# Coverage for pygeodesy/hausdorff.py : 93%

## 184 statements 172 run 12 missing 6 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 | # -*- coding: utf-8 -*- u'''Classes L{Hausdorff}, L{HausdorffDegrees}, L{HausdorffRadians}, L{HausdorffEquirectangular}, L{HausdorffEuclidean}, L{HausdorffHaversine}, L{HausdorffKarney} and L{HausdorffVincentys} to compute U{Hausdorff <https://WikiPedia.org/wiki/Hausdorff_distance>} distances between two sets of C{LatLon}, C{NumPy}, C{tuples} or other types of points. Only L{HausdorffKarney} depends on an external package, Charles Karney's U{geographiclib<https://PyPI.org/project/geographiclib>}. Typical usage is as follows. First, create a C{Hausdorff} calculator from a given set of C{LatLon} points, called the C{model} or C{template} points. C{h = HausdorffXyz(points1, ...)} Get the C{directed} or C{symmetric} Hausdorff distance to a second set of C{LatLon} points, named the C{target} points, by using C{t6 = h.directed(points2)} respectively C{t6 = h.symmetric(points2)}. Or, use function C{hausdorff_} with a proper C{distance} function and optionally a C{point} function passed as keyword arguments as follows C{t6 = hausdorff_(points1, points2, ..., distance=..., point=...)}. In all cases, the returned result C{t6} is a L{Hausdorff6Tuple}. 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{Hausdorff} sub-class with the appropriate C{distance} method overloading L{Hausdorff.distance} and optionally a C{point} method overriding L{Hausdorff.point} as the next example. >>> from pygeodesy import Hausdorff, hypot_ >>> >>> class H3D(Hausdorff): >>> """Custom Hausdorff example. >>> """ >>> def distance(self, p1, p2): >>> return hypot_(p1.x - p2.x, p1.y - p2.y, p1.z - p2.z) >>> >>> h3D = H3D(xyz1, ..., units="...") >>> d6 = h3D.directed(xyz2) Transcribed from the original SciPy U{Directed Hausdorff Code <https://GitHub.com/scipy/scipy/blob/master/scipy/spatial/_hausdorff.pyx>} version 0.19.0, Copyright (C) Tyler Reddy, Richard Gowers, and Max Linke, 2016, distributed under the same BSD license as SciPy, including C{early breaking} and C{random sampling} as in U{Abdel Aziz Taha, Allan Hanbury "An Efficient Algorithm for Calculating the Exact Hausdorff Distance" <https://Publik.TUWien.ac.AT/files/PubDat_247739.pdf>}, IEEE Trans. Pattern Analysis Machine Intelligence (PAMI), vol 37, no 11, pp 2153-2163, Nov 2015. ''' from pygeodesy.datum import Datum from pygeodesy.fmath import hypot2, INF, _IsNotError from pygeodesy.formy import euclidean_, haversine_, points2, \ _scaler, vincentys_ from pygeodesy.lazily import _ALL_LAZY, _ALL_DOCS from pygeodesy.named import _Named, _NamedTuple, PhiLam2Tuple from pygeodesy.utily import property_RO, unroll180, unrollPI from math import radians from random import Random __all__ = _ALL_LAZY.hausdorff + _ALL_DOCS('Hausdorff6Tuple') __version__ = '20.02.09' class HausdorffError(ValueError): '''Hausdorff issue. ''' pass class Hausdorff6Tuple(_NamedTuple): '''6-Tuple C{(hd, i, j, mn, md, units)} with the U{Hausdorff <https://WikiPedia.org/wiki/Hausdorff_distance>} distance C{hd}, indices C{i} and C{j}, the total count C{mn}, the C{I{mean} Hausdorff} distance C{md} and the name of the distance C{units}. For C{directed Hausdorff} distances, count C{mn} is the number of model points considered. For C{symmetric Hausdorff} distances count C{mn} twice that. Indices C{i} and C{j} are the C{model} respectively C{target} point with the C{hd} distance. Mean distance C{md} is C{None} if an C{early break} occurred and U{early breaking<https://Publik.TUWien.ac.AT/files/PubDat_247739.pdf>} was enabled by keyword argument C{early=True}. ''' _Names_ = ('hd', 'i', 'j', 'mn', 'md', 'units') class Hausdorff(_Named): '''Hausdorff base class, requires method L{Hausdorff.distance} to be overloaded. ''' _model = () _seed = None _units = '' def __init__(self, points, seed=None, name='', units=''): '''New L{Hausdorff} calculator. @param points: Initial set of points, aka the C{model} or C{template} (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @keyword seed: Random sampling seed (C{any}) or C{None}, C{0} or C{False} for no U{random sampling<https:// Publik.TUWien.ac.AT/files/PubDat_247739.pdf>}. @keyword name: Optional calculator name (C{str}). @keyword units: Optional, distance units (C{str}). @raise HausdorffError: Insufficient number of B{C{points}} or invalid B{C{seed}}. ''' _, self._model = points2(points, closed=False, Error=HausdorffError) if seed: self.seed = seed if name: self.name = name if units: self.units = units def directed(self, points, early=True): '''Compute only the C{forward Hausdorff} distance. @param points: Second set of points, aka the C{target} (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @keyword early: Enable or disable U{early breaking<https:// Publik.TUWien.ac.AT/files/PubDat_247739.pdf>} (C{bool}). @return: A L{Hausdorff6Tuple}C{(hd, i, j, mn, md, units)}. @raise HausdorffError: Insufficient number of B{C{points}}. ''' _, ps2 = points2(points, closed=False, Error=HausdorffError) return _hausdorff_(self._model, ps2, False, early, self.seed, self.units, self.distance, self.point) def distance(self, point1, point2): '''Distance between 2 points from C{.point}. @note: This method I{must be overloaded}. @raise AssertionError: Not overloaded. ''' self._notOverloaded(self.distance.__name__, point1, point2) def point(self, point): '''Convert a C{model} or C{target} point for the C{.distance} method. ''' return point # pass thru @property def seed(self): '''Get the random sampling seed (C{any} or C{None}). ''' return self._seed @seed.setter # PYCHOK setter! def seed(self, seed): '''Set the random sampling seed. @param seed: Valid L{Random(seed)} or C{None}, C{0} or C{False} for no U{random sampling<https:// Publik.TUWien.ac.AT/files/PubDat_247739.pdf>}. @raise HausdorffError: Invalid B{C{seed}}. ''' if seed: try: Random(seed) except (TypeError, ValueError): raise HausdorffError('%s invalid: %r' % ('seed', seed)) self._seed = seed else: self._seed = None def symmetric(self, points, early=True): '''Compute the combined C{forward and reverse Hausdorff} distance. @param points: Second set of points, aka the C{target} (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @keyword early: Enable or disable U{early breaking<https:// Publik.TUWien.ac.AT/files/PubDat_247739.pdf>} (C{bool}). @return: A L{Hausdorff6Tuple}C{(hd, i, j, mn, md, units)}. @raise HausdorffError: Insufficient number of B{C{points}}. ''' _, ps2 = points2(points, closed=False, Error=HausdorffError) return _hausdorff_(self._model, ps2, True, early, self.seed, self.units, self.distance, self.point) @property 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. @param units: New units name (C{str}). ''' self._units = str(units or "") class HausdorffDegrees(Hausdorff): '''L{Hausdorff} base class for distances in C{degrees} from C{LatLon} points in C{degrees}. ''' _units = 'degrees' directed = Hausdorff.directed # for __doc__ symmetric = Hausdorff.symmetric # for __doc__ class HausdorffRadians(Hausdorff): '''L{Hausdorff} base class for distances in C{radians} from C{LatLon} points converted from C{degrees} to C{radians}. ''' _units = 'radians' directed = Hausdorff.directed # for __doc__ symmetric = Hausdorff.symmetric # 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 HausdorffEquirectangular(HausdorffRadians): '''Compute the C{Hausdorff} distance based on the C{equirectangular} distance (in radians squared) like function L{equirectangular_}. @see: L{HausdorffEuclidean}, L{HausdorffHaversine}, L{HausdorffKarney} and L{HausdorffVincentys}. ''' _adjust = True _wrap = False def __init__(self, points, adjust=True, wrap=False, seed=None, name=''): '''New L{HausdorffEquirectangular} calculator. @param points: Initial set of points, aka the C{model} or C{template} (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @keyword adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @keyword seed: Random seed (C{any}) or C{None}, C{0} or C{False} for no U{random sampling<https:// Publik.TUWien.ac.AT/files/PubDat_247739.pdf>}. @keyword name: Optional calculator name (C{str}). @raise HausdorffError: 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(HausdorffRadians, self).__init__(points, seed=seed, 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 directed = Hausdorff.directed # for __doc__ symmetric = Hausdorff.symmetric # for __doc__ class HausdorffEuclidean(HausdorffRadians): '''Compute the C{Hausdorff} distance based on the C{Euclidean} distance (in radians) from function L{euclidean_}. @see: L{HausdorffEquirectangular}, L{HausdorffHaversine}, L{HausdorffKarney} and L{HausdorffVincentys}. ''' _adjust = True def __init__(self, points, adjust=True, seed=None, name=''): '''New L{HausdorffEuclidean} calculator. @param points: Initial set of points, aka the C{model} or C{template} (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @keyword adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @keyword seed: Random sampling seed (C{any}) or C{None}, C{0} or C{False} for no U{random sampling<https:// Publik.TUWien.ac.AT/files/PubDat_247739.pdf>}. @keyword name: Optional calculator name (C{str}). @raise HausdorffError: Insufficient number of B{C{points}} or invalid B{C{seed}}. ''' if not adjust: self._adjust = False super(HausdorffRadians, self).__init__(points, seed=seed, 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) directed = Hausdorff.directed # for __doc__ symmetric = Hausdorff.symmetric # for __doc__ class HausdorffHaversine(HausdorffRadians): '''Compute the C{Hausdorff} distance based on the I{angular} C{Haversine} distance (in radians) from function L{haversine_}. @note: See note under L{HausdorffVincentys}. @see: L{HausdorffEquirectangular}, L{HausdorffEuclidean}, L{HausdorffKarney} and L{HausdorffVincentys}. ''' _wrap = False def __init__(self, points, wrap=False, seed=None, name=''): '''New L{HausdorffHaversine} calculator. @param points: Initial set of points, aka the C{model} or C{template} (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @keyword seed: Random sampling seed (C{any}) or C{None}, C{0} or C{False} for no U{random sampling<https:// Publik.TUWien.ac.AT/files/PubDat_247739.pdf>}. @keyword name: Optional calculator name (C{str}). @raise HausdorffError: Insufficient number of B{C{points}} or invalid B{C{seed}}. ''' if wrap: self._wrap = True super(HausdorffRadians, self).__init__(points, seed=seed, 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) directed = Hausdorff.directed # for __doc__ symmetric = Hausdorff.symmetric # for __doc__ class HausdorffKarney(HausdorffDegrees): '''Compute the C{Hausdorff} distance based on the I{angular} distance (in degrees) from I{Charles Karney's} U{GeographicLib <https://PyPI.org/project/geographiclib>} U{Geodesic <https://geographiclib.sourceforge.io/1.49/python/code.html>} Inverse method. @see: L{HausdorffEquirectangular}, L{HausdorffEuclidean}, L{HausdorffHaversine} and L{HausdorffVincentys}. ''' _datum = None _Inverse = None _wrap = False def __init__(self, points, datum=None, wrap=False, seed=None, name=''): '''New L{HausdorffKarney} calculator. @param points: Initial set of points, aka the C{model} or C{template} (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @keyword datum: Optional datum (L{Datum} to use, overriding the default C{I{model} points[0].datum}. @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @keyword seed: Random sampling seed (C{any}) or C{None}, C{0} or C{False} for no U{random sampling<https:// Publik.TUWien.ac.AT/files/PubDat_247739.pdf>}. @keyword name: Optional calculator name (C{str}). @raise HausdorffError: Insufficient number of B{C{points}} or invalid B{C{seed}}. @raise ImportError: Package U{GeographicLib <https://PyPI.org/project/geographiclib>} missing. @raise TypeError: Invalid B{C{datum}}. ''' if wrap: self._wrap = True super(HausdorffDegrees, self).__init__(points, seed=seed, name=name) try: self._datum = self._model[0].datum if datum is None else datum if not isinstance(self.datum, Datum): raise TypeError except (AttributeError, TypeError): raise _IsNotError('valid', datum=self.datum or datum) self._Inverse = self.datum.ellipsoid.geodesic.Inverse @property_RO def datum(self): '''Get the datum of this calculator (L{Datum}). ''' return self._datum def distance(self, p1, p2): '''Return the non-negative I{angular} distance in C{degrees}. ''' # see .ellipsoidalKarney.LatLon._inverse _, lon2 = unroll180(p1.lon, p2.lon, wrap=self._wrap) # g.LONG_UNROLL # XXX g.DISTANCE needed for 's12', distance in meters? return abs(self._Inverse(p1.lat, p1.lon, p2.lat, lon2)['a12']) directed = Hausdorff.directed # for __doc__ symmetric = Hausdorff.symmetric # for __doc__ class HausdorffVincentys(HausdorffRadians): '''Compute the C{Hausdorff} distance based on the I{angular} C{Vincenty} distance (in radians) from function L{vincentys_}. @note: See note under L{vincentys_}. @see: L{HausdorffEquirectangular}, L{HausdorffEuclidean}, L{HausdorffHaversine} and L{HausdorffKarney}. ''' _wrap = False def __init__(self, points, wrap=False, seed=None, name=''): '''New L{HausdorffVincentys} calculator. @param points: Initial set of points, aka the C{model} or C{template} (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @keyword seed: Random sampling seed (C{any}) or C{None}, C{0} or C{False} for no U{random sampling<https:// Publik.TUWien.ac.AT/files/PubDat_247739.pdf>}. @keyword name: Optional calculator name (C{str}). @raise HausdorffError: Insufficient number of B{C{points}} or invalid B{C{seed}}. ''' if wrap: self._wrap = True super(HausdorffRadians, self).__init__(points, seed=seed, 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) directed = Hausdorff.directed # for __doc__ symmetric = Hausdorff.symmetric # for __doc__ def _hausdorff_(ps1, ps2, both, early, seed, units, distance, point): '''(INTERNAL) Core of function L{hausdorff.hausdorff} and methods C{directed} and C{symmetric} of classes C{hausdorff.Hausdorff...}. ''' # shuffling the points generally increases the # chance of an early break in the inner j loop rr = randomrangenerator(seed) if seed else range hd = -INF hi = hj = m = mn = 0 md = 0.0 # forward or forward and backward for fb in range(2 if both else 1): n = len(ps2) for i in rr(len(ps1)): p1 = point(ps1[i]) dh, dj = INF, 0 for j in rr(n): p2 = point(ps2[j]) d = distance(p1, p2) if early and d < hd: break # early elif d < dh: dh, dj = d, j else: # no early break if hd < dh: hd = dh if fb: hi, hj = dj, i else: hi, hj = i, dj md += dh mn += 1 m += 1 # swap model and target ps1, ps2 = ps2, ps1 md = None if mn < m else (md / float(m)) return Hausdorff6Tuple(hd, hi, hj, m, md, units) def _point(p): '''Default B{C{point}} callable for function L{hausdorff_}. @param p: The original C{model} or C{target} point (C{any}). @return: The point, suitable for the L{hausdorff_} B{C{distance}} callable. ''' return p def hausdorff_(model, target, both=False, early=True, seed=None, units='', distance=None, point=_point): '''Compute the C{directed} or C{symmetric} U{Hausdorff distance<https:// WikiPedia.org/wiki/Hausdorff_distance>} between 2 sets of points with or without U{early breaking<https://Publik.TUWien.ac.AT/files/PubDat_247739.pdf>} and U{random sampling<https://Publik.TUWien.ac.AT/files/PubDat_247739.pdf>}. @param model: First set of points (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @param target: Second set of points (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @keyword both: Return the C{directed} (forward only) or the C{symmetric} (combined forward and reverse) C{Hausdorff} distance (C{bool}). @keyword early: Enable or disable U{early breaking<https://Publik.TUWien.ac.AT/ files/PubDat_247739.pdf>} (C{bool}). @keyword seed: Random sampling seed (C{any}) or C{None}, C{0} or C{False} for no U{random sampling<https://Publik.TUWien.ac.AT/files/PubDat_247739.pdf>}. @keyword units: Optional, name of the distance units (C{str}). @keyword distance: Callable returning the distance between a B{C{model}} and B{C{target}} point (signature C{(point1, point2)}). @Keyword point: Callable returning the B{C{model}} or B{C{target}} point suitable for B{C{distance}} (signature C{(point)}). @return: A L{Hausdorff6Tuple}C{(hd, i, j, mn, md, units)}. @raise HausdorffError: Insufficient number of B{C{model}} or B{C{target}} points. @raise TypeError: If B{C{distance}} or B{C{point}} is not callable. ''' if not callable(distance): raise _IsNotError(callable.__name__, distance=distance) if not callable(point): raise _IsNotError(callable.__name__, point=point) _, ps1 = points2(model, closed=False, Error=HausdorffError) _, ps2 = points2(target, closed=False, Error=HausdorffError) return _hausdorff_(ps1, ps2, both, early, seed, units, distance, point) def randomrangenerator(seed): '''Return a C{seed}ed random range function generator. @param seed: Initial, internal L{Random} state (C{hashable}). @note: L{Random} B{C{seed}} C{None} seeds from the current time or from a platform-specific randomness source, if available. @return: A function to generatore random ranges. @example: >>> rrange = randomrangenerator('R') >>> for r in rrange(n): >>> ... # r is random in 0..n-1 ''' R = Random(seed) def _range(n, *stop_step): '''Like standard L{range}C{start, stop=..., step=...)}, except the returned values are in random order. @note: Especially C{range(n)} behaves like standard L{Random.sample}C{(range(n), n)} but avoids creating a tuple with the entire C{population} and a list containing all sample values (for large C{n}). ''' if stop_step: s = range(n, *stop_step) elif n > 32: r = R.randrange # Random._randbelow s = set() for _ in range(n - 32): i = r(n) while i in s: i = r(n) s.add(i) yield i s = set(range(n)) - s # [i for i in range(n) if i not in s] else: s = range(n) s = list(s) R.shuffle(s) while s: yield s.pop(0) return _range # **) 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.