{lat1, lon1, azi1, lat2, lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1}, C{lon1}, C{azi1} and arc length C{a12} always included, except when C{a12=NAN}. @note: By default, C{B{outmask}=STANDARD}, meaning thc C{lat1}, C{lon1}, C{azi1}, C{lat2}, C{lon2}, C{azi2}, C{s12} and C{a12} entries are returned, except when C{a12=NAN}. @note: This L{GeodesicLineExact} instance must have been constructed with capability C{Caps.DISTANCE_IN} set. ''' return self._GDictPosition(False, s12, outmask) @Property_RO def s13(self): '''Get the distance from the first to the reference point C({meter}). @see: Method L{SetDistance}. ''' return self._s13 def SetArc(self, a13): '''Set reference point 3 in terms of distance to the first point. @arg a13: Spherical arc length from the first to the reference point (C{degrees}). @return: The distance C{s13} (C{meter}) between the first and the reference point. ''' self._a13 = a13 # In case the GeodesicLineExact doesn't have the DISTANCE capability. self._s13 = s13 = self._GDictPosition(True, a13, Caps.DISTANCE).s12 return s13 def SetDistance(self, s13): '''Set reference point 3 in terms of distance to the first point. @arg s13: Distance from the first to the reference point C({meter}). @return: The arc length C{a13} (C{degrees}) between the first and the reference point or C{NAN}. ''' self._s13 = s13 # _a13 will be_NAN if the GeodesicLineExact # doesn't have the DISTANCE_IN capability self._a13 = a13 = self._GDictPosition(False, s13, 0).a12 return a13 @Property_RO def _stau1_ctau1(self): '''(INTERNAL) Cached/memoized. ''' s, c = sincos2(self._E1) # tau1 = sig1 + B11 return _sincos12(-s, c, self._ssig1, self._csig1) # unnecessary because Einv inverts E # return -self._gX._eF.deltaEinv(stau1, ctau1) def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature '''Return this C{GeodesicExactLine} as string. @kwarg prec: The C{float} precision, number of decimal digits (0..9). Trailing zero decimals are stripped for B{C{prec}} values of 1 and above, but kept for negative B{C{prec}} values. @kwarg sep: Optional separator to join (C{str}). @return: C{GeodesicExactLine} (C{str}). ''' d = dict(geodesic=self.geodesic, lat1=self.lat1, lon1=self.lon1, azi1=self.azi1, a13=self.a13, s13=self.s13) return sep.join(pairs(d, prec=prec)) __all__ += _ALL_DOCS(_GeodesicLineExact) # **) MIT License # # Copyright (C) 2016-2021 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.