# Coverage for pygeodesy/frechet.py : 92%

## 178 statements 164 run 14 missing 8 excluded

Hot-keys on this page

r m x p toggle line displays

j k next/prev highlighted chunk

0 (zero) top of page

1 (one) first highlighted chunk

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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 | # -*- coding: utf-8 -*- u'''Classes L{Frechet}, L{FrechetDegrees}, L{FrechetRadians}, L{FrechetEquirectangular}, L{FrechetEuclidean}, L{FrechetHaversine}, and L{FrechetVincentys} to compute I{discrete} U{Fréchet <https://WikiPedia.org/wiki/Frechet_distance>} distances between two sets of C{LatLon}, C{NumPy}, C{tuples} or other types of points. Typical usage is as follows. First, create a C{Frechet} calculator from one set of C{LatLon} points. C{f = FrechetXyz(points1, ...)} Get the I{discrete} Fréchet distance to another set of C{LatLon} points by C{t6 = f.discrete(points2)} Or, use function C{frechet_} with a proper C{distance} function passed as keyword arguments as follows C{t6 = frechet_(points1, points2, ..., distance=...)}. In both cases, the returned result C{t6} is a L{Frechet6Tuple}. For C{(lat, lon, ...)} points in a C{NumPy} array or plain C{tuples}, wrap the points in a L{Numpy2LatLon} respectively L{Tuple2LatLon} instance, more details in the documentation thereof. For other points, create a L{Frechet} sub-class with the appropriate C{distance} method overloading L{Frechet.distance} as in this example. >>> from pygeodesy import Frechet, hypot_ >>> >>> class F3D(Frechet): >>> """Custom Frechet example. >>> """ >>> def distance(self, p1, p2): >>> return hypot_(p1.x - p2.x, p1.y - p2.y, p1.z - p2.z) >>> >>> f3D = F3D(xyz1, ..., units="...") >>> t6 = f3D.discrete(xyz2) Transcribed from the original U{Computing Discrete Fréchet Distance <https://www.kr.TUWien.ac.AT/staff/eiter/et-archive/cdtr9464.pdf>} by Eiter, T. and Mannila, H., 1994, April 25, Technical Report CD-TR 94/64, Information Systems Department/Christian Doppler Laboratory for Expert Systems, Technical University Vienna, Austria. This L{Frechet.discrete} implementation optionally generates intermediate points for each point set separately. For example, using keyword argument C{fraction=0.5} adds one additional point halfway between each pair of points. Or using C{fraction=0.1} interpolates nine additional points between each points pair. The L{Frechet6Tuple} attributes C{fi1} and/or C{fi2} will be I{fractional} indices of type C{float} if keyword argument C{fraction} is used. Otherwise, C{fi1} and/or C{fi2} are simply type C{int} indices into the respective points set. For example, C{fractional} index value 2.5 means an intermediate point halfway between points[2] and points[3]. Use function L{fractional} to obtain the intermediate point for a I{fractional} index in the corresponding set of points. The C{Fréchet} distance was introduced in 1906 by U{Maurice Fréchet <https://WikiPedia.org/wiki/Maurice_Rene_Frechet>}, see U{reference [6]<https://www.kr.TUWien.ac.AT/staff/eiter/et-archive/cdtr9464.pdf>}. It is a measure of similarity between curves that takes into account the location and ordering of the points. Therefore, it is often a better metric than the well-known C{Hausdorff} distance, see the L{hausdorff} module. ''' from pygeodesy.basics import EPS, EPS1, INF, _isnotError, \ isscalar, property_doc_, property_RO from pygeodesy.fmath import favg, hypot2 from pygeodesy.formy import euclidean_, haversine_, points2 as _points2, \ _scaler, vincentys_ from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY from pygeodesy.named import LatLon2Tuple, _Named, _NamedTuple, \ notOverloaded, PhiLam2Tuple from pygeodesy.utily import unrollPI from collections import defaultdict from math import radians __all__ = _ALL_LAZY.frechet + _ALL_DOCS('Frechet6Tuple') __version__ = '20.03.23' if not 0 < EPS < EPS1 < 1: raise AssertionError('%s < %s: 0 < %.6g < %.6g < 1' % ('EPS', 'EPS1', EPS, EPS1)) class FrechetError(ValueError): '''Fréchet issue. ''' pass def _fraction(fraction, n): f = 1 # int, no fractional indices if fraction in (None, 1): pass elif not (isscalar(fraction) and EPS < fraction < EPS1 and (float(n) - fraction) < n): raise FrechetError('%s invalid: %r' % ('fraction', fraction)) elif fraction < EPS1: f = float(fraction) return f class Frechet6Tuple(_NamedTuple): '''6-Tuple C{(fd, fi1, fi2, r, n, units)} with the I{discrete} U{Fréchet<https://WikiPedia.org/wiki/Frechet_distance>} distance C{fd}, I{fractional} indices C{fi1} and C{fi2}, the recursion depth C{r}, the number of distances computed C{n} and the name of the distance C{units}. If I{fractional} indices C{fi1} and C{fi2} are type C{int}, the returned C{fd} is the distance between C{points1[fi1]} and C{points2[fi2]}. For type C{float} indices, the distance is between an intermediate point along C{points1[int(fi1)]} and C{points1[int(fi1) + 1]} respectively an intermediate point along C{points2[int(fi2)]} and C{points2[int(fi2) + 1]}. Use function L{fractional} to compute the point at a fractional index. ''' _Names_ = ('fd', 'fi1', 'fi2', 'r', 'n', 'units') # def __gt__(self, other): # _TypeError(Frechet6Tuple, other=other) # return self if self.fd > other.fd else other # PYCHOK .fd=[0] # # def __lt__(self, other): # _TypeError(Frechet6Tuple, other=other) # return self if self.fd < other.fd else other # PYCHOK .fd=[0] class Frechet(_Named): '''Frechet base class, requires method L{Frechet.distance} to be overloaded. ''' _adjust = None _f1 = 1 _n1 = 0 _ps1 = None _units = '' _wrap = None def __init__(self, points, fraction=None, name='', units=''): '''New L{Frechet} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @kwarg units: Optional, distance units (C{str}). @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{fraction}}. ''' self._n1, self._ps1 = _points2(points, closed=False, Error=FrechetError) if fraction: self.fraction = fraction if name: self.name = name if units: self.units = units @property_RO def adjust(self): '''Get the adjust setting (C{bool} or C{None} if not applicable). ''' return self._adjust def discrete(self, points, fraction=None): '''Compute the C{forward, discrete Fréchet} distance. @arg points: Second set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @return: A L{Frechet6Tuple}C{(fd, fi1, fi2, r, n, units)}. @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{fraction}}. @raise RecursionError: Recursion depth exceeded, see U{sys.getrecursionlimit() <https://docs.Python.org/3/library/sys.html#sys.getrecursionlimit>}. ''' n2, ps2 = _points2(points, closed=False, Error=FrechetError) f2 = _fraction(fraction, n2) p2 = self.points_fraction if f2 < EPS1 else self.points_ # PYCHOK expected f1 = self.fraction p1 = self.points_fraction if f1 < EPS1 else self.points_ # PYCHOK expected def dF(fi1, fi2): return self.distance(p1(self._ps1, fi1), p2(ps2, fi2)) return _frechet_(self._n1, f1, n2, f2, dF, self.units) def distance(self, point1, point2): '''(INTERNAL) I{must be overloaded}. ''' notOverloaded(self, self.distance.__name__, point1, point2) @property_doc_(''' the index fraction (C{float}).''') def fraction(self): '''Get the index fraction (C{float} or C{1}). ''' return self._f1 @fraction.setter # PYCHOK setter! def fraction(self, fraction): '''Set the the index fraction (C{float} or C{1}). @arg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @raise FrechetError: Invalid B{C{fraction}}. ''' self._f1 = _fraction(fraction, self._n1) def point(self, point): '''Convert a point for the C{.distance} method. @arg point: The point to convert ((C{LatLon}, L{Numpy2LatLon}, L{Tuple2LatLon} or C{other}). @return: The converted B{C{point}}. ''' return point # pass thru def points_(self, points, i): '''Get and convert a point for the C{.distance} method. @arg points: The orignal B{C{points}} to convert ((C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @arg i: The B{C{points}} index (C{int}). @return: The converted B{C{points[i]}}. ''' return self.point(points[i]) def points_fraction(self, points, fi): '''Get and convert I{fractional} index point for the C{.distance} method. @arg points: The orignal B{C{points}} to convert ((C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @arg fi: The I{fractional} index in B{C{points}} (C{float} or C{int}). @return: The interpolated, converted, intermediate B{C{points[fi]}}. ''' return self.point(_fractional(points, fi)) @property_doc_(''' the distance units (C{str}).''') def units(self): '''Get the distance units (C{str} or C{""}). ''' return self._units @units.setter # PYCHOK setter! def units(self, units): '''Set the distance units. @arg units: New units name (C{str}). ''' self._units = str(units or "") @property_RO def wrap(self): '''Get the wrap setting (C{bool} or C{None} if not applicable). ''' return self._wrap class FrechetDegrees(Frechet): '''L{Frechet} base class for distances in C{degrees} from C{LatLon} points in C{degrees}. ''' _units = 'degrees' discrete = Frechet.discrete # for __doc__ class FrechetRadians(Frechet): '''L{Frechet} base class for distances in C{radians} from C{LatLon} points converted from C{degrees} to C{radians}. ''' _units = 'radians' discrete = Frechet.discrete # for __doc__ def point(self, point): '''Convert C{(lat, lon)} point in degrees to C{(a, b)} in radians. @return: An L{PhiLam2Tuple}C{(phi, lam)}. ''' return PhiLam2Tuple(radians(point.lat), radians(point.lon)) class FrechetEquirectangular(FrechetRadians): '''Compute the C{Frechet} distance based on the C{equirectangular} distance (in radians squared) like function L{equirectangular_}. @see: L{FrechetEuclidean}, L{FrechetHaversine} and L{FrechetVincentys}. ''' _adjust = True _wrap = False def __init__(self, points, adjust=True, wrap=False, fraction=None, name=''): '''New L{FrechetEquirectangular} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg wrap: Wrap and L{unroll180} longitudes (C{bool}). @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{adjust}} or B{C{seed}}. ''' if not adjust: self._adjust = False if wrap: self._wrap = True super(FrechetRadians, self).__init__(points, fraction=fraction, name=name) # distance**2 def distance(self, p1, p2): '''Return the L{equirectangular_} distance in C{radians squared}. ''' d, _ = unrollPI(p1.lam, p2.lam, wrap=self.wrap) if self.adjust: d *= _scaler(p1.phi, p2.phi) return hypot2(d, p2.phi - p1.phi) # like equirectangular_ d2 discrete = Frechet.discrete # for __doc__ class FrechetEuclidean(FrechetRadians): '''Compute the C{Frechet} distance based on the C{Euclidean} distance (in radians) from function L{euclidean_}. @see: L{FrechetEquirectangular}, L{FrechetHaversine} and L{FrechetVincentys}. ''' _adjust = True def __init__(self, points, adjust=True, fraction=None, name=''): '''New L{FrechetEuclidean} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{fraction}}. ''' if not adjust: self._adjust = False super(FrechetRadians, self).__init__(points, fraction=fraction, name=name) def distance(self, p1, p2): '''Return the L{euclidean_} distance in C{radians}. ''' return euclidean_(p2.phi, p1.phi, p2.lam - p1.lam, adjust=self.adjust) discrete = Frechet.discrete # for __doc__ class FrechetHaversine(FrechetRadians): '''Compute the C{Frechet} distance based on the I{angular} C{Haversine} distance (in radians) from function L{haversine_}. @note: See note under L{FrechetVincentys}. @see: L{FrechetEquirectangular}, L{FrechetEuclidean} and L{FrechetVincentys}. ''' _wrap = False def __init__(self, points, wrap=False, fraction=None, name=''): '''New L{FrechetHaversine} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg wrap: Wrap and L{unroll180} longitudes (C{bool}). @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{fraction}}. ''' if wrap: self._wrap = True super(FrechetRadians, self).__init__(points, fraction=fraction, name=name) def distance(self, p1, p2): '''Return the L{haversine_} distance in C{radians}. ''' d, _ = unrollPI(p1.lam, p2.lam, wrap=self.wrap) return haversine_(p2.phi, p1.phi, d) discrete = Frechet.discrete # for __doc__ class FrechetVincentys(FrechetRadians): '''Compute the C{Frechet} distance based on the I{angular} C{Vincenty} distance (in radians) from function L{vincentys_}. @note: See note under L{vincentys_}. @see: L{FrechetEquirectangular}, L{FrechetEuclidean} and L{FrechetHaversine}. ''' _wrap = False def __init__(self, points, wrap=False, fraction=None, name=''): '''New L{FrechetVincentys} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg wrap: Wrap and L{unroll180} longitudes (C{bool}). @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{fraction}}. ''' if wrap: self._wrap = True super(FrechetRadians, self).__init__(points, fraction=fraction, name=name) def distance(self, p1, p2): '''Return the L{vincentys_} distance in C{radians}. ''' d, _ = unrollPI(p1.lam, p2.lam, wrap=self.wrap) return vincentys_(p2.phi, p1.phi, d) discrete = Frechet.discrete # for __doc__ def _fractional(points, fi): '''(INTERNAL) Compute point at I{fractional} index. ''' i = int(fi) p = points[i] f = fi - float(i) if f > EPS: if f < EPS1: q = points[i + 1] p = LatLon2Tuple(favg(p.lat, q.lat, f=f), favg(p.lon, q.lon, f=f)) else: p = points[i + 1] return p def fractional(points, fi, LatLon=None, **LatLon_kwds): '''Return the point at a given I{fractional} index. @arg points: The points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @arg fi: The fractional index (C{float} or C{int}). @kwarg LatLon: Optional class to return the I{intermediate} point (C{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional B{C{LatLon}} keyword arguments, ignored of B{C{LatLon=None}}. @return: A B{C{LatLon}} or if B{C{LatLon}} is C{None}, a L{LatLon2Tuple}C{(lat, lon)} for B{C{points[fi]}} if I{fractional} index B{C{fi}} is C{int}, otherwise the intermediate point between B{C{points[int(fi)]}} and B{C{points[int(fi) + 1]}} for C{float} I{fractional} index B{C{fi}}. @raise IndexError: Fractional index B{C{fi}} invalid or B{C{points}} not subscriptable. ''' try: if not (isscalar(fi) and 0 <= fi < len(points)): raise IndexError p = _fractional(points, fi) except (IndexError, TypeError): raise IndexError('%s invalid: %r' % (fractional.__name__, fi)) if LatLon and isinstance(p, LatLon2Tuple): p = LatLon(*p, **LatLon_kwds) return p def _frechet_(ni, fi, nj, fj, dF, units): # MCCABE 14 '''(INTERNAL) Recursive core of function L{frechet_} and method C{discrete} of C{Frechet...} classes. ''' iFs = {} def iF(i): # cache index, depth ints and floats return iFs.setdefault(i, i) def rF(i, j, r): # recursive Fréchet i = iF(i) j = iF(j) try: t = cF[i][j] except KeyError: r = iF(r + 1) try: if i > 0: if j > 0: t = min(rF(i - fi, j, r), rF(i - fi, j - fj, r), rF(i, j - fj, r)) elif j < 0: raise IndexError else: # j == 0 t = rF(i - fi, 0, r) elif i < 0: raise IndexError elif j > 0: # i == 0 t = rF(0, j - fj, r) elif j < 0: # i == 0 raise IndexError else: # i == j == 0 t = (-INF, i, j, r) d = dF(i, j) if d > t[0]: t = (d, i, j, r) except IndexError: t = (INF, i, j, r) cF[i][j] = t return t cF = defaultdict(dict) t = rF(ni - 1, nj - 1, 0) t += (sum(map(len, cF.values())), units) # del cF, iFs return Frechet6Tuple(*t) def frechet_(points1, points2, distance=None, units=''): '''Compute the I{discrete} U{Fréchet<https://WikiPedia.org/wiki/Frechet_distance>} distance between two paths given as sets of points. @arg points1: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @arg points2: Second set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg distance: Callable returning the distance between a B{C{points1}} and a B{C{points2}} point (signature C{(point1, point2)}). @kwarg units: Optional, name of the distance units (C{str}). @return: A L{Frechet6Tuple}C{(fd, fi1, fi2, r, n, units)} where C{fi1} and C{fi2} are type C{int} indices into B{C{points1}} respectively B{C{points2}}. @raise FrechetError: Insufficient number of B{C{points1}} or B{C{points2}}. @raise RecursionError: Recursion depth exceeded, see U{sys.getrecursionlimit() <https://docs.Python.org/3/library/sys.html#sys.getrecursionlimit>}. @raise TypeError: If B{C{distance}} is not a callable. @note: Keyword arguments C{fraction}, intermediate B{C{points1}} and B{C{points2}} and I{fractional} indices are I{not} supported in this L{frechet_} function. ''' if not callable(distance): raise _isnotError(callable.__name__, distance=distance) n1, ps1 = _points2(points1, closed=False, Error=FrechetError) n2, ps2 = _points2(points2, closed=False, Error=FrechetError) def dF(i1, i2): return distance(ps1[i1], ps2[i2]) return _frechet_(n1, 1, n2, 1, dF, units) # **) MIT License # # Copyright (C) 2016-2020 -- 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.