# Coverage for pygeodesy/heights.py : 95%

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Except for L{HeightIDWequirectangular}, L{HeightIDWeuclidean}, L{HeightIDWhaversine} and L{HeightIDWvincentys}, the height interpolators in this module require the packages U{numpy <https://PyPI.org/project/numpy>} and U{scipy<https://SciPy.org>} or U{geographiclib<https://PyPI.org/project/geographiclib>} to be installed. Typical usage is as follows. First create an interpolator from a given set of C{LatLon} points with known heights, called C{knots}. C{hinterpolator = HeightXyz(knots, **options)} 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)} # C{list, tuple, generator, ...} For separate lat-/longitudes invoke the C{.height} method C{h = hinterpolator.height(lat, lon)} or C{h0, h1, h2, ... = hinterpolator.height(lats, lons)} # C{list, ...} 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 EPS, _isnotError, isscalar, \ len2, map1, map2, property_RO from pygeodesy.datum import Datum from pygeodesy.fmath import fidw, hypot2 from pygeodesy.formy import euclidean_, haversine_, _scaler, vincentys_ from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY from pygeodesy.named import _Named, notOverloaded from pygeodesy.points import LatLon_ from pygeodesy.utily import PI, PI2, PI_2, radiansPI, radiansPI2, \ unroll180, unrollPI __all__ = _ALL_LAZY.heights + _ALL_DOCS('_HeightBase') __version__ = '20.03.23' class HeightError(ValueError): # imported by .geoids '''Height interpolator C{Height...} or interpolation issue. ''' pass class SciPyError(HeightError): '''Error raised for C{SciPy} errors. ''' pass class SciPyWarning(HeightError): '''Exception thrown for C{SciPy} warnings. To raise C{SciPy} warnings as L{SciPyWarning} exceptions, Python C{warnings} must be filtered as U{warnings.filterwarnings('error') <https://docs.Python.org/3/library/warnings.html#the-warnings-filter>} I{prior to} C{import scipy} or by setting environment variable U{PYTHONWARNINGS<https://docs.Python.org/3/using/cmdline.html #envvar-PYTHONWARNINGS>} or with C{python} command line option U{-W<https://docs.Python.org/3/using/cmdline.html#cmdoption-w>} as C{error}. ''' pass def _alist(ais): # return tuple 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 Error('insufficient %s: %s, need %s' % ('llis', n, m)) 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('len[%r] = %s == 1' % (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)) # unzip return _as, atype(xis), atype(yis), llis 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 _SciPyIssue(x, *extras): # imported by .geoids # PYCHOK no cover t = ' '.join(str(x).strip().split() + map(str, extras)) if isinstance(x, (RuntimeWarning, UserWarning)): return SciPyWarning(t) else: return SciPyError(t) # PYCHOK not really def _xyhs(lls, off=True): # 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 ll in 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: raise HeightError('%s: %r' % (x, ll)) 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)) # PYCHOK unzip n = len(hs) if n < m: raise HeightError('insufficient %s: %s, need %s' % ('knots', n, m)) return map1(atype, xs, ys, hs) class _HeightBase(_Named): # imported by .geoids '''(INTERNAL) Interpolator base class. ''' _adjust = None # not applicable _kmin = 2 # min number of knots _np = None # numpy _np_v = None # version _spi = None # scipy.interpolate _sp_v = None # version _wrap = None # not applicable def __call__(self, *args): '''(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) def _ev(self, *args): '''(INTERNAL) I{Must be overloaded}. ''' notOverloaded(self, self._ev.__name__, *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): if isscalar(lats) and isscalar(lons): llis = LatLon_(lats, lons) else: n, lats = len2(lats) m, lons = len2(lons) if n != m: raise Error('non-matching %s: %s vs %s' % ('len', n, m)) llis = [LatLon_(*ll) 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}. ''' 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') import scipy as sp import scipy.interpolate as spi import numpy as np _HeightBase._np = np _HeightBase._np_v = np.__version__ _HeightBase._spi = spi _HeightBase._sp_v = sp.__version__ return np, spi 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=''): '''New L{HeightCubic} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg name: Optional height interpolator name (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 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=''): '''New L{HeightLinear} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg name: Optional height interpolator name (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. ''' HeightCubic.__init__(self, knots, name=name) __call__ = HeightCubic.__call__ # for __doc__ height = HeightCubic.height # for __doc__ 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=''): '''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 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}}, 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 _distances(self, x, y): # PYCHOK unused (x, y) radians '''Must be overloaded. ''' raise NotImplementedError('method: %s' % ('_distances',)) 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 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}}. ''' try: b = int(beta) if b != beta or 1 > b or b > 3: raise ValueError except (TypeError, ValueError): raise HeightError('%s invalid: %r' % ('beta', beta)) self._beta = b 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 HeightIDWequirectangular(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the C{equirectangular} distance (in radians squared) like function L{equirectangular_}. @see: L{HeightIDWeuclidean}, L{HeightIDWhaversine}, L{HeightIDWvincentys}, U{Inverse distance weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>}, 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=''): '''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{unroll180} longitudes (C{bool}). @kwarg name: Optional height interpolator name (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or invalid B{C{knot}}. ''' if not adjust: self._adjust = False if wrap: self._wrap = True _HeightIDW.__init__(self, knots, beta=1, name=name) # distance**2 def _distances(self, x, y): # (x, y) radians for xk, yk in zip(self._xs, self._ys): d, _ = unrollPI(xk, x, wrap=self._wrap) if self.adjust: d *= _scaler(yk, y) yield hypot2(d, yk - y) # like equirectangular_ distance2 __call__ = _HeightIDW.__call__ # for __doc__ height = _HeightIDW.height # for __doc__ class HeightIDWeuclidean(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the C{Euclidean} distance from function L{euclidean_}. @see: L{HeightIDWequirectangular}, L{HeightIDWhaversine}, L{HeightIDWkarney}, L{HeightIDWvincentys}, U{Inverse distance weighting<https://WikiPedia.org/wiki/Inverse_distance_weighting>}, 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=''): '''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 height interpolator name (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or invalid B{C{knot}} or B{C{beta}}. ''' if not adjust: self._adjust = False _HeightIDW.__init__(self, knots, beta=beta, name=name) 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) __call__ = _HeightIDW.__call__ # for __doc__ height = _HeightIDW.height # for __doc__ class HeightIDWhaversine(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} C{Haversine} distance from function L{haversine_}. @note: See note under L{HeightIDWvincentys}. @see: L{HeightIDWequirectangular}, L{HeightIDWeuclidean}, L{HeightIDWkarney}, L{HeightIDWvincentys}, U{Inverse distance weighting<https://WikiPedia.org/wiki/Inverse_distance_weighting>}, 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=''): '''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{unroll180} longitudes (C{bool}). @kwarg name: Optional height interpolator name (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or invalid B{C{knot}} or B{C{beta}}. ''' if wrap: self._wrap = True _HeightIDW.__init__(self, knots, beta=beta, name=name) def _distances(self, x, y): # (x, y) radians for xk, yk in zip(self._xs, self._ys): d, _ = unrollPI(xk, x, wrap=self._wrap) yield haversine_(yk, y, d) __call__ = _HeightIDW.__call__ # for __doc__ height = _HeightIDW.height # for __doc__ class HeightIDWkarney(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} distance from I{Charles F. F. Karney's} U{GeographicLib<https://PyPI.org/project/geographiclib>} U{Geodesic <https://geographiclib.sourceforge.io/1.49/python/code.html>} Inverse method. @see: L{HeightIDWequirectangular}, L{HeightIDWeuclidean}, L{HeightIDWhaversine}, L{HeightIDWvincentys}, U{Inverse distance weighting<https://WikiPedia.org/wiki/Inverse_distance_weighting>}, 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 = None _geodesic = None _wrap = False def __init__(self, knots, datum=None, beta=2, wrap=False, name=''): '''New L{HeightIDWhaversine} interpolator. @arg knots: The points with known height (C{LatLon}s). @kwarg datum: Optional datum (L{Datum} to use, overriding the default B{C{knots[0].datum}} @kwarg beta: Inverse distance power (C{int} 1, 2, or 3). @kwarg wrap: Wrap and L{unroll180} longitudes (C{bool}). @kwarg name: Optional height interpolator name (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or 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._lls = len2(knots) if n < self._kmin: raise HeightError('insufficient %s: %s, need %s' % ('knots', n, self._kmin)) try: self._datum = self._lls[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._geodesic = self.datum.ellipsoid.geodesic self.beta = beta if wrap: self._wrap = True if name: self.name = name def _distances(self, x, y): # (x, y) degrees g = self._geodesic for ll in self._lls: # see .ellipsoidalKarney.LatLon._inverse _, lon = unroll180(x, ll.lon, wrap=self._wrap) # g.LONG_UNROLL # XXX g.DISTANCE needed for 's12', distance in meters? yield abs(g.Inverse(y, x, ll.lat, lon)['a12']) @property_RO def _hs(self): for ll in self._lls: yield ll.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}}, invalid B{C{lli}} or an L{fidw} issue. ''' def _xy2(lls): try: # like _xyhs above, but keeping degrees for ll in lls: yield ll.lon, ll.lat except AttributeError as x: raise HeightError('%s: %r' % (x, ll)) _as, llis = _allis2(llis) return _as(map(self._hIDW, *zip(*_xy2(llis)))) @property_RO def datum(self): '''Get the datum of this interpolator (L{Datum}). ''' return self._datum height = _HeightIDW.height # for __doc__ class HeightIDWvincentys(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} C{Vincenty} distance from function L{vincentys_}. @note: See note under L{vincentys_}. @see: L{HeightIDWequirectangular}, L{HeightIDWeuclidean}, L{HeightIDWhaversine}, L{HeightIDWkarney}, U{Inverse distance weighting<https://WikiPedia.org/wiki/Inverse_distance_weighting>}, 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=''): '''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{unroll180} longitudes (C{bool}). @kwarg name: Optional height interpolator name (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or invalid B{C{knot}} or B{C{beta}}. ''' if wrap: self._wrap = True _HeightIDW.__init__(self, knots, beta=beta, name=name) def _distances(self, x, y): # (x, y) radians for xk, yk in zip(self._xs, self._ys): d, _ = unrollPI(xk, x, wrap=self._wrap) yield vincentys_(yk, y, d) __call__ = _HeightIDW.__call__ # for __doc__ height = _HeightIDW.height # for __doc__ 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=''): '''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 height interpolator name (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or B{C{weight}}s or invalid B{C{knot}} or B{C{weight}}. @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('%s invalid: %.6F' % ('weight', w)) w = [w] * n elif w is not None: m, w = len2(w) if m != n: raise HeightError('%s invalid: %s, not %s' % ( 'number of weights', m, n)) w = map2(float, w) m = min(w) if m <= 0: raise HeightError('%s[%s] invalid: %.6F' % ( 'weight', w.find(m), 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 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=''): '''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 height interpolator name (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or 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() if s < 4: raise HeightError('%s too small: %s' % ('smoothing', s)) 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 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) # **) 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.