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# -*- 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 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__ = '19.10.30' 

 

 

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 d**2 + (p2.phi - p1.phi)**2 # 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. 

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# 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: 

# 

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