# Coverage for pygeodesy/heights.py : 95%

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1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 | # -*- coding: utf-8 -*- u'''Classes L{HeightCubic}, L{HeightIDWcosineAndoyerLambert}, L{HeightIDWcosineForsytheAndoyerLambert}, L{HeightIDWcosineLaw}, L{HeightIDWdistanceTo}, L{HeightIDWequirectangular}, L{HeightIDWeuclidean}, L{HeightIDWflatLocal}, L{HeightIDWflatPolar}, L{HeightIDWhaversine}, L{HeightIDWhubeny}, L{HeightIDWkarney}, L{HeightIDWthomas}, L{HeightIDWvincentys}, L{HeightLinear}, L{HeightLSQBiSpline} and L{HeightSmoothBiSpline} to interpolate the height of C{LatLon} locations or separate lat-/longitudes from a set of C{LatLon} points with C{known} heights. Classes L{HeightCubic} and L{HeightLinear} require package U{numpy <https://PyPI.org/project/numpy>}, classes L{HeightLSQBiSpline} and L{HeightSmoothBiSpline} require package U{scipy<https://SciPy.org>}. Classes L{HeightIDWkarney} and L{HeightIDWdistanceTo} -iff used with L{ellipsoidalKarney.LatLon} points- require I{Karney}'s U{geographiclib <https://PyPI.org/project/geographiclib>} to be installed. B{Typical usage} is as follows. First, create an interpolator from a given set of C{LatLon} points with C{known} heights, called C{knots}. C{>>> hinterpolator = HeightXyz(knots, **options)} Then, get the interpolated height of other C{LatLon} location(s) with C{>>> h = hinterpolator(ll)} or C{>>> h0, h1, h2, ... = hinterpolator(ll0, ll1, ll2, ...)} or C{>>> hs = hinterpolator(lls) # list, tuple, generator, ...} For separate lat- and longitudes invoke the C{.height} method C{>>> h = hinterpolator.height(lat, lon)} or C{>>> h0, h1, h2, ... = hinterpolator.height(lats, lons) # lists, tuples, ...} The C{knots} do not need to be ordered for any of the height interpolators. Errors from C{scipy} as raised as L{SciPyError}s. Warnings issued by C{scipy} can be thrown as L{SciPyWarning} exceptions, provided Python C{warnings} are filtered accordingly, see L{SciPyWarning}. @see: U{SciPy<https://docs.SciPy.org/doc/scipy/reference/interpolate.html>}. ''' from pygeodesy.basics import isscalar, len2, map1, map2, property_RO, \ _xnumpy, _xscipy from pygeodesy.datums import Datums, _ellipsoidal_datum from pygeodesy.errors import _AssertionError, LenError, PointsError, _SciPyIssue from pygeodesy.fmath import fidw, hypot2 from pygeodesy.formy import cosineAndoyerLambert_, cosineForsytheAndoyerLambert_, \ cosineLaw_, euclidean_, flatPolar_, haversine_, \ _scale_rad, thomas_, vincentys_ from pygeodesy.interns import EPS, NN, PI, PI2, PI_2, _cubic_, _datum_, \ _distanceTo_, _knots_, _len_, _linear_, _scipy_, \ _0_0 from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _FOR_DOCS from pygeodesy.named import _Named, notOverloaded from pygeodesy.points import LatLon_ from pygeodesy.streprs import _boolkwds, Fmt from pygeodesy.units import Int_ from pygeodesy.utily import radiansPI, radiansPI2, unrollPI __all__ = _ALL_LAZY.heights __version__ = '20.12.18' class HeightError(PointsError): '''Height interpolator C{Height...} or interpolation issue. ''' pass def _alist(ais): # return list of floats, not numpy.float64s return list(map(float, ais)) def _allis2(llis, m=1, Error=HeightError): # imported by .geoids # dtermine return type and convert lli C{LatLon}s to list if not isinstance(llis, tuple): # llis are *args raise _AssertionError('type(%s): %r' % ('*llis', llis)) n = len(llis) if n == 1: # convert single lli to 1-item list llis = llis[0] try: n, llis = len2(llis) _as = _alist # return list of interpolated heights except TypeError: # single lli n, llis = 1, [llis] _as = _ascalar # return single interpolated heights else: # of 0, 2 or more llis _as = _atuple # return tuple of interpolated heights if n < m: raise _insufficientError(m, Error=Error, llis=n) return _as, llis def _ascalar(ais): # imported by .geoids # return single float, not numpy.float64 ais = list(ais) # np.array, etc. to list if len(ais) != 1: raise _AssertionError('%s(%r): %s != 1' % (_len_, ais, len(ais))) return float(ais[0]) # remove np.<type> def _atuple(ais): # return tuple of floats, not numpy.float64s return tuple(map(float, ais)) def _axyllis4(atype, llis, m=1, off=True): # convert lli C{LatLon}s to tuples or C{NumPy} arrays of # C{SciPy} sphericals and determine the return type _as, llis = _allis2(llis, m=m) xis, yis, _ = zip(*_xyhs(llis, off=off)) # PYCHOK unzip return _as, atype(xis), atype(yis), llis def _insufficientError(need, Error=HeightError, **name_value): # create an insufficient Error instance t = 'insufficient, need %s' % (need,) return Error(txt=t, **name_value) def _ordedup(ts, lo=EPS, hi=PI2-EPS): # clip, order and remove duplicates p, ks = 0, [] for k in sorted(max(lo, min(hi, t)) for t in ts): if k > p: ks.append(k) p = k return ks def _xyhs(lls, off=True, name='llis'): # map (lat, lon, h) to (x, y, h) in radians, offset as # x: 0 <= lon <= PI2, y: 0 <= lat <= PI if off is True # else x: -PI <= lon <= PI, y: -PI_2 <= lat <= PI_2 if off: xf = yf = _0_0 else: # undo offset xf, yf = PI, PI_2 try: for i, ll in enumerate(lls): yield (max(0.0, radiansPI2(ll.lon + 180.0)) - xf), \ (max(0.0, radiansPI( ll.lat + 90.0)) - yf), ll.height except AttributeError as x: i = Fmt.SQUARE(name, i) raise HeightError(i, ll, txt=str(x)) def _xyhs3(atype, m, knots, off=True): # convert knot C{LatLon}s to tuples or C{NumPy} arrays and C{SciPy} sphericals xs, ys, hs = zip(*_xyhs(knots, off=off, name=_knots_)) # PYCHOK unzip n = len(hs) if n < m: raise _insufficientError(m, knots=n) return map1(atype, xs, ys, hs) class _HeightBase(_Named): # imported by .geoids '''(INTERNAL) Interpolator base class. ''' _adjust = None # not applicable _datum = None # ._height datum _kmin = 2 # min number of knots _LLis = LatLon_ # ._height class _np = None # numpy _np_v = None # version _spi = None # scipy.interpolate _sp_v = None # version _wrap = None # not applicable def __call__(self, *args): # PYCHOK no cover '''(INTERNAL) I{Must be overloaded}. ''' notOverloaded(self, '__call__', *args) @property_RO def adjust(self): '''Get the adjust setting (C{bool} or C{None} if not applicable). ''' return self._adjust def _axyllis4(self, llis): return _axyllis4(self._np.array, llis) @property_RO def datum(self): '''Get the datum (L{Datum} or C{None} if not applicable). ''' return self._datum def _ev(self, *args): # PYCHOK no cover '''(INTERNAL) I{Must be overloaded}. ''' notOverloaded(self, self._ev, *args) def _eval(self, llis): # XXX single arg, not *args _as, xis, yis, _ = self._axyllis4(llis) try: # SciPy .ev signature: y first, then x! return _as(self._ev(yis, xis)) except Exception as x: raise _SciPyIssue(x) def _height(self, lats, lons, Error=HeightError): LLis, d = self._LLis, self.datum if isscalar(lats) and isscalar(lons): llis = LLis(lats, lons, datum=d) else: n, lats = len2(lats) m, lons = len2(lons) if n != m: # format a LenError, but raise an Error e = LenError(self.__class__, lats=n, lons=m, txt=None) raise e if Error is LenError else Error(str(e)) llis = [LLis(*ll, datum=d) for ll in zip(lats, lons)] return self(llis) # __call__(lli) or __call__(llis) @property_RO def kmin(self): '''Get the minimum number of knots (C{int}). ''' return self._kmin def _NumSciPy(self, throwarnings=False): '''(INTERNAL) Import C{numpy} and C{scipy}, once. ''' if throwarnings: # raise SciPyWarnings, but ... # ... not if scipy has been imported already import sys if _scipy_ not in sys.modules: import warnings warnings.filterwarnings('error') np = _HeightBase._np spi = _HeightBase._spi if None in (np, spi): sp = _xscipy(self.__class__, 1, 2) import scipy.interpolate as spi np = _xnumpy(self.__class__, 1, 9) _HeightBase._np = np _HeightBase._np_v = np.__version__ _HeightBase._spi = spi _HeightBase._sp_v = sp.__version__ return np, spi # XXX spi not sp! def _xyhs3(self, knots): return _xyhs3(self._np.array, self._kmin, knots) @property_RO def wrap(self): '''Get the wrap setting (C{bool} or C{None} if not applicable). ''' return self._wrap class HeightCubic(_HeightBase): '''Height interpolator based on C{SciPy} U{interp2d<https://docs.SciPy.org/ doc/scipy/reference/generated/scipy.interpolate.interp2d.html>} C{kind='cubic'}. ''' _interp2d = None _kind = _cubic_ _kmin = 16 def __init__(self, knots, name=NN): '''New L{HeightCubic} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg name: Optional name for this height interpolator (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or invalid B{C{knot}}. @raise ImportError: Package C{numpy} or C{scipy} not found or not installed. @raise SciPyError: A C{scipy.interpolate.interp2d} issue. @raise SciPyWarning: A C{scipy.interpolate.interp2d} warning as exception. ''' _, spi = self._NumSciPy() xs, ys, hs = self._xyhs3(knots) try: # SciPy.interpolate.interp2d kind 'linear' or 'cubic' self._interp2d = spi.interp2d(xs, ys, hs, kind=self._kind) except Exception as x: raise _SciPyIssue(x) if name: self.name = name def __call__(self, *llis): '''Interpolate the height for one or several locations. @arg llis: The location or locations (C{LatLon}, ... or C{LatLon}s). @return: A single interpolated height (C{float}) or a list or tuple of interpolated heights (C{float}s). @raise HeightError: Insufficient number of B{C{llis}} or an invalid B{C{lli}}. @raise SciPyError: A C{scipy.interpolate.interp2d} issue. @raise SciPyWarning: A C{scipy.interpolate.interp2d} warning as exception. ''' return _HeightBase._eval(self, llis) def _ev(self, yis, xis): # PYCHOK expected # to make SciPy .interp2d signature(x, y), single (x, y) # match SciPy .ev signature(ys, xs), flipped multiples return map(self._interp2d, xis, yis) def height(self, lats, lons): '''Interpolate the height for one or several lat-/longitudes. @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s). @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s). @return: A single interpolated height (C{float}) or a list of interpolated heights (C{float}s). @raise HeightError: Insufficient or non-matching number of B{C{lats}} and B{C{lons}}. @raise SciPyError: A C{scipy.interpolate.interp2d} issue. @raise SciPyWarning: A C{scipy.interpolate.interp2d} warning as exception. ''' return _HeightBase._height(self, lats, lons) class HeightLinear(HeightCubic): '''Height interpolator based on C{SciPy} U{interp2d<https://docs.SciPy.org/ doc/scipy/reference/generated/scipy.interpolate.interp2d.html>} C{kind='linear'}. ''' _kind = _linear_ _kmin = 2 def __init__(self, knots, name=NN): '''New L{HeightLinear} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg name: Optional name for this height interpolator (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or an invalid B{C{knot}}. @raise ImportError: Package C{numpy} or C{scipy} not found or not installed. @raise SciPyError: A C{scipy.interpolate.interp2d} issue. @raise SciPyWarning: A C{scipy.interpolate.interp2d} warning as exception. ''' HeightCubic.__init__(self, knots, name=name) if _FOR_DOCS: __call__ = HeightCubic.__call__ height = HeightCubic.height class _HeightIDW(_HeightBase): '''(INTERNAL) Base class for U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) height interpolators. ''' _beta = 0 # inverse distance power _hs = () # known heights _xs = () # knot lons _ys = () # knot lats def __init__(self, knots, beta=2, name=NN, **wrap_adjust): '''New L{_HeightIDW} interpolator. ''' self._xs, self._ys, self._hs = _xyhs3(tuple, self._kmin, knots, off=False) self.beta = beta if name: self.name = name if wrap_adjust: _boolkwds(self, **wrap_adjust) def __call__(self, *llis): '''Interpolate the height for one or several locations. @arg llis: The location or locations (C{LatLon}, ... or C{LatLon}s). @return: A single interpolated height (C{float}) or a list or tuple of interpolated heights (C{float}s). @raise HeightError: Insufficient number of B{C{llis}}, an invalid B{C{lli}} or an L{fidw} issue. ''' _as, xis, yis, _ = _axyllis4(tuple, llis, off=False) return _as(map(self._hIDW, xis, yis)) def _datum_setter(self, datum, knots): '''(INTERNAL) Set the datum. @raise TypeError: Invalid B{C{datum}}. ''' d = datum or getattr(knots[0], _datum_, datum) if d not in (None, self._datum): self._datum = _ellipsoidal_datum(d, name=self.name) def _distances(self, x, y): # PYCHOK unused (x, y) radians '''(INTERNAL) I{Must be overloaded}. ''' notOverloaded(self, self._distances, x, y) def _distances_angular_(self, func_, x, y): # return angular distances from func_ for xk, yk in zip(self._xs, self._ys): r, _ = unrollPI(xk, x, wrap=self._wrap) yield func_(yk, y, r) def _distances_angular_datum_(self, func_, x, y): # return angular distances from func_ for xk, yk in zip(self._xs, self._ys): r, _ = unrollPI(xk, x, wrap=self._wrap) yield func_(yk, y, r, datum=self._datum) def _hIDW(self, x, y): # interpolate height at (x, y) radians or degrees try: ds = self._distances(x, y) return fidw(self._hs, ds, beta=self._beta) except (TypeError, ValueError) as x: raise HeightError(str(x)) @property def beta(self): '''Get the inverse distance power (C{int}). ''' return self._beta @beta.setter # PYCHOK setter! def beta(self, beta): '''Set the inverse distance power. @arg beta: New inverse distance power (C{int} 1, 2, or 3). @raise HeightError: Invalid B{C{beta}}. ''' self._beta = Int_(beta=beta, Error=HeightError, low=1, high=3) def height(self, lats, lons): '''Interpolate the height for one or several lat-/longitudes. @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s). @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s). @return: A single interpolated height (C{float}) or a list of interpolated heights (C{float}s). @raise HeightError: Insufficient or non-matching number of B{C{lats}} and B{C{lons}} or an L{fidw} issue. ''' return _HeightBase._height(self, lats, lons) class HeightIDWcosineAndoyerLambert(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} distance in C{radians} from function L{cosineAndoyerLambert_}. @see: L{HeightIDWcosineForsytheAndoyerLambert}, L{HeightIDWdistanceTo}, L{HeightIDWflatLocal}, L{HeightIDWhubeny}, L{HeightIDWthomas}, U{IDW<https://www.Geo.FU-Berlin.DE/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. ''' _datum = Datums.WGS84 _wrap = False def __init__(self, knots, datum=None, beta=2, wrap=False, name=NN): '''New L{HeightIDWcosineAndoyerLambert} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg datum: Optional datum overriding the default C{Datums.WGS84} and first B{C{knots}}' datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg beta: Inverse distance power (C{int} 1, 2, or 3). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}). @kwarg name: Optional name for this height interpolator (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or an invalid B{C{knot}} or B{C{beta}}. @raise TypeError: Invalid B{C{datum}}. ''' _HeightIDW.__init__(self, knots, beta=beta, name=name, wrap=wrap) self._datum_setter(datum, knots) def _distances(self, x, y): # (x, y) radians return self._distances_angular_datum_(cosineAndoyerLambert_, x, y) if _FOR_DOCS: __call__ = _HeightIDW.__call__ height = _HeightIDW.height class HeightIDWcosineForsytheAndoyerLambert(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} distance in C{radians} from function L{cosineForsytheAndoyerLambert_}. @see: L{HeightIDWcosineAndoyerLambert}, L{HeightIDWdistanceTo}, L{HeightIDWflatLocal}, L{HeightIDWhubeny}, L{HeightIDWthomas}, U{IDW<https://www.Geo.FU-Berlin.DE/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. ''' _datum = Datums.WGS84 _wrap = False def __init__(self, knots, datum=None, beta=2, wrap=False, name=NN): '''New L{HeightIDWcosineForsytheAndoyerLambert} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg datum: Optional datum overriding the default C{Datums.WGS84} and first B{C{knots}}' datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg beta: Inverse distance power (C{int} 1, 2, or 3). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}). @kwarg name: Optional name for this height interpolator (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or an invalid B{C{knot}} or B{C{beta}}. @raise TypeError: Invalid B{C{datum}}. ''' _HeightIDW.__init__(self, knots, beta=beta, name=name, wrap=wrap) self._datum_setter(datum, knots) def _distances(self, x, y): # (x, y) radians return self._distances_angular_datum_(cosineForsytheAndoyerLambert_, x, y) if _FOR_DOCS: __call__ = _HeightIDW.__call__ height = _HeightIDW.height class HeightIDWcosineLaw(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} distance in C{radians} from function L{cosineLaw_}. @see: L{HeightIDWequirectangular}, L{HeightIDWeuclidean}, L{HeightIDWflatPolar}, L{HeightIDWhaversine}, L{HeightIDWvincentys}, U{IDW<https://www.Geo.FU-Berlin.DE/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. @note: See note at function L{vincentys_}. ''' _wrap = False def __init__(self, knots, beta=2, wrap=False, name=NN): '''New L{HeightIDWcosineLaw} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg beta: Inverse distance power (C{int} 1, 2, or 3). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}). @kwarg name: Optional name for this height interpolator (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or an invalid B{C{knot}} or B{C{beta}}. ''' _HeightIDW.__init__(self, knots, beta=beta, name=name, wrap=wrap) def _distances(self, x, y): # (x, y) radians return self._distances_angular_(cosineLaw_, x, y) if _FOR_DOCS: __call__ = _HeightIDW.__call__ height = _HeightIDW.height class HeightIDWdistanceTo(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the distance from the points' C{LatLon.distanceTo} method, conventionally in C{meter}. @see: L{HeightIDWcosineAndoyerLambert}, L{HeightIDWcosineForsytheAndoyerLambert}, L{HeightIDWflatPolar}, L{HeightIDWkarney}, L{HeightIDWthomas}, U{IDW<https://www.Geo.FU-Berlin.DE/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. ''' _distanceTo_kwds = {} _ks = () def __init__(self, knots, beta=2, name=NN, **distanceTo_kwds): '''New L{HeightIDWdistanceTo} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg beta: Inverse distance power (C{int} 1, 2, or 3). @kwarg name: Optional name for this height interpolator (C{str}). @kwarg distanceTo_kwds: Optional keyword arguments for the B{C{points}}' C{LatLon.distanceTo} method. @raise HeightError: Insufficient number of B{C{knots}} or an invalid B{C{knot}} or B{C{beta}}. @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} missing iff B{C{points}} are L{ellipsoidalKarney.LatLon}s. @note: All B{C{points}} I{must} be instances of the same ellipsoidal or spherical C{LatLon} class, I{not checked however}. ''' n, self._ks = len2(knots) if n < self._kmin: raise _insufficientError(self._kmin, knots=n) for i, k in enumerate(self._ks): if not callable(getattr(k, _distanceTo_, None)): i = Fmt.SQUARE(_knots_, i) raise HeightError(i, k, txt=_distanceTo_) # use knots[0] class and datum to create # compatible points in _HeightBase._height # instead of class LatLon_ and datum None self._datum = self._ks[0].datum self._LLis = self._ks[0].classof self.beta = beta if name: self.name = name if distanceTo_kwds: self._distanceTo_kwds = distanceTo_kwds def __call__(self, *llis): '''Interpolate the height for one or several locations. @arg llis: The location or locations (C{LatLon}, ... or C{LatLon}s). @return: A single interpolated height (C{float}) or a list or tuple of interpolated heights (C{float}s). @raise HeightError: Insufficient number of B{C{llis}}, an invalid B{C{lli}} or an L{fidw} issue. ''' _as, llis = _allis2(llis) return _as(map(self._hIDW, llis)) if _FOR_DOCS: height = _HeightIDW.height def _hIDW(self, lli): # PYCHOK expected # interpolate height at point lli try: kwds = self._distanceTo_kwds ds = (k.distanceTo(lli, **kwds) for k in self._ks) return fidw(self._hs, ds, beta=self._beta) except (TypeError, ValueError) as x: raise HeightError(str(x)) @property_RO def _hs(self): # see HeightIDWkarney for k in self._ks: yield k.height class HeightIDWequirectangular(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} distance in C{radians squared} like function L{equirectangular_}. @see: L{HeightIDWeuclidean}, L{HeightIDWflatPolar}, L{HeightIDWhaversine}, L{HeightIDWvincentys}, U{IDW<https://www.Geo.FU-Berlin.DE/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. ''' _adjust = True _wrap = False def __init__(self, knots, adjust=True, wrap=False, name=NN): '''New L{HeightIDWequirectangular} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}). @kwarg name: Optional name for this height interpolator (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or an invalid B{C{knot}}. ''' _HeightIDW.__init__(self, knots, beta=1, name=name, wrap=wrap, adjust=adjust) def _distances(self, x, y): # (x, y) radians**2 for xk, yk in zip(self._xs, self._ys): d, _ = unrollPI(xk, x, wrap=self._wrap) if self._adjust: d *= _scale_rad(yk, y) yield hypot2(d, yk - y) # like equirectangular_ distance2 if _FOR_DOCS: __call__ = _HeightIDW.__call__ height = _HeightIDW.height class HeightIDWeuclidean(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} distance in C{radians} from function L{euclidean_}. @see: L{HeightIDWcosineLaw}, L{HeightIDWequirectangular}, L{HeightIDWhaversine}, L{HeightIDWvincentys}, U{IDW<https://www.Geo.FU-Berlin.DE/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. ''' _adjust = True def __init__(self, knots, adjust=True, beta=2, name=NN): '''New L{HeightIDWeuclidean} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg adjust: Adjust the longitudinal delta by the cosine of the mean latitude for B{C{adjust}}=C{True}. @kwarg beta: Inverse distance power (C{int} 1, 2, or 3). @kwarg name: Optional name for this height interpolator (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or an invalid B{C{knot}} or B{C{beta}}. ''' _HeightIDW.__init__(self, knots, beta=beta, name=name, adjust=adjust) def _distances(self, x, y): # (x, y) radians for xk, yk in zip(self._xs, self._ys): yield euclidean_(yk, y, xk - x, adjust=self._adjust) if _FOR_DOCS: __call__ = _HeightIDW.__call__ height = _HeightIDW.height class HeightIDWflatLocal(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} distance in C{radians squared} like function L{flatLocal_}/L{hubeny_}. @see: L{HeightIDWcosineAndoyerLambert}, L{HeightIDWcosineForsytheAndoyerLambert}, L{HeightIDWdistanceTo}, L{HeightIDWhubeny}, L{HeightIDWthomas}, U{IDW<https://www.Geo.FU-Berlin.DE/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. ''' _datum = Datums.WGS84 _wrap = False def __init__(self, knots, datum=None, beta=2, wrap=False, name=NN): '''New L{HeightIDWflatLocal}/L{HeightIDWhubeny} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg datum: Optional datum overriding the default C{Datums.WGS84} and first B{C{knots}}' datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg beta: Inverse distance power (C{int} 1, 2, or 3). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}). @kwarg name: Optional name for this height interpolator (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or an invalid B{C{knot}} or B{C{beta}}. @raise TypeError: Invalid B{C{datum}}. ''' _HeightIDW.__init__(self, knots, beta=beta, name=name, wrap=wrap) self._datum_setter(datum, knots) def _distances(self, x, y): # (x, y) radians _r2_ = self._datum.ellipsoid._hubeny2_ return self._distances_angular_(_r2_, x, y) # radians**2 if _FOR_DOCS: __call__ = _HeightIDW.__call__ height = _HeightIDW.height class HeightIDWflatPolar(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} distance in C{radians} from function L{flatPolar_}. @see: L{HeightIDWcosineLaw}, L{HeightIDWequirectangular}, L{HeightIDWeuclidean}, L{HeightIDWhaversine}, L{HeightIDWvincentys}, U{IDW<https://www.Geo.FU-Berlin.DE/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. ''' _wrap = False def __init__(self, knots, beta=2, wrap=False, name=NN): '''New L{HeightIDWflatPolar} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg beta: Inverse distance power (C{int} 1, 2, or 3). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}). @kwarg name: Optional name for this height interpolator (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or an invalid B{C{knot}} or B{C{beta}}. ''' _HeightIDW.__init__(self, knots, beta=beta, name=name, wrap=wrap) def _distances(self, x, y): # (x, y) radians return self._distances_angular_(flatPolar_, x, y) if _FOR_DOCS: __call__ = _HeightIDW.__call__ height = _HeightIDW.height class HeightIDWhaversine(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} distance in C{radians} from function L{haversine_}. @see: L{HeightIDWcosineLaw}, L{HeightIDWequirectangular}, L{HeightIDWeuclidean}, L{HeightIDWflatPolar}, L{HeightIDWvincentys}, U{IDW<https://www.Geo.FU-Berlin.DE/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. @note: See note at function L{vincentys_}. ''' _wrap = False def __init__(self, knots, beta=2, wrap=False, name=NN): '''New L{HeightIDWhaversine} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg beta: Inverse distance power (C{int} 1, 2, or 3). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}). @kwarg name: Optional name for this height interpolator (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or an B{C{knot}} or B{C{beta}}. ''' _HeightIDW.__init__(self, knots, beta=beta, name=name, wrap=wrap) def _distances(self, x, y): # (x, y) radians return self._distances_angular_(haversine_, x, y) if _FOR_DOCS: __call__ = _HeightIDW.__call__ height = _HeightIDW.height class HeightIDWhubeny(HeightIDWflatLocal): # for Karl Hubeny if _FOR_DOCS: __doc__ = HeightIDWflatLocal.__doc__ __init__ = HeightIDWflatLocal.__init__ __call__ = HeightIDWflatLocal.__call__ height = HeightIDWflatLocal.height class HeightIDWkarney(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} distance in C{degrees} from I{Karney}'s U{geographiclib<https://PyPI.org/project/geographiclib>} U{Geodesic <https://GeographicLib.SourceForge.io/html/python/code.html>} Inverse method. @see: L{HeightIDWcosineAndoyerLambert}, L{HeightIDWcosineForsytheAndoyerLambert}, L{HeightIDWdistanceTo}, L{HeightIDWflatLocal}, L{HeightIDWhubeny}, L{HeightIDWthomas}, U{IDW<https://www.Geo.FU-Berlin.DE/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. ''' _datum = Datums.WGS84 _Inverse1 = None _ks = () _wrap = False def __init__(self, knots, datum=None, beta=2, wrap=False, name=NN): '''New L{HeightIDWkarney} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg datum: Optional datum overriding the default C{Datums.WGS84} and first B{C{knots}}' datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg beta: Inverse distance power (C{int} 1, 2, or 3). @kwarg wrap: Wrap and L{unroll180} longitudes (C{bool}). @kwarg name: Optional name for this height interpolator (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or an invalid B{C{knot}}, B{C{datum}} or B{C{beta}}. @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} missing. @raise TypeError: Invalid B{C{datum}}. ''' n, self._ks = len2(knots) if n < self._kmin: raise _insufficientError(self._kmin, knots=n) self._datum_setter(datum, self._ks) self._Inverse1 = self.datum.ellipsoid.geodesic.Inverse1 self.beta = beta if wrap: self._wrap = True if name: self.name = name def _distances(self, x, y): # (x, y) degrees for k in self._ks: # non-negative I{angular} distance in C{degrees} yield self._Inverse1(y, x, k.lat, k.lon, wrap=self._wrap) @property_RO def _hs(self): # see HeightIDWdistanceTo for k in self._ks: yield k.height def __call__(self, *llis): '''Interpolate the height for one or several locations. @arg llis: The location or locations (C{LatLon}, ... or C{LatLon}s). @return: A single interpolated height (C{float}) or a list or tuple of interpolated heights (C{float}s). @raise HeightError: Insufficient number of B{C{llis}}, an invalid B{C{lli}} or an L{fidw} issue. ''' def _xy2(lls): try: # like _xyhs above, but keeping degrees for i, ll in enumerate(lls): yield ll.lon, ll.lat except AttributeError as x: i = Fmt.SQUARE(llis=i) raise HeightError(i, ll, txt=str(x)) _as, llis = _allis2(llis) return _as(map(self._hIDW, *zip(*_xy2(llis)))) if _FOR_DOCS: height = _HeightIDW.height class HeightIDWthomas(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} distance in C{radians} from function L{thomas_}. @see: L{HeightIDWcosineAndoyerLambert}, L{HeightIDWcosineForsytheAndoyerLambert}, L{HeightIDWdistanceTo}, L{HeightIDWflatLocal}, L{HeightIDWhubeny}, U{IDW<https://www.Geo.FU-Berlin.DE/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. ''' _datum = Datums.WGS84 _wrap = False def __init__(self, knots, datum=None, beta=2, wrap=False, name=NN): '''New L{HeightIDWthomas} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg datum: Optional datum overriding the default C{Datums.WGS84} and first B{C{knots}}' datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg beta: Inverse distance power (C{int} 1, 2, or 3). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}). @kwarg name: Optional name for this height interpolator (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or an invalid B{C{knot}} or B{C{beta}}. @raise TypeError: Invalid B{C{datum}}. ''' _HeightIDW.__init__(self, knots, beta=beta, name=name, wrap=wrap) self._datum_setter(datum, knots) def _distances(self, x, y): # (x, y) radians return self._distances_angular_datum_(thomas_, x, y) if _FOR_DOCS: __call__ = _HeightIDW.__call__ height = _HeightIDW.height class HeightIDWvincentys(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} distance in C{radians} from function L{vincentys_}. @see: L{HeightIDWcosineLaw}, L{HeightIDWequirectangular}, L{HeightIDWeuclidean}, L{HeightIDWflatPolar}, L{HeightIDWhaversine}, U{IDW<https://www.Geo.FU-Berlin.DE/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. @note: See note at function L{vincentys_}. ''' _wrap = False def __init__(self, knots, beta=2, wrap=False, name=NN): '''New L{HeightIDWvincentys} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg beta: Inverse distance power (C{int} 1, 2, or 3). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}). @kwarg name: Optional name for this height interpolator (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or an invalid B{C{knot}} or B{C{beta}}. ''' _HeightIDW.__init__(self, knots, beta=beta, name=name, wrap=wrap) def _distances(self, x, y): # (x, y) radians return self._distances_angular_(vincentys_, x, y) if _FOR_DOCS: __call__ = _HeightIDW.__call__ height = _HeightIDW.height class HeightLSQBiSpline(_HeightBase): '''Height interpolator using C{SciPy} U{LSQSphereBivariateSpline <https://docs.SciPy.org/doc/scipy/reference/generated/scipy. interpolate.LSQSphereBivariateSpline.html>}. ''' _kmin = 16 # k = 3, always def __init__(self, knots, weight=None, name=NN): '''New L{HeightLSQBiSpline} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg weight: Optional weight or weights for each B{C{knot}} (C{scalar} or C{scalar}s). @kwarg name: Optional name for this height interpolator (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or an invalid B{C{knot}} or B{C{weight}}. @raise LenError: Unequal number of B{C{knots}} and B{C{weight}}s. @raise ImportError: Package C{numpy} or C{scipy} not found or not installed. @raise SciPyError: A C{LSQSphereBivariateSpline} issue. @raise SciPyWarning: A C{LSQSphereBivariateSpline} warning as exception. ''' np, spi = self._NumSciPy() xs, ys, hs = self._xyhs3(knots) n = len(hs) w = weight if isscalar(w): w = float(w) if w <= 0: raise HeightError(weight=w) w = [w] * n elif w is not None: m, w = len2(w) if m != n: raise LenError(HeightLSQBiSpline, weight=m, knots=n) w = map2(float, w) m = min(w) if m <= 0: w = Fmt.SQUARE(weight=w.find(m)) raise HeightError(w, m) try: T = 1.0e-4 # like SciPy example ps = np.array(_ordedup(xs, T, PI2 - T)) ts = np.array(_ordedup(ys, T, PI - T)) self._ev = spi.LSQSphereBivariateSpline(ys, xs, hs, ts, ps, eps=EPS, w=w).ev except Exception as x: raise _SciPyIssue(x) if name: self.name = name def __call__(self, *llis): '''Interpolate the height for one or several locations. @arg llis: The location or locations (C{LatLon}, ... or C{LatLon}s). @return: A single interpolated height (C{float}) or a list or tuple of interpolated heights (C{float}s). @raise HeightError: Insufficient number of B{C{llis}} or an invalid B{C{lli}}. @raise SciPyError: A C{LSQSphereBivariateSpline} issue. @raise SciPyWarning: A C{LSQSphereBivariateSpline} warning as exception. ''' return _HeightBase._eval(self, llis) def height(self, lats, lons): '''Interpolate the height for one or several lat-/longitudes. @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s). @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s). @return: A single interpolated height (C{float}) or a list of interpolated heights (C{float}s). @raise HeightError: Insufficient or non-matching number of B{C{lats}} and B{C{lons}}. @raise SciPyError: A C{LSQSphereBivariateSpline} issue. @raise SciPyWarning: A C{LSQSphereBivariateSpline} warning as exception. ''' return _HeightBase._height(self, lats, lons) class HeightSmoothBiSpline(_HeightBase): '''Height interpolator using C{SciPy} U{SmoothSphereBivariateSpline <https://docs.SciPy.org/doc/scipy/reference/generated/scipy. interpolate.SmoothSphereBivariateSpline.html>}. ''' _kmin = 16 # k = 3, always def __init__(self, knots, s=4, name=NN): '''New L{HeightSmoothBiSpline} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg s: The spline smoothing factor (C{4}). @kwarg name: Optional name for this height interpolator (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or an invalid B{C{knot}} or B{C{s}}. @raise ImportError: Package C{numpy} or C{scipy} not found or not installed. @raise SciPyError: A C{SmoothSphereBivariateSpline} issue. @raise SciPyWarning: A C{SmoothSphereBivariateSpline} warning as exception. ''' _, spi = self._NumSciPy() s = Int_(s, name='smoothing', Error=HeightError, low=4) xs, ys, hs = self._xyhs3(knots) try: self._ev = spi.SmoothSphereBivariateSpline(ys, xs, hs, eps=EPS, s=s).ev except Exception as x: raise _SciPyIssue(x) if name: self.name = name def __call__(self, *llis): '''Interpolate the height for one or several locations. @arg llis: The location or locations (C{LatLon}, ... or C{LatLon}s). @return: A single interpolated height (C{float}) or a list or tuple of interpolated heights (C{float}s). @raise HeightError: Insufficient number of B{C{llis}} or an invalid B{C{lli}}. @raise SciPyError: A C{SmoothSphereBivariateSpline} issue. @raise SciPyWarning: A C{SmoothSphereBivariateSpline} warning as exception. ''' return _HeightBase._eval(self, llis) def height(self, lats, lons): '''Interpolate the height for one or several lat-/longitudes. @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s). @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s). @return: A single interpolated height (C{float}) or a list of interpolated heights (C{float}s). @raise HeightError: Insufficient or non-matching number of B{C{lats}} and B{C{lons}}. @raise SciPyError: A C{SmoothSphereBivariateSpline} issue. @raise SciPyWarning: A C{SmoothSphereBivariateSpline} warning as exception. ''' return _HeightBase._height(self, lats, lons) __all__ += _ALL_DOCS(_HeightBase) # **) MIT License # # Copyright (C) 2016-2021 -- 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.