# Coverage for pygeodesy/geoids.py : 94%

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1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 | # -*- coding: utf-8 -*- u'''Classes L{GeoidG2012B}, L{GeoidKarney} and L{GeoidPGM} to interpolate the height of various U{geoid<https://WikiPedia.org/wiki/Geoid>}s at C{LatLon} locations or separate lat-/longitudes using different interpolation methods and C{geoid} files. L{GeoidKarney} is a transcription of I{Charles Karney's} C++ class U{Geoid <https://GeographicLib.SourceForge.io/html/geoid.html>} to pure Python. The L{GeoidG2012B} and L{GeoidPGM} interpolators both depend on U{scipy<https://SciPy.org>} and U{numpy<https://PyPI.org/project/numpy>} and require those packages to be installed. In addition, each geoid interpolator needs C{grid knots} to be (down)loaded from a geoid file, specific to the interpolator, more details below. For each interpolator, there are several interpolation choices, like I{linear}, I{cubic}, etc. Typical usage is as follows. First create an interpolator from a geoid file, also referred to as the C{grid knots}. C{ginterpolator = GeoidXyz(grid_file, **options)} Get the interpolated geoid height of C{LatLon} location(s) with C{h = ginterpolator(ll)} or C{h0, h1, h2, ... = ginterpolator(ll0, ll1, ll2, ...)} or C{hs = ginterpolator(lls)} # C{list, tuple, generator, ...} For separate lat-/longitudes invoke the C{.height} method C{h = ginterpolator.height(lat, lon)} or C{h0, h1, h2, ... = ginterpolator.height(lats, lons)} # C{list, ...} Errors from C{scipy} are 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: Charles Karney's U{GeographicLib<https://GeographicLib.SourceForge.io/ html/index.html>}, U{Geoid height<https://GeographicLib.SourceForge.io/ html/geoid.html>} and U{Installing the Geoid datasets<https:// GeographicLib.SourceForge.io/html/geoid.html#geoidinst>}, U{SciPy <https://docs.SciPy.org/doc/scipy/reference/interpolate.html>} interpolation U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/ reference/generated/scipy.interpolate.RectBivariateSpline.html>} and U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/ scipy.interpolate.interp2d.html>} and the functions L{elevations.elevation2} and L{elevations.geoidHeight2}. ''' from pygeodesy.basics import EPS, InvalidError, len2, map1, map2, \ property_RO, RangeError from pygeodesy.datum import Datum, Datums from pygeodesy.dms import parseDMS2 from pygeodesy.fmath import favg, Fdot, fdot, Fhorner, frange from pygeodesy.heights import _allis2, _ascalar, \ _HeightBase, HeightError, _SciPyIssue from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _FOR_DOCS from pygeodesy.named import GeoidHeight5Tuple, LatLon3Tuple, \ _Named, notOverloaded from pygeodesy.streprs import attrs, fstr, pairs from math import floor import os.path as _os_path from os import SEEK_CUR as _SEEK_CUR, SEEK_SET as _SEEK_SET from struct import calcsize as _calcsize, unpack as _unpack try: from StringIO import StringIO as _BytesIO # reads bytes _b2str = str # convert bytes to str except ImportError: # Python 3+ from io import BytesIO as _BytesIO # PYCHOK expected def _b2str(bs): # used only for egm*.pgm text return bs.decode('utf-8') __all__ = _ALL_LAZY.geoids + _ALL_DOCS('_GeoidBase') __version__ = '20.04.09' # temporarily hold a single instance for each int value _intCs = {} _interp2d_ks = {-2: 'linear', -3: 'cubic', -5: 'quintic'} class GeoidError(HeightError): '''Geoid interpolator C{Geoid...} or interpolation issue. ''' pass class PGMError(GeoidError): '''Issue parsing or cropping an C{egm*.pgm} geoid dataset. ''' pass class _GeoidBase(_HeightBase): '''(INTERNAL) Base class for C{Geoid...}s. ''' _cropped = None _datum = Datums.WGS84 _endian = 'tbd' _geoid = 'n/a' _hs_y_x = None # numpy 2darray, row-major order _interp2d = None # interp2d interpolation _kind = 3 # order for interp2d, RectBivariateSpline _knots = 0 # nlat * nlon _mean = None # _name = '' # _Named _nBytes = 0 # numpy size in bytes, float64 _pgm = None _sizeB = 0 # geoid file size in bytes _smooth = 0 # used only for RectBivariateSpline _stdev = None _lat_d = 0.0 # increment, +tive _lat_lo = 0.0 # lower lat, south _lat_hi = 0.0 # upper lat, noth _lon_d = 0.0 # increment, +tive _lon_lo = 0.0 # left lon, west _lon_hi = 0.0 # right lon, east _lon_of = 0.0 # forward lon offset _lon_og = 0.0 # reverse lon offset _center = None # (lat, lon, height) _highest = None # (lat, lon, height) _lowerleft = None # (lat, lon, height) _lowerright = None # (lat, lon, height) _lowest = None # (lat, lon, height) _upperleft = None # (lat, lon, height) _upperright = None # (lat, lon, height) _yx_hits = None # cache hits, ala Karney def __init__(self, hs, p): '''(INTERNAL) Set up the grid axes, the C{SciPy} interpolator and several internal geoid attributes. @arg hs: Grid knots with known height (C{numpy 2darray}). @arg p: The C{slat, wlon, nlat, nlon, dlat, dlon} and other geoid parameters (C{INTERNAL}). @raise GeoidError: Invalid B{C{kind}}. @raise SciPyError: A C{scipy.interpolate.inter2d} or C{-.RectBivariateSpline} issue. @raise SciPyWarning: A C{scipy.interpolate.inter2d} or C{-.RectBivariateSpline} warning as exception. ''' # for 2d scipy.interpolate.interp2d(xs, ys, hs, ...) and # scipy.interpolate.RectBivariateSpline(ys, xs, hs, ...) # require the shape of hs to be (len(ys), len(xs)), note # the different (xs, ys, ...) and (ys, xs, ...) orders if (p.nlat, p.nlon) != hs.shape: raise GeoidError('%s %s vs %r' % ('shape', hs.shape, (p.nlat, p.nlon))) # both axes and bounding box ys, self._lat_d = self._gaxis2(p.slat, p.dlat, p.nlat, 'lats') xs, self._lon_d = self._gaxis2(p.wlon, p.dlon, p.nlon, 'lons') bb = ys[0], ys[-1], xs[0], xs[-1] + p.dlon # fudge lon_hi # geoid grids are typically stored in row-major order, some # with rows (90..-90) reversed and columns (0..360) wrapped # to Easten longitude, 0 <= east < 180 and 180 <= west < 0 k = self._kind if k in _interp2d_ks: self._interp2d = self._spi.interp2d(xs, ys, hs, kind=_interp2d_ks[k]) elif 1 <= k <= 5: self._ev = self._spi.RectBivariateSpline(ys, xs, hs, bbox=bb, ky=k, kx=k, s=self._smooth).ev else: raise InvalidError(kind=k, Error=GeoidError) self._hs_y_x = hs # numpy 2darray, row-major self._nBytes = hs.nbytes # numpy size in bytes self._knots = p.knots # grid knots self._lon_of = float(p.flon) # forward offset self._lon_og = float(p.glon) # reverse offset # shrink the box by 1 unit on every side # bb += self._lat_d, -self._lat_d, self._lon_d, -self._lon_d self._lat_lo = float(bb[0]) self._lat_hi = float(bb[1]) self._lon_lo = float(bb[2] - p.glon) self._lon_hi = float(bb[3] - p.glon) def __call__(self, *llis): '''Interpolate the geoid height for one or several locations. @arg llis: The location or locations (C{LatLon}, ... or C{LatLon}s). @return: A single interpolated geoid height (C{float}) or a list or tuple of interpolated geoid heights (C{float}s). @raise GeoidError: Insufficient number of B{C{llis}} or an invalid B{C{lli}}. @raise RangeError: An B{C{lli}} is outside this geoid's lat- or longitude range. @raise SciPyError: A C{scipy.interpolate.inter2d} or C{-.RectBivariateSpline} issue. @raise SciPyWarning: A C{scipy.interpolate.inter2d} or C{-.RectBivariateSpline} warning as exception. ''' return self._called(llis, True) def __repr__(self): return self.toStr() def __str__(self): return '%s(%r)' % (self.classname, self.name) def _called(self, llis, scipy): # handle __call__ _as, llis = _allis2(llis, Error=GeoidError) hs = [] for i, lli in enumerate(llis): try: hs.append(self._hGeoid(lli.lat, lli.lon)) except (GeoidError, RangeError) as x: # XXX avoid str(LatLon()) degree symbols i = '' if _as is _ascalar else '[%s]' % (i,) lli = fstr((lli.lat, lli.lon), prec=6) raise x.__class__('location%s (%s) %s' % (i, lli, x)) except Exception as x: if scipy and self.scipy: raise _SciPyIssue(x) else: raise return _as(hs) def _ev(self, y, x): # PYCHOK expected # only used for .interpolate.interp2d, but # overwritten for .RectBivariateSpline, # note (y, x) must be flipped! return self._interp2d(x, y) def _gaxis2(self, lo, d, n, name): # build grid axis, hi = lo + (n - 1) * d m, a = len2(frange(lo, n, d)) if m != n: raise GeoidError('len(%s) = %s != %s' % (name, m, n)) if d < 0: d, a = -d, list(reversed(a)) for i in range(1, m): e = a[i] - a[i-1] if e < EPS: # non-increasing axis raise GeoidError('%s[%s]: %.12F' % (name, i, e)) return self._np.array(a), d def _g2ll2(self, lat, lon): # PYCHOK no cover notOverloaded(self, self._g2ll2, lat, lon) def _gyx2g2(self, y, x): # convert grid (y, x) indices to grid (lat, lon) return ((self._lat_lo + self._lat_d * y), (self._lon_lo + self._lon_of + self._lon_d * x)) def _hGeoid(self, lat, lon): out = self.outside(lat, lon) if out: raise RangeError('outside on %s' % (out,)) return float(self._ev(*self._ll2g2(lat, lon))) def _ll2g2(self, lat, lon): # PYCHOK no cover notOverloaded(self, self._ll2g2, lat, lon) def _llh3(self, lat, lon): r = LatLon3Tuple(lat, lon, self._hGeoid(lat, lon)) return self._xnamed(r) def _llh3LL(self, llh, LatLon): return llh if LatLon is None else LatLon(*llh) def _llh3minmax(self, highest=True, *unused): hs, np = self._hs_y_x, self._np # <https://docs.SciPy.org/doc/numpy/reference/generated/ # numpy.argmin.html#numpy.argmin> arg = self._np.argmax if highest else self._np.argmin y, x = np.unravel_index(arg(hs, axis=None), hs.shape) return self._g2ll2(*self._gyx2g2(y, x)) + (float(hs[y, x]),) def _load(self, g, dtype, n, offset=0): # numpy.fromfile, like .frombuffer g.seek(offset, _SEEK_SET) return self._np.fromfile(g, dtype, n) def _open(self, geoid, datum, kind, name, smooth): # open the geoid file try: self._geoid = _os_path.basename(geoid) self._sizeB = _os_path.getsize(geoid) g = open(geoid, 'rb') except (IOError, OSError) as x: raise GeoidError(str(x)) if datum and isinstance(datum, Datum): self._datum = datum self._kind = int(kind) if name: _HeightBase.name.fset(self, name) # recursion if smooth: if int(smooth) < 0: raise InvalidError(smooth=smooth, Error=GeoidError) self._smooth = int(smooth) return g def _swne(self, crop): # crop box to 4-tuple (s, w, n, e) try: if len(crop) == 2: try: # sw, ne LatLons swne = (crop[0].lat, crop[0].lon, crop[1].lat, crop[1].lon) except AttributeError: # (s, w), (n, e) swne = tuple(crop[0]) + tuple(crop[1]) else: # (s, w, n, e) swne = crop if len(swne) == 4: s, w, n, e = map(float, swne) if -90 <= s <= (n - 1) <= 89 and \ -180 <= w <= (e - 1) <= 179: return s, w, n, e except (IndexError, TypeError, ValueError): pass raise InvalidError(crop=crop, Error=GeoidError) def center(self, LatLon=None): '''Return the center location and height of this geoid. @kwarg LatLon: Optional class to return the location and height (C{LatLon}) or C{None}. @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat, lon, height)} otherwise a B{C{LatLon}} instance with the lat-, longitude and height of the grid center location. ''' if self._center is None: self._center = self._llh3(favg(self._lat_lo, self._lat_hi), favg(self._lon_lo, self._lon_hi)) return self._llh3LL(self._center, LatLon) @property_RO def cropped(self): '''Is geoid cropped (C{bool} or C{None} if crop not supported). ''' return self._cropped @property_RO def dtype(self): '''Get the grid C{scipy} U{dtype<https://docs.SciPy.org/doc/numpy/ reference/generated/numpy.ndarray.dtype.html>} (C{numpy.dtype}). ''' return self._hs_y_x.dtype @property_RO def endian(self): '''Get the geoid endianess and U{dtype<https://docs.SciPy.org/ doc/numpy/reference/generated/numpy.dtype.html>} (C{str}). ''' return self._endian def height(self, lats, lons): '''Interpolate the geoid 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 geoid height (C{float}) or a list of interpolated geoid heights (C{float}s). @raise GeoidError: Insufficient or non-matching number of B{C{lats}} and B{C{lons}}. @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this geoid's lat- or longitude range. @raise SciPyError: A C{scipy.interpolate.inter2d} or C{-.RectBivariateSpline} issue. @raise SciPyWarning: A C{scipy.interpolate.inter2d} or C{-.RectBivariateSpline} warning as exception. ''' return _HeightBase._height(self, lats, lons, Error=GeoidError) def highest(self, LatLon=None, **unused): '''Return the location and largest height of this geoid. @kwarg LatLon: Optional class to return the location and height (C{LatLon}) or C{None}. @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat, lon, height)} otherwise a B{C{LatLon}} instance with the lat-, longitude and height of the highest grid location. ''' if self._highest is None: self._highest = self._llh3minmax(True) return self._llh3LL(self._highest, LatLon) @property_RO def hits(self): '''Get the number of cache hits (C{int} or C{None}). ''' return self._yx_hits @property_RO def kind(self): '''Get the interpolator kind and order (C{int}). ''' return self._kind @property_RO def knots(self): '''Get the number of grid knots (C{int}). ''' return self._knots def lowerleft(self, LatLon=None): '''Return the lower-left location and height of this geoid. @kwarg LatLon: Optional class to return the location (C{LatLon}) and height or C{None}. @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat, lon, height)} otherwise a B{C{LatLon}} instance with the lat-, longitude and height of the lower-left, SW grid corner. ''' if self._lowerleft is None: self._lowerleft = self._llh3(self._lat_lo, self._lon_lo) return self._llh3LL(self._lowerleft, LatLon) def lowerright(self, LatLon=None): '''Return the lower-right location and height of this geoid. @kwarg LatLon: Optional class to return the location and height (C{LatLon}) or C{None}. @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat, lon, height)} otherwise a B{C{LatLon}} instance with the lat-, longitude and height of the lower-right, SE grid corner. ''' if self._lowerright is None: self._lowerright = self._llh3(self._lat_lo, self._lon_hi) return self._llh3LL(self._lowerright, LatLon) def lowest(self, LatLon=None, **unused): '''Return the location and the lowest height of this geoid. @kwarg LatLon: Optional class to return the location and height (C{LatLon}) or C{None}. @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat, lon, height)} otherwise a B{C{LatLon}} instance with the lat-, longitude and height of the lowest grid location. ''' if self._lowest is None: self._lowest = self._llh3minmax(False) return self._llh3LL(self._lowest, LatLon) @property_RO def mean(self): '''Get the mean of this geoid's heights (C{float}). ''' if self._mean is None: self._mean = float(self._np.mean(self._hs_y_x)) return self._mean @property_RO def name(self): '''Get the name of this geoid (C{str}). ''' return _HeightBase.name.fget(self) or self._geoid # recursion @property_RO def nBytes(self): '''Get the grid in-memory size in bytes (C{int}). ''' return self._nBytes @property_RO def numpy(self): '''Get the imported C{numpy} version (C{str}). ''' return self._np_v def outside(self, lat, lon): '''Check whether a location is outside this geoid's lat-/longitude or crop range. @arg lat: The latitude (C{degrees}). @arg lon: The longitude (C{degrees}). @return: A 1- or 2-character C{str} if outside or an empty C{str} if inside. ''' return ('S' if lat < self._lat_lo else ('N' if lat > self._lat_hi else '')) + \ ('W' if lon < self._lon_lo else ('E' if lon > self._lon_hi else '')) @property_RO def pgm(self): '''Get the PGM attributes (C{_PGM} or C{None} if not available/applicable). ''' return self._pgm @property_RO def scipy(self): '''Get the imported C{scipy} version (C{str}). ''' return self._sp_v @property_RO def sizeB(self): '''Get the geoid grid file size in bytes (C{int}). ''' return self._sizeB @property_RO def smooth(self): '''Get the C{RectBivariateSpline} smoothing (C{int}). ''' return self._smooth @property_RO def stdev(self): '''Get the standard deviation of this geoid's heights (C{float}). ''' if self._stdev is None: self._stdev = float(self._np.std(self._hs_y_x)) return self._stdev def toStr(self, prec=3, sep=', '): # PYCHOK signature '''This geoid and all geoid attributes as a string. @kwarg prec: Optional number of decimal digits (0..9 or C{None} for default). Trailing zero decimals are stripped for B{C{prec}} values of 1 and above, but kept for negative B{C{prec}} values. @kwarg sep: Optional separator (C{str}). @return: Geoid name and attributes (C{str}). ''' s = 1 if self.kind < 0 else 2 t = tuple('%s(%s)' % (m.__name__, fstr(m(), prec=prec)) for m in (self.lowerleft, self.upperright, self.center, self.highest, self.lowest)) + \ attrs( 'mean', 'stdev', prec=prec, Nones=False) + \ attrs(('kind', 'smooth')[:s], prec=prec, Nones=False) + \ attrs( 'cropped', 'dtype', 'endian', 'hits', 'knots', 'nBytes', 'sizeB', 'scipy', 'numpy', prec=prec, Nones=False) return '%s: %s' % (self, sep.join(t)) def upperleft(self, LatLon=None): '''Return the upper-left location and height of this geoid. @kwarg LatLon: Optional class to return the location and height (C{LatLon}) or C{None}. @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat, lon, height)} otherwise a B{C{LatLon}} instance with the lat-, longitude and height of the upper-left, NW grid corner. ''' if self._upperleft is None: self._upperleft = self._llh3(self._lat_hi, self._lon_lo) return self._llh3LL(self._upperleft, LatLon) def upperright(self, LatLon=None): '''Return the upper-right location and height of this geoid. @kwarg LatLon: Optional class to return the location and height (C{LatLon}) or C{None}. @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat, lon, height)} otherwise a B{C{LatLon}} instance with the lat-, longitude and height of the upper-right, NE grid corner. ''' if self._upperright is None: self._upperright = self._llh3(self._lat_hi, self._lon_hi) return self._llh3LL(self._upperright, LatLon) class GeoidG2012B(_GeoidBase): '''Geoid height interpolator for U{GEOID12B Model <https://www.NGS.NOAA.gov/GEOID/GEOID12B/>} grids U{CONUS <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_CONUS.shtml>}, U{Alaska<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_AK.shtml>}, U{Hawaii<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_HI.shtml>}, U{Guam and Northern Mariana Islands <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_GMNI.shtml>}, U{Puerto Rico and U.S. Virgin Islands <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_PRVI.shtml>} and U{American Samoa<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_AS.shtml>} based on C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/doc/ scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>} or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/ scipy.interpolate.interp2d.html>} interpolation. Use any of the binary C{le} (little endian) or C{be} (big endian) C{g2012b*.bin} grid files. ''' def __init__(self, g2012b_bin, crop=None, datum=None, # NAD 83 Ellipsoid kind=3, name='', smooth=0): '''New L{GeoidG2012B} interpolator. @arg g2012b_bin: A C{GEOID12B} grid file name (C{.bin}). @kwarg crop: Optional crop box, not supported (C{None}). @kwarg datum: Optional grid datum (C{Datum}), default C{WGS84}. @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/ reference/generated/scipy.interpolate.RectBivariateSpline.html>}, -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/ reference/generated/scipy.interpolate.interp2d.html>}, -3 for C{interp2d cubic} or -5 for C{interp2d quintic}. @kwarg name: Optional geoid name (C{str}). @kwarg smooth: Smoothing factor for U{RectBivariateSpline <https://docs.SciPy.org/doc/scipy/reference/generated/ scipy.interpolate.RectBivariateSpline.html>} only (C{int}). @raise GeoidError: G2012B grid file B{C{g2012b_bin}} issue, non-C{None} B{C{crop}} or invalid B{C{kind}} or B{C{smooth}}. @raise ImportError: Package C{numpy} or C{scipy} not found or not installed. @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue. @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d} warning as exception. ''' if crop is not None: raise GeoidError('not supported: %s=%r' % ('crop', crop)) np, _ = self._NumSciPy() g = self._open(g2012b_bin, datum, kind, name, smooth) try: p = _Gpars() n = self.sizeB // 4 - 11 # number of f4 heights # U{numpy dtype formats are different from Python struct formats # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>} for en_f4 in ('<f4', '>f4'): en_ = en_f4[:1] # skip 4xf8, get 3xi4 p.nlat, p.nlon, ien = map(int, self._load(g, en_+'i4', 3, 32)) if ien == 1: # correct endian p.knots = p.nlat * p.nlon if p.knots == n and 1 < p.nlat < n \ and 1 < p.nlon < n: self._endian = en_f4 break else: # couldn't validate endian raise GeoidError('endianess') # get the first 4xf8 p.slat, p.wlon, p.dlat, p.dlon = map(float, self._load(g, en_+'f8', 4)) # read all f4 heights, ignoring the first 4xf8 and 3xi4 hs = self._load(g, en_f4, n, 44).reshape(p.nlat, p.nlon) p.wlon -= 360 # western-most East longitude to earth (..., lon) _GeoidBase.__init__(self, hs, p) except Exception as x: raise _SciPyIssue(x, 'in', repr(g2012b_bin)) finally: g.close() def _g2ll2(self, lat, lon): # convert grid (lat, lon) to earth (lat, lon) return lat, lon def _ll2g2(self, lat, lon): # convert earth (lat, lon) to grid (lat, lon) return lat, lon if _FOR_DOCS: # PYCHOK no cover __call__ = _GeoidBase.__call__ height = _GeoidBase.height def _I(i): '''(INTERNAL) Cache a single C{int} constant. ''' return _intCs.setdefault(i, i) # PYCHOK undefined due to del _intCs def _T(*cs): '''(INTERNAL) Cache a tuple of single C{int} constants. ''' return map1(_I, *cs) class GeoidKarney(_GeoidBase): '''Geoid height interpolator for Charles Karney's U{GeographicLib Earth Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/ html/geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/ html/geoid.html#geoidinst>} datasets using bilinear or U{cubic <https://dl.ACM.org/citation.cfm?id=368443>} interpolation and U{caching <https://GeographicLib.SourceForge.io/html/geoid.html#geoidcache>} in pure Python transcribed from Karney's U{C++ class Geoid <https://GeographicLib.SourceForge.io/html/geoid.html#geoidinterp>}. Use any of the geoid U{egm84-, egm96- or egm2008-*.pgm <https://GeographicLib.SourceForge.io/html/geoid.html#geoidinst>} datasets. ''' _C0 = (372.0, 240.0, 372.0) # n, _ and s common denominators # matrices c3n_, c3, c3s_, transposed from GeographicLib/Geoid.cpp _C3 = ((_T(0, 0, 62, 124, 124, 62, 0, 0, 0, 0, 0, 0), _T(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), _T(-131, 7, -31, -62, -62, -31, 45, 216, 156, -45, -55, -7), _T(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), _T(138, -138, 0, 0, 0, 0, -183, 33, 153, -3, 48, -48), # PYCHOK indent _T(144, 42, -62, -124, -124, -62, -9, 87, 99, 9, 42, -42), _T(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), _T(0, 0, 0, 0, 0, 0, 93, -93, -93, 93, 0, 0), _T(-102, 102, 0, 0, 0, 0, 18, 12, -12, -18, -84, 84), _T(-31, -31, 31, 62, 62, 31, 0, -93, -93, 0, 31, 31)), # PYCHOK indent (_T(9, -9, 9, 186, 54, -9, -9, 54, -54, 9, -9, 9), _T(-18, 18, -88, -42, 162, -32, 8, -78, 78, -8, 18, -18), _T(-88, 8, -18, -42, -78, 18, 18, 162, 78, -18, -32, -8), _T(0, 0, 90, -150, 30, 30, 30, -90, 90, -30, 0, 0), _T(96, -96, 96, -96, -24, 24, -96, -24, 144, -24, 24, -24), # PYCHOK indent _T(90, 30, 0, -150, -90, 0, 0, 30, 90, 0, 30, -30), _T(0, 0, -20, 60, -60, 20, -20, 60, -60, 20, 0, 0), _T(0, 0, -60, 60, 60, -60, 60, -60, -60, 60, 0, 0), _T(-60, 60, 0, 60, -60, 0, 0, 60, -60, 0, -60, 60), _T(-20, -20, 0, 60, 60, 0, 0, -60, -60, 0, 20, 20)), (_T(18, -18, 36, 210, 162, -36, 0, 0, 0, 0, -18, 18), # PYCHOK indent _T(-36, 36, -165, 45, 141, -21, 0, 0, 0, 0, 36, -36), _T(-122, -2, -27, -111, -75, 27, 62, 124, 124, 62, -64, 2), _T(0, 0, 93, -93, -93, 93, 0, 0, 0, 0, 0, 0), _T(120, -120, 147, -57, -129, 39, 0, 0, 0, 0, 66, -66), # PYCHOK indent _T(135, 51, -9, -192, -180, 9, 31, 62, 62, 31, 51, -51), _T(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), _T(0, 0, -93, 93, 93, -93, 0, 0, 0, 0, 0, 0), _T(-84, 84, 18, 12, -12, -18, 0, 0, 0, 0, -102, 102), _T(-31, -31, 0, 93, 93, 0, -31, -62, -62, -31, 31, 31))) _BT = (_T(0, 0), # bilinear 4-tuple [i, j] indices _T(1, 0), _T(0, 1), _T(1, 1)) _CM = (_T( 0, -1), # 10x12 cubic matrix [i, j] indices _T( 1, -1), _T(-1, 0), _T( 0, 0), _T( 1, 0), _T( 2, 0), _T(-1, 1), _T( 0, 1), _T( 1, 1), _T( 2, 1), _T( 0, 2), _T( 1, 2)) _egm = None # open geoid file _endian = '>H' # struct.unpack 1 ushort (big endian, unsigned short) _4endian = '>4H' # struct.unpack 4 ushorts _Rendian = '' # struct.unpack a row of ushorts # _highest = (-8.4, 147.367, 85.839) if egm2008-1.pgm else ( # (-8.167, 147.25, 85.422) if egm96-5.pgm else # (-4.5, 148.75, 81.33) # egm84-15.pgm) # _lowest = (4.7, 78.767, -106.911) if egm2008-1.pgm else ( # (4.667, 78.833, -107.043) if egm96-5.pgm else # (4.75, 79.25, -107.34) # egm84-15.pgm _mean = -1.317 # from egm2008-1, -1.438 egm96-5, -0.855 egm84-15 _nBytes = None # not applicable _nterms = len(_C3[0]) # columns length, number of row _smooth = None # not applicable _stdev = 29.244 # from egm2008-1, 29.227 egm96-5, 29.183 egm84-15 _u2B = _calcsize(_endian) # pixelsize_ in bytes _4u2B = _calcsize(_4endian) # 4 pixelsize_s in bytes _Ru2B = 0 # row of pixelsize_s in bytes _yxH = () # cache (y, x) indices _yxHt = () # cached 4- or 10-tuple for _ev2H resp. _ev3H _yx_hits = 0 # cache hits def __init__(self, egm_pgm, crop=None, datum=None, # WGS84 kind=3, name='', smooth=None): '''New L{GeoidKarney} interpolator. @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/ html/geoid.html#geoidinst>} file name (C{egm*.pgm}). @kwarg crop: Optional box to limit geoid locations, a 4-tuple (C{south, west, north, east}), 2-tuple (C{(south, west), (north, east)}) or 2, in C{degrees90} lat- and C{degrees180} longitudes or a 2-tuple (C{LatLonSW, LatLonNE}) of C{LatLon} instances. @kwarg datum: Optional grid datum (C{Datum}), default C{WGS84}. @kwarg kind: Interpolation order (C{int}), 2 for C{bilinear} or 3 for C{cubic}. @kwarg name: Optional geoid name (C{str}). @kwarg smooth: Smoothing factor, unsupported (C{None}). @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid B{C{crop}}, B{C{kind}} or B{C{smooth}}. @see: Class L{GeoidPGM} and function L{egmGeoidHeights}. ''' if smooth is not None: raise GeoidError('not supported: %s=%r' % ('smooth', smooth)) if kind in (2,): self._evH = self._ev2H elif kind not in (3,): raise InvalidError(kind=kind, Error=GeoidError) self._egm = g = self._open(egm_pgm, datum, kind, name, smooth) self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB) self._Rendian = self._4endian.replace('4', str(p.nlon)) self._Ru2B = _calcsize(self._Rendian) self._knots = p.knots # grid knots self._lon_of = float(p.flon) # forward offset self._lon_og = float(p.glon) # reverse offset # set earth (lat, lon) limits (s, w, n, e) self._lat_lo, \ self._lon_lo, \ self._lat_hi, \ self._lon_hi = self._swne(crop if crop else p.crop4) self._cropped = True if crop else False def __call__(self, *llis): '''Interpolate the geoid height for one or several locations. @arg llis: The location or locations (C{LatLon}, ... or C{LatLon}s). @return: A single interpolated geoid height (C{float}) or a list or tuple of interpolated geoid heights (C{float}s). @raise GeoidError: Insufficient number of B{C{llis}} or an invalid B{C{lli}}. @raise RangeError: An B{C{lli}} is outside this geoid's lat- or longitude range. ''' return self._called(llis, False) def _c0c3v(self, y, x): # get the common denominator, the 10x12 cubic matrix and # the 12 cubic v-coefficients around geoid index (y, x) p = self._pgm if 0 < x < (p.nlon - 2) and 0 < y < (p.nlat - 2): # read 4x4 ushorts, drop the 4 corners g = self._egm e = self._4endian n = self._4u2B R = self._Ru2B b = self._seek(y - 1, x - 1) v = _unpack(e, g.read(n))[1:3] b += R g.seek(b, _SEEK_SET) v += _unpack(e, g.read(n)) b += R g.seek(b, _SEEK_SET) v += _unpack(e, g.read(n)) b += R g.seek(b, _SEEK_SET) v += _unpack(e, g.read(n))[1:3] j = 1 else: # likely some wrapped y and/or x's v = self._raws(y, x, GeoidKarney._CM) j = 0 if y < 1 else (1 if y < (p.nlat - 2) else 2) return GeoidKarney._C0[j], GeoidKarney._C3[j], v def _ev(self, lat, lon): # PYCHOK expected # interpolate the geoid height at grid (lat, lon) fy, fx = self._g2yx2(lat, lon) y, x = int(floor(fy)), int(floor(fx)) fy -= y fx -= x H = self._evH(fy, fx, y, x) # ._ev3H or ._ev2H H *= self._pgm.Scale # H.fmul(self._pgm.Scale) H += self._pgm.Offset # H.fadd(self._pgm.Offset) return H.fsum() def _ev2H(self, fy, fx, *yx): # compute the bilinear 4-tuple and interpolate raw H if self._yxH == yx: t = self._yxHt self._yx_hits += 1 else: y, x = self._yxH = yx self._yxHt = t = self._raws(y, x, GeoidKarney._BT) v = 1.0, -fx, fx H = Fdot(v, t[0], t[0], t[1]) # a H -= H * fy # c = (1 - fy) * a H += Fdot(v, t[2], t[2], t[3]) * fy # c += b * fy return H def _ev3H(self, fy, fx, *yx): # compute the cubic 10-tuple and interpolate raw H if self._yxH == yx: t = self._yxHt self._yx_hits += 1 else: self._yxH = yx c0, c3, v = self._c0c3v(*yx) t = [fdot(v, *c3[i]) / c0 for i in range(self._nterms)] self._yxHt = t = tuple(t) # GeographicLib/Geoid.cpp Geoid::height(lat, lon) ... # real h = t[0] + fx * (t[1] + fx * (t[3] + fx * t[6])) + # fy * (t[2] + fx * (t[4] + fx * t[7]) + # fy * (t[5] + fx * t[8] + fy * t[9])); H = Fdot((1, fx, fy), t[5], t[8], t[9]) * fy H = (Fhorner(fx, t[2], t[4], t[7]) + H) * fy H += Fhorner(fx, t[0], t[1], t[3], t[6]) return H _evH = _ev3H # overriden for kind == 2 def _g2ll2(self, lat, lon): # convert grid (lat, lon) to earth (lat, lon), uncropped while lon > 180: lon -= 360 return lat, lon def _g2yx2(self, lat, lon): # convert grid (lat, lon) to grid (y, x) indices p = self._pgm # note, slat = +90, rlat < 0 makes y >=0 return ((lat - p.slat) * p.rlat), ((lon - p.wlon) * p.rlon) def _gyx2g2(self, y, x): # convert grid (y, x) indices to grid (lat, lon) p = self._pgm return (p.slat + p.dlat * y), (p.wlon + p.dlon * x) def _lat2y2(self, lat2): # convert earth lat(s) to min and max grid y indices ys, m = [], self._pgm.nlat - 1 for lat in lat2: y, _ = self._g2yx2(*self._ll2g2(lat, 0)) ys.append(max(min(int(y), m), 0)) return min(ys), max(ys) + 1 def _ll2g2(self, lat, lon): # convert earth (lat, lon) to grid (lat, lon), uncropped while lon < 0: lon += 360 return lat, lon def _llh3minmax(self, highest=True, *lat2): # find highest or lowest, takes 10+ secs for egm2008-1.pgm geoid # (Python 2.7.16, macOS 10.13.6 High Sierra, iMac 3 GHz Core i3) y = x = 0 h = self._raw(y, x) if highest: for j, r in self._raw2(*lat2): m = max(r) if m > h: h, y, x = m, j, r.index(m) else: # lowest for j, r in self._raw2(*lat2): m = min(r) if m < h: h, y, x = m, j, r.index(m) h *= self._pgm.Scale h += self._pgm.Offset return self._g2ll2(*self._gyx2g2(y, x)) + (h,) def _raw(self, y, x): # get the ushort geoid height at geoid index (y, x), # like GeographicLib/Geoid.hpp real rawval(is, iy) p = self._pgm if x < 0: x += p.nlon elif x >= p.nlon: x -= p.nlon h = p.nlon // 2 if y < 0: y = -y elif y >= p.nlat: y = (p.nlat - 1) * 2 - y else: h = 0 x += h if x < h else -h self._seek(y, x) h = _unpack(self._endian, self._egm.read(self._u2B)) return h[0] def _raws(self, y, x, ijs): # get bilinear 4-tuple or 10x12 cubic matrix return tuple(self._raw(y + j, x + i) for i, j in ijs) def _raw2(self, *lat2): # yield a 2-tuple (y, ushorts) for each row or for # the rows between two (or more) earth lat values p = self._pgm g = self._egm e = self._Rendian n = self._Ru2B # min(lat2) <= lat <= max(lat2) or 0 <= y < p.nlat s, t = self._lat2y2(lat2) if lat2 else (0, p.nlat) self._seek(s, 0) # to start of row s for y in range(s, t): yield y, _unpack(e, g.read(n)) def _seek(self, y, x): # position geoid to grid index (y, x) p = self._pgm b = p.skip + (y * p.nlon + x) * self._u2B self._egm.seek(b, _SEEK_SET) return b # position @property_RO def dtype(self): '''Get the geoid's grid data type (C{str}). ''' return 'ushort' def height(self, lats, lons): '''Interpolate the geoid 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 geoid height (C{float}) or a list of interpolated geoid heights (C{float}s). @raise GeoidError: Insufficient or non-matching number of B{C{lats}} and B{C{lons}}. @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this geoid's lat- or longitude range. ''' return _HeightBase._height(self, lats, lons, Error=GeoidError) def highest(self, LatLon=None, full=False): # PYCHOK full '''Return the location and largest height of this geoid. @kwarg LatLon: Optional class to return the location and height (C{LatLon}) or C{None}. @kwarg full: Search the full or limited latitude range (C{bool}). @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat, lon, height)} otherwise a B{C{LatLon}} instance with the lat-, longitude and height of the highest grid location. ''' if self._highest is None: lat2 = () if full or self.cropped else (-12, -4) self._highest = self._llh3minmax(True, *lat2) return self._llh3LL(self._highest, LatLon) def lowest(self, LatLon=None, full=False): # PYCHOK full '''Return the location and the lowest height of this geoid. @kwarg LatLon: Optional class to return the location and height (C{LatLon}) or C{None}. @kwarg full: Search the full or limited latitude range (C{bool}). @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat, lon, height)} otherwise a B{C{LatLon}} instance with the lat-, longitude and height of the lowest grid location. ''' if self._lowest is None: lat2 = () if full or self.cropped else (0, 8) self._lowest = self._llh3minmax(False, *lat2) return self._llh3LL(self._lowest, LatLon) @property_RO def u2B(self): '''Get the PGM itemsize in bytes (C{int}). ''' return self._u2B class GeoidPGM(_GeoidBase): '''Geoid height interpolator for Charles Karney's U{GeographicLib Earth Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/ html/geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/ html/geoid.html#geoidinst>} datasets but based on C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/reference/ generated/scipy.interpolate.RectBivariateSpline.html>} or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/ scipy.interpolate.interp2d.html>} interpolation. Use any of the U{egm84-, egm96- or egm2008-*.pgm <https://GeographicLib.SourceForge.io/html/geoid.html#geoidinst>} datasets. However, unless cropped, an entire C{egm*.pgm} dataset is loaded into the C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/ doc/scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>} or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/ scipy.interpolate.interp2d.html>} interpolator and converted from 2-byte C{int} to 8-byte C{dtype float64}. Therefore, internal memory usage is 4x the U{egm*.pgm<https://GeographicLib.SourceForge.io/html/ geoid.html#geoidinst>} file size and may exceed the available memory, especially with 32-bit Python, see properties C{.nBytes} and C{.sizeB}. ''' _endian = '>u2' _u2B = 0 # np.itemsize def __init__(self, egm_pgm, crop=None, datum=None, # WGS84 kind=3, name='', smooth=0): '''New L{GeoidPGM} interpolator. @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/ html/geoid.html#geoidinst>} file name (C{egm*.pgm}). @kwarg crop: Optional box to crop B{C{egm_pgm}}, a 4-tuple (C{south, west, north, east}) or 2-tuple (C{(south, west), (north, east)}), in C{degrees90} lat- and C{degrees180} longitudes or a 2-tuple (C{LatLonSW, LatLonNE}) of C{LatLon} instances. @kwarg datum: Optional grid datum (C{Datum}), default C{WGS84}. @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/ reference/generated/scipy.interpolate.RectBivariateSpline.html>}, -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/ reference/generated/scipy.interpolate.interp2d.html>}, -3 for C{interp2d cubic} or -5 for C{interp2d quintic}. @kwarg name: Optional geoid name (C{str}). @kwarg smooth: Smoothing factor for U{RectBivariateSpline <https://docs.SciPy.org/doc/scipy/reference/generated/ scipy.interpolate.RectBivariateSpline.html>} only (C{int}). @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid B{C{crop}}, B{C{kind}} or B{C{smooth}}. @raise ImportError: Package C{numpy} or C{scipy} not found or not installed. @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue. @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d} warning as exception. @note: The U{GeographicLib egm*.pgm<https://GeographicLib.SourceForge.io/ html/geoid.html#geoidinst>} file sizes are based on a 2-byte C{int} height converted to 8-byte C{dtype float64} for C{scipy} interpolators. Therefore, internal memory usage is 4 times the C{egm*.pgm} file size and may exceed the available memory, especially with 32-bit Python. To reduce memory usage, set keyword argument B{C{crop}} to the region of interest. For example B{crop=(20, -125, 50, -65)} covers the U{conterminous US<https:// www.NGS.NOAA.gov/GEOID/GEOID12B/maps/GEOID12B_CONUS_grids.png>} (CONUS), less than 3% of the entire C{egm2008-1.pgm} dataset. @see: Class L{GeoidKarney} and function L{egmGeoidHeights}. ''' np, _ = self._NumSciPy() self._u2B = np.dtype(self.endian).itemsize g = self._open(egm_pgm, datum, kind, name, smooth) self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB) if crop: g = p._cropped(g, abs(kind) + 1, *self._swne(crop)) self._g2ll2 = self._g2ll2_cropped self._ll2g2 = self._ll2g2_cropped if map2(int, self.numpy.split('.')[:2]) < (1, 9): g = open(g.name, 'rb') # reopen tempfile for numpy 1.8.0- self._cropped = True else: self._cropped = False try: # U{numpy dtype formats are different from Python struct formats # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>} # read all heights, skipping the PGM header lines, converted to float hs = self._load(g, self.endian, p.knots, p.skip).reshape(p.nlat, p.nlon) * p.Scale if p.Offset: # offset hs = p.Offset + hs if p.dlat < 0: # flip the rows hs = np.flipud(hs) _GeoidBase.__init__(self, hs, p) except Exception as x: raise _SciPyIssue(x, 'in', repr(egm_pgm)) finally: g.close() def _g2ll2(self, lat, lon): # convert grid (lat, lon) to earth (lat, lon), uncropped while lon > 180: lon -= 360 return lat, lon def _g2ll2_cropped(self, lat, lon): # convert cropped grid (lat, lon) to earth (lat, lon) return lat, lon - self._lon_og def _ll2g2(self, lat, lon): # convert earth (lat, lon) to grid (lat, lon), uncropped while lon < 0: lon += 360 return lat, lon def _ll2g2_cropped(self, lat, lon): # convert earth (lat, lon) to cropped grid (lat, lon) return lat, lon + self._lon_of if _FOR_DOCS: # PYCHOK no cover __call__ = _GeoidBase.__call__ height = _GeoidBase.height @property_RO def u2B(self): '''Get the PGM itemsize in bytes (C{int}). ''' return self._u2B class _Gpars(_Named): '''(INTERNAL) Basic geoid parameters. ''' # interpolator parameters dlat = 0 # +/- latitude resolution in C{degrees}. dlon = 0 # longitude resolution in C{degrees}. nlat = 1 # number of latitude knots (C{int}). nlon = 0 # number of longitude knots (C{int}) rlat = 0 # +/- latitude resolution in C{float}, 1 / .dlat. rlon = 0 # longitude resolution in C{float}, 1 / .dlon. slat = 0 # nothern- or southern most latitude (C{degrees90}). wlon = 0 # western-most longitude in Eastern lon (C{degrees360}). flon = 0 # forward, earth to grid longitude offset glon = 0 # reverse, grid to earth longitude offset knots = 0 # number of knots, nlat * nlon (C{int}). skip = 0 # header bytes to skip (C{int}). def __repr__(self): t = ', '.join(pairs((a, getattr(self, a)) for a in dir(self.__class__) if a[:1].isupper())) return '%s: %s' % (self, t) def __str__(self): return '%s(%r)' % (self.classname, self.name) class _PGM(_Gpars): '''(INTERNAL) Parse an C{egm*.pgm} geoid dataset file. # Geoid file in PGM format for the GeographicLib::Geoid class # Description WGS84 EGM96, 5-minute grid # URL https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html # DateTime 2009-08-29 18:45:03 # MaxBilinearError 0.140 # RMSBilinearError 0.005 # MaxCubicError 0.003 # RMSCubicError 0.001 # Offset -108 # Scale 0.003 # Origin 90N 0E # AREA_OR_POINT Point # Vertical_Datum WGS84 <width> <height> <pixel> ... ''' crop4 = () # 4-tuple (C{south, west, north, east}). egm = None glon = 180 # reverse offset, uncropped # pgm = '' # name sizeB = 0 u2B = 2 # item size of grid height (C{int}). @staticmethod def _llstr2floats(latlon): # llstr to (lat, lon) floats lat, lon = latlon.split() return parseDMS2(lat, lon) # PGM file attributes, CamelCase but not .istitle() AREA_OR_POINT = str DateTime = str Description = str # 'WGS84 EGM96, 5-minute grid' Geoid = str # 'file in PGM format for the GeographicLib::Geoid class' MaxBilinearError = float MaxCubicError = float Offset = float Origin = _llstr2floats Pixel = 0 RMSBilinearError = float RMSCubicError = float Scale = float URL = str # 'https://Earth-Info.NGA.mil/GandG/wgs84/...' Vertical_Datum = str def __init__(self, g, pgm='', itemsize=0, sizeB=0): # MCCABE 22 '''(INTERNAL) New C{_PGM} parsed C{egm*.pgm} geoid dataset. ''' self.name = pgm # geoid file name if itemsize: self._u2B = itemsize if sizeB: self.sizeB = sizeB t = g.readline() # make sure newline == '\n' if t != b'P5\n' or t.strip() != b'P5': raise self._Errorf('header %r', t) while True: # read all # Attr ... lines, try: # ignore empty ones or comments t = g.readline().strip() if t.startswith(b'#'): t = t.lstrip(b'#').lstrip() a, v = map(_b2str, t.split(None, 1)) f = getattr(_PGM, a, None) if callable(f) and a[:1].isupper(): setattr(self, a, f(v)) elif t: break except (TypeError, ValueError): raise self._Errorf('Attr %r', t) else: # should never get here raise self._Errorf('header %r', g.tell()) try: # must be (even) width and (odd) height nlon, nlat = map(int, t.split()) if nlon < 2 or nlon > (360 * 60) or (nlon & 1) != 0 or \ nlat < 2 or nlat > (181 * 60) or (nlat & 1) == 0: raise ValueError except (TypeError, ValueError): raise self._Errorf('width height %r', t) try: # must be 16 bit pixel height t = g.readline().strip() self.Pixel = int(t) if not 255 < self.Pixel < 65536: # >u2 or >H only raise ValueError except (TypeError, ValueError): raise self._Errorf('pixel %r', t) for a in dir(_PGM): # set undefined # Attr ... to None if a[:1].isupper() and callable(getattr(self, a)): setattr(self, a, None) if self.Origin is None: raise self._Errorf('Origin %r', self.Origin) if self.Offset is None or self.Offset > 0: raise self._Errorf('Offset %r', self.Offset) if self.Scale is None or self.Scale < EPS: raise self._Errorf('Scale %r', self.Scale) self.skip = g.tell() self.knots = nlat * nlon self.nlat, self.nlon = nlat, nlon self.slat, self.wlon = self.Origin # note, negative .dlat and .rlat since rows # are from .slat 90N down in decreasing lat self.dlat, self.dlon = 180.0 / (1 - nlat), 360.0 / nlon self.rlat, self.rlon = (1 - nlat) / 180.0, nlon / 360.0 # grid corners in earth (lat, lon), .slat = 90, .dlat < 0 n = float(self.slat) s = n + self.dlat * (nlat - 1) w = self.wlon - self.glon e = w + self.dlon * nlon self.crop4 = s, w, n, e n = self.sizeB - self.skip if n > 0 and n != (self.knots * self.u2B): raise self._Errorf('assert(%s x %s != %s)', nlat, nlon, n) def _cropped(self, g, k1, south, west, north, east): # MCCABE 15 '''Crop the geoid to (south, west, north, east) box. ''' # flon offset for both west and east f = 360 if west < 0 else 0 # earth (lat, lon) to grid indices (y, x), # note y is decreasing, i.e. n < s s, w = self._lle2yx2(south, west, f) n, e = self._lle2yx2(north, east, f) s += 1 # s > n e += 1 # e > w hi, wi = self.nlat, self.nlon # handle special cases if (s - n) > hi: n, s = 0, hi # entire lat range if (e - w) > wi: w, e, f = 0, wi, 180 # entire lon range if s == hi and w == n == 0 and e == wi: return g # use entire geoid as-is if (e - w) < k1 or (s - n) < (k1 + 1): raise self._Errorf('swne %r', (north - south, east - west)) if e > wi > w: # wrap around # read w..wi and 0..e r, p = (wi - w), (e - wi) elif e > w: r, p = (e - w), 0 else: raise self._Errorf('assert(%s < %s)', w, e) # convert to bytes r *= self.u2B p *= self.u2B q = wi * self.u2B # stride # number of rows and cols to skip from # the original (.slat, .wlon) origin z = self.skip + (n * wi + w) * self.u2B # sanity check if r < 2 or p < 0 or q < 2 or z < self.skip \ or z > self.sizeB: raise self._Errorf('assert%r', (r, p, q, z)) # can't use _BytesIO since numpy # needs .fileno attr in .fromfile t, c = 0, self._tmpfile() # reading (s - n) rows, forward for y in range(n, s): # PYCHOK y unused g.seek(z, _SEEK_SET) # Python 2 tmpfile.write returns None t += c.write(g.read(r)) or r if p: # wrap around to start of row g.seek(-q, _SEEK_CUR) # assert(g.tell() == (z - w * self.u2B)) # Python 2 tmpfile.write returns None t += c.write(g.read(p)) or p z += q c.flush() g.close() s -= n # nlat e -= w # nlon k = s * e # knots z = k * self.u2B if t != z: raise self._Errorf('assert(%s != %s) %s', t, z, self) # update the _Gpars accordingly, note attributes # .dlat, .dlon, .rlat and .rlon remain unchanged self.slat += n * self.dlat self.wlon += w * self.dlon self.nlat = s self.nlon = e self.flon = self.glon = f self.crop4 = south, west, north, east self.knots = k self.skip = 0 # no header lines in c c.seek(0, _SEEK_SET) # c = open(c.name, 'rb') # reopen for numpy 1.8.0- return c def _Errorf(self, fmt, *args): # PYCHOK no cover e = self.pgm or '' if e: e = ' in %r' % (e,) return PGMError('%s%s' % ((fmt % args), e)) def _lle2yx2(self, lat, lon, flon): # earth (lat, lon) to grid indices (y, x) # with .dlat decreasing from 90N .slat lat -= self.slat lon += flon - self.wlon return (min(self.nlat - 1, max(0, int(lat * self.rlat))), max(0, int(lon * self.rlon))) def _tmpfile(self): # create a tmpfile to hold the cropped geoid grid try: from tempfile import NamedTemporaryFile as tmpfile except ImportError: # Python 2.7.16- from os import tmpfile t = _os_path.splitext(_os_path.basename(self.pgm))[0] f = tmpfile(mode='w+b', prefix=t or 'egm') f.seek(0, _SEEK_SET) # force overwrite return f @property_RO def pgm(self): '''Get the geoid file name (C{str}). ''' return self.name def egmGeoidHeights(GeoidHeights_dat): '''Generate geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/ html/geoid.html#geoidinst>} height tests from U{GeoidHeights.dat <https://SourceForge.net/projects/geographiclib/files/testdata/>} U{Test data for Geoids<https://GeographicLib.SourceForge.io/html/ geoid.html#testgeoid>}. @arg GeoidHeights_dat: The un-gz-ed C{GeoidHeights.dat} file (C{str} or C{file} handle). @return: For each test, yield a L{GeoidHeight5Tuple}C{(lat, lon, egm84, egm96, egm2008)}. @raise GeoidError: Invalid B{C{GeoidHeights_dat}}. @note: Function L{egmGeoidHeights} is used to test the geoids L{GeoidKarney} and L{GeoidPGM}, see PyGeodesy module C{test/testGeoids.py}. ''' dat = GeoidHeights_dat if isinstance(dat, bytes): dat = _BytesIO(dat) try: dat.seek(0, _SEEK_SET) # reset except AttributeError: raise GeoidError('%s invalid: %s' % ('GeoidHeights_dat', type(dat))) for t in dat.readlines(): t = t.strip() if t and not t.startswith(b'#'): lat, lon, egm84, egm96, egm2008 = map(float, t.split()) while lon > 180: # EasternLon to earth lon lon -= 360 yield GeoidHeight5Tuple(lat, lon, egm84, egm96, egm2008) if __name__ == '__main__': import sys _crop = () _GeoidEGM = GeoidKarney _kind = 3 geoids = sys.argv[1:] while geoids: geoid = geoids.pop(0) if '-crop'.startswith(geoid.lower()): _crop = 20, -125, 50, -65 # CONUS elif '-karney'.startswith(geoid.lower()): _GeoidEGM = GeoidKarney elif '-kind'.startswith(geoid.lower()): _kind = int(geoids.pop(0)) elif '-pgm'.startswith(geoid.lower()): _GeoidEGM = GeoidPGM elif geoid[-4:].lower() in ('.pgm',): g = _GeoidEGM(geoid, crop=_crop, kind=_kind) print('\n%s\n' % (g.toStr(),)) print('%r\n' % (g.pgm,)) # <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>: # The height of the EGM96 geoid at Timbuktu # echo 16:46:33N 3:00:34W | GeoidEval # => 28.7068 -0.02e-6 -1.73e-6 # The 1st number is the height of the geoid, the 2nd and # 3rd are its slopes in northerly and easterly direction t = 'Timbuktu %s' % (g,) k = {'egm84-15.pgm': '31.2979', 'egm96-5.pgm': '28.7067', 'egm2008-1.pgm': '28.7880'}.get(g.name.lower(), '28.7880') ll = parseDMS2('16:46:33N', '3:00:34W', sep=':') for ll in (ll, (16.776, -3.009),): try: h, ll = g.height(*ll), fstr(ll, prec=6) print('%s.height(%s): %.4F vs %s' % (t, ll, h, k)) except (GeoidError, RangeError) as x: print('%s: %s' % (t, x)) elif geoid[-4:].lower() in ('.bin',): g = GeoidG2012B(geoid, kind=_kind) print(g.toStr()) else: raise GeoidError('unknown grid: %r' % (geoid,)) _I = int # PYCHOK unused _I del _intCs # trash ints cache # **) 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. # <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval> # _lowerleft = -90, -179, -30.1500 # egm2008-1.pgm # _lowerleft = -90, -179, -29.5350 # egm96-5.pgm # _lowerleft = -90, -179, -29.7120 # egm84-15.pgm # _center = 0, 0, 17.2260 # egm2008-1.pgm # _center = 0, 0, 17.1630 # egm96-5.pgm # _center = 0, 0, 18.3296 # egm84-15.pgm # _upperright = 90, 180, 14.8980 # egm2008-1.pgm # _upperright = 90, 180, 13.6050 # egm96-5.pgm # _upperright = 90, 180, 13.0980 # egm84-15.pgm # % python pygeodesy/geoids.py [-Karney] ../geoids/egm*.pgm # # GeoidKarney('egm2008-1.pgm'): lowerleft(-90.0, -180.0, -30.15), upperright(90.0, 180.0, 14.898), center(0.0, 0.0, 17.226), # highest(-8.4, -32.633, 85.839), lowest(4.683, -101.25, -106.911), mean=-1.317, stdev=29.244, # kind=3, dtype='ushort', endian='>H', hits=0, knots=233301600, sizeB=466603604 # _PGM('../geoids/egm2008-1.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-31 06:54:00', Description='WGS84 EGM2008, 1-minute grid', # Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.025, MaxCubicError=0.003, # Offset=-108.0, Origin=(90, 0.0), Pixel=65535, RMSBilinearError=0.001, RMSCubicError=0.001, Scale=0.003, # URL='https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm2008', Vertical_Datum='WGS84', crop4=(-90.0, -180.0, 90.0, 180.0), # dlat=-0.016666666666666666, dlon=0.016666666666666666, egm=None, flon=0, glon=180, knots=233301600, nlat=10801, nlon=21600, # pgm='../geoids/egm2008-1.pgm', rlat=-60.0, rlon=60.0, sizeB=466603604, skip=404, slat=90, u2B=2, wlon=0.0 # Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880 # Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880 # # GeoidKarney('egm84-15.pgm'): lowerleft(-90.0, -180.0, -29.712), upperright(90.0, 180.0, 13.098), center(0.0, 0.0, 18.33), # highest(-8.4, -32.633, 85.839), lowest(4.683, -101.25, -106.911), mean=-1.317, stdev=29.244, # kind=3, dtype='ushort', endian='>H', hits=0, knots=1038240, sizeB=2076896 # _PGM('../geoids/egm84-15.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-29 18:45:02', Description='WGS84 EGM84, 15-minute grid', # Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.413, MaxCubicError=0.02, # Offset=-108.0, Origin=(90, 0.0), Pixel=65535, RMSBilinearError=0.018, RMSCubicError=0.001, Scale=0.003, # URL='https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/wgs84_180/wgs84_180.html', Vertical_Datum='WGS84', crop4=(-90.0, -180.0, 90.0, 180.0), # dlat=-0.25, dlon=0.25, egm=None, flon=0, glon=180, knots=1038240, nlat=721, nlon=1440, # pgm='../geoids/egm84-15.pgm', rlat=-4.0, rlon=4.0, sizeB=2076896, skip=416, slat=90, u2B=2, wlon=0.0 # Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979 # Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979 # # GeoidKarney('egm96-5.pgm'): lowerleft(-90.0, -180.0, -29.535), upperright(90.0, 180.0, 13.605), center(0.0, 0.0, 17.163), # highest(-8.4, -32.633, 85.839), lowest(4.683, -101.25, -106.911), mean=-1.317, stdev=29.244, # kind=3, dtype='ushort', endian='>H', hits=0, knots=9335520, sizeB=18671448 # _PGM('../geoids/egm96-5.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-29 18:45:03', Description='WGS84 EGM96, 5-minute grid', # Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.14, MaxCubicError=0.003, # Offset=-108.0, Origin=(90, 0.0), Pixel=65535, RMSBilinearError=0.005, RMSCubicError=0.001, Scale=0.003, # URL='https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html', Vertical_Datum='WGS84', crop4=(), # dlat=-0.08333333333333333, dlon=0.08333333333333333, egm=None, flon=0, glon=180, knots=9335520, nlat=2161, nlon=4320, # pgm='../geoids/egm96-5.pgm', rlat=-12.0, rlon=12.0, sizeB=18671448, skip=408, slat=90, u2B=2, wlon=0.0 # Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067 # Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067 # % python pygeodesy/geoids.py -PGM ../geoids/egm*.pgm # # GeoidPGM('egm2008-1.pgm'): lowerleft(-90.0, -180.0, -30.15), upperright(90.0, 180.0, 14.898), center(0.0, 0.0, 17.226), # highest(-8.4, -32.633, 85.839), lowest(4.683, -101.25, -106.911), mean=-1.317, stdev=29.244, # kind=3, smooth=0, dtype=dtype('float64'), endian='>u2', knots=233301600, nBytes=1866412800, sizeB=466603604, scipy='1.2.1', numpy='1.16.1' # _PGM('../geoids/egm2008-1.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-31 06:54:00', Description='WGS84 EGM2008, 1-minute grid', # Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.025, MaxCubicError=0.003, # Offset=-108.0, Origin=(90, 0.0), Pixel=65535, RMSBilinearError=0.001, RMSCubicError=0.001, Scale=0.003, # URL='https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm2008', Vertical_Datum='WGS84', crop4=(-90.0, -180.0, 90.0, 180.0), # dlat=-0.016666666666666666, dlon=0.016666666666666666, egm=None, flon=0, glon=180, knots=233301600, nlat=10801, nlon=21600, # pgm='../geoids/egm2008-1.pgm', rlat=-60.0, rlon=60.0, sizeB=466603604, skip=404, slat=90, u2B=2, wlon=0.0 # Timbuktu GeoidPGM('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880 # Timbuktu GeoidPGM('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880 # # GeoidPGM('egm84-15.pgm'): lowerleft(-90.0, -180.0, -29.712), upperright(90.0, 180.0, 13.098), center(0.0, 0.0, 18.33), # highest(-4.5, -31.25, 81.33), lowest(4.75, -100.75, -107.34), mean=-0.855, stdev=29.183, # kind=3, smooth=0, dtype=dtype('float64'), endian='>u2', knots=1038240, nBytes=8305920, sizeB=2076896, scipy='1.2.1', numpy='1.16.1' # _PGM('../geoids/egm84-15.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-29 18:45:02', Description='WGS84 EGM84, 15-minute grid', # Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.413, MaxCubicError=0.02, # Offset=-108.0, Origin=(90, 0.0), Pixel=65535, RMSBilinearError=0.018, RMSCubicError=0.001, Scale=0.003, # URL='https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/wgs84_180/wgs84_180.html', Vertical_Datum='WGS84', crop4=(-90.0, -180.0, 90.0, 180.0), # dlat=-0.25, dlon=0.25, egm=None, flon=0, glon=180, knots=1038240, nlat=721, nlon=1440, # pgm='../geoids/egm84-15.pgm', rlat=-4.0, rlon=4.0, sizeB=2076896, skip=416, slat=90, u2B=2, wlon=0.0 # Timbuktu GeoidPGM('egm84-15.pgm').height(16.775833, -3.009444): 31.2979 vs 31.2979 # Timbuktu GeoidPGM('egm84-15.pgm').height(16.776, -3.009): 31.2975 vs 31.2979 # # GeoidPGM('egm96-5.pgm'): lowerleft(-90.0, -180.0, -29.535), upperright(90.0, 180.0, 13.605), center(0.0, -0.0, 17.179), # highest(-8.167, -32.75, 85.422), lowest(4.667, -101.167, -107.043), mean=-1.438, stdev=29.227, # kind=3, smooth=0, dtype=dtype('float64'), endian='>u2', knots=9335520, nBytes=74684160, sizeB=18671448, scipy='1.2.1', numpy='1.16.1' # _PGM('../geoids/egm96-5.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-29 18:45:03', Description='WGS84 EGM96, 5-minute grid', # Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.14, MaxCubicError=0.003, # Offset=-108.0, Origin=(90, 0.0), Pixel=65535, RMSBilinearError=0.005, RMSCubicError=0.001, Scale=0.003, # URL='https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html', Vertical_Datum='WGS84', crop4=(-90.0, -180.0, 90.0, 180.0), # dlat=-0.08333333333333333, dlon=0.08333333333333333, egm=None, flon=0, glon=180, knots=9335520, nlat=2161, nlon=4320, # pgm='../geoids/egm96-5.pgm', rlat=-12.0, rlon=12.0, sizeB=18671448, skip=408, slat=90, u2B=2, wlon=0.0 # Timbuktu GeoidPGM('egm96-5.pgm').height(16.775833, -3.009444): 28.7065 vs 28.7067 # Timbuktu GeoidPGM('egm96-5.pgm').height(16.776, -3.009): 28.7064 vs 28.7067