Coverage for pygeodesy/geoids.py: 96%
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« prev ^ index » next coverage.py v7.6.1, created at 2024-11-12 16:17 -0500
2# -*- coding: utf-8 -*-
4u'''Geoid models and geoid height interpolations.
6Classes L{GeoidG2012B}, L{GeoidKarney} and L{GeoidPGM} to interpolate the
7height of various U{geoid<https://WikiPedia.org/wiki/Geoid>}s at C{LatLon}
8locations or separate lat-/longitudes using different interpolation methods
9and C{geoid} model files.
11L{GeoidKarney} is a transcoding of I{Charles Karney}'s C++ class U{Geoid
12<https://GeographicLib.SourceForge.io/C++/doc/geoid.html>} to pure Python.
13The L{GeoidG2012B} and L{GeoidPGM} interpolators both depend on U{scipy
14<https://SciPy.org>} and U{numpy<https://PyPI.org/project/numpy>} and
15require those packages to be installed.
17In addition, each geoid interpolator needs C{grid knots} (down)loaded from
18a C{geoid} model file, I{specific to the interpolator}. More details below
19and in the documentation of the interpolator class. For each interpolator,
20there are several interpolation choices, like I{linear}, I{cubic}, etc.
22Typical usage
23=============
251. Choose one of the interpolator classes L{GeoidG2012B}, L{GeoidKarney}
26or L{GeoidPGM} and download a C{geoid} model file, containing locations with
27known heights also referred to as the C{grid knots}. See the documentation
28of the interpolator class for references to available C{grid} models.
30C{>>> from pygeodesy import GeoidG2012B # or -Karney or -PGM as GeoidXyz}
322. Instantiate an interpolator with the C{geoid} model file and use keyword
33arguments to select different interpolation options
35C{>>> ginterpolator = GeoidXyz(geoid_model_file, **options)}
373. Get the interpolated geoid height of other C{LatLon} location(s) with
39C{>>> ll = LatLon(1, 2, ...)}
41C{>>> h = ginterpolator(ll)}
43or
45C{>>> h1, h2, h3, ... = ginterpolator(ll1, ll2, ll3, ...)}
47or a list, tuple, generator, etc. of C{LatLon}s
49C{>>> hs = ginterpolator(lls)}
514. For separate lat- and longitudes invoke the C{.height} method as
53C{>>> h = ginterpolator.height(lat, lon)}
55or as 2 lists, 2 tuples, etc.
57C{>>> hs = ginterpolator.height(lats, lons)}
595. An example is in U{issue #64<https://GitHub.com/mrJean1/PyGeodesy/issues/64>},
60courtesy of SBFRF.
62@note: Classes L{GeoidG2012B} and L{GeoidPGM} require both U{numpy
63 <https://PyPI.org/project/numpy>} and U{scipy<https://PyPI.org/project/scipy>}
64 to be installed.
66@note: Errors from C{scipy} are raised as L{SciPyError}s. Warnings issued by C{scipy} can
67 be thrown as L{SciPyWarning} exceptions, provided Python C{warnings} are filtered
68 accordingly, see L{SciPyWarning}.
70@see: I{Karney}'s U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/index.html>},
71 U{Geoid height<https://GeographicLib.SourceForge.io/C++/doc/geoid.html>} and U{Installing
72 the Geoid datasets<https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>},
73 U{SciPy<https://docs.SciPy.org/doc/scipy/reference/interpolate.html>} interpolation
74 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/reference/generated/scipy.interpolate.
75 RectBivariateSpline.html>}, U{bisplrep/-ev<https://docs.scipy.org/doc/scipy/reference/generated/
76 scipy.interpolate.bisplrep.html>} and U{interp2d<https://docs.SciPy.org/doc/scipy/reference/
77 generated/scipy.interpolate.interp2d.html>}, functions L{elevations.elevation2} and
78 L{elevations.geoidHeight2}, U{I{Ellispoid vs Orthometric Elevations}<https://www.YouTube.com/
79 watch?v=dX6a6kCk3Po>} and U{6.22.1 Avoiding Pitfalls Related to Ellipsoid Height and Height
80 Above Mean Sea Level<https://Wiki.ROS.org/mavros>}.
81'''
82# make sure int/int division yields float quotient, see .basics
83from __future__ import division as _; del _ # PYCHOK semicolon
85from pygeodesy.basics import len2, map1, isodd, ub2str as _ub2str
86from pygeodesy.constants import EPS, _float as _F, _1_0, _N_90_0, _180_0, \
87 _N_180_0, _360_0
88# from pygeodesy.datums import _ellipsoidal_datum # from .heights
89# from pygeodesy.dms import parseDMS2 # _MODS
90from pygeodesy.errors import _incompatible, LenError, RangeError, _SciPyIssue, \
91 _xkwds_pop2
92from pygeodesy.fmath import favg, Fdot, fdot, Fhorner, frange
93# from pygoedesy.formy import heightOrthometric # _MODS
94from pygeodesy.heights import _as_llis2, _ascalar, _HeightBase, HeightError, \
95 _ellipsoidal_datum, _Wrap
96# from pygeodesy.internals import _version2 # _MODS
97from pygeodesy.interns import NN, _COLONSPACE_, _COMMASPACE_, _E_, _height_, \
98 _in_, _kind_, _lat_, _lon_, _mean_, _N_, _n_a_, \
99 _numpy_, _on_, _outside_, _S_, _s_, _scipy_, \
100 _SPACE_, _stdev_, _tbd_, _W_, _width_, _4_
101from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _FOR_DOCS
102from pygeodesy.named import _name__, _Named, _NamedTuple
103# from pygeodesy.namedTuples import LatLon3Tuple # _MODS
104from pygeodesy.props import Property_RO, property_RO, property_ROver
105from pygeodesy.streprs import attrs, Fmt, fstr, pairs
106from pygeodesy.units import Height, Int_, Lat, Lon
107# from pygeodesy.utily import _Wrap # from .heights
109from math import floor as _floor
110# from os import SEEK_CUR, SEEK_SET # _MODS
111# import os.path # _MODS
112from struct import calcsize as _calcsize, unpack as _unpack
113try:
114 from StringIO import StringIO as _BytesIO # reads bytes
115 _ub2str = str # PYCHOK convert bytes to str for egm*.pgm text
117except ImportError: # Python 3+
118 from io import BytesIO as _BytesIO # PYCHOK expected
120__all__ = _ALL_LAZY.geoids
121__version__ = '24.11.05'
123_assert_ = 'assert'
124_bHASH_ = b'#'
125_endian_ = 'endian'
126_format_ = '%s %r'
127_header_ = 'header'
128_intCs = {} # cache int value
129_lli_ = 'lli'
130_non_increasing_ = 'non-increasing'
131_rb_ = 'rb'
132_supported_ = 'supported'
135class GeoidError(HeightError):
136 '''Geoid interpolator C{Geoid...} or interpolation issue.
137 '''
138 pass
141class _GeoidBase(_HeightBase):
142 '''(INTERNAL) Base class for C{Geoid...}s.
143 '''
144 _center = None # (lat, lon, height)
145 _cropped = None
146# _datum = _WGS84 # from _HeightBase
147 _egm = None # open C{egm*.pgm} geoid file
148 _endian = _tbd_
149 _Error = GeoidError # in ._HeightBase._as_lls, ...
150 _geoid = _n_a_
151 _hs_y_x = None # numpy 2darray, row-major order
152 _kind = 3 # order for interp2d, RectBivariateSpline
153# _kmin = 2 # min number of knots
154 _knots = 0 # nlat * nlon
155 _mean = None # fixed in GeoidKarney
156 _nBytes = 0 # numpy size in bytes, float64
157 _pgm = None # PGM attributes, C{_PGM} or C{None}
158 _sizeB = 0 # geoid file size in bytes
159 _smooth = 0 # used only for RectBivariateSpline
160 _stdev = None # fixed in GeoidKarney
161 _u2B = 0 # np.itemsize or undefined
162 _yx_hits = None # cache hits, ala Karney's
164# _lat_d = _0_0 # increment, +tive
165# _lat_lo = _0_0 # lower lat, south
166# _lat_hi = _0_0 # upper lat, noth
167# _lon_d = _0_0 # increment, +tive
168# _lon_lo = _0_0 # left lon, west
169# _lon_hi = _0_0 # right lon, east
170# _lon_of = _0_0 # forward lon offset
171# _lon_og = _0_0 # reverse lon offset
173 def __init__(self, hs, p):
174 '''(INTERNAL) Set up the grid axes, the C{SciPy} interpolator and
175 several internal geoid attributes.
177 @arg hs: Grid knots with known height (C{numpy 2darray}).
178 @arg p: The C{slat, wlon, nlat, nlon, dlat, dlon} and other
179 geoid parameters (C{INTERNAL}).
180 '''
181 spi = self.scipy_interpolate
182 # for 2d scipy.interpolate.interp2d(xs, ys, hs, ...) and
183 # scipy.interpolate.RectBivariateSpline(ys, xs, hs, ...)
184 # require the shape of hs to be (len(ys), len(xs)), note
185 # the different (xs, ys, ...) and (ys, xs, ...) orders
186 if (p.nlat, p.nlon) != hs.shape:
187 raise GeoidError(shape=hs.shape, txt=_incompatible((p.nlat, p.nlon)))
189 # both axes and bounding box
190 ys, self._lat_d = self._gaxis2(p.slat, p.dlat, p.nlat, _lat_ + _s_)
191 xs, self._lon_d = self._gaxis2(p.wlon, p.dlon, p.nlon, _lon_ + _s_)
193 bb = ys[0], ys[-1], xs[0], xs[-1] + p.dlon # fudge lon_hi
194 # geoid grids are typically stored in row-major order, some
195 # with rows (90..-90) reversed and columns (0..360) wrapped
196 # to Easten longitude, 0 <= east < 180 and 180 <= west < 360
197 k = self.kind
198 if k in self._k2interp2d: # see _HeightBase
199 self._interp2d(xs, ys, hs, kind=k)
200 else: # XXX order ys and xs, see HeightLSQBiSpline
201 k = self._kxky(k)
202 self._ev = spi.RectBivariateSpline(ys, xs, hs, bbox=bb, ky=k, kx=k,
203 s=self._smooth).ev
204 self._hs_y_x = hs # numpy 2darray, row-major
205 self._nBytes = hs.nbytes # numpy size in bytes
206 self._knots = p.knots # grid knots
207 self._lon_of = float(p.flon) # forward offset
208 self._lon_og = g = float(p.glon) # reverse offset
209 # shrink the bounding box by 1 unit on every side:
210 # +self._lat_d, -self._lat_d, +self._lon_d, -self._lon_d
211 self._lat_lo, \
212 self._lat_hi, \
213 self._lon_lo, \
214 self._lon_hi = map(float, bb)
215 self._lon_lo -= g
216 self._lon_hi -= g
218 def __call__(self, *llis, **wrap_H):
219 '''Interpolate the geoid height for one or several locations.
221 @arg llis: One or more locations (C{LatLon}s), all positional.
222 @kwarg wrap_H: Keyword arguments C{B{wrap}=False} (C{bool}) and
223 C{B{H}=False} (C{bool}). If C{B{wrap} is True},
224 wrap or I{normalize} all B{C{llis}} locations. If
225 C{B{H} is True}, return the I{orthometric} height
226 instead of the I{geoid} height at each location.
228 @return: A single interpolated geoid (or orthometric) height
229 (C{float}) or a list or tuple of interpolated geoid
230 (or orthometric) heights (C{float}s).
232 @raise GeoidError: Insufficient number of B{C{llis}}, an invalid
233 B{C{lli}} or the C{egm*.pgm} geoid file is closed.
235 @raise RangeError: An B{C{lli}} is outside this geoid's lat- or
236 longitude range.
238 @raise SciPyError: A C{scipy} issue.
240 @raise SciPyWarning: A C{scipy} warning as exception.
242 @note: To obtain I{orthometric} heights, each B{C{llis}} location
243 must have an ellipsoid C{height} or C{h} attribute, otherwise
244 C{height=0} is used.
246 @see: Function L{pygeodesy.heightOrthometric}.
247 '''
248 return self._called(llis, True, **wrap_H)
250 def __enter__(self):
251 '''Open context.
252 '''
253 return self
255 def __exit__(self, *unused): # PYCHOK exc_type, exc_value, exc_traceback)
256 '''Close context.
257 '''
258 self.close()
259 # return None # XXX False
261 def __repr__(self):
262 return self.toStr()
264 def __str__(self):
265 return Fmt.PAREN(self.classname, repr(self.name))
267 def _called(self, llis, iscipy, wrap=False, H=False):
268 # handle __call__
269 _H = self._heightOrthometric if H else None
270 _as, llis = _as_llis2(llis, Error=GeoidError)
271 hs, _w = [], _Wrap._latlonop(wrap)
272 _a, _h = hs.append, self._hGeoid
273 try:
274 for i, lli in enumerate(llis):
275 N = _h(*_w(lli.lat, lli.lon))
276 # orthometric or geoid height
277 _a(_H(lli, N) if _H else N)
278 return _as(hs)
279 except (GeoidError, RangeError) as x:
280 # XXX avoid str(LatLon()) degree symbols
281 t = _lli_ if _as is _ascalar else Fmt.INDEX(llis=i)
282 lli = fstr((lli.lat, lli.lon), strepr=repr)
283 raise type(x)(t, lli, wrap=wrap, H=H, cause=x)
284 except Exception as x:
285 if iscipy and self.scipy:
286 raise _SciPyIssue(x, self._ev_name)
287 else:
288 raise
290 @Property_RO
291 def _center(self):
292 ''' Cache for method L{center}.
293 '''
294 return self._llh3(favg(self._lat_lo, self._lat_hi),
295 favg(self._lon_lo, self._lon_hi))
297 def center(self, LatLon=None):
298 '''Return the center location and height of this geoid.
300 @kwarg LatLon: Optional class to return the location and height
301 (C{LatLon}) or C{None}.
303 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,
304 height)} otherwise a B{C{LatLon}} instance with the lat-,
305 longitude and geoid height of the center grid location.
306 '''
307 return self._llh3LL(self._center, LatLon)
309 def close(self):
310 '''Close the C{egm*.pgm} geoid file if open (and applicable).
311 '''
312 if not self.closed:
313 self._egm.close()
314 self._egm = None
316 @property_RO
317 def closed(self):
318 '''Get the C{egm*.pgm} geoid file status.
319 '''
320 return self._egm is None
322 @Property_RO
323 def cropped(self):
324 '''Is geoid cropped (C{bool} or C{None} if crop not supported).
325 '''
326 return self._cropped
328 @Property_RO
329 def dtype(self):
330 '''Get the grid C{scipy} U{dtype<https://docs.SciPy.org/doc/numpy/
331 reference/generated/numpy.ndarray.dtype.html>} (C{numpy.dtype}).
332 '''
333 return self._hs_y_x.dtype
335 @Property_RO
336 def endian(self):
337 '''Get the geoid endianess and U{dtype<https://docs.SciPy.org/
338 doc/numpy/reference/generated/numpy.dtype.html>} (C{str}).
339 '''
340 return self._endian
342 def _ev(self, y, x): # PYCHOK overwritten with .RectBivariateSpline.ev
343 # see methods _HeightBase._ev and -._interp2d
344 return self._ev2d(x, y) # (y, x) flipped!
346 def _gaxis2(self, lo, d, n, name):
347 # build grid axis, hi = lo + (n - 1) * d
348 m, a = len2(frange(lo, n, d))
349 if m != n:
350 raise LenError(self.__class__, grid=m, **{name: n})
351 if d < 0:
352 d, a = -d, list(reversed(a))
353 for i in range(1, m):
354 e = a[i] - a[i-1]
355 if e < EPS: # non-increasing axis
356 i = Fmt.INDEX(name, i)
357 raise GeoidError(i, e, txt=_non_increasing_)
358 return self.numpy.array(a), d
360 def _g2ll2(self, lat, lon): # PYCHOK no cover
361 '''(INTERNAL) I{Must be overloaded}.'''
362 self._notOverloaded(lat, lon)
364 def _gyx2g2(self, y, x):
365 # convert grid (y, x) indices to grid (lat, lon)
366 return ((self._lat_lo + self._lat_d * y),
367 (self._lon_lo + self._lon_of + self._lon_d * x))
369 def height(self, lats, lons, **wrap):
370 '''Interpolate the geoid height for one or several lat-/longitudes.
372 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s).
373 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s).
374 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{lats}}
375 and B{C{lons}} locations (C{bool}).
377 @return: A single interpolated geoid height (C{float}) or a
378 list of interpolated geoid heights (C{float}s).
380 @raise GeoidError: Insufficient or non-matching number of
381 B{C{lats}} and B{C{lons}}.
383 @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this
384 geoid's lat- or longitude range.
386 @raise SciPyError: A C{scipy} issue.
388 @raise SciPyWarning: A C{scipy} warning as exception.
389 '''
390 lls = self._as_lls(lats, lons)
391 return self(lls, **wrap) # __call__(ll) or __call__(lls)
393 @property_ROver
394 def _heightOrthometric(self):
395 return _MODS.formy.heightOrthometric # overwrite property_ROver
397 def _hGeoid(self, lat, lon):
398 out = self.outside(lat, lon)
399 if out:
400 lli = fstr((lat, lon), strepr=repr)
401 raise RangeError(lli=lli, txt=_SPACE_(_outside_, _on_, out))
402 return float(self._ev(*self._ll2g2(lat, lon)))
404 @Property_RO
405 def _highest(self):
406 '''(INTERNAL) Cache for C{.highest}.
407 '''
408 return self._LL3T(self._llh3minmax(True), name__=self.highest)
410 def highest(self, LatLon=None, **unused):
411 '''Return the location and largest height of this geoid.
413 @kwarg LatLon: Optional class to return the location and height
414 (C{LatLon}) or C{None}.
416 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,
417 height)} otherwise a B{C{LatLon}} instance with the lat-,
418 longitude and geoid height of the highest grid location.
419 '''
420 return self._llh3LL(self._highest, LatLon)
422 @Property_RO
423 def hits(self):
424 '''Get the number of cache hits (C{int} or C{None}).
425 '''
426 return self._yx_hits
428 @Property_RO
429 def kind(self):
430 '''Get the interpolator kind and order (C{int}).
431 '''
432 return self._kind
434 @Property_RO
435 def knots(self):
436 '''Get the number of grid knots (C{int}).
437 '''
438 return self._knots
440 def _ll2g2(self, lat, lon): # PYCHOK no cover
441 '''(INTERNAL) I{Must be overloaded}.'''
442 self._notOverloaded(lat, lon)
444 @property_ROver
445 def _LL3T(self):
446 '''(INTERNAL) Get L{LatLon3Tuple}, I{once}.
447 '''
448 return _MODS.namedTuples.LatLon3Tuple # overwrite property_ROver
450 def _llh3(self, lat, lon):
451 return self._LL3T(lat, lon, self._hGeoid(lat, lon), name=self.name)
453 def _llh3LL(self, llh, LatLon):
454 return llh if LatLon is None else self._xnamed(LatLon(*llh))
456 def _llh3minmax(self, highest, *unused):
457 hs, np = self._hs_y_x, self.numpy
458 # <https://docs.SciPy.org/doc/numpy/reference/generated/
459 # numpy.argmin.html#numpy.argmin>
460 arg = np.argmax if highest else np.argmin
461 y, x = np.unravel_index(arg(hs, axis=None), hs.shape)
462 return self._g2ll2(*self._gyx2g2(y, x)) + (float(hs[y, x]),)
464 def _load(self, g, dtype, n, offset=0):
465 # numpy.fromfile, like .frombuffer
466 g.seek(offset, _MODS.os.SEEK_SET)
467 return self.numpy.fromfile(g, dtype, n)
469 @Property_RO
470 def _lowerleft(self):
471 '''(INTERNAL) Cache for C{.lowerleft}.
472 '''
473 return self._llh3(self._lat_lo, self._lon_lo)
475 def lowerleft(self, LatLon=None):
476 '''Return the lower-left location and height of this geoid.
478 @kwarg LatLon: Optional class to return the location
479 (C{LatLon}) and height or C{None}.
481 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)}
482 otherwise a B{C{LatLon}} instance with the lat-, longitude and
483 geoid height of the lower-left, SW grid corner.
484 '''
485 return self._llh3LL(self._lowerleft, LatLon)
487 @Property_RO
488 def _loweright(self):
489 '''(INTERNAL) Cache for C{.loweright}.
490 '''
491 return self._llh3(self._lat_lo, self._lon_hi)
493 def loweright(self, LatLon=None):
494 '''Return the lower-right location and height of this geoid.
496 @kwarg LatLon: Optional class to return the location and height
497 (C{LatLon}) or C{None}.
499 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)}
500 otherwise a B{C{LatLon}} instance with the lat-, longitude and
501 geoid height of the lower-right, SE grid corner.
502 '''
503 return self._llh3LL(self._loweright, LatLon)
505 lowerright = loweright # synonymous
507 @Property_RO
508 def _lowest(self):
509 '''(INTERNAL) Cache for C{.lowest}.
510 '''
511 return self._LL3T(self._llh3minmax(False), name__=self.lowest)
513 def lowest(self, LatLon=None, **unused):
514 '''Return the location and lowest height of this geoid.
516 @kwarg LatLon: Optional class to return the location and height
517 (C{LatLon}) or C{None}.
519 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,
520 height)} otherwise a B{C{LatLon}} instance with the lat-,
521 longitude and geoid height of the lowest grid location.
522 '''
523 return self._llh3LL(self._lowest, LatLon)
525 @Property_RO
526 def mean(self):
527 '''Get the mean of this geoid's heights (C{float}).
528 '''
529 if self._mean is None: # see GeoidKarney
530 self._mean = float(self.numpy.mean(self._hs_y_x))
531 return self._mean
533 @property_RO
534 def name(self):
535 '''Get the name of this geoid (C{str}).
536 '''
537 return _HeightBase.name.fget(self) or self._geoid # recursion
539 @Property_RO
540 def nBytes(self):
541 '''Get the grid in-memory size in bytes (C{int}).
542 '''
543 return self._nBytes
545 def _open(self, geoid, datum, kind, name, smooth):
546 # open the geoid file
547 try:
548 self._geoid = _MODS.os.path.basename(geoid)
549 self._sizeB = _MODS.os.path.getsize(geoid)
550 g = open(geoid, _rb_)
551 except (IOError, OSError) as x:
552 raise GeoidError(geoid=geoid, cause=x)
554 if datum not in (None, self._datum):
555 self._datum = _ellipsoidal_datum(datum, name=name)
556 self._kind = int(kind)
557 if name:
558 _HeightBase.name.fset(self, name) # rename
559 if smooth:
560 self._smooth = Int_(smooth=smooth, Error=GeoidError, low=0)
562 return g
564 def outside(self, lat, lon):
565 '''Check whether a location is outside this geoid's
566 lat-/longitude or crop range.
568 @arg lat: The latitude (C{degrees}).
569 @arg lon: The longitude (C{degrees}).
571 @return: A 1- or 2-character C{str} if outside or an
572 empty C{str} if inside.
573 '''
574 return (_S_ if lat < self._lat_lo else
575 (_N_ if lat > self._lat_hi else NN)) + \
576 (_W_ if lon < self._lon_lo else
577 (_E_ if lon > self._lon_hi else NN))
579 @Property_RO
580 def pgm(self):
581 '''Get the PGM attributes (C{_PGM} or C{None} if not available/applicable).
582 '''
583 return self._pgm
585 @Property_RO
586 def sizeB(self):
587 '''Get the geoid grid file size in bytes (C{int}).
588 '''
589 return self._sizeB
591 @Property_RO
592 def smooth(self):
593 '''Get the C{RectBivariateSpline} smoothing (C{int}).
594 '''
595 return self._smooth
597 @Property_RO
598 def stdev(self):
599 '''Get the standard deviation of this geoid's heights (C{float}) or C{None}.
600 '''
601 if self._stdev is None: # see GeoidKarney
602 self._stdev = float(self.numpy.std(self._hs_y_x))
603 return self._stdev
605 def _swne(self, crop):
606 # crop box to 4-tuple (s, w, n, e)
607 try:
608 if len(crop) == 2:
609 try: # sw, ne LatLons
610 swne = (crop[0].lat, crop[0].lon,
611 crop[1].lat, crop[1].lon)
612 except AttributeError: # (s, w), (n, e)
613 swne = tuple(crop[0]) + tuple(crop[1])
614 else: # (s, w, n, e)
615 swne = crop
616 if len(swne) == 4:
617 s, w, n, e = map(float, swne)
618 if _N_90_0 <= s <= (n - _1_0) <= 89.0 and \
619 _N_180_0 <= w <= (e - _1_0) <= 179.0:
620 return s, w, n, e
621 except (IndexError, TypeError, ValueError):
622 pass
623 raise GeoidError(crop=crop)
625 def toStr(self, prec=3, sep=_COMMASPACE_): # PYCHOK signature
626 '''This geoid and all geoid attributes as a string.
628 @kwarg prec: Number of decimal digits (0..9 or C{None} for
629 default). Trailing zero decimals are stripped
630 for B{C{prec}} values of 1 and above, but kept
631 for negative B{C{prec}} values.
632 @kwarg sep: Separator to join (C{str}).
634 @return: Geoid name and attributes (C{str}).
635 '''
636 s = 1 if self.kind < 0 else 2
637 t = tuple(Fmt.PAREN(m.__name__, fstr(m(), prec=prec)) for m in
638 (self.lowerleft, self.upperright,
639 self.center,
640 self.highest, self.lowest)) + \
641 attrs( _mean_, _stdev_, prec=prec, Nones=False) + \
642 attrs((_kind_, 'smooth')[:s], prec=prec, Nones=False) + \
643 attrs( 'cropped', 'dtype', _endian_, 'hits', 'knots', 'nBytes',
644 'sizeB', _scipy_, _numpy_, prec=prec, Nones=False)
645 return _COLONSPACE_(self, sep.join(t))
647 @Property_RO
648 def u2B(self):
649 '''Get the PGM itemsize in bytes (C{int}).
650 '''
651 return self._u2B
653 @Property_RO
654 def _upperleft(self):
655 '''(INTERNAL) Cache for C{.upperleft}.
656 '''
657 return self._llh3(self._lat_hi, self._lon_lo)
659 def upperleft(self, LatLon=None):
660 '''Return the upper-left location and height of this geoid.
662 @kwarg LatLon: Optional class to return the location and height
663 (C{LatLon}) or C{None}.
665 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)}
666 otherwise a B{C{LatLon}} instance with the lat-, longitude and
667 geoid height of the upper-left, NW grid corner.
668 '''
669 return self._llh3LL(self._upperleft, LatLon)
671 @Property_RO
672 def _upperright(self):
673 '''(INTERNAL) Cache for C{.upperright}.
674 '''
675 return self._llh3(self._lat_hi, self._lon_hi)
677 def upperright(self, LatLon=None):
678 '''Return the upper-right location and height of this geoid.
680 @kwarg LatLon: Optional class to return the location and height
681 (C{LatLon}) or C{None}.
683 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)}
684 otherwise a B{C{LatLon}} instance with the lat-, longitude and
685 geoid height of the upper-right, NE grid corner.
686 '''
687 return self._llh3LL(self._upperright, LatLon)
690class GeoidG2012B(_GeoidBase):
691 '''Geoid height interpolator for U{GEOID12B Model
692 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/>} grids U{CONUS
693 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_CONUS.shtml>},
694 U{Alaska<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_AK.shtml>},
695 U{Hawaii<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_HI.shtml>},
696 U{Guam and Northern Mariana Islands
697 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_GMNI.shtml>},
698 U{Puerto Rico and U.S. Virgin Islands
699 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_PRVI.shtml>} and
700 U{American Samoa<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_AS.shtml>}
701 based on C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/
702 reference/generated/scipy.interpolate.RectBivariateSpline.html>}, U{interp2d
703 <https://docs.SciPy.org/doc/scipy/reference/generated/scipy.interpolate
704 .interp2d.html>} or U{bisplrep/-ev<https://docs.scipy.org/doc/scipy/reference/
705 generated/scipy.interpolate.bisplrep.html>} interpolation.
707 Use any of the binary C{le} (little endian) or C{be} (big endian)
708 C{g2012b*.bin} grid files.
709 '''
710 def __init__(self, g2012b_bin, datum=None, # NAD 83 Ellipsoid
711 kind=3, smooth=0, **name_crop):
712 '''New L{GeoidG2012B} interpolator.
714 @arg g2012b_bin: A C{GEOID12B} grid file name (C{.bin}).
715 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
716 L{a_f2Tuple}), default C{WGS84}.
717 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for U{RectBivariateSpline
718 <https://docs.SciPy.org/doc/scipy/ reference/generated/scipy.interpolate.
719 RectBivariateSpline.html>} or -1, -3 or -5 for U{bisplrep/-ev<https://
720 docs.SciPy.org/doc/scipy/reference/generated/scipy.interpolate.bisplrep.html>}
721 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/scipy.
722 interpolate.interp2d.html>} C{linear}, C{cubic} respectively C{quintic},
723 see note for more details.
724 @kwarg smooth: Smoothing factor for C{B{kind}=1..5} only (C{int}).
725 @kwarg name_crop: Optional geoid C{B{name}=NN} (C{str}) and UNSUPPORTED keyword argument
726 C{B{crop}=None}.
728 @raise GeoidError: Invalid B{C{crop}}, B{C{kind}} or B{C{smooth}} or a G2012B grid file
729 B{C{g2012b_bin}} issue.
731 @raise ImportError: Package C{numpy} or C{scipy} not found or not installed.
733 @raise LenError: Grid file B{C{g2012b_bin}} axis mismatch.
735 @raise SciPyError: A C{scipy} issue.
737 @raise SciPyWarning: A C{scipy} warning as exception.
739 @raise TypeError: Invalid B{C{datum}}.
741 @note: Specify C{B{kind}=-1, -3 or -5} to use C{scipy.interpolate.interp2d}
742 before or C{scipy.interpolate.bisplrep/-ev} since C{Scipy} version 1.14.
743 '''
744 crop, name = _xkwds_pop2(name_crop, crop=None)
745 if crop is not None:
746 raise GeoidError(crop=crop, txt_not_=_supported_)
748 g = self._open(g2012b_bin, datum, kind, _name__(**name), smooth)
749 _ = self.numpy # import numpy for ._load and
751 try:
752 p = _Gpars()
753 n = (self.sizeB // 4) - 11 # number of f4 heights
754 # U{numpy dtype formats are different from Python struct formats
755 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>}
756 for en_ in ('<', '>'):
757 # skip 4xf8, get 3xi4
758 p.nlat, p.nlon, ien = map(int, self._load(g, en_+'i4', 3, 32))
759 if ien == 1: # correct endian
760 p.knots = p.nlat * p.nlon
761 if p.knots == n and 1 < p.nlat < n \
762 and 1 < p.nlon < n:
763 self._endian = en_+'f4'
764 break
765 else: # couldn't validate endian
766 raise GeoidError(_endian_)
768 # get the first 4xf8
769 p.slat, p.wlon, p.dlat, p.dlon = map(float, self._load(g, en_+'f8', 4))
770 # read all f4 heights, ignoring the first 4xf8 and 3xi4
771 hs = self._load(g, self._endian, n, 44).reshape(p.nlat, p.nlon)
772 p.wlon -= _360_0 # western-most East longitude to earth (..., lon)
773 _GeoidBase.__init__(self, hs, p)
775 except Exception as x:
776 raise _SciPyIssue(x, _in_, repr(g2012b_bin))
777 finally:
778 g.close()
780 def _g2ll2(self, lat, lon):
781 # convert grid (lat, lon) to earth (lat, lon)
782 return lat, lon
784 def _ll2g2(self, lat, lon):
785 # convert earth (lat, lon) to grid (lat, lon)
786 return lat, lon
788 if _FOR_DOCS:
789 __call__ = _GeoidBase.__call__
790 height = _GeoidBase.height
793class GeoidHeight5Tuple(_NamedTuple): # .geoids.py
794 '''5-Tuple C{(lat, lon, egm84, egm96, egm2008)} for U{GeoidHeights.dat
795 <https://SourceForge.net/projects/geographiclib/files/testdata/>}
796 tests with the heights for 3 different EGM grids at C{degrees90}
797 and C{degrees180} degrees (after converting C{lon} from original
798 C{0 <= EasterLon <= 360}).
799 '''
800 _Names_ = (_lat_, _lon_, 'egm84', 'egm96', 'egm2008')
801 _Units_ = ( Lat, Lon, Height, Height, Height)
804def _I(i):
805 '''(INTERNAL) Cache a single C{int} constant.
806 '''
807 return _intCs.setdefault(i, i) # PYCHOK undefined due to del _intCs
810def _T(*cs):
811 '''(INTERNAL) Cache a tuple of single C{int} constants.
812 '''
813 return map1(_I, *cs)
815_T0s12 = (_I(0),) * 12 # PYCHOK _T(0, 0, ..., 0)
818class GeoidKarney(_GeoidBase):
819 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth
820 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/
821 geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/
822 C++/doc/geoid.html#geoidinst>} datasets using bilinear or U{cubic
823 <https://dl.ACM.org/citation.cfm?id=368443>} interpolation and U{caching
824 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidcache>}
825 in pure Python, transcoded from I{Karney}'s U{C++ class Geoid
826 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinterp>}.
828 Use any of the geoid U{egm84-, egm96- or egm2008-*.pgm
829 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>}
830 datasets.
831 '''
832 _C0 = _F(372), _F(240), _F(372) # n, _ and s common denominators
833 # matrices c3n_, c3, c3s_, transposed from GeographicLib/Geoid.cpp
834 _C3 = ((_T(0, 0, 62, 124, 124, 62, 0, 0, 0, 0, 0, 0),
835 _T0s12,
836 _T(-131, 7, -31, -62, -62, -31, 45, 216, 156, -45, -55, -7),
837 _T0s12,
838 _T(138, -138, 0, 0, 0, 0, -183, 33, 153, -3, 48, -48), # PYCHOK indent
839 _T(144, 42, -62, -124, -124, -62, -9, 87, 99, 9, 42, -42),
840 _T0s12,
841 _T(0, 0, 0, 0, 0, 0, 93, -93, -93, 93, 0, 0),
842 _T(-102, 102, 0, 0, 0, 0, 18, 12, -12, -18, -84, 84),
843 _T(-31, -31, 31, 62, 62, 31, 0, -93, -93, 0, 31, 31)), # PYCHOK indent
845 (_T(9, -9, 9, 186, 54, -9, -9, 54, -54, 9, -9, 9),
846 _T(-18, 18, -88, -42, 162, -32, 8, -78, 78, -8, 18, -18),
847 _T(-88, 8, -18, -42, -78, 18, 18, 162, 78, -18, -32, -8),
848 _T(0, 0, 90, -150, 30, 30, 30, -90, 90, -30, 0, 0),
849 _T(96, -96, 96, -96, -24, 24, -96, -24, 144, -24, 24, -24), # PYCHOK indent
850 _T(90, 30, 0, -150, -90, 0, 0, 30, 90, 0, 30, -30),
851 _T(0, 0, -20, 60, -60, 20, -20, 60, -60, 20, 0, 0),
852 _T(0, 0, -60, 60, 60, -60, 60, -60, -60, 60, 0, 0),
853 _T(-60, 60, 0, 60, -60, 0, 0, 60, -60, 0, -60, 60),
854 _T(-20, -20, 0, 60, 60, 0, 0, -60, -60, 0, 20, 20)),
856 (_T(18, -18, 36, 210, 162, -36, 0, 0, 0, 0, -18, 18), # PYCHOK indent
857 _T(-36, 36, -165, 45, 141, -21, 0, 0, 0, 0, 36, -36),
858 _T(-122, -2, -27, -111, -75, 27, 62, 124, 124, 62, -64, 2),
859 _T(0, 0, 93, -93, -93, 93, 0, 0, 0, 0, 0, 0),
860 _T(120, -120, 147, -57, -129, 39, 0, 0, 0, 0, 66, -66), # PYCHOK indent
861 _T(135, 51, -9, -192, -180, 9, 31, 62, 62, 31, 51, -51),
862 _T0s12,
863 _T(0, 0, -93, 93, 93, -93, 0, 0, 0, 0, 0, 0),
864 _T(-84, 84, 18, 12, -12, -18, 0, 0, 0, 0, -102, 102),
865 _T(-31, -31, 0, 93, 93, 0, -31, -62, -62, -31, 31, 31)))
867 _BT = (_T(0, 0), # bilinear 4-tuple [i, j] indices
868 _T(1, 0),
869 _T(0, 1),
870 _T(1, 1))
872 _CM = (_T( 0, -1), # 10x12 cubic matrix [i, j] indices
873 _T( 1, -1),
874 _T(-1, 0),
875 _T( 0, 0),
876 _T( 1, 0),
877 _T( 2, 0),
878 _T(-1, 1),
879 _T( 0, 1),
880 _T( 1, 1),
881 _T( 2, 1),
882 _T( 0, 2),
883 _T( 1, 2))
885# _cropped = None
886 _endian = '>H' # struct.unpack 1 ushort (big endian, unsigned short)
887 _4endian = '>4H' # struct.unpack 4 ushorts
888 _Rendian = NN # struct.unpack a row of ushorts
889# _highest = (-8.4, 147.367, 85.839) if egm2008-1.pgm else (
890# (-8.167, 147.25, 85.422) if egm96-5.pgm else
891# (-4.5, 148.75, 81.33)) # egm84-15.pgm
892# _lowest = (4.7, 78.767, -106.911) if egm2008-1.pgm else (
893# (4.667, 78.833, -107.043) if egm96-5.pgm else
894# (4.75, 79.25, -107.34)) # egm84-15.pgm
895 _mean = _F(-1.317) # from egm2008-1, -1.438 egm96-5, -0.855 egm84-15
896 _nBytes = None # not applicable
897 _nterms = len(_C3[0]) # columns length, number of row
898 _smooth = None # not applicable
899 _stdev = _F(29.244) # from egm2008-1, 29.227 egm96-5, 29.183 egm84-15
900 _u2B = _calcsize(_endian) # pixelsize_ in bytes
901 _4u2B = _calcsize(_4endian) # 4 pixelsize_s in bytes
902 _Ru2B = 0 # row of pixelsize_s in bytes
903 _yx_hits = 0 # cache hits
904 _yx_i = () # cached (y, x) indices
905 _yx_t = () # cached 4- or 10-tuple for _ev2k resp. _ev3k
907 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84
908 kind=3, **name_smooth):
909 '''New L{GeoidKarney} interpolator.
911 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/
912 C++/doc/geoid.html#geoidinst>} file name (C{egm*.pgm}), see
913 note below.
914 @kwarg crop: Optional box to limit geoid locations, a 4-tuple (C{south,
915 west, north, east}), 2-tuple (C{(south, west), (north, east)})
916 with 2 C{degrees90} lat- and C{degrees180} longitudes or as
917 2-tuple (C{LatLonSW, LatLonNE}) of C{LatLon} instances.
918 @kwarg datum: Optional grid datum (C{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
919 L{a_f2Tuple}), default C{WGS84}.
920 @kwarg kind: Interpolation order (C{int}), 2 for C{bilinear} or 3 for C{cubic}.
921 @kwarg name_smooth: Optional geoid C{B{name}=NN} (C{str}) and UNSUPPORTED
922 keyword argument C{B{smooth}}, use C{B{smooth}=None} to ignore.
924 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid B{C{crop}},
925 B{C{kind}} or B{C{smooth}}.
927 @raise TypeError: Invalid B{C{datum}}.
929 @see: Class L{GeoidPGM} and function L{egmGeoidHeights}.
931 @note: Geoid file B{C{egm_pgm}} remains open and I{must be closed} by calling
932 method C{close} or by using C{with B{GeoidKarney}(...) as ...:} context.
933 '''
934 smooth, name = _xkwds_pop2(name_smooth, smooth=None)
935 if smooth is not None:
936 raise GeoidError(smooth=smooth, txt_not_=_supported_)
938 if kind in (2,):
939 self._ev2d = self._ev2k # see ._ev_name
940 elif kind not in (3,):
941 raise GeoidError(kind=kind)
943 self._egm = g = self._open(egm_pgm, datum, kind, _name__(**name), None)
944 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB)
946 self._Rendian = self._4endian.replace(_4_, str(p.nlon))
947 self._Ru2B = _calcsize(self._Rendian)
949 self._knots = p.knots # grid knots
950 self._lon_of = float(p.flon) # forward offset
951 self._lon_og = float(p.glon) # reverse offset
952 # set earth (lat, lon) limits (s, w, n, e)
953 self._lat_lo, self._lon_lo, \
954 self._lat_hi, self._lon_hi = self._swne(crop if crop else p.crop4)
955 self._cropped = bool(crop)
957 def __call__(self, *llis, **wrap_H):
958 '''Interpolate the geoid height for one or several locations.
960 @arg llis: One or more locations (C{LatLon}s), all positional.
961 @kwarg wrap_H: Keyword arguments C{B{wrap}=False, B{H}=False}.
962 If C{B{wrap} is True}, wrap or I{normalize} all
963 B{C{llis}} locations (C{bool}). If C{B{H} is True},
964 return the I{orthometric} height instead of the
965 I{geoid} height at each location (C{bool}).
967 @return: A single interpolated geoid (or orthometric) height
968 (C{float}) or a list or tuple of interpolated geoid
969 (or orthometric) heights (C{float}s).
971 @raise GeoidError: Insufficient number of B{C{llis}}, an invalid
972 B{C{lli}} or the C{egm*.pgm} geoid file is closed.
974 @raise RangeError: An B{C{lli}} is outside this geoid's lat- or
975 longitude range.
977 @note: To obtain I{orthometric} heights, each B{C{llis}} location
978 must have an ellipsoid C{height} or C{h} attribute, otherwise
979 C{height=0} is used.
981 @see: Function L{pygeodesy.heightOrthometric}.
982 '''
983 return self._called(llis, False, **wrap_H)
985 def _c0c3v(self, y, x):
986 # get the common denominator, the 10x12 cubic matrix and
987 # the 12 cubic v-coefficients around geoid index (y, x)
988 p = self._pgm
989 if 0 < x < (p.nlon - 2) and 0 < y < (p.nlat - 2):
990 # read 4x4 ushorts, drop the 4 corners
991 S = _MODS.os.SEEK_SET
992 e = self._4endian
993 g = self._egm
994 n = self._4u2B
995 R = self._Ru2B
996 b = self._seek(y - 1, x - 1)
997 v = _unpack(e, g.read(n))[1:3]
998 b += R
999 g.seek(b, S)
1000 v += _unpack(e, g.read(n))
1001 b += R
1002 g.seek(b, S)
1003 v += _unpack(e, g.read(n))
1004 b += R
1005 g.seek(b, S)
1006 v += _unpack(e, g.read(n))[1:3]
1007 j = 1
1009 else: # likely some wrapped y and/or x's
1010 v = self._raws(y, x, GeoidKarney._CM)
1011 j = 0 if y < 1 else (1 if y < (p.nlat - 2) else 2)
1013 return GeoidKarney._C0[j], GeoidKarney._C3[j], v
1015 @Property_RO
1016 def dtype(self):
1017 '''Get the geoid's grid data type (C{str}).
1018 '''
1019 return 'ushort'
1021 def _ev(self, lat, lon): # PYCHOK expected
1022 # interpolate the geoid height at grid (lat, lon)
1023 fy, fx = self._g2yx2(lat, lon)
1024 y, x = int(_floor(fy)), int(_floor(fx))
1025 fy -= y
1026 fx -= x
1027 H = self._ev2d(fy, fx, y, x) # PYCHOK ._ev2k or ._ev3k
1028 H *= self._pgm.Scale # H.fmul(self._pgm.Scale)
1029 H += self._pgm.Offset # H.fadd(self._pgm.Offset)
1030 return H.fsum() # float(H)
1032 def _ev2k(self, fy, fx, *yx):
1033 # compute the bilinear 4-tuple and interpolate raw H
1034 if self._yx_i == yx:
1035 self._yx_hits += 1
1036 else:
1037 y, x = self._yx_i = yx
1038 self._yx_t = self._raws(y, x, GeoidKarney._BT)
1039 t = self._yx_t
1040 v = _1_0, -fx, fx
1041 H = Fdot(v, t[0], t[0], t[1]).fmul(_1_0 - fy) # c = a * (1 - fy)
1042 H += Fdot(v, t[2], t[2], t[3]).fmul(fy) # c += b * fy
1043 return H
1045 def _ev3k(self, fy, fx, *yx):
1046 # compute the cubic 10-tuple and interpolate raw H
1047 if self._yx_i == yx:
1048 self._yx_hits += 1
1049 else:
1050 c0, c3, v = self._c0c3v(*yx)
1051 # assert len(c3) == self._nterms
1052 self._yx_t = tuple(fdot(v, *r3) / c0 for r3 in c3)
1053 self._yx_i = yx
1054 # GeographicLib/Geoid.cpp Geoid::height(lat, lon) ...
1055 # real h = t[0] + fx * (t[1] + fx * (t[3] + fx * t[6])) +
1056 # fy * (t[2] + fx * (t[4] + fx * t[7]) +
1057 # fy * (t[5] + fx * t[8] + fy * t[9]));
1058 t = self._yx_t
1059 v = _1_0, fx, fy
1060 H = Fdot(v, t[5], t[8], t[9])
1061 H *= fy
1062 H += Fhorner(fx, t[2], t[4], t[7])
1063 H *= fy
1064 H += Fhorner(fx, t[0], t[1], t[3], t[6])
1065 return H
1067 _ev2d = _ev3k # overriden for kind=2, see ._ev_name
1069 def _g2ll2(self, lat, lon):
1070 # convert grid (lat, lon) to earth (lat, lon), uncropped
1071 while lon > _180_0:
1072 lon -= _360_0
1073 return lat, lon
1075 def _g2yx2(self, lat, lon):
1076 # convert grid (lat, lon) to grid (y, x) indices
1077 p = self._pgm
1078 # note, slat = +90, rlat < 0 makes y >=0
1079 return ((lat - p.slat) * p.rlat), ((lon - p.wlon) * p.rlon)
1081 def _gyx2g2(self, y, x):
1082 # convert grid (y, x) indices to grid (lat, lon)
1083 p = self._pgm
1084 return (p.slat + p.dlat * y), (p.wlon + p.dlon * x)
1086 def height(self, lats, lons, **wrap):
1087 '''Interpolate the geoid height for one or several lat-/longitudes.
1089 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s).
1090 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s).
1091 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{lats}}
1092 and B{C{lons}} locations (C{bool}).
1094 @return: A single interpolated geoid height (C{float}) or a
1095 list of interpolated geoid heights (C{float}s).
1097 @raise GeoidError: Insufficient or non-matching number of
1098 B{C{lats}} and B{C{lons}} or the C{egm*.pgm}
1099 geoid file is closed.
1101 @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this
1102 geoid's lat- or longitude range.
1103 '''
1104 lls = self._as_lls(lats, lons)
1105 return self(lls, **wrap) # __call__(ll) or __call__(lls)
1107 @Property_RO
1108 def _highest_ltd(self):
1109 '''(INTERNAL) Cache for C{.highest}.
1110 '''
1111 return self._LL3T(self._llh3minmax(True, -12, -4), name__=self.highest)
1113 def highest(self, LatLon=None, full=False): # PYCHOK full
1114 '''Return the location and largest height of this geoid.
1116 @kwarg LatLon: Optional class to return the location and height
1117 (C{LatLon}) or C{None}.
1118 @kwarg full: Search the full or limited latitude range (C{bool}).
1120 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,
1121 height)} otherwise a B{C{LatLon}} instance with the lat-,
1122 longitude and geoid height of the highest grid location.
1123 '''
1124 llh = self._highest if full or self.cropped else self._highest_ltd
1125 return self._llh3LL(llh, LatLon)
1127 def _lat2y2(self, lat2):
1128 # convert earth lat(s) to min and max grid y indices
1129 ys, m = [], self._pgm.nlat - 1
1130 for lat in lat2:
1131 y, _ = self._g2yx2(*self._ll2g2(lat, 0))
1132 ys.append(max(min(int(y), m), 0))
1133 return min(ys), max(ys) + 1
1135 def _ll2g2(self, lat, lon):
1136 # convert earth (lat, lon) to grid (lat, lon), uncropped
1137 while lon < 0:
1138 lon += _360_0
1139 return lat, lon
1141 def _llh3minmax(self, highest, *lat2):
1142 # find highest or lowest, takes 10+ secs for egm2008-1.pgm geoid
1143 # (Python 2.7.16, macOS 10.13.6 High Sierra, iMac 3 GHz Core i3)
1144 if highest:
1145 def _mt(r, h):
1146 m = max(r)
1147 return m, (m > h)
1149 else: # lowest
1150 def _mt(r, h): # PYCHOK redef
1151 m = min(r)
1152 return m, (m < h)
1154 y = x = 0
1155 h = self._raw(y, x)
1156 for j, r in self._raw2(*lat2):
1157 m, t = _mt(r, h)
1158 if t:
1159 h, y, x = m, j, r.index(m)
1160 h *= self._pgm.Scale
1161 h += self._pgm.Offset
1162 return self._g2ll2(*self._gyx2g2(y, x)) + (h,)
1164 @Property_RO
1165 def _lowest_ltd(self):
1166 '''(INTERNAL) Cache for C{.lowest}.
1167 '''
1168 return self._LL3T(self._llh3minmax(False, 0, 8), name__=self.lowest)
1170 def lowest(self, LatLon=None, full=False): # PYCHOK full
1171 '''Return the location and lowest height of this geoid.
1173 @kwarg LatLon: Optional class to return the location and height
1174 (C{LatLon}) or C{None}.
1175 @kwarg full: Search the full or limited latitude range (C{bool}).
1177 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,
1178 height)} otherwise a B{C{LatLon}} instance with the lat-,
1179 longitude and geoid height of the lowest grid location.
1180 '''
1181 llh = self._lowest if full or self.cropped else self._lowest_ltd
1182 return self._llh3LL(llh, LatLon)
1184 def _raw(self, y, x):
1185 # get the ushort geoid height at geoid index (y, x),
1186 # like GeographicLib/Geoid.hpp real rawval(is, iy)
1187 p = self._pgm
1188 if x < 0:
1189 x += p.nlon
1190 elif x >= p.nlon:
1191 x -= p.nlon
1192 h = p.nlon // 2
1193 if y < 0:
1194 y = -y
1195 elif y >= p.nlat:
1196 y = (p.nlat - 1) * 2 - y
1197 else:
1198 h = 0
1199 x += h if x < h else -h
1200 self._seek(y, x)
1201 h = _unpack(self._endian, self._egm.read(self._u2B))
1202 return h[0]
1204 def _raws(self, y, x, ijs):
1205 # get bilinear 4-tuple or 10x12 cubic matrix
1206 return tuple(self._raw(y + j, x + i) for i, j in ijs)
1208 def _raw2(self, *lat2):
1209 # yield a 2-tuple (y, ushorts) for each row or for
1210 # the rows between two (or more) earth lat values
1211 p = self._pgm
1212 g = self._egm
1213 e = self._Rendian
1214 n = self._Ru2B
1215 # min(lat2) <= lat <= max(lat2) or 0 <= y < p.nlat
1216 s, t = self._lat2y2(lat2) if lat2 else (0, p.nlat)
1217 self._seek(s, 0) # to start of row s
1218 for y in range(s, t):
1219 yield y, _unpack(e, g.read(n))
1221 def _seek(self, y, x):
1222 # position geoid to grid index (y, x)
1223 p, g = self._pgm, self._egm
1224 if g:
1225 b = p.skip + (y * p.nlon + x) * self._u2B
1226 g.seek(b, _MODS.os.SEEK_SET)
1227 return b # position
1228 raise GeoidError('closed file', txt=repr(p.egm)) # IOError
1231class GeoidPGM(_GeoidBase):
1232 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth
1233 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/geoid.html>}
1234 geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>}
1235 datasets but based on C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/
1236 reference/generated/scipy.interpolate.RectBivariateSpline.html>}, U{bisplrep/-ev
1237 <https://docs.SciPy.org/doc/scipy/reference/generated/scipy.interpolate.bisplrep.html>}
1238 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/scipy.interpolate.
1239 interp2d.html>} interpolation.
1241 Use any of the U{egm84-, egm96- or egm2008-*.pgm <https://GeographicLib.SourceForge.io/
1242 C++/doc/geoid.html#geoidinst>} datasets. However, unless cropped, an entire C{egm*.pgm}
1243 dataset is loaded into the C{SciPy} interpolator and converted from 2-byte C{int} to
1244 8-byte C{dtype float64}. Therefore, internal memory usage is 4x the U{egm*.pgm
1245 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>} file size and may
1246 exceed the available memory, especially with 32-bit Python, see properties C{.nBytes}
1247 and C{.sizeB}.
1248 '''
1249 _cropped = False
1250 _endian = '>u2'
1252 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84
1253 kind=3, smooth=0, **name):
1254 '''New L{GeoidPGM} interpolator.
1256 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/
1257 C++/doc/geoid.html#geoidinst>} file name (C{egm*.pgm}).
1258 @kwarg crop: Optional box to crop B{C{egm_pgm}}, a 4-tuple (C{south, west,
1259 north, east}) or 2-tuple (C{(south, west), (north, east)}),
1260 in C{degrees90} lat- and C{degrees180} longitudes or a 2-tuple
1261 (C{LatLonSW, LatLonNE}) of C{LatLon} instances.
1262 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
1263 L{a_f2Tuple}), default C{WGS84}.
1264 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for U{RectBivariateSpline
1265 <https://docs.SciPy.org/doc/scipy/reference/generated/scipy.interpolate.
1266 RectBivariateSpline.html>} or -1, -3 or -5 for U{bisplrep/-ev<https://
1267 docs.SciPy.org/doc/scipy/reference/generated/scipy.interpolate.bisplrep.html>}
1268 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/scipy.
1269 interpolate.interp2d.html>} C{linear}, C{cubic} respectively C{quintic},
1270 see note for more details.
1271 @kwarg smooth: Smoothing factor for C{B{kind}=1..5} only (C{int}).
1272 @kwarg name: Optional geoid C{B{name}=NN} (C{str}).
1274 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid B{C{crop}}, B{C{kind}}
1275 or B{C{smooth}}.
1277 @raise ImportError: Package C{numpy} or C{scipy} not found or not installed.
1279 @raise LenError: EGM dataset B{C{egm_pgm}} axis mismatch.
1281 @raise SciPyError: A C{scipy} issue.
1283 @raise SciPyWarning: A C{scipy} warning as exception.
1285 @raise TypeError: Invalid B{C{datum}} or unexpected argument.
1287 @note: Specify C{B{kind}=-1, -3 or -5} to use C{scipy.interpolate.interp2d}
1288 before or C{scipy.interpolate.bisplrep/-ev} since C{Scipy} version 1.14.
1290 @note: The U{GeographicLib egm*.pgm<https://GeographicLib.SourceForge.io/C++/doc/
1291 geoid.html#geoidinst>} file sizes are based on a 2-byte C{int} height
1292 converted to 8-byte C{dtype float64} for C{scipy} interpolators. Therefore,
1293 internal memory usage is 4 times the C{egm*.pgm} file size and may exceed
1294 the available memory, especially with 32-bit Python. To reduce memory
1295 usage, set keyword argument B{C{crop}} to the region of interest. For
1296 example C{B{crop}=(20, -125, 50, -65)} covers the U{conterminous US
1297 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/maps/GEOID12B_CONUS_grids.png>}
1298 (CONUS), less than 3% of the entire C{egm2008-1.pgm} dataset.
1300 @see: Class L{GeoidKarney} and function L{egmGeoidHeights}.
1301 '''
1302 np = self.numpy
1303 self._u2B = np.dtype(self.endian).itemsize
1305 g = self._open(egm_pgm, datum, kind, _name__(**name), smooth)
1306 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB)
1307 if crop:
1308 g = p._cropped(g, abs(kind) + 1, *self._swne(crop))
1309 if _MODS.internals._version2(np.__version__) < (1, 9):
1310 g = open(g.name, _rb_) # reopen tempfile for numpy 1.8.0-
1311 self._cropped = True
1312 try:
1313 # U{numpy dtype formats are different from Python struct formats
1314 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>}
1315 # read all heights, skipping the PGM header lines, converted to float
1316 hs = self._load(g, self.endian, p.knots, p.skip).reshape(p.nlat, p.nlon) * p.Scale
1317 if p.Offset: # offset
1318 hs = p.Offset + hs
1319 if p.dlat < 0: # flip the rows
1320 hs = np.flipud(hs)
1321 _GeoidBase.__init__(self, hs, p)
1322 except Exception as x:
1323 raise _SciPyIssue(x, _in_, repr(egm_pgm))
1324 finally:
1325 g.close()
1327 def _g2ll2(self, lat, lon):
1328 # convert grid (lat, lon) to earth (lat, lon), un-/cropped
1329 if self._cropped:
1330 lon -= self._lon_of
1331 else:
1332 while lon > _180_0:
1333 lon -= _360_0
1334 return lat, lon
1336 def _ll2g2(self, lat, lon):
1337 # convert earth (lat, lon) to grid (lat, lon), un-/cropped
1338 if self._cropped:
1339 lon += self._lon_of
1340 else:
1341 while lon < 0:
1342 lon += _360_0
1343 return lat, lon
1345 if _FOR_DOCS:
1346 __call__ = _GeoidBase.__call__
1347 height = _GeoidBase.height
1350class _Gpars(_Named):
1351 '''(INTERNAL) Basic geoid parameters.
1352 '''
1353 # interpolator parameters
1354 dlat = 0 # +/- latitude resolution in C{degrees}
1355 dlon = 0 # longitude resolution in C{degrees}
1356 nlat = 1 # number of latitude knots (C{int})
1357 nlon = 0 # number of longitude knots (C{int})
1358 rlat = 0 # +/- latitude resolution in C{float}, 1 / .dlat
1359 rlon = 0 # longitude resolution in C{float}, 1 / .dlon
1360 slat = 0 # nothern- or southern most latitude (C{degrees90})
1361 wlon = 0 # western-most longitude in Eastern lon (C{degrees360})
1363 flon = 0 # forward, earth to grid longitude offset
1364 glon = 0 # reverse, grid to earth longitude offset
1366 knots = 0 # number of knots, nlat * nlon (C{int})
1367 skip = 0 # header bytes to skip (C{int})
1369 def __repr__(self):
1370 t = _COMMASPACE_.join(pairs((a, getattr(self, a)) for
1371 a in dir(self.__class__)
1372 if a[:1].isupper()))
1373 return _COLONSPACE_(self, t)
1375 def __str__(self):
1376 return Fmt.PAREN(self.classname, repr(self.name))
1379class _PGM(_Gpars):
1380 '''(INTERNAL) Parse an C{egm*.pgm} geoid dataset file.
1382 # Geoid file in PGM format for the GeographicLib::Geoid class
1383 # Description WGS84 EGM96, 5-minute grid
1384 # URL https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html
1385 # DateTime 2009-08-29 18:45:03
1386 # MaxBilinearError 0.140
1387 # RMSBilinearError 0.005
1388 # MaxCubicError 0.003
1389 # RMSCubicError 0.001
1390 # Offset -108
1391 # Scale 0.003
1392 # Origin 90N 0E
1393 # AREA_OR_POINT Point
1394 # Vertical_Datum WGS84
1395 <width> <height>
1396 <pixel>
1397 ...
1398 '''
1399 crop4 = () # 4-tuple (C{south, west, north, east}).
1400 egm = None
1401 glon = 180 # reverse offset, uncropped
1402# pgm = NN # name
1403 sizeB = 0
1404 u2B = 2 # item size of grid height (C{int}).
1406 @staticmethod
1407 def _llstr2floats(latlon):
1408 # llstr to (lat, lon) floats
1409 lat, lon = latlon.split()
1410 return _MODS.dms.parseDMS2(lat, lon)
1412 # PGM file attributes, CamelCase but not .istitle()
1413 AREA_OR_POINT = str
1414 DateTime = str
1415 Description = str # 'WGS84 EGM96, 5-minute grid'
1416 Geoid = str # 'file in PGM format for the GeographicLib::Geoid class'
1417 MaxBilinearError = float
1418 MaxCubicError = float
1419 Offset = float
1420 Origin = _llstr2floats
1421 Pixel = 0
1422 RMSBilinearError = float
1423 RMSCubicError = float
1424 Scale = float
1425 URL = str # 'https://Earth-Info.NGA.mil/GandG/wgs84/...'
1426 Vertical_Datum = str
1428 def __init__(self, g, pgm=NN, itemsize=0, sizeB=0): # MCCABE 22
1429 '''(INTERNAL) New C{_PGM} parsed C{egm*.pgm} geoid dataset.
1430 '''
1431 self.name = pgm # geoid file name
1432 if itemsize:
1433 self._u2B = itemsize
1434 if sizeB:
1435 self.sizeB = sizeB
1437 t = g.readline() # make sure newline == '\n'
1438 if t != b'P5\n' and t.strip() != b'P5':
1439 raise self._Errorf(_format_, _header_, t)
1441 while True: # read all # Attr ... lines,
1442 try: # ignore empty ones or comments
1443 t = g.readline().strip()
1444 if t.startswith(_bHASH_):
1445 t = t.lstrip(_bHASH_).lstrip()
1446 a, v = map(_ub2str, t.split(None, 1))
1447 f = getattr(_PGM, a, None)
1448 if callable(f) and a[:1].isupper():
1449 setattr(self, a, f(v))
1450 elif t:
1451 break
1452 except (TypeError, ValueError):
1453 raise self._Errorf(_format_, 'Attr', t)
1454 else: # should never get here
1455 raise self._Errorf(_format_, _header_, g.tell())
1457 try: # must be (even) width and (odd) height
1458 nlon, nlat = map(int, t.split())
1459 if nlon < 2 or nlon > (360 * 60) or isodd(nlon) or \
1460 nlat < 2 or nlat > (181 * 60) or not isodd(nlat):
1461 raise ValueError
1462 except (TypeError, ValueError):
1463 raise self._Errorf(_format_, _SPACE_(_width_, _height_), t)
1465 try: # must be 16 bit pixel height
1466 t = g.readline().strip()
1467 self.Pixel = int(t)
1468 if not 255 < self.Pixel < 65536: # >u2 or >H only
1469 raise ValueError
1470 except (TypeError, ValueError):
1471 raise self._Errorf(_format_, 'pixel', t)
1473 for a in dir(_PGM): # set undefined # Attr ... to None
1474 if a[:1].isupper() and callable(getattr(self, a)):
1475 setattr(self, a, None)
1477 if self.Origin is None:
1478 raise self._Errorf(_format_, 'Origin', self.Origin)
1479 if self.Offset is None or self.Offset > 0:
1480 raise self._Errorf(_format_, 'Offset', self.Offset)
1481 if self.Scale is None or self.Scale < EPS:
1482 raise self._Errorf(_format_, 'Scale', self.Scale)
1484 self.skip = g.tell()
1485 self.knots = nlat * nlon
1487 self.nlat, self.nlon = nlat, nlon
1488 self.slat, self.wlon = self.Origin
1489 # note, negative .dlat and .rlat since rows
1490 # are from .slat 90N down in decreasing lat
1491 self.dlat, self.dlon = _180_0 / (1 - nlat), _360_0 / nlon
1492 self.rlat, self.rlon = (1 - nlat) / _180_0, nlon / _360_0
1494 # grid corners in earth (lat, lon), .slat = 90, .dlat < 0
1495 n = float(self.slat)
1496 s = n + self.dlat * (nlat - 1)
1497 w = self.wlon - self.glon
1498 e = w + self.dlon * nlon
1499 self.crop4 = s, w, n, e
1501 n = self.sizeB - self.skip
1502 if n > 0 and n != (self.knots * self.u2B):
1503 raise self._Errorf('%s(%s x %s != %s)', _assert_, nlat, nlon, n)
1505 def _cropped(self, g, k1, south, west, north, east): # MCCABE 15
1506 '''Crop the geoid to (south, west, north, east) box.
1507 '''
1508 # flon offset for both west and east
1509 f = 360 if west < 0 else 0
1510 # earth (lat, lon) to grid indices (y, x),
1511 # note y is decreasing, i.e. n < s
1512 s, w = self._lle2yx2(south, west, f)
1513 n, e = self._lle2yx2(north, east, f)
1514 s += 1 # s > n
1515 e += 1 # e > w
1517 hi, wi = self.nlat, self.nlon
1518 # handle special cases
1519 if (s - n) > hi:
1520 n, s = 0, hi # entire lat range
1521 if (e - w) > wi:
1522 w, e, f = 0, wi, 180 # entire lon range
1523 if s == hi and w == n == 0 and e == wi:
1524 return g # use entire geoid as-is
1526 if (e - w) < k1 or (s - n) < (k1 + 1):
1527 raise self._Errorf(_format_, 'swne', (north - south, east - west))
1529 if e > wi > w: # wrap around
1530 # read w..wi and 0..e
1531 r, p = (wi - w), (e - wi)
1532 elif e > w:
1533 r, p = (e - w), 0
1534 else:
1535 raise self._Errorf('%s(%s < %s)', _assert_, w, e)
1537 # convert to bytes
1538 r *= self.u2B
1539 p *= self.u2B
1540 q = wi * self.u2B # stride
1541 # number of rows and cols to skip from
1542 # the original (.slat, .wlon) origin
1543 z = self.skip + (n * wi + w) * self.u2B
1544 # sanity check
1545 if r < 2 or p < 0 or q < 2 or z < self.skip \
1546 or z > self.sizeB:
1547 raise self._Errorf(_format_, _assert_, (r, p, q, z))
1549 # can't use _BytesIO since numpy
1550 # needs .fileno attr in .fromfile
1551 t, c = 0, self._tmpfile()
1552 # reading (s - n) rows, forward
1553 for y in range(n, s): # PYCHOK y unused
1554 g.seek(z, _MODS.os.SEEK_SET)
1555 # Python 2 tmpfile.write returns None
1556 t += c.write(g.read(r)) or r
1557 if p: # wrap around to start of row
1558 g.seek(-q, _MODS.os.SEEK_CUR)
1559 # assert(g.tell() == (z - w * self.u2B))
1560 # Python 2 tmpfile.write returns None
1561 t += c.write(g.read(p)) or p
1562 z += q
1563 c.flush()
1564 g.close()
1566 s -= n # nlat
1567 e -= w # nlon
1568 k = s * e # knots
1569 z = k * self.u2B
1570 if t != z:
1571 raise self._Errorf('%s(%s != %s) %s', _assert_, t, z, self)
1573 # update the _Gpars accordingly, note attributes
1574 # .dlat, .dlon, .rlat and .rlon remain unchanged
1575 self.slat += n * self.dlat
1576 self.wlon += w * self.dlon
1577 self.nlat = s
1578 self.nlon = e
1579 self.flon = self.glon = f
1581 self.crop4 = south, west, north, east
1582 self.knots = k
1583 self.skip = 0 # no header lines in c
1585 c.seek(0, _MODS.os.SEEK_SET)
1586 # c = open(c.name, _rb_) # reopen for numpy 1.8.0-
1587 return c
1589 def _Errorf(self, fmt, *args): # PYCHOK no cover
1590 t = fmt % args
1591 e = self.pgm or NN
1592 if e:
1593 t = _SPACE_(t, _in_, repr(e))
1594 return PGMError(t)
1596 def _lle2yx2(self, lat, lon, flon):
1597 # earth (lat, lon) to grid indices (y, x)
1598 # with .dlat decreasing from 90N .slat
1599 lat -= self.slat
1600 lon += flon - self.wlon
1601 return (min(self.nlat - 1, max(0, int(lat * self.rlat))),
1602 max(0, int(lon * self.rlon)))
1604 def _tmpfile(self):
1605 # create a tmpfile to hold the cropped geoid grid
1606 try:
1607 from tempfile import NamedTemporaryFile as tmpfile
1608 except ImportError: # Python 2.7.16-
1609 from _MODS.os import tmpfile
1610 t = _MODS.os.path.basename(self.pgm)
1611 t = _MODS.os.path.splitext(t)[0]
1612 f = tmpfile(mode='w+b', prefix=t or 'egm')
1613 f.seek(0, _MODS.os.SEEK_SET) # force overwrite
1614 return f
1616 @Property_RO
1617 def pgm(self):
1618 '''Get the geoid file name (C{str}).
1619 '''
1620 return self.name
1623class PGMError(GeoidError):
1624 '''An issue while parsing or cropping an C{egm*.pgm} geoid dataset.
1625 '''
1626 pass
1629def egmGeoidHeights(GeoidHeights_dat):
1630 '''Generate geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/
1631 C++/doc/geoid.html#geoidinst>} height tests from U{GeoidHeights.dat
1632 <https://SourceForge.net/projects/geographiclib/files/testdata/>}
1633 U{Test data for Geoids<https://GeographicLib.SourceForge.io/C++/doc/
1634 geoid.html#testgeoid>}.
1636 @arg GeoidHeights_dat: The un-gz-ed C{GeoidHeights.dat} file
1637 (C{str} or C{file} handle).
1639 @return: For each test, yield a L{GeoidHeight5Tuple}C{(lat, lon,
1640 egm84, egm96, egm2008)}.
1642 @raise GeoidError: Invalid B{C{GeoidHeights_dat}}.
1644 @note: Function L{egmGeoidHeights} is used to test the geoids
1645 L{GeoidKarney} and L{GeoidPGM}, see PyGeodesy module
1646 C{test/testGeoids.py}.
1647 '''
1648 dat = GeoidHeights_dat
1649 if isinstance(dat, bytes):
1650 dat = _BytesIO(dat)
1652 try:
1653 dat.seek(0, _MODS.os.SEEK_SET) # reset
1654 except AttributeError as x:
1655 raise GeoidError(GeoidHeights_dat=type(dat), cause=x)
1657 for t in dat.readlines():
1658 t = t.strip()
1659 if t and not t.startswith(_bHASH_):
1660 lat, lon, egm84, egm96, egm2008 = map(float, t.split())
1661 while lon > _180_0: # EasternLon to earth lon
1662 lon -= _360_0
1663 yield GeoidHeight5Tuple(lat, lon, egm84, egm96, egm2008)
1666__all__ += _ALL_DOCS(_GeoidBase)
1668if __name__ == '__main__': # MCCABE 14
1670 from pygeodesy.internals import printf, _secs2str, _versions, _sys
1671 from time import time
1673 _crop = ()
1674 _GeoidEGM = GeoidKarney
1675 _kind = 3
1677 geoids = _sys.argv[1:]
1678 while geoids:
1679 geoid = geoids.pop(0)
1681 if '-crop'.startswith(geoid.lower()):
1682 _crop = 20, -125, 50, -65 # CONUS
1684 elif '-karney'.startswith(geoid.lower()):
1685 _GeoidEGM = GeoidKarney
1687 elif '-kind'.startswith(geoid.lower()):
1688 _kind = int(geoids.pop(0))
1690 elif '-pgm'.startswith(geoid.lower()):
1691 _GeoidEGM = GeoidPGM
1693 elif geoid[-4:].lower() in ('.pgm',):
1694 g = _GeoidEGM(geoid, crop=_crop, kind=_kind)
1695 t = time()
1696 _ = g.highest()
1697 t = _secs2str(time() - t)
1698 printf('%s: %s (%s)', g.toStr(), t, _versions(), nl=1, nt=1)
1699 printf(repr(g.pgm), nt=1)
1700 # <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>:
1701 # The height of the EGM96 geoid at Timbuktu
1702 # echo 16:46:33N 3:00:34W | GeoidEval
1703 # => 28.7068 -0.02e-6 -1.73e-6
1704 # The 1st number is the height of the geoid, the 2nd and
1705 # 3rd are its slopes in northerly and easterly direction
1706 t = 'Timbuktu %s' % (g,)
1707 k = {'egm84-15.pgm': '31.2979',
1708 'egm96-5.pgm': '28.7067',
1709 'egm2008-1.pgm': '28.7880'}.get(g.name.lower(), '28.7880')
1710 ll = _MODS.dms.parseDMS2('16:46:33N', '3:00:34W', sep=':')
1711 for ll in (ll, (16.776, -3.009),):
1712 try:
1713 h, ll = g.height(*ll), fstr(ll, prec=6)
1714 printf('%s.height(%s): %.4F vs %s', t, ll, h, k)
1715 except (GeoidError, RangeError) as x:
1716 printf(_COLONSPACE_(t, str(x)))
1718 elif geoid[-4:].lower() in ('.bin',):
1719 g = GeoidG2012B(geoid, kind=_kind)
1720 printf(g.toStr())
1722 else:
1723 raise GeoidError(grid=repr(geoid))
1725_I = int # PYCHOK unused _I
1726del _intCs # trash ints cache
1729# <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>
1730# _lowerleft = -90, -179, -30.1500 # egm2008-1.pgm
1731# _lowerleft = -90, -179, -29.5350 # egm96-5.pgm
1732# _lowerleft = -90, -179, -29.7120 # egm84-15.pgm
1734# _center = 0, 0, 17.2260 # egm2008-1.pgm
1735# _center = 0, 0, 17.1630 # egm96-5.pgm
1736# _center = 0, 0, 18.3296 # egm84-15.pgm
1738# _upperright = 90, 180, 14.8980 # egm2008-1.pgm
1739# _upperright = 90, 180, 13.6050 # egm96-5.pgm
1740# _upperright = 90, 180, 13.0980 # egm84-15.pgm
1743# % python3.12 -m pygeodesy.geoids -Karney ../testGeoids/egm*.pgm
1744#
1745# 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, 147.367, 85.839), lowest(4.7, 78.767, -106.911): 204.334 ms (pygeodesy 24.8.24 Python 3.12.5 64bit arm64 macOS 14.6.1)
1746#
1747# _PGM('../testGeoids/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=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.001, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008', Vertical_Datum='WGS84'
1748#
1749# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880
1750# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880
1751#
1752# 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(-4.5, 148.75, 81.33), lowest(4.75, 79.25, -107.34): 1.007 ms (pygeodesy 24.8.24 Python 3.12.5 64bit arm64 macOS 14.6.1)
1753#
1754# _PGM('../testGeoids/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=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.018, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/wgs84_180/wgs84_180.html', Vertical_Datum='WGS84'
1755#
1756# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979
1757# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979
1758#
1759# 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(-8.167, 147.25, 85.422), lowest(4.667, 78.833, -107.043): 8.509 ms (pygeodesy 24.8.24 Python 3.12.5 64bit arm64 macOS 14.6.1)
1760#
1761# _PGM('../testGeoids/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=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.005, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm96/egm96.html', Vertical_Datum='WGS84'
1762#
1763# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067
1764# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067
1767# % python3.8 -m pygeodesy.geoids -Karney ../testGeoids/egm*.pgm
1768#
1769# 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, 147.367, 85.839), lowest(4.7, 78.767, -106.911): 353.050 ms (pygeodesy 24.8.24 Python 3.8.10 64bit arm64_x86_64 macOS 10.16)
1770#
1771# _PGM('../testGeoids/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=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.001, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008', Vertical_Datum='WGS84'
1772#
1773# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880
1774# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880
1775#
1776# 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(-4.5, 148.75, 81.33), lowest(4.75, 79.25, -107.34): 1.727 ms (pygeodesy 24.8.24 Python 3.8.10 64bit arm64_x86_64 macOS 10.16)
1777#
1778# _PGM('../testGeoids/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=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.018, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/wgs84_180/wgs84_180.html', Vertical_Datum='WGS84'
1779#
1780# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979
1781# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979
1782#
1783# 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(-8.167, 147.25, 85.422), lowest(4.667, 78.833, -107.043): 14.807 ms (pygeodesy 24.8.24 Python 3.8.10 64bit arm64_x86_64 macOS 10.16)
1784#
1785# _PGM('../testGeoids/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=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.005, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm96/egm96.html', Vertical_Datum='WGS84'
1786#
1787# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067
1788# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067
1791# % python2 -m pygeodesy.geoids -Karney ../testGeoids/egm*.pgm
1792#
1793# 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, 147.367, 85.839), lowest(4.7, 78.767, -106.911): 283.362 ms (pygeodesy 24.8.24 Python 2.7.18 64bit arm64_x86_64 macOS 10.16)
1794#
1795# _PGM('../testGeoids/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=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.001, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008', Vertical_Datum='WGS84'
1796#
1797# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880
1798# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880
1799#
1800# 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(-4.5, 148.75, 81.33), lowest(4.75, 79.25, -107.34): 1.378 ms (pygeodesy 24.8.24 Python 2.7.18 64bit arm64_x86_64 macOS 10.16)
1801#
1802# _PGM('../testGeoids/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=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.018, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/wgs84_180/wgs84_180.html', Vertical_Datum='WGS84'
1803#
1804# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979
1805# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979
1806#
1807# 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(-8.167, 147.25, 85.422), lowest(4.667, 78.833, -107.043): 11.612 ms (pygeodesy 24.8.24 Python 2.7.18 64bit arm64_x86_64 macOS 10.16)
1808#
1809# _PGM('../testGeoids/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=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.005, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm96/egm96.html', Vertical_Datum='WGS84'
1810#
1811# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067
1812# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067
1815# % python3.12 -m pygeodesy.geoids -PGM ../testGeoids/egm*.pgm
1816#
1817# 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): 543.148 ms (pygeodesy 24.8.24 Python 3.12.5 64bit arm64 macOS 14.6.1)
1818#
1819# _PGM('../testGeoids/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=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.001, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008', Vertical_Datum='WGS84'
1820#
1821# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880
1822# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880
1823#
1824# 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): 1.762 ms (pygeodesy 24.8.24 Python 3.12.5 64bit arm64 macOS 14.6.1)
1825#
1826# _PGM('../testGeoids/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=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.018, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/wgs84_180/wgs84_180.html', Vertical_Datum='WGS84'
1827#
1828# Timbuktu GeoidPGM('egm84-15.pgm').height(16.775833, -3.009444): 31.2979 vs 31.2979
1829# Timbuktu GeoidPGM('egm84-15.pgm').height(16.776, -3.009): 31.2975 vs 31.2979
1830#
1831# 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): 12.594 ms (pygeodesy 24.8.24 Python 3.12.5 64bit arm64 macOS 14.6.1)
1832#
1833# _PGM('../testGeoids/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=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.005, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm96/egm96.html', Vertical_Datum='WGS84'
1834#
1835# Timbuktu GeoidPGM('egm96-5.pgm').height(16.775833, -3.009444): 28.7065 vs 28.7067
1836# Timbuktu GeoidPGM('egm96-5.pgm').height(16.776, -3.009): 28.7064 vs 28.7067
1838# **) MIT License
1839#
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