# Coverage for pygeodesy/frechet.py : 91%

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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.fmath import EPS, EPS1, favg, INF, isscalar, _IsNotError from pygeodesy.formy import euclidean_, haversine_, points2 as _points2, \ _scaler, vincentys_ from pygeodesy.lazily import _ALL_LAZY, _ALL_DOCS from pygeodesy.named import LatLon2Tuple, _Named, _NamedTuple, PhiLam2Tuple from pygeodesy.utily import unrollPI from collections import defaultdict from math import radians __all__ = _ALL_LAZY.frechet + _ALL_DOCS('Frechet6Tuple') __version__ = '19.12.29' 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}[C{fi1}] and C{points2}[C{fi2}]. For type C{float} indices, the distance is between an intermediate point along C{points1}[C{int(fi1)}] and C{points1}[C{int(fi1)+1}] respectively an intermediate point along C{points2}[C{int(fi2)}] and C{points2}[C{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 = False _f1 = 1 _n1 = 0 _ps1 = None _units = '' _warp = False def __init__(self, points, fraction=None, name='', units=''): '''New L{Frechet} calculator/interpolator. @param points: First set of points (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @keyword fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or C{None} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @keyword name: Optional calculator/interpolator name (C{str}). @keyword 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 def discrete(self, points, fraction=None): '''Compute the C{forward, discrete Fréchet} distance. @param points: Second set of points (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @keyword fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or C{None} 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): '''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) @property 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}). @param fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or C{None} 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. @param point: The point to convert ((C{LatLon}, C{Numpy2LatLon}, C{Tuple2LatLon} or C{other}). @return: The converted B{C{point}}. ''' return point # pass thru def points_(self, points, i): '''Get and convert B{C{points}}[B{C{i}}] for the C{.distance} method. @param points: The orignal B{C{points}} to convert ((C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @param i: The B{C{points}} index (C{int}). @return: The converted B{C{points}[B{C{i}}]}. ''' return self.point(points[i]) def points_fraction(self, points, fi): '''Get and convert I{fractional} B{C{points}}[B{C{fi}}] for the C{.distance} method. @param points: The orignal B{C{points}} to convert ((C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @param fi: The I{fractional} index in B{C{points}} (C{float} or C{int}). @return: The interpolated, converted, intermediate B{C{points}[B{C{fi}}]}. ''' return self.point(_fractional(points, fi)) @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 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. @param points: First set of points (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 fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or C{None} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @keyword 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 d**2 + (p2.phi - p1.phi)**2 # 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. @param points: First set of points (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 fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or C{None} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @keyword 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. @param points: First set of points (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @keyword fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or C{None} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @keyword 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. @param points: First set of points (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @keyword fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or C{None} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @keyword 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): '''Return the point at a given I{fractional} index. @param points: The points (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @param fi: The fractional index (C{float} or C{int}). @keyword LatLon: Optional (sub-)class to return the I{intermediate} point (C{LatLon}) or C{None}. @return: A B{C{LatLon}} or a L{LatLon2Tuple}C{(lat, lon)} if B{C{LatLon}} is C{None} with B{C{points}}[B{C{fi}}] if I{fractional} index B{C{fi}} is C{int}, otherwise the intermediate point between B{C{points}}[C{int(B{fi})}] and B{C{points}}[C{int(B{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) 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. @param points1: First set of points (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @param points2: Second set of points (C{LatLon}[], C{Numpy2LatLon}[], C{Tuple2LatLon}[] or C{other}[]). @keyword distance: Callable returning the distance between a B{C{points1}} and a B{C{points2}} point (signature C{(point1, point2)}). @keyword 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 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.