Coverage for pygeodesy/geoids.py: 96%
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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{>>> h0, h1, h2, ... = ginterpolator(ll0, ll1, ll2, ...)}
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
67 C{scipy} can be thrown as L{SciPyWarning} exceptions, provided Python
68 C{warnings} are filtered 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.
75 interpolate.RectBivariateSpline.html>} and U{interp2d<https://docs.SciPy.org/doc/scipy/
76 reference/generated/scipy.interpolate.interp2d.html>}, functions L{elevations.elevation2}
77 and L{elevations.geoidHeight2}, U{I{Ellispoid vs Orthometric Elevations}<https://
78 www.YouTube.com/watch?v=dX6a6kCk3Po>} and U{I{Pitfalls Related to Ellipsoid Height
79 and Height Above Mean Sea Level (AMSL)}<https://Wiki.ROS.org/mavros#mavros.2FPlugins.
80 Avoiding_Pitfalls_Related_to_Ellipsoid_Height_and_Height_Above_Mean_Sea_Level>}.
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, _0_0, _1_0, _180_0, _360_0
87# from pygeodesy.datums import _ellipsoidal_datum # from .heights
88# from pygeodesy.dms import parseDMS2 # _MODS
89from pygeodesy.errors import _incompatible, LenError, RangeError, SciPyError, \
90 _SciPyIssue, _xkwds_pop2
91from pygeodesy.fmath import favg, Fdot, fdot, Fhorner, frange
92# from pygoedesy.formy import heightOrthometric # _MODS
93from pygeodesy.heights import _as_llis2, _ascalar, _height_called, HeightError, \
94 _HeightsBase, _ellipsoidal_datum, _Wrap
95# from pygeodesy.internals import _version2 # _MODS
96from pygeodesy.interns import MISSING, NN, _4_, _COLONSPACE_, _COMMASPACE_, _cubic_, \
97 _E_, _height_, _in_, _kind_, _lat_, _linear_, _lon_, \
98 _mean_, _N_, _n_a_, _numpy_, _on_, _outside_, _S_, _s_, \
99 _scipy_, _SPACE_, _stdev_, _tbd_, _W_, _width_
100from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _FOR_DOCS
101from pygeodesy.named import _name__, _Named, _NamedTuple
102# from pygeodesy.namedTuples import LatLon3Tuple # _MODS
103from pygeodesy.props import deprecated_method, Property_RO, property_RO, property_ROver
104from pygeodesy.streprs import attrs, Fmt, fstr, pairs
105from pygeodesy.units import Height, Int_, Lat, Lon
106# from pygeodesy.utily import _Wrap # from .heights
108from math import floor
109import os.path as _os_path
110from os import SEEK_CUR as _SEEK_CUR, SEEK_SET as _SEEK_SET
111from struct import calcsize as _calcsize, unpack as _unpack
112try:
113 from StringIO import StringIO as _BytesIO # reads bytes
114 _ub2str = str # PYCHOK convert bytes to str for egm*.pgm text
116except ImportError: # Python 3+
117 from io import BytesIO as _BytesIO # PYCHOK expected
119__all__ = _ALL_LAZY.geoids
120__version__ = '24.07.12'
122_assert_ = 'assert'
123_bHASH_ = b'#'
124_endian_ = 'endian'
125_format_ = '%s %r'
126_header_ = 'header'
127_intCs = {} # cache int value
128_interp2d_ks = {-2: _linear_,
129 -3: _cubic_,
130 -5: 'quintic'}
131_lli_ = 'lli'
132_non_increasing_ = 'non-increasing'
133_rb_ = 'rb'
134_supported_ = 'supported'
137class _GeoidBase(_HeightsBase):
138 '''(INTERNAL) Base class for C{Geoid...}s.
139 '''
140 _cropped = None
141# _datum = _WGS84 # from _HeightsBase
142 _egm = None # open C{egm*.pgm} geoid file
143 _endian = _tbd_
144 _geoid = _n_a_
145 _hs_y_x = None # numpy 2darray, row-major order
146 _interp2d = None # interp2d interpolation
147 _kind = 3 # order for interp2d, RectBivariateSpline
148# _kmin = 2 # min number of knots
149 _knots = 0 # nlat * nlon
150 _mean = None # fixed in GeoidKarney
151# _name = NN # _Named
152 _nBytes = 0 # numpy size in bytes, float64
153 _pgm = None # PGM attributes, C{_PGM} or C{None}
154 _sizeB = 0 # geoid file size in bytes
155 _smooth = 0 # used only for RectBivariateSpline
156 _stdev = None # fixed in GeoidKarney
157 _u2B = 0 # np.itemsize or undefined
159 _lat_d = _0_0 # increment, +tive
160 _lat_lo = _0_0 # lower lat, south
161 _lat_hi = _0_0 # upper lat, noth
162 _lon_d = _0_0 # increment, +tive
163 _lon_lo = _0_0 # left lon, west
164 _lon_hi = _0_0 # right lon, east
165 _lon_of = _0_0 # forward lon offset
166 _lon_og = _0_0 # reverse lon offset
168 _center = None # (lat, lon, height)
169 _yx_hits = None # cache hits, ala Karney
171 def __init__(self, hs, p):
172 '''(INTERNAL) Set up the grid axes, the C{SciPy} interpolator
173 and several internal geoid attributes.
175 @arg hs: Grid knots with known height (C{numpy 2darray}).
176 @arg p: The C{slat, wlon, nlat, nlon, dlat, dlon} and
177 other geoid parameters (C{INTERNAL}).
179 @raise GeoidError: Incompatible grid B{C{hs}} shape or
180 invalid B{C{kind}}.
182 @raise LenError: Mismatch grid B{C{hs}} axis.
184 @raise SciPyError: A C{scipy.interpolate.inter2d} or
185 C{-.RectBivariateSpline} issue.
187 @raise SciPyWarning: A C{scipy.interpolate.inter2d} or
188 C{-.RectBivariateSpline} warning as
189 exception.
191 @note: C{scipy.interpolate.interp2d} has been C{DEPRECATED},
192 specify keyword argument C{B{kind}=1..5} to use
193 C{scipy.interpolate.RectBivariateSpline}.
194 '''
195 spi = self.scipy_interpolate
196 # for 2d scipy.interpolate.interp2d(xs, ys, hs, ...) and
197 # scipy.interpolate.RectBivariateSpline(ys, xs, hs, ...)
198 # require the shape of hs to be (len(ys), len(xs)), note
199 # the different (xs, ys, ...) and (ys, xs, ...) orders
200 if (p.nlat, p.nlon) != hs.shape:
201 raise GeoidError(shape=hs.shape, txt=_incompatible((p.nlat, p.nlon)))
203 # both axes and bounding box
204 ys, self._lat_d = self._gaxis2(p.slat, p.dlat, p.nlat, _lat_ + _s_)
205 xs, self._lon_d = self._gaxis2(p.wlon, p.dlon, p.nlon, _lon_ + _s_)
207 bb = ys[0], ys[-1], xs[0], xs[-1] + p.dlon # fudge lon_hi
208 # geoid grids are typically stored in row-major order, some
209 # with rows (90..-90) reversed and columns (0..360) wrapped
210 # to Easten longitude, 0 <= east < 180 and 180 <= west < 360
211 k = self.kind
212 if k in _interp2d_ks: # .interp2d DEPRECATED since scipy 1.10
213 if self._scipy_version() < (1, 10):
214 self._interp2d = spi.interp2d(xs, ys, hs, kind=_interp2d_ks[k])
215 else: # call and overwrite the DEPRECATED .interp2d
216 self._interp2d = self._interp2d(xs, ys, hs, k)
217 elif 1 <= k <= 5:
218 self._ev = spi.RectBivariateSpline(ys, xs, hs, bbox=bb, ky=k, kx=k,
219 s=self._smooth).ev
220 else:
221 raise GeoidError(kind=k)
223 self._hs_y_x = hs # numpy 2darray, row-major
224 self._nBytes = hs.nbytes # numpy size in bytes
225 self._knots = p.knots # grid knots
226 self._lon_of = float(p.flon) # forward offset
227 self._lon_og = float(p.glon) # reverse offset
228 # shrink the box by 1 unit on every side
229 # bb += self._lat_d, -self._lat_d, self._lon_d, -self._lon_d
230 self._lat_lo = float(bb[0])
231 self._lat_hi = float(bb[1])
232 self._lon_lo = float(bb[2] - p.glon)
233 self._lon_hi = float(bb[3] - p.glon)
235 def __call__(self, *llis, **wrap_H):
236 '''Interpolate the geoid height for one or several locations.
238 @arg llis: One or more locations (C{LatLon}s), all positional.
239 @kwarg wrap_H: Keyword arguments C{B{wrap}=False} (C{bool}) and
240 C{B{H}=False} (C{bool}). If C{B{wrap} is True},
241 wrap or I{normalize} all B{C{llis}} locations. If
242 C{B{H} is True}, return the I{orthometric} height
243 instead of the I{geoid} height at each location.
245 @return: A single interpolated geoid (or orthometric) height
246 (C{float}) or a list or tuple of interpolated geoid
247 (or orthometric) heights (C{float}s).
249 @raise GeoidError: Insufficient number of B{C{llis}}, an
250 invalid B{C{lli}} or the C{egm*.pgm}
251 geoid file is closed.
253 @raise RangeError: An B{C{lli}} is outside this geoid's lat-
254 or longitude range.
256 @raise SciPyError: A C{scipy.interpolate.inter2d} or
257 C{-.RectBivariateSpline} issue.
259 @raise SciPyWarning: A C{scipy.interpolate.inter2d} or
260 C{-.RectBivariateSpline} warning as
261 exception.
263 @note: To obtain I{orthometric} heights, each B{C{llis}}
264 location must have an ellipsoid C{height} or C{h}
265 attribute, otherwise C{height=0} is used.
267 @see: Function L{pygeodesy.heightOrthometric}.
268 '''
269 return self._called(llis, True, **wrap_H)
271 def __enter__(self):
272 '''Open context.
273 '''
274 return self
276 def __exit__(self, *unused): # PYCHOK exc_type, exc_value, exc_traceback)
277 '''Close context.
278 '''
279 self.close()
280 # return None # XXX False
282 def __repr__(self):
283 return self.toStr()
285 def __str__(self):
286 return Fmt.PAREN(self.classname, repr(self.name))
288 def _called(self, llis, scipy, wrap=False, H=False):
289 # handle __call__
290 _H = _MODS.formy.heightOrthometric if H else None
291 _as, llis = _as_llis2(llis, Error=GeoidError)
292 hs, _w = [], _Wrap._latlonop(wrap)
293 _a, _h = hs.append, self._hGeoid
294 try:
295 for i, lli in enumerate(llis):
296 N = _h(*_w(lli.lat, lli.lon))
297 # orthometric or geoid height
298 _a(_H(lli, N) if _H else N)
299 return _as(hs)
301 except (GeoidError, RangeError) as x:
302 # XXX avoid str(LatLon()) degree symbols
303 t = _lli_ if _as is _ascalar else Fmt.INDEX(llis=i)
304 lli = fstr((lli.lat, lli.lon), strepr=repr)
305 raise type(x)(t, lli, wrap=wrap, H=H, cause=x)
306 except Exception as x:
307 if scipy and self.scipy:
308 raise _SciPyIssue(x)
309 else:
310 raise
312 @Property_RO
313 def _center(self):
314 ''' Cache for method L{center}.
315 '''
316 return self._llh3(favg(self._lat_lo, self._lat_hi),
317 favg(self._lon_lo, self._lon_hi))
319 def center(self, LatLon=None):
320 '''Return the center location and height of this geoid.
322 @kwarg LatLon: Optional class to return the location and height
323 (C{LatLon}) or C{None}.
325 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,
326 height)} otherwise a B{C{LatLon}} instance with the lat-,
327 longitude and geoid height of the center grid location.
328 '''
329 return self._llh3LL(self._center, LatLon)
331 def close(self):
332 '''Close the C{egm*.pgm} geoid file if open (and applicable).
333 '''
334 if not self.closed:
335 self._egm.close()
336 self._egm = None
338 @property_RO
339 def closed(self):
340 '''Get the C{egm*.pgm} geoid file status.
341 '''
342 return self._egm is None
344 @Property_RO
345 def cropped(self):
346 '''Is geoid cropped (C{bool} or C{None} if crop not supported).
347 '''
348 return self._cropped
350 @Property_RO
351 def dtype(self):
352 '''Get the grid C{scipy} U{dtype<https://docs.SciPy.org/doc/numpy/
353 reference/generated/numpy.ndarray.dtype.html>} (C{numpy.dtype}).
354 '''
355 return self._hs_y_x.dtype
357 @Property_RO
358 def endian(self):
359 '''Get the geoid endianess and U{dtype<https://docs.SciPy.org/
360 doc/numpy/reference/generated/numpy.dtype.html>} (C{str}).
361 '''
362 return self._endian
364 def _ev(self, y, x): # PYCHOK expected
365 # only used for .interpolate.interp2d, but
366 # overwritten for .RectBivariateSpline,
367 # note (y, x) must be flipped!
368 return self._interp2d(x, y)
370 def _gaxis2(self, lo, d, n, name):
371 # build grid axis, hi = lo + (n - 1) * d
372 m, a = len2(frange(lo, n, d))
373 if m != n:
374 raise LenError(self.__class__, grid=m, **{name: n})
375 if d < 0:
376 d, a = -d, list(reversed(a))
377 for i in range(1, m):
378 e = a[i] - a[i-1]
379 if e < EPS: # non-increasing axis
380 i = Fmt.INDEX(name, i)
381 raise GeoidError(i, e, txt=_non_increasing_)
382 return self.numpy.array(a), d
384 def _g2ll2(self, lat, lon): # PYCHOK no cover
385 '''(INTERNAL) I{Must be overloaded}.'''
386 self._notOverloaded(lat, lon)
388 def _gyx2g2(self, y, x):
389 # convert grid (y, x) indices to grid (lat, lon)
390 return ((self._lat_lo + self._lat_d * y),
391 (self._lon_lo + self._lon_of + self._lon_d * x))
393 def height(self, lats, lons, **wrap):
394 '''Interpolate the geoid height for one or several lat-/longitudes.
396 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s).
397 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s).
398 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{lats}}
399 and B{C{lons}} locations (C{bool}).
401 @return: A single interpolated geoid height (C{float}) or a
402 list of interpolated geoid heights (C{float}s).
404 @raise GeoidError: Insufficient or non-matching number of
405 B{C{lats}} and B{C{lons}}.
407 @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this
408 geoid's lat- or longitude range.
410 @raise SciPyError: A C{scipy.interpolate.inter2d} or
411 C{-.RectBivariateSpline} issue.
413 @raise SciPyWarning: A C{scipy.interpolate.inter2d} or
414 C{-.RectBivariateSpline} warning as
415 exception.
416 '''
417 return _height_called(self, lats, lons, Error=GeoidError, **wrap)
419 def _hGeoid(self, lat, lon):
420 out = self.outside(lat, lon)
421 if out:
422 lli = fstr((lat, lon), strepr=repr)
423 raise RangeError(lli=lli, txt=_SPACE_(_outside_, _on_, out))
424 return float(self._ev(*self._ll2g2(lat, lon)))
426 @Property_RO
427 def _highest(self):
428 '''(INTERNAL) Cache for L{highest} method.
429 '''
430 return self._llh3minmax(True)
432 def highest(self, LatLon=None, **unused):
433 '''Return the location and largest height of this geoid.
435 @kwarg LatLon: Optional class to return the location and height
436 (C{LatLon}) or C{None}.
438 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,
439 height)} otherwise a B{C{LatLon}} instance with the lat-,
440 longitude and geoid height of the highest grid location.
441 '''
442 return self._llh3LL(self._highest, LatLon)
444 @Property_RO
445 def hits(self):
446 '''Get the number of cache hits (C{int} or C{None}).
447 '''
448 return self._yx_hits
450 @deprecated_method
451 def _interp2d(self, xs, ys, hs=(), k=0): # overwritten in .__init__ above
452 '''DEPRECATED on 23.01.06, use keyword argument C{B{kind}=1..5}.'''
453 # assert k in _interp2d_ks # and len(hs) == len(xs) == len(ys)
454 try:
455 return self.scipy_interpolate.interp2d(xs, ys, hs, kind=_interp2d_ks[k])
456 except AttributeError as x:
457 raise SciPyError(interp2d=MISSING, kind=k, cause=x)
459 @Property_RO
460 def kind(self):
461 '''Get the interpolator kind and order (C{int}).
462 '''
463 return self._kind
465 @Property_RO
466 def knots(self):
467 '''Get the number of grid knots (C{int}).
468 '''
469 return self._knots
471 def _ll2g2(self, lat, lon): # PYCHOK no cover
472 '''(INTERNAL) I{Must be overloaded}.'''
473 self._notOverloaded(lat, lon)
475 @property_ROver
476 def _LL3T(self):
477 '''(INTERNAL) Get L{LatLon3Tuple}, I{once}.
478 '''
479 return _MODS.namedTuples.LatLon3Tuple # overwrite property_ROver
481 def _llh3(self, lat, lon):
482 return self._LL3T(lat, lon, self._hGeoid(lat, lon), name=self.name)
484 def _llh3LL(self, llh, LatLon):
485 return llh if LatLon is None else self._xnamed(LatLon(*llh))
487 def _llh3minmax(self, highest=True, *unused):
488 hs, np = self._hs_y_x, self.numpy
489 # <https://docs.SciPy.org/doc/numpy/reference/generated/
490 # numpy.argmin.html#numpy.argmin>
491 arg = np.argmax if highest else np.argmin
492 y, x = np.unravel_index(arg(hs, axis=None), hs.shape)
493 return self._g2ll2(*self._gyx2g2(y, x)) + (float(hs[y, x]),)
495 def _load(self, g, dtype, n, offset=0):
496 # numpy.fromfile, like .frombuffer
497 g.seek(offset, _SEEK_SET)
498 return self.numpy.fromfile(g, dtype, n)
500 @Property_RO
501 def _lowerleft(self):
502 '''(INTERNAL) Cache for L{lowerleft}.
503 '''
504 return self._llh3(self._lat_lo, self._lon_lo)
506 def lowerleft(self, LatLon=None):
507 '''Return the lower-left location and height of this geoid.
509 @kwarg LatLon: Optional class to return the location
510 (C{LatLon}) and height or C{None}.
512 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)}
513 otherwise a B{C{LatLon}} instance with the lat-, longitude and
514 geoid height of the lower-left, SW grid corner.
515 '''
516 return self._llh3LL(self._lowerleft, LatLon)
518 @Property_RO
519 def _loweright(self):
520 '''(INTERNAL) Cache for L{loweright}.
521 '''
522 return self._llh3(self._lat_lo, self._lon_hi)
524 def loweright(self, LatLon=None):
525 '''Return the lower-right location and height of this geoid.
527 @kwarg LatLon: Optional class to return the location and height
528 (C{LatLon}) or C{None}.
530 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)}
531 otherwise a B{C{LatLon}} instance with the lat-, longitude and
532 geoid height of the lower-right, SE grid corner.
533 '''
535 return self._llh3LL(self._loweright, LatLon)
537 lowerright = loweright # synonymous
539 @Property_RO
540 def _lowest(self):
541 '''(INTERNAL) Cache for L{lowest}.
542 '''
543 return self._llh3minmax(False)
545 def lowest(self, LatLon=None, **unused):
546 '''Return the location and lowest height of this geoid.
548 @kwarg LatLon: Optional class to return the location and height
549 (C{LatLon}) or C{None}.
551 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,
552 height)} otherwise a B{C{LatLon}} instance with the lat-,
553 longitude and geoid height of the lowest grid location.
554 '''
555 return self._llh3LL(self._lowest, LatLon)
557 @Property_RO
558 def mean(self):
559 '''Get the mean of this geoid's heights (C{float}).
560 '''
561 if self._mean is None: # see GeoidKarney
562 self._mean = float(self.numpy.mean(self._hs_y_x))
563 return self._mean
565 @property_RO
566 def name(self):
567 '''Get the name of this geoid (C{str}).
568 '''
569 return _HeightsBase.name.fget(self) or self._geoid # recursion
571 @Property_RO
572 def nBytes(self):
573 '''Get the grid in-memory size in bytes (C{int}).
574 '''
575 return self._nBytes
577 def _open(self, geoid, datum, kind, name, smooth):
578 # open the geoid file
579 try:
580 self._geoid = _os_path.basename(geoid)
581 self._sizeB = _os_path.getsize(geoid)
582 g = open(geoid, _rb_)
583 except (IOError, OSError) as x:
584 raise GeoidError(geoid=geoid, cause=x)
586 if datum not in (None, self._datum):
587 self._datum = _ellipsoidal_datum(datum, name=name)
588 self._kind = int(kind)
589 if name:
590 _HeightsBase.name.fset(self, name) # rename
591 if smooth:
592 self._smooth = Int_(smooth=smooth, Error=GeoidError, low=0)
594 return g
596 def outside(self, lat, lon):
597 '''Check whether a location is outside this geoid's
598 lat-/longitude or crop range.
600 @arg lat: The latitude (C{degrees}).
601 @arg lon: The longitude (C{degrees}).
603 @return: A 1- or 2-character C{str} if outside or an
604 empty C{str} if inside.
605 '''
606 return (_S_ if lat < self._lat_lo else
607 (_N_ if lat > self._lat_hi else NN)) + \
608 (_W_ if lon < self._lon_lo else
609 (_E_ if lon > self._lon_hi else NN))
611 @Property_RO
612 def pgm(self):
613 '''Get the PGM attributes (C{_PGM} or C{None} if not available/applicable).
614 '''
615 return self._pgm
617 @Property_RO
618 def sizeB(self):
619 '''Get the geoid grid file size in bytes (C{int}).
620 '''
621 return self._sizeB
623 @Property_RO
624 def smooth(self):
625 '''Get the C{RectBivariateSpline} smoothing (C{int}).
626 '''
627 return self._smooth
629 @Property_RO
630 def stdev(self):
631 '''Get the standard deviation of this geoid's heights (C{float}) or C{None}.
632 '''
633 if self._stdev is None: # see GeoidKarney
634 self._stdev = float(self.numpy.std(self._hs_y_x))
635 return self._stdev
637 def _swne(self, crop):
638 # crop box to 4-tuple (s, w, n, e)
639 try:
640 if len(crop) == 2:
641 try: # sw, ne LatLons
642 swne = (crop[0].lat, crop[0].lon,
643 crop[1].lat, crop[1].lon)
644 except AttributeError: # (s, w), (n, e)
645 swne = tuple(crop[0]) + tuple(crop[1])
646 else: # (s, w, n, e)
647 swne = crop
648 if len(swne) == 4:
649 s, w, n, e = map(float, swne)
650 if -90 <= s <= (n - _1_0) <= 89 and \
651 -180 <= w <= (e - _1_0) <= 179:
652 return s, w, n, e
653 except (IndexError, TypeError, ValueError):
654 pass
655 raise GeoidError(crop=crop)
657 def toStr(self, prec=3, sep=_COMMASPACE_): # PYCHOK signature
658 '''This geoid and all geoid attributes as a string.
660 @kwarg prec: Number of decimal digits (0..9 or C{None} for
661 default). Trailing zero decimals are stripped
662 for B{C{prec}} values of 1 and above, but kept
663 for negative B{C{prec}} values.
664 @kwarg sep: Separator to join (C{str}).
666 @return: Geoid name and attributes (C{str}).
667 '''
668 s = 1 if self.kind < 0 else 2
669 t = tuple(Fmt.PAREN(m.__name__, fstr(m(), prec=prec)) for m in
670 (self.lowerleft, self.upperright,
671 self.center,
672 self.highest, self.lowest)) + \
673 attrs( _mean_, _stdev_, prec=prec, Nones=False) + \
674 attrs((_kind_, 'smooth')[:s], prec=prec, Nones=False) + \
675 attrs( 'cropped', 'dtype', _endian_, 'hits', 'knots', 'nBytes',
676 'sizeB', _scipy_, _numpy_, prec=prec, Nones=False)
677 return _COLONSPACE_(self, sep.join(t))
679 @Property_RO
680 def u2B(self):
681 '''Get the PGM itemsize in bytes (C{int}).
682 '''
683 return self._u2B
685 @Property_RO
686 def _upperleft(self):
687 '''(INTERNAL) Cache for method L{upperleft}.
688 '''
689 return self._llh3(self._lat_hi, self._lon_lo)
691 def upperleft(self, LatLon=None):
692 '''Return the upper-left location and height of this geoid.
694 @kwarg LatLon: Optional class to return the location and height
695 (C{LatLon}) or C{None}.
697 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)}
698 otherwise a B{C{LatLon}} instance with the lat-, longitude and
699 geoid height of the upper-left, NW grid corner.
700 '''
701 return self._llh3LL(self._upperleft, LatLon)
703 @Property_RO
704 def _upperright(self):
705 '''(INTERNAL) Cache for method L{upperright}.
706 '''
707 return self._llh3(self._lat_hi, self._lon_hi)
709 def upperright(self, LatLon=None):
710 '''Return the upper-right location and height of this geoid.
712 @kwarg LatLon: Optional class to return the location and height
713 (C{LatLon}) or C{None}.
715 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)}
716 otherwise a B{C{LatLon}} instance with the lat-, longitude and
717 geoid height of the upper-right, NE grid corner.
718 '''
719 return self._llh3LL(self._upperright, LatLon)
722class GeoidError(HeightError):
723 '''Geoid interpolator C{Geoid...} or interpolation issue.
724 '''
725 pass
728class GeoidG2012B(_GeoidBase):
729 '''Geoid height interpolator for U{GEOID12B Model
730 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/>} grids U{CONUS
731 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_CONUS.shtml>},
732 U{Alaska<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_AK.shtml>},
733 U{Hawaii<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_HI.shtml>},
734 U{Guam and Northern Mariana Islands
735 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_GMNI.shtml>},
736 U{Puerto Rico and U.S. Virgin Islands
737 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_PRVI.shtml>} and
738 U{American Samoa<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_AS.shtml>}
739 based on C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/doc/
740 scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>}
741 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/
742 scipy.interpolate.interp2d.html>} interpolation.
744 Use any of the binary C{le} (little endian) or C{be} (big endian)
745 C{g2012b*.bin} grid files.
746 '''
747 def __init__(self, g2012b_bin, datum=None, # NAD 83 Ellipsoid
748 kind=3, smooth=0, **name_crop):
749 '''New L{GeoidG2012B} interpolator.
751 @arg g2012b_bin: A C{GEOID12B} grid file name (C{.bin}).
752 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
753 or L{a_f2Tuple}), default C{WGS84}.
754 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for
755 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/
756 reference/generated/scipy.interpolate.RectBivariateSpline.html>},
757 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/
758 reference/generated/scipy.interpolate.interp2d.html>}, -3
759 for C{interp2d cubic} or -5 for C{interp2d quintic}.
760 @kwarg smooth: Smoothing factor for U{RectBivariateSpline
761 <https://docs.SciPy.org/doc/scipy/reference/generated/
762 scipy.interpolate.RectBivariateSpline.html>}
763 only (C{int}).
764 @kwarg name_crop: Optional geoid C{B{name}=NN} (C{str}) and UNSUPPORTED
765 keyword argument C{B{crop}}, use C{B{crop}=None} to ignore.
767 @raise GeoidError: G2012B grid file B{C{g2012b_bin}} issue or invalid
768 B{C{crop}}, B{C{kind}} or B{C{smooth}}.
770 @raise ImportError: Package C{numpy} or C{scipy} not found or not
771 installed.
773 @raise LenError: Grid file B{C{g2012b_bin}} axis mismatch.
775 @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue.
777 @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d}
778 warning as exception.
780 @raise TypeError: Invalid B{C{datum}}.
782 @note: C{scipy.interpolate.interp2d} has been C{DEPRECATED}, specify
783 C{B{kind}=1..5} for C{scipy.interpolate.RectBivariateSpline}.
784 '''
785 crop, name = _xkwds_pop2(name_crop, crop=None)
786 if crop is not None:
787 raise GeoidError(crop=crop, txt_not_=_supported_)
789 g = self._open(g2012b_bin, datum, kind, _name__(**name), smooth)
790 _ = self.numpy # import numpy for ._load and
792 try:
793 p = _Gpars()
794 n = (self.sizeB // 4) - 11 # number of f4 heights
795 # U{numpy dtype formats are different from Python struct formats
796 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>}
797 for en_ in ('<', '>'):
798 # skip 4xf8, get 3xi4
799 p.nlat, p.nlon, ien = map(int, self._load(g, en_+'i4', 3, 32))
800 if ien == 1: # correct endian
801 p.knots = p.nlat * p.nlon
802 if p.knots == n and 1 < p.nlat < n \
803 and 1 < p.nlon < n:
804 self._endian = en_+'f4'
805 break
806 else: # couldn't validate endian
807 raise GeoidError(_endian_)
809 # get the first 4xf8
810 p.slat, p.wlon, p.dlat, p.dlon = map(float, self._load(g, en_+'f8', 4))
811 # read all f4 heights, ignoring the first 4xf8 and 3xi4
812 hs = self._load(g, self._endian, n, 44).reshape(p.nlat, p.nlon)
813 p.wlon -= _360_0 # western-most East longitude to earth (..., lon)
814 _GeoidBase.__init__(self, hs, p)
816 except Exception as x:
817 raise _SciPyIssue(x, _in_, repr(g2012b_bin))
818 finally:
819 g.close()
821 def _g2ll2(self, lat, lon):
822 # convert grid (lat, lon) to earth (lat, lon)
823 return lat, lon
825 def _ll2g2(self, lat, lon):
826 # convert earth (lat, lon) to grid (lat, lon)
827 return lat, lon
829 if _FOR_DOCS:
830 __call__ = _GeoidBase.__call__
831 height = _GeoidBase.height
834class GeoidHeight5Tuple(_NamedTuple): # .geoids.py
835 '''5-Tuple C{(lat, lon, egm84, egm96, egm2008)} for U{GeoidHeights.dat
836 <https://SourceForge.net/projects/geographiclib/files/testdata/>}
837 tests with the heights for 3 different EGM grids at C{degrees90}
838 and C{degrees180} degrees (after converting C{lon} from original
839 C{0 <= EasterLon <= 360}).
840 '''
841 _Names_ = (_lat_, _lon_, 'egm84', 'egm96', 'egm2008')
842 _Units_ = ( Lat, Lon, Height, Height, Height)
845def _I(i):
846 '''(INTERNAL) Cache a single C{int} constant.
847 '''
848 return _intCs.setdefault(i, i) # PYCHOK undefined due to del _intCs
851def _T(*cs):
852 '''(INTERNAL) Cache a tuple of single C{int} constants.
853 '''
854 return map1(_I, *cs)
856_T0s12 = (_I(0),) * 12 # PYCHOK _T(0, 0, ..., 0)
859class GeoidKarney(_GeoidBase):
860 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth
861 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/
862 geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/
863 C++/doc/geoid.html#geoidinst>} datasets using bilinear or U{cubic
864 <https://dl.ACM.org/citation.cfm?id=368443>} interpolation and U{caching
865 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidcache>}
866 in pure Python, transcoded from I{Karney}'s U{C++ class Geoid
867 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinterp>}.
869 Use any of the geoid U{egm84-, egm96- or egm2008-*.pgm
870 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>}
871 datasets.
872 '''
873 _C0 = _F(372), _F(240), _F(372) # n, _ and s common denominators
874 # matrices c3n_, c3, c3s_, transposed from GeographicLib/Geoid.cpp
875 _C3 = ((_T(0, 0, 62, 124, 124, 62, 0, 0, 0, 0, 0, 0),
876 _T0s12,
877 _T(-131, 7, -31, -62, -62, -31, 45, 216, 156, -45, -55, -7),
878 _T0s12,
879 _T(138, -138, 0, 0, 0, 0, -183, 33, 153, -3, 48, -48), # PYCHOK indent
880 _T(144, 42, -62, -124, -124, -62, -9, 87, 99, 9, 42, -42),
881 _T0s12,
882 _T(0, 0, 0, 0, 0, 0, 93, -93, -93, 93, 0, 0),
883 _T(-102, 102, 0, 0, 0, 0, 18, 12, -12, -18, -84, 84),
884 _T(-31, -31, 31, 62, 62, 31, 0, -93, -93, 0, 31, 31)), # PYCHOK indent
886 (_T(9, -9, 9, 186, 54, -9, -9, 54, -54, 9, -9, 9),
887 _T(-18, 18, -88, -42, 162, -32, 8, -78, 78, -8, 18, -18),
888 _T(-88, 8, -18, -42, -78, 18, 18, 162, 78, -18, -32, -8),
889 _T(0, 0, 90, -150, 30, 30, 30, -90, 90, -30, 0, 0),
890 _T(96, -96, 96, -96, -24, 24, -96, -24, 144, -24, 24, -24), # PYCHOK indent
891 _T(90, 30, 0, -150, -90, 0, 0, 30, 90, 0, 30, -30),
892 _T(0, 0, -20, 60, -60, 20, -20, 60, -60, 20, 0, 0),
893 _T(0, 0, -60, 60, 60, -60, 60, -60, -60, 60, 0, 0),
894 _T(-60, 60, 0, 60, -60, 0, 0, 60, -60, 0, -60, 60),
895 _T(-20, -20, 0, 60, 60, 0, 0, -60, -60, 0, 20, 20)),
897 (_T(18, -18, 36, 210, 162, -36, 0, 0, 0, 0, -18, 18), # PYCHOK indent
898 _T(-36, 36, -165, 45, 141, -21, 0, 0, 0, 0, 36, -36),
899 _T(-122, -2, -27, -111, -75, 27, 62, 124, 124, 62, -64, 2),
900 _T(0, 0, 93, -93, -93, 93, 0, 0, 0, 0, 0, 0),
901 _T(120, -120, 147, -57, -129, 39, 0, 0, 0, 0, 66, -66), # PYCHOK indent
902 _T(135, 51, -9, -192, -180, 9, 31, 62, 62, 31, 51, -51),
903 _T0s12,
904 _T(0, 0, -93, 93, 93, -93, 0, 0, 0, 0, 0, 0),
905 _T(-84, 84, 18, 12, -12, -18, 0, 0, 0, 0, -102, 102),
906 _T(-31, -31, 0, 93, 93, 0, -31, -62, -62, -31, 31, 31)))
908 _BT = (_T(0, 0), # bilinear 4-tuple [i, j] indices
909 _T(1, 0),
910 _T(0, 1),
911 _T(1, 1))
913 _CM = (_T( 0, -1), # 10x12 cubic matrix [i, j] indices
914 _T( 1, -1),
915 _T(-1, 0),
916 _T( 0, 0),
917 _T( 1, 0),
918 _T( 2, 0),
919 _T(-1, 1),
920 _T( 0, 1),
921 _T( 1, 1),
922 _T( 2, 1),
923 _T( 0, 2),
924 _T( 1, 2))
926 _endian = '>H' # struct.unpack 1 ushort (big endian, unsigned short)
927 _4endian = '>4H' # struct.unpack 4 ushorts
928 _Rendian = NN # struct.unpack a row of ushorts
929# _highest = (-8.4, 147.367, 85.839) if egm2008-1.pgm else (
930# (-8.167, 147.25, 85.422) if egm96-5.pgm else
931# (-4.5, 148.75, 81.33)) # egm84-15.pgm
932# _lowest = (4.7, 78.767, -106.911) if egm2008-1.pgm else (
933# (4.667, 78.833, -107.043) if egm96-5.pgm else
934# (4.75, 79.25, -107.34)) # egm84-15.pgm
935 _mean = _F(-1.317) # from egm2008-1, -1.438 egm96-5, -0.855 egm84-15
936 _nBytes = None # not applicable
937 _nterms = len(_C3[0]) # columns length, number of row
938 _smooth = None # not applicable
939 _stdev = _F(29.244) # from egm2008-1, 29.227 egm96-5, 29.183 egm84-15
940 _u2B = _calcsize(_endian) # pixelsize_ in bytes
941 _4u2B = _calcsize(_4endian) # 4 pixelsize_s in bytes
942 _Ru2B = 0 # row of pixelsize_s in bytes
943 _yxH = () # cache (y, x) indices
944 _yxHt = () # cached 4- or 10-tuple for _ev2H resp. _ev3H
945 _yx_hits = 0 # cache hits
947 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84
948 kind=3, **name_smooth):
949 '''New L{GeoidKarney} interpolator.
951 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/
952 C++/doc/geoid.html#geoidinst>} file name (C{egm*.pgm}), see
953 note below.
954 @kwarg crop: Optional box to limit geoid locations, a 4-tuple (C{south,
955 west, north, east}), 2-tuple (C{(south, west), (north,
956 east)}) or 2, in C{degrees90} lat- and C{degrees180}
957 longitudes or a 2-tuple (C{LatLonSW, LatLonNE}) of
958 C{LatLon} instances.
959 @kwarg datum: Optional grid datum (C{Datum}, L{Ellipsoid}, L{Ellipsoid2}
960 or L{a_f2Tuple}), default C{WGS84}.
961 @kwarg kind: Interpolation order (C{int}), 2 for C{bilinear} or 3
962 for C{cubic}.
963 @kwarg name_smooth: Optional geoid C{B{name}=NN} (C{str}) and UNSUPPORTED
964 keyword argument C{B{smooth}}, use C{B{smooth}=None} to ignore.
966 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid
967 B{C{crop}}, B{C{kind}} or B{C{smooth}}.
969 @raise TypeError: Invalid B{C{datum}}.
971 @see: Class L{GeoidPGM} and function L{egmGeoidHeights}.
973 @note: Geoid file B{C{egm_pgm}} remains open and must be closed
974 by calling the C{close} method or by using this instance
975 in a C{with B{GeoidKarney}(...) as ...} context.
976 '''
977 smooth, name = _xkwds_pop2(name_smooth, smooth=None)
978 if smooth is not None:
979 raise GeoidError(smooth=smooth, txt_not_=_supported_)
981 if kind in (2,):
982 self._evH = self._ev2H
983 elif kind not in (3,):
984 raise GeoidError(kind=kind)
986 self._egm = g = self._open(egm_pgm, datum, kind, _name__(**name), None)
987 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB)
989 self._Rendian = self._4endian.replace(_4_, str(p.nlon))
990 self._Ru2B = _calcsize(self._Rendian)
992 self._knots = p.knots # grid knots
993 self._lon_of = float(p.flon) # forward offset
994 self._lon_og = float(p.glon) # reverse offset
995 # set earth (lat, lon) limits (s, w, n, e)
996 self._lat_lo, self._lon_lo, \
997 self._lat_hi, self._lon_hi = self._swne(crop if crop else p.crop4)
998 self._cropped = True if crop else False
1000 def __call__(self, *llis, **wrap_H):
1001 '''Interpolate the geoid height for one or several locations.
1003 @arg llis: One or more locations (C{LatLon}s), all positional.
1004 @kwarg wrap_H: Keyword arguments C{B{wrap}=False, B{H}=False}.
1005 If C{B{wrap} is True}, wrap or I{normalize} all
1006 B{C{llis}} locations (C{bool}). If C{B{H} is True},
1007 return the I{orthometric} height instead of the
1008 I{geoid} height at each location (C{bool}).
1010 @return: A single interpolated geoid (or orthometric) height
1011 (C{float}) or a list or tuple of interpolated geoid
1012 (or orthometric) heights (C{float}s).
1014 @raise GeoidError: Insufficient number of B{C{llis}}, an
1015 invalid B{C{lli}} or the C{egm*.pgm}
1016 geoid file is closed.
1018 @raise RangeError: An B{C{lli}} is outside this geoid's lat-
1019 or longitude range.
1021 @note: To obtain I{orthometric} heights, each B{C{llis}}
1022 location must have an ellipsoid C{height} or C{h}
1023 attribute, otherwise C{height=0} is used.
1025 @see: Function L{pygeodesy.heightOrthometric}.
1026 '''
1027 return self._called(llis, False, **wrap_H)
1029 def _c0c3v(self, y, x):
1030 # get the common denominator, the 10x12 cubic matrix and
1031 # the 12 cubic v-coefficients around geoid index (y, x)
1032 p = self._pgm
1033 if 0 < x < (p.nlon - 2) and 0 < y < (p.nlat - 2):
1034 # read 4x4 ushorts, drop the 4 corners
1035 g = self._egm
1036 e = self._4endian
1037 n = self._4u2B
1038 R = self._Ru2B
1040 b = self._seek(y - 1, x - 1)
1041 v = _unpack(e, g.read(n))[1:3]
1042 b += R
1043 g.seek(b, _SEEK_SET)
1044 v += _unpack(e, g.read(n))
1045 b += R
1046 g.seek(b, _SEEK_SET)
1047 v += _unpack(e, g.read(n))
1048 b += R
1049 g.seek(b, _SEEK_SET)
1050 v += _unpack(e, g.read(n))[1:3]
1051 j = 1
1053 else: # likely some wrapped y and/or x's
1054 v = self._raws(y, x, GeoidKarney._CM)
1055 j = 0 if y < 1 else (1 if y < (p.nlat - 2) else 2)
1057 return GeoidKarney._C0[j], GeoidKarney._C3[j], v
1059 @Property_RO
1060 def dtype(self):
1061 '''Get the geoid's grid data type (C{str}).
1062 '''
1063 return 'ushort'
1065 def _ev(self, lat, lon): # PYCHOK expected
1066 # interpolate the geoid height at grid (lat, lon)
1067 fy, fx = self._g2yx2(lat, lon)
1068 y, x = int(floor(fy)), int(floor(fx))
1069 fy -= y
1070 fx -= x
1071 H = self._evH(fy, fx, y, x) # ._ev3H or ._ev2H
1072 H *= self._pgm.Scale # H.fmul(self._pgm.Scale)
1073 H += self._pgm.Offset # H.fadd(self._pgm.Offset)
1074 return H.fsum()
1076 def _ev2H(self, fy, fx, *yx):
1077 # compute the bilinear 4-tuple and interpolate raw H
1078 if self._yxH == yx:
1079 t = self._yxHt
1080 self._yx_hits += 1
1081 else:
1082 y, x = self._yxH = yx
1083 self._yxHt = t = self._raws(y, x, GeoidKarney._BT)
1084 v = _1_0, -fx, fx
1085 H = Fdot(v, t[0], t[0], t[1]).fmul(_1_0 - fy) # c = a * (1 - fy)
1086 H += Fdot(v, t[2], t[2], t[3]).fmul(fy) # c += b * fy
1087 return H
1089 def _ev3H(self, fy, fx, *yx):
1090 # compute the cubic 10-tuple and interpolate raw H
1091 if self._yxH == yx:
1092 t = self._yxHt
1093 self._yx_hits += 1
1094 else:
1095 self._yxH = yx
1096 c0, c3, v = self._c0c3v(*yx)
1097 t = [fdot(v, *c3[i]) / c0 for i in range(self._nterms)]
1098 self._yxHt = t = tuple(t)
1099 # GeographicLib/Geoid.cpp Geoid::height(lat, lon) ...
1100 # real h = t[0] + fx * (t[1] + fx * (t[3] + fx * t[6])) +
1101 # fy * (t[2] + fx * (t[4] + fx * t[7]) +
1102 # fy * (t[5] + fx * t[8] + fy * t[9]));
1103 v = _1_0, fx, fy
1104 H = Fdot(v, t[5], t[8], t[9])
1105 H *= fy
1106 H += Fhorner(fx, t[2], t[4], t[7])
1107 H *= fy
1108 H += Fhorner(fx, t[0], t[1], t[3], t[6])
1109 return H
1111 _evH = _ev3H # overriden for kind == 2
1113 def _g2ll2(self, lat, lon):
1114 # convert grid (lat, lon) to earth (lat, lon), uncropped
1115 while lon > _180_0:
1116 lon -= _360_0
1117 return lat, lon
1119 def _g2yx2(self, lat, lon):
1120 # convert grid (lat, lon) to grid (y, x) indices
1121 p = self._pgm
1122 # note, slat = +90, rlat < 0 makes y >=0
1123 return ((lat - p.slat) * p.rlat), ((lon - p.wlon) * p.rlon)
1125 def _gyx2g2(self, y, x):
1126 # convert grid (y, x) indices to grid (lat, lon)
1127 p = self._pgm
1128 return (p.slat + p.dlat * y), (p.wlon + p.dlon * x)
1130 def height(self, lats, lons, **wrap):
1131 '''Interpolate the geoid height for one or several lat-/longitudes.
1133 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s).
1134 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s).
1135 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{lats}}
1136 and B{C{lons}} locations (C{bool}).
1138 @return: A single interpolated geoid height (C{float}) or a
1139 list of interpolated geoid heights (C{float}s).
1141 @raise GeoidError: Insufficient or non-matching number of
1142 B{C{lats}} and B{C{lons}} or the C{egm*.pgm}
1143 geoid file is closed.
1145 @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this
1146 geoid's lat- or longitude range.
1147 '''
1148 return _height_called(self, lats, lons, Error=GeoidError, **wrap)
1150 @Property_RO
1151 def _highest_ltd(self):
1152 '''(INTERNAL) Cache for L{highest} mesthod.
1153 '''
1154 return self._llh3minmax(True, -12, -4)
1156 def highest(self, LatLon=None, full=False): # PYCHOK full
1157 '''Return the location and largest height of this geoid.
1159 @kwarg LatLon: Optional class to return the location and height
1160 (C{LatLon}) or C{None}.
1161 @kwarg full: Search the full or limited latitude range (C{bool}).
1163 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,
1164 height)} otherwise a B{C{LatLon}} instance with the lat-,
1165 longitude and geoid height of the highest grid location.
1166 '''
1167 llh = self._highest if full or self.cropped else self._highest_ltd
1168 return self._llh3LL(llh, LatLon)
1170 def _lat2y2(self, lat2):
1171 # convert earth lat(s) to min and max grid y indices
1172 ys, m = [], self._pgm.nlat - 1
1173 for lat in lat2:
1174 y, _ = self._g2yx2(*self._ll2g2(lat, 0))
1175 ys.append(max(min(int(y), m), 0))
1176 return min(ys), max(ys) + 1
1178 def _ll2g2(self, lat, lon):
1179 # convert earth (lat, lon) to grid (lat, lon), uncropped
1180 while lon < 0:
1181 lon += _360_0
1182 return lat, lon
1184 def _llh3minmax(self, highest=True, *lat2):
1185 # find highest or lowest, takes 10+ secs for egm2008-1.pgm geoid
1186 # (Python 2.7.16, macOS 10.13.6 High Sierra, iMac 3 GHz Core i3)
1187 y = x = 0
1188 h = self._raw(y, x)
1189 if highest:
1190 for j, r in self._raw2(*lat2):
1191 m = max(r)
1192 if m > h:
1193 h, y, x = m, j, r.index(m)
1194 else: # lowest
1195 for j, r in self._raw2(*lat2):
1196 m = min(r)
1197 if m < h:
1198 h, y, x = m, j, r.index(m)
1199 h *= self._pgm.Scale
1200 h += self._pgm.Offset
1201 return self._g2ll2(*self._gyx2g2(y, x)) + (h,)
1203 @Property_RO
1204 def _lowest_ltd(self):
1205 '''(INTERNAL) Cache for L{lowest}.
1206 '''
1207 return self._llh3minmax(False, 0, 8)
1209 def lowest(self, LatLon=None, full=False): # PYCHOK full
1210 '''Return the location and lowest height of this geoid.
1212 @kwarg LatLon: Optional class to return the location and height
1213 (C{LatLon}) or C{None}.
1214 @kwarg full: Search the full or limited latitude range (C{bool}).
1216 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,
1217 height)} otherwise a B{C{LatLon}} instance with the lat-,
1218 longitude and geoid height of the lowest grid location.
1219 '''
1220 llh = self._lowest if full or self.cropped else self._lowest_ltd
1221 return self._llh3LL(llh, LatLon)
1223 def _raw(self, y, x):
1224 # get the ushort geoid height at geoid index (y, x),
1225 # like GeographicLib/Geoid.hpp real rawval(is, iy)
1226 p = self._pgm
1227 if x < 0:
1228 x += p.nlon
1229 elif x >= p.nlon:
1230 x -= p.nlon
1231 h = p.nlon // 2
1232 if y < 0:
1233 y = -y
1234 elif y >= p.nlat:
1235 y = (p.nlat - 1) * 2 - y
1236 else:
1237 h = 0
1238 x += h if x < h else -h
1239 self._seek(y, x)
1240 h = _unpack(self._endian, self._egm.read(self._u2B))
1241 return h[0]
1243 def _raws(self, y, x, ijs):
1244 # get bilinear 4-tuple or 10x12 cubic matrix
1245 return tuple(self._raw(y + j, x + i) for i, j in ijs)
1247 def _raw2(self, *lat2):
1248 # yield a 2-tuple (y, ushorts) for each row or for
1249 # the rows between two (or more) earth lat values
1250 p = self._pgm
1251 g = self._egm
1252 e = self._Rendian
1253 n = self._Ru2B
1254 # min(lat2) <= lat <= max(lat2) or 0 <= y < p.nlat
1255 s, t = self._lat2y2(lat2) if lat2 else (0, p.nlat)
1256 self._seek(s, 0) # to start of row s
1257 for y in range(s, t):
1258 yield y, _unpack(e, g.read(n))
1260 def _seek(self, y, x):
1261 # position geoid to grid index (y, x)
1262 p, g = self._pgm, self._egm
1263 if g:
1264 b = p.skip + (y * p.nlon + x) * self._u2B
1265 g.seek(b, _SEEK_SET)
1266 return b # position
1267 raise GeoidError('closed file', txt=repr(p.egm)) # IOError
1270class GeoidPGM(_GeoidBase):
1271 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth
1272 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/
1273 geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/
1274 C++/doc/geoid.html#geoidinst>} datasets but based on C{SciPy}
1275 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/reference/
1276 generated/scipy.interpolate.RectBivariateSpline.html>} or
1277 U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/
1278 scipy.interpolate.interp2d.html>} interpolation.
1280 Use any of the U{egm84-, egm96- or egm2008-*.pgm
1281 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>}
1282 datasets. However, unless cropped, an entire C{egm*.pgm} dataset
1283 is loaded into the C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/
1284 doc/scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>}
1285 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/
1286 scipy.interpolate.interp2d.html>} interpolator and converted from
1287 2-byte C{int} to 8-byte C{dtype float64}. Therefore, internal memory
1288 usage is 4x the U{egm*.pgm<https://GeographicLib.SourceForge.io/C++/doc/
1289 geoid.html#geoidinst>} file size and may exceed the available memory,
1290 especially with 32-bit Python, see properties C{.nBytes} and C{.sizeB}.
1291 '''
1292 _cropped = False
1293 _endian = '>u2'
1295 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84
1296 kind=3, smooth=0, **name):
1297 '''New L{GeoidPGM} interpolator.
1299 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/
1300 C++/doc/geoid.html#geoidinst>} file name (C{egm*.pgm}).
1301 @kwarg crop: Optional box to crop B{C{egm_pgm}}, a 4-tuple (C{south, west,
1302 north, east}) or 2-tuple (C{(south, west), (north, east)}),
1303 in C{degrees90} lat- and C{degrees180} longitudes or a
1304 2-tuple (C{LatLonSW, LatLonNE}) of C{LatLon} instances.
1305 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
1306 or L{a_f2Tuple}), default C{WGS84}.
1307 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for
1308 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/
1309 reference/generated/scipy.interpolate.RectBivariateSpline.html>},
1310 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/
1311 reference/generated/scipy.interpolate.interp2d.html>}, -3
1312 for C{interp2d cubic} or -5 for C{interp2d quintic}.
1313 @kwarg smooth: Smoothing factor for U{RectBivariateSpline
1314 <https://docs.SciPy.org/doc/scipy/reference/generated/
1315 scipy.interpolate.RectBivariateSpline.html>}
1316 only (C{int}).
1317 @kwarg name: Optional geoid C{B{name}=NN} (C{str}).
1319 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid B{C{crop}},
1320 B{C{kind}} or B{C{smooth}}.
1322 @raise ImportError: Package C{numpy} or C{scipy} not found or not installed.
1324 @raise LenError: EGM dataset B{C{egm_pgm}} axis mismatch.
1326 @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue.
1328 @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d}
1329 warning as exception.
1331 @raise TypeError: Invalid B{C{datum}} or unexpected argument.
1333 @note: C{scipy.interpolate.interp2d} has been C{DEPRECATED}, specify
1334 C{B{kind}=1..5} for C{scipy.interpolate.RectBivariateSpline}.
1336 @note: The U{GeographicLib egm*.pgm<https://GeographicLib.SourceForge.io/
1337 C++/doc/geoid.html#geoidinst>} file sizes are based on a 2-byte
1338 C{int} height converted to 8-byte C{dtype float64} for C{scipy}
1339 interpolators. Therefore, internal memory usage is 4 times the
1340 C{egm*.pgm} file size and may exceed the available memory,
1341 especially with 32-bit Python. To reduce memory usage, set
1342 keyword argument B{C{crop}} to the region of interest. For example
1343 C{B{crop}=(20, -125, 50, -65)} covers the U{conterminous US<https://
1344 www.NGS.NOAA.gov/GEOID/GEOID12B/maps/GEOID12B_CONUS_grids.png>}
1345 (CONUS), less than 3% of the entire C{egm2008-1.pgm} dataset.
1347 @see: Class L{GeoidKarney} and function L{egmGeoidHeights}.
1348 '''
1349 np = self.numpy
1350 self._u2B = np.dtype(self.endian).itemsize
1352 g = self._open(egm_pgm, datum, kind, _name__(**name), smooth)
1353 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB)
1354 if crop:
1355 g = p._cropped(g, abs(kind) + 1, *self._swne(crop))
1356 if _MODS.internals._version2(np.__version__) < (1, 9):
1357 g = open(g.name, _rb_) # reopen tempfile for numpy 1.8.0-
1358 self._cropped = True
1359 try:
1360 # U{numpy dtype formats are different from Python struct formats
1361 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>}
1362 # read all heights, skipping the PGM header lines, converted to float
1363 hs = self._load(g, self.endian, p.knots, p.skip).reshape(p.nlat, p.nlon) * p.Scale
1364 if p.Offset: # offset
1365 hs = p.Offset + hs
1366 if p.dlat < 0: # flip the rows
1367 hs = np.flipud(hs)
1368 _GeoidBase.__init__(self, hs, p)
1369 except Exception as x:
1370 raise _SciPyIssue(x, _in_, repr(egm_pgm))
1371 finally:
1372 g.close()
1374 def _g2ll2(self, lat, lon):
1375 # convert grid (lat, lon) to earth (lat, lon), un-/cropped
1376 if self._cropped:
1377 lon -= self._lon_of
1378 else:
1379 while lon > _180_0:
1380 lon -= _360_0
1381 return lat, lon
1383 def _ll2g2(self, lat, lon):
1384 # convert earth (lat, lon) to grid (lat, lon), un-/cropped
1385 if self._cropped:
1386 lon += self._lon_of
1387 else:
1388 while lon < 0:
1389 lon += _360_0
1390 return lat, lon
1392 if _FOR_DOCS:
1393 __call__ = _GeoidBase.__call__
1394 height = _GeoidBase.height
1397class _Gpars(_Named):
1398 '''(INTERNAL) Basic geoid parameters.
1399 '''
1400 # interpolator parameters
1401 dlat = 0 # +/- latitude resolution in C{degrees}
1402 dlon = 0 # longitude resolution in C{degrees}
1403 nlat = 1 # number of latitude knots (C{int})
1404 nlon = 0 # number of longitude knots (C{int})
1405 rlat = 0 # +/- latitude resolution in C{float}, 1 / .dlat
1406 rlon = 0 # longitude resolution in C{float}, 1 / .dlon
1407 slat = 0 # nothern- or southern most latitude (C{degrees90})
1408 wlon = 0 # western-most longitude in Eastern lon (C{degrees360})
1410 flon = 0 # forward, earth to grid longitude offset
1411 glon = 0 # reverse, grid to earth longitude offset
1413 knots = 0 # number of knots, nlat * nlon (C{int})
1414 skip = 0 # header bytes to skip (C{int})
1416 def __repr__(self):
1417 t = _COMMASPACE_.join(pairs((a, getattr(self, a)) for
1418 a in dir(self.__class__)
1419 if a[:1].isupper()))
1420 return _COLONSPACE_(self, t)
1422 def __str__(self):
1423 return Fmt.PAREN(self.classname, repr(self.name))
1426class _PGM(_Gpars):
1427 '''(INTERNAL) Parse an C{egm*.pgm} geoid dataset file.
1429 # Geoid file in PGM format for the GeographicLib::Geoid class
1430 # Description WGS84 EGM96, 5-minute grid
1431 # URL https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html
1432 # DateTime 2009-08-29 18:45:03
1433 # MaxBilinearError 0.140
1434 # RMSBilinearError 0.005
1435 # MaxCubicError 0.003
1436 # RMSCubicError 0.001
1437 # Offset -108
1438 # Scale 0.003
1439 # Origin 90N 0E
1440 # AREA_OR_POINT Point
1441 # Vertical_Datum WGS84
1442 <width> <height>
1443 <pixel>
1444 ...
1445 '''
1446 crop4 = () # 4-tuple (C{south, west, north, east}).
1447 egm = None
1448 glon = 180 # reverse offset, uncropped
1449# pgm = NN # name
1450 sizeB = 0
1451 u2B = 2 # item size of grid height (C{int}).
1453 @staticmethod
1454 def _llstr2floats(latlon):
1455 # llstr to (lat, lon) floats
1456 lat, lon = latlon.split()
1457 return _MODS.dms.parseDMS2(lat, lon)
1459 # PGM file attributes, CamelCase but not .istitle()
1460 AREA_OR_POINT = str
1461 DateTime = str
1462 Description = str # 'WGS84 EGM96, 5-minute grid'
1463 Geoid = str # 'file in PGM format for the GeographicLib::Geoid class'
1464 MaxBilinearError = float
1465 MaxCubicError = float
1466 Offset = float
1467 Origin = _llstr2floats
1468 Pixel = 0
1469 RMSBilinearError = float
1470 RMSCubicError = float
1471 Scale = float
1472 URL = str # 'https://Earth-Info.NGA.mil/GandG/wgs84/...'
1473 Vertical_Datum = str
1475 def __init__(self, g, pgm=NN, itemsize=0, sizeB=0): # MCCABE 22
1476 '''(INTERNAL) New C{_PGM} parsed C{egm*.pgm} geoid dataset.
1477 '''
1478 self.name = pgm # geoid file name
1479 if itemsize:
1480 self._u2B = itemsize
1481 if sizeB:
1482 self.sizeB = sizeB
1484 t = g.readline() # make sure newline == '\n'
1485 if t != b'P5\n' and t.strip() != b'P5':
1486 raise self._Errorf(_format_, _header_, t)
1488 while True: # read all # Attr ... lines,
1489 try: # ignore empty ones or comments
1490 t = g.readline().strip()
1491 if t.startswith(_bHASH_):
1492 t = t.lstrip(_bHASH_).lstrip()
1493 a, v = map(_ub2str, t.split(None, 1))
1494 f = getattr(_PGM, a, None)
1495 if callable(f) and a[:1].isupper():
1496 setattr(self, a, f(v))
1497 elif t:
1498 break
1499 except (TypeError, ValueError):
1500 raise self._Errorf(_format_, 'Attr', t)
1501 else: # should never get here
1502 raise self._Errorf(_format_, _header_, g.tell())
1504 try: # must be (even) width and (odd) height
1505 nlon, nlat = map(int, t.split())
1506 if nlon < 2 or nlon > (360 * 60) or isodd(nlon) or \
1507 nlat < 2 or nlat > (181 * 60) or not isodd(nlat):
1508 raise ValueError
1509 except (TypeError, ValueError):
1510 raise self._Errorf(_format_, _SPACE_(_width_, _height_), t)
1512 try: # must be 16 bit pixel height
1513 t = g.readline().strip()
1514 self.Pixel = int(t)
1515 if not 255 < self.Pixel < 65536: # >u2 or >H only
1516 raise ValueError
1517 except (TypeError, ValueError):
1518 raise self._Errorf(_format_, 'pixel', t)
1520 for a in dir(_PGM): # set undefined # Attr ... to None
1521 if a[:1].isupper() and callable(getattr(self, a)):
1522 setattr(self, a, None)
1524 if self.Origin is None:
1525 raise self._Errorf(_format_, 'Origin', self.Origin)
1526 if self.Offset is None or self.Offset > 0:
1527 raise self._Errorf(_format_, 'Offset', self.Offset)
1528 if self.Scale is None or self.Scale < EPS:
1529 raise self._Errorf(_format_, 'Scale', self.Scale)
1531 self.skip = g.tell()
1532 self.knots = nlat * nlon
1534 self.nlat, self.nlon = nlat, nlon
1535 self.slat, self.wlon = self.Origin
1536 # note, negative .dlat and .rlat since rows
1537 # are from .slat 90N down in decreasing lat
1538 self.dlat, self.dlon = _180_0 / (1 - nlat), _360_0 / nlon
1539 self.rlat, self.rlon = (1 - nlat) / _180_0, nlon / _360_0
1541 # grid corners in earth (lat, lon), .slat = 90, .dlat < 0
1542 n = float(self.slat)
1543 s = n + self.dlat * (nlat - 1)
1544 w = self.wlon - self.glon
1545 e = w + self.dlon * nlon
1546 self.crop4 = s, w, n, e
1548 n = self.sizeB - self.skip
1549 if n > 0 and n != (self.knots * self.u2B):
1550 raise self._Errorf('%s(%s x %s != %s)', _assert_, nlat, nlon, n)
1552 def _cropped(self, g, k1, south, west, north, east): # MCCABE 15
1553 '''Crop the geoid to (south, west, north, east) box.
1554 '''
1555 # flon offset for both west and east
1556 f = 360 if west < 0 else 0
1557 # earth (lat, lon) to grid indices (y, x),
1558 # note y is decreasing, i.e. n < s
1559 s, w = self._lle2yx2(south, west, f)
1560 n, e = self._lle2yx2(north, east, f)
1561 s += 1 # s > n
1562 e += 1 # e > w
1564 hi, wi = self.nlat, self.nlon
1565 # handle special cases
1566 if (s - n) > hi:
1567 n, s = 0, hi # entire lat range
1568 if (e - w) > wi:
1569 w, e, f = 0, wi, 180 # entire lon range
1570 if s == hi and w == n == 0 and e == wi:
1571 return g # use entire geoid as-is
1573 if (e - w) < k1 or (s - n) < (k1 + 1):
1574 raise self._Errorf(_format_, 'swne', (north - south, east - west))
1576 if e > wi > w: # wrap around
1577 # read w..wi and 0..e
1578 r, p = (wi - w), (e - wi)
1579 elif e > w:
1580 r, p = (e - w), 0
1581 else:
1582 raise self._Errorf('%s(%s < %s)', _assert_, w, e)
1584 # convert to bytes
1585 r *= self.u2B
1586 p *= self.u2B
1587 q = wi * self.u2B # stride
1588 # number of rows and cols to skip from
1589 # the original (.slat, .wlon) origin
1590 z = self.skip + (n * wi + w) * self.u2B
1591 # sanity check
1592 if r < 2 or p < 0 or q < 2 or z < self.skip \
1593 or z > self.sizeB:
1594 raise self._Errorf(_format_, _assert_, (r, p, q, z))
1596 # can't use _BytesIO since numpy
1597 # needs .fileno attr in .fromfile
1598 t, c = 0, self._tmpfile()
1599 # reading (s - n) rows, forward
1600 for y in range(n, s): # PYCHOK y unused
1601 g.seek(z, _SEEK_SET)
1602 # Python 2 tmpfile.write returns None
1603 t += c.write(g.read(r)) or r
1604 if p: # wrap around to start of row
1605 g.seek(-q, _SEEK_CUR)
1606 # assert(g.tell() == (z - w * self.u2B))
1607 # Python 2 tmpfile.write returns None
1608 t += c.write(g.read(p)) or p
1609 z += q
1610 c.flush()
1611 g.close()
1613 s -= n # nlat
1614 e -= w # nlon
1615 k = s * e # knots
1616 z = k * self.u2B
1617 if t != z:
1618 raise self._Errorf('%s(%s != %s) %s', _assert_, t, z, self)
1620 # update the _Gpars accordingly, note attributes
1621 # .dlat, .dlon, .rlat and .rlon remain unchanged
1622 self.slat += n * self.dlat
1623 self.wlon += w * self.dlon
1624 self.nlat = s
1625 self.nlon = e
1626 self.flon = self.glon = f
1628 self.crop4 = south, west, north, east
1629 self.knots = k
1630 self.skip = 0 # no header lines in c
1632 c.seek(0, _SEEK_SET)
1633 # c = open(c.name, _rb_) # reopen for numpy 1.8.0-
1634 return c
1636 def _Errorf(self, fmt, *args): # PYCHOK no cover
1637 t = fmt % args
1638 e = self.pgm or NN
1639 if e:
1640 t = _SPACE_(t, _in_, repr(e))
1641 return PGMError(t)
1643 def _lle2yx2(self, lat, lon, flon):
1644 # earth (lat, lon) to grid indices (y, x)
1645 # with .dlat decreasing from 90N .slat
1646 lat -= self.slat
1647 lon += flon - self.wlon
1648 return (min(self.nlat - 1, max(0, int(lat * self.rlat))),
1649 max(0, int(lon * self.rlon)))
1651 def _tmpfile(self):
1652 # create a tmpfile to hold the cropped geoid grid
1653 try:
1654 from tempfile import NamedTemporaryFile as tmpfile
1655 except ImportError: # Python 2.7.16-
1656 from os import tmpfile
1657 t = _os_path.splitext(_os_path.basename(self.pgm))[0]
1658 f = tmpfile(mode='w+b', prefix=t or 'egm')
1659 f.seek(0, _SEEK_SET) # force overwrite
1660 return f
1662 @Property_RO
1663 def pgm(self):
1664 '''Get the geoid file name (C{str}).
1665 '''
1666 return self.name
1669class PGMError(GeoidError):
1670 '''Issue parsing or cropping an C{egm*.pgm} geoid dataset.
1671 '''
1672 pass
1675def egmGeoidHeights(GeoidHeights_dat):
1676 '''Generate geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/
1677 C++/doc/geoid.html#geoidinst>} height tests from U{GeoidHeights.dat
1678 <https://SourceForge.net/projects/geographiclib/files/testdata/>}
1679 U{Test data for Geoids<https://GeographicLib.SourceForge.io/C++/doc/
1680 geoid.html#testgeoid>}.
1682 @arg GeoidHeights_dat: The un-gz-ed C{GeoidHeights.dat} file
1683 (C{str} or C{file} handle).
1685 @return: For each test, yield a L{GeoidHeight5Tuple}C{(lat, lon,
1686 egm84, egm96, egm2008)}.
1688 @raise GeoidError: Invalid B{C{GeoidHeights_dat}}.
1690 @note: Function L{egmGeoidHeights} is used to test the geoids
1691 L{GeoidKarney} and L{GeoidPGM}, see PyGeodesy module
1692 C{test/testGeoids.py}.
1693 '''
1694 dat = GeoidHeights_dat
1695 if isinstance(dat, bytes):
1696 dat = _BytesIO(dat)
1698 try:
1699 dat.seek(0, _SEEK_SET) # reset
1700 except AttributeError as x:
1701 raise GeoidError(GeoidHeights_dat=type(dat), cause=x)
1703 for t in dat.readlines():
1704 t = t.strip()
1705 if t and not t.startswith(_bHASH_):
1706 lat, lon, egm84, egm96, egm2008 = map(float, t.split())
1707 while lon > _180_0: # EasternLon to earth lon
1708 lon -= _360_0
1709 yield GeoidHeight5Tuple(lat, lon, egm84, egm96, egm2008)
1712__all__ += _ALL_DOCS(_GeoidBase)
1714if __name__ == '__main__':
1716 from pygeodesy.internals import printf, _sys
1718 _crop = ()
1719 _GeoidEGM = GeoidKarney
1720 _kind = 3
1722 geoids = _sys.argv[1:]
1723 while geoids:
1724 geoid = geoids.pop(0)
1726 if '-crop'.startswith(geoid.lower()):
1727 _crop = 20, -125, 50, -65 # CONUS
1729 elif '-karney'.startswith(geoid.lower()):
1730 _GeoidEGM = GeoidKarney
1732 elif '-kind'.startswith(geoid.lower()):
1733 _kind = int(geoids.pop(0))
1735 elif '-pgm'.startswith(geoid.lower()):
1736 _GeoidEGM = GeoidPGM
1738 elif geoid[-4:].lower() in ('.pgm',):
1739 g = _GeoidEGM(geoid, crop=_crop, kind=_kind)
1740 printf(g.toStr(), nt=1, nl=1)
1741 printf(repr(g.pgm), nt=1)
1742 # <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>:
1743 # The height of the EGM96 geoid at Timbuktu
1744 # echo 16:46:33N 3:00:34W | GeoidEval
1745 # => 28.7068 -0.02e-6 -1.73e-6
1746 # The 1st number is the height of the geoid, the 2nd and
1747 # 3rd are its slopes in northerly and easterly direction
1748 t = 'Timbuktu %s' % (g,)
1749 k = {'egm84-15.pgm': '31.2979',
1750 'egm96-5.pgm': '28.7067',
1751 'egm2008-1.pgm': '28.7880'}.get(g.name.lower(), '28.7880')
1752 ll = _MODS.dms.parseDMS2('16:46:33N', '3:00:34W', sep=':')
1753 for ll in (ll, (16.776, -3.009),):
1754 try:
1755 h, ll = g.height(*ll), fstr(ll, prec=6)
1756 printf('%s.height(%s): %.4F vs %s', t, ll, h, k)
1757 except (GeoidError, RangeError) as x:
1758 printf(_COLONSPACE_(t, str(x)))
1760 elif geoid[-4:].lower() in ('.bin',):
1761 g = GeoidG2012B(geoid, kind=_kind)
1762 printf(g.toStr())
1764 else:
1765 raise GeoidError(grid=repr(geoid))
1767_I = int # PYCHOK unused _I
1768del _intCs # trash ints cache
1770# **) MIT License
1771#
1772# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1773#
1774# Permission is hereby granted, free of charge, to any person obtaining a
1775# copy of this software and associated documentation files (the "Software"),
1776# to deal in the Software without restriction, including without limitation
1777# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1778# and/or sell copies of the Software, and to permit persons to whom the
1779# Software is furnished to do so, subject to the following conditions:
1780#
1781# The above copyright notice and this permission notice shall be included
1782# in all copies or substantial portions of the Software.
1783#
1784# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1785# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1786# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1787# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1788# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1789# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1790# OTHER DEALINGS IN THE SOFTWARE.
1792# <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>
1793# _lowerleft = -90, -179, -30.1500 # egm2008-1.pgm
1794# _lowerleft = -90, -179, -29.5350 # egm96-5.pgm
1795# _lowerleft = -90, -179, -29.7120 # egm84-15.pgm
1797# _center = 0, 0, 17.2260 # egm2008-1.pgm
1798# _center = 0, 0, 17.1630 # egm96-5.pgm
1799# _center = 0, 0, 18.3296 # egm84-15.pgm
1801# _upperright = 90, 180, 14.8980 # egm2008-1.pgm
1802# _upperright = 90, 180, 13.6050 # egm96-5.pgm
1803# _upperright = 90, 180, 13.0980 # egm84-15.pgm
1806# % python3 -m pygeodesy.geoids [-Karney] ../testGeoids/egm*.pgm
1807#
1808# 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)
1809#
1810# _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'
1811#
1812# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880
1813# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880
1814#
1815# 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)
1816#
1817# _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'
1818#
1819# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979
1820# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979
1821#
1822# 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)
1823#
1824# _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'
1825#
1826# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067
1827# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067
1830# % python3 -m pygeodesy.geoids -Karney ../testGeoids/egm*.pgm
1831#
1832# 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)
1833#
1834# _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'
1835#
1836# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880
1837# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880
1838#
1839# 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)
1840#
1841# _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'
1842#
1843# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979
1844# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979
1845#
1846# 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)
1847#
1848# _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'
1849#
1850# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067
1851# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067
1854# % python2 -m pygeodesy.geoids -PGM ../testGeoids/egm*.pgm
1855#
1856# 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)
1857#
1858# _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'
1859#
1860# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880
1861# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880
1862#
1863# 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)
1864#
1865# _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'
1866#
1867# Timbuktu GeoidPGM('egm84-15.pgm').height(16.775833, -3.009444): 31.2979 vs 31.2979
1868# Timbuktu GeoidPGM('egm84-15.pgm').height(16.776, -3.009): 31.2975 vs 31.2979
1869#
1870# 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)
1871#
1872# _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'
1873#
1874# Timbuktu GeoidPGM('egm96-5.pgm').height(16.775833, -3.009444): 28.7065 vs 28.7067
1875# Timbuktu GeoidPGM('egm96-5.pgm').height(16.776, -3.009): 28.7064 vs 28.7067