# Coverage for pygeodesy/hausdorff.py : 90%

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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.