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_, \
97 _cubic_, _E_, _height_, _in_, _kind_, _lat_, \
98 _linear_, _lon_, _mean_, _N_, _n_a_, _numpy_, \
99 _on_, _outside_, _S_, _s_, _scipy_, _SPACE_, \
100 _stdev_, _tbd_, _W_, _width_
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 deprecated_method, Property_RO, property_RO
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
110import os.path as _os_path
111from os import SEEK_CUR as _SEEK_CUR, SEEK_SET as _SEEK_SET
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__ = '24.05.23'
123_assert_ = 'assert'
124_bHASH_ = b'#'
125_endian_ = 'endian'
126_format_ = '%s %r'
127_header_ = 'header'
128_intCs = {} # cache int value
129_interp2d_ks = {-2: _linear_,
130 -3: _cubic_,
131 -5: 'quintic'}
132_lli_ = 'lli'
133_non_increasing_ = 'non-increasing'
134_rb_ = 'rb'
135_supported_ = 'supported'
138class _GeoidBase(_HeightsBase):
139 '''(INTERNAL) Base class for C{Geoid...}s.
140 '''
141 _cropped = None
142# _datum = _WGS84 # from _HeightsBase
143 _egm = None # open C{egm*.pgm} geoid file
144 _endian = _tbd_
145 _geoid = _n_a_
146 _hs_y_x = None # numpy 2darray, row-major order
147 _interp2d = None # interp2d interpolation
148 _kind = 3 # order for interp2d, RectBivariateSpline
149# _kmin = 2 # min number of knots
150 _knots = 0 # nlat * nlon
151 _mean = None # fixed in GeoidKarney
152# _name = NN # _Named
153 _nBytes = 0 # numpy size in bytes, float64
154 _pgm = None # PGM attributes, C{_PGM} or C{None}
155 _sizeB = 0 # geoid file size in bytes
156 _smooth = 0 # used only for RectBivariateSpline
157 _stdev = None # fixed in GeoidKarney
158 _u2B = 0 # np.itemsize or undefined
160 _lat_d = _0_0 # increment, +tive
161 _lat_lo = _0_0 # lower lat, south
162 _lat_hi = _0_0 # upper lat, noth
163 _lon_d = _0_0 # increment, +tive
164 _lon_lo = _0_0 # left lon, west
165 _lon_hi = _0_0 # right lon, east
166 _lon_of = _0_0 # forward lon offset
167 _lon_og = _0_0 # reverse lon offset
169 _center = None # (lat, lon, height)
170 _yx_hits = None # cache hits, ala Karney
172 def __init__(self, hs, p):
173 '''(INTERNAL) Set up the grid axes, the C{SciPy} interpolator
174 and several internal geoid attributes.
176 @arg hs: Grid knots with known height (C{numpy 2darray}).
177 @arg p: The C{slat, wlon, nlat, nlon, dlat, dlon} and
178 other geoid parameters (C{INTERNAL}).
180 @raise GeoidError: Incompatible grid B{C{hs}} shape or
181 invalid B{C{kind}}.
183 @raise LenError: Mismatch grid B{C{hs}} axis.
185 @raise SciPyError: A C{scipy.interpolate.inter2d} or
186 C{-.RectBivariateSpline} issue.
188 @raise SciPyWarning: A C{scipy.interpolate.inter2d} or
189 C{-.RectBivariateSpline} warning as
190 exception.
192 @note: C{scipy.interpolate.interp2d} has been C{DEPRECATED},
193 specify keyword argument C{B{kind}=1..5} to use
194 C{scipy.interpolate.RectBivariateSpline}.
195 '''
196 spi = self.scipy_interpolate
197 # for 2d scipy.interpolate.interp2d(xs, ys, hs, ...) and
198 # scipy.interpolate.RectBivariateSpline(ys, xs, hs, ...)
199 # require the shape of hs to be (len(ys), len(xs)), note
200 # the different (xs, ys, ...) and (ys, xs, ...) orders
201 if (p.nlat, p.nlon) != hs.shape:
202 raise GeoidError(shape=hs.shape, txt=_incompatible((p.nlat, p.nlon)))
204 # both axes and bounding box
205 ys, self._lat_d = self._gaxis2(p.slat, p.dlat, p.nlat, _lat_ + _s_)
206 xs, self._lon_d = self._gaxis2(p.wlon, p.dlon, p.nlon, _lon_ + _s_)
208 bb = ys[0], ys[-1], xs[0], xs[-1] + p.dlon # fudge lon_hi
209 # geoid grids are typically stored in row-major order, some
210 # with rows (90..-90) reversed and columns (0..360) wrapped
211 # to Easten longitude, 0 <= east < 180 and 180 <= west < 360
212 k = self.kind
213 if k in _interp2d_ks: # .interp2d DEPRECATED since scipy 1.10
214 if self._scipy_version() < (1, 10):
215 self._interp2d = spi.interp2d(xs, ys, hs, kind=_interp2d_ks[k])
216 else: # call and overwrite the DEPRECATED .interp2d
217 self._interp2d = self._interp2d(xs, ys, hs, k)
218 elif 1 <= k <= 5:
219 self._ev = spi.RectBivariateSpline(ys, xs, hs, bbox=bb, ky=k, kx=k,
220 s=self._smooth).ev
221 else:
222 raise GeoidError(kind=k)
224 self._hs_y_x = hs # numpy 2darray, row-major
225 self._nBytes = hs.nbytes # numpy size in bytes
226 self._knots = p.knots # grid knots
227 self._lon_of = float(p.flon) # forward offset
228 self._lon_og = float(p.glon) # reverse offset
229 # shrink the box by 1 unit on every side
230 # bb += self._lat_d, -self._lat_d, self._lon_d, -self._lon_d
231 self._lat_lo = float(bb[0])
232 self._lat_hi = float(bb[1])
233 self._lon_lo = float(bb[2] - p.glon)
234 self._lon_hi = float(bb[3] - p.glon)
236 def __call__(self, *llis, **wrap_H):
237 '''Interpolate the geoid height for one or several locations.
239 @arg llis: One or more locations (C{LatLon}s), all positional.
240 @kwarg wrap_H: Keyword arguments C{B{wrap}=False} (C{bool}) and
241 C{B{H}=False} (C{bool}). If C{B{wrap} is True},
242 wrap or I{normalize} all B{C{llis}} locations. If
243 C{B{H} is True}, return the I{orthometric} height
244 instead of the I{geoid} height at each location.
246 @return: A single interpolated geoid (or orthometric) height
247 (C{float}) or a list or tuple of interpolated geoid
248 (or orthometric) heights (C{float}s).
250 @raise GeoidError: Insufficient number of B{C{llis}}, an
251 invalid B{C{lli}} or the C{egm*.pgm}
252 geoid file is closed.
254 @raise RangeError: An B{C{lli}} is outside this geoid's lat-
255 or longitude range.
257 @raise SciPyError: A C{scipy.interpolate.inter2d} or
258 C{-.RectBivariateSpline} issue.
260 @raise SciPyWarning: A C{scipy.interpolate.inter2d} or
261 C{-.RectBivariateSpline} warning as
262 exception.
264 @note: To obtain I{orthometric} heights, each B{C{llis}}
265 location must have an ellipsoid C{height} or C{h}
266 attribute, otherwise C{height=0} is used.
268 @see: Function L{pygeodesy.heightOrthometric}.
269 '''
270 return self._called(llis, True, **wrap_H)
272 def __enter__(self):
273 '''Open context.
274 '''
275 return self
277 def __exit__(self, *unused): # PYCHOK exc_type, exc_value, exc_traceback)
278 '''Close context.
279 '''
280 self.close()
281 # return None # XXX False
283 def __repr__(self):
284 return self.toStr()
286 def __str__(self):
287 return Fmt.PAREN(self.classname, repr(self.name))
289 def _called(self, llis, scipy, wrap=False, H=False):
290 # handle __call__
291 _H = _MODS.formy.heightOrthometric if H else None
292 _as, llis = _as_llis2(llis, Error=GeoidError)
293 hs, _w = [], _Wrap._latlonop(wrap)
294 _a, _h = hs.append, self._hGeoid
295 try:
296 for i, lli in enumerate(llis):
297 N = _h(*_w(lli.lat, lli.lon))
298 # orthometric or geoid height
299 _a(_H(lli, N) if _H else N)
300 return _as(hs)
302 except (GeoidError, RangeError) as x:
303 # XXX avoid str(LatLon()) degree symbols
304 t = _lli_ if _as is _ascalar else Fmt.INDEX(llis=i)
305 lli = fstr((lli.lat, lli.lon), strepr=repr)
306 raise type(x)(t, lli, wrap=wrap, H=H, cause=x)
307 except Exception as x:
308 if scipy and self.scipy:
309 raise _SciPyIssue(x)
310 else:
311 raise
313 @Property_RO
314 def _center(self):
315 ''' Cache for method L{center}.
316 '''
317 return self._llh3(favg(self._lat_lo, self._lat_hi),
318 favg(self._lon_lo, self._lon_hi))
320 def center(self, LatLon=None):
321 '''Return the center location and height of this geoid.
323 @kwarg LatLon: Optional class to return the location and height
324 (C{LatLon}) or C{None}.
326 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,
327 lon, height)} otherwise a B{C{LatLon}} instance
328 with the lat-, longitude and geoid height of the
329 center grid location.
330 '''
331 return self._llh3LL(self._center, LatLon)
333 def close(self):
334 '''Close the C{egm*.pgm} geoid file if open (and applicable).
335 '''
336 if not self.closed:
337 self._egm.close()
338 self._egm = None
340 @property_RO
341 def closed(self):
342 '''Get the C{egm*.pgm} geoid file status.
343 '''
344 return self._egm is None
346 @Property_RO
347 def cropped(self):
348 '''Is geoid cropped (C{bool} or C{None} if crop not supported).
349 '''
350 return self._cropped
352 @Property_RO
353 def dtype(self):
354 '''Get the grid C{scipy} U{dtype<https://docs.SciPy.org/doc/numpy/
355 reference/generated/numpy.ndarray.dtype.html>} (C{numpy.dtype}).
356 '''
357 return self._hs_y_x.dtype
359 @Property_RO
360 def endian(self):
361 '''Get the geoid endianess and U{dtype<https://docs.SciPy.org/
362 doc/numpy/reference/generated/numpy.dtype.html>} (C{str}).
363 '''
364 return self._endian
366 def _ev(self, y, x): # PYCHOK expected
367 # only used for .interpolate.interp2d, but
368 # overwritten for .RectBivariateSpline,
369 # note (y, x) must be flipped!
370 return self._interp2d(x, y)
372 def _gaxis2(self, lo, d, n, name):
373 # build grid axis, hi = lo + (n - 1) * d
374 m, a = len2(frange(lo, n, d))
375 if m != n:
376 raise LenError(self.__class__, grid=m, **{name: n})
377 if d < 0:
378 d, a = -d, list(reversed(a))
379 for i in range(1, m):
380 e = a[i] - a[i-1]
381 if e < EPS: # non-increasing axis
382 i = Fmt.INDEX(name, i)
383 raise GeoidError(i, e, txt=_non_increasing_)
384 return self.numpy.array(a), d
386 def _g2ll2(self, lat, lon): # PYCHOK no cover
387 '''(INTERNAL) I{Must be overloaded}.'''
388 self._notOverloaded(lat, lon)
390 def _gyx2g2(self, y, x):
391 # convert grid (y, x) indices to grid (lat, lon)
392 return ((self._lat_lo + self._lat_d * y),
393 (self._lon_lo + self._lon_of + self._lon_d * x))
395 def height(self, lats, lons, **wrap):
396 '''Interpolate the geoid height for one or several lat-/longitudes.
398 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s).
399 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s).
400 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{lats}}
401 and B{C{lons}} locations (C{bool}).
403 @return: A single interpolated geoid height (C{float}) or a
404 list of interpolated geoid heights (C{float}s).
406 @raise GeoidError: Insufficient or non-matching number of
407 B{C{lats}} and B{C{lons}}.
409 @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this
410 geoid's lat- or longitude range.
412 @raise SciPyError: A C{scipy.interpolate.inter2d} or
413 C{-.RectBivariateSpline} issue.
415 @raise SciPyWarning: A C{scipy.interpolate.inter2d} or
416 C{-.RectBivariateSpline} warning as
417 exception.
418 '''
419 return _height_called(self, lats, lons, Error=GeoidError, **wrap)
421 def _hGeoid(self, lat, lon):
422 out = self.outside(lat, lon)
423 if out:
424 lli = fstr((lat, lon), strepr=repr)
425 raise RangeError(lli=lli, txt=_SPACE_(_outside_, _on_, out))
426 return float(self._ev(*self._ll2g2(lat, lon)))
428 @Property_RO
429 def _highest(self):
430 '''(INTERNAL) Cache for L{highest} method.
431 '''
432 return self._llh3minmax(True)
434 def highest(self, LatLon=None, **unused):
435 '''Return the location and largest height of this geoid.
437 @kwarg LatLon: Optional class to return the location and height
438 (C{LatLon}) or C{None}.
440 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,
441 lon, height)} otherwise a B{C{LatLon}} instance
442 with the lat-, longitude and geoid height of the
443 highest grid location.
444 '''
445 return self._llh3LL(self._highest, LatLon)
447 @Property_RO
448 def hits(self):
449 '''Get the number of cache hits (C{int} or C{None}).
450 '''
451 return self._yx_hits
453 @deprecated_method
454 def _interp2d(self, xs, ys, hs=(), k=0): # overwritten in .__init__ above
455 '''DEPRECATED on 23.01.06, use keyword argument C{B{kind}=1..5}.'''
456 # assert k in _interp2d_ks # and len(hs) == len(xs) == len(ys)
457 try:
458 return self.scipy_interpolate.interp2d(xs, ys, hs, kind=_interp2d_ks[k])
459 except AttributeError as x:
460 raise SciPyError(interp2d=MISSING, kind=k, cause=x)
462 @Property_RO
463 def kind(self):
464 '''Get the interpolator kind and order (C{int}).
465 '''
466 return self._kind
468 @Property_RO
469 def knots(self):
470 '''Get the number of grid knots (C{int}).
471 '''
472 return self._knots
474 def _ll2g2(self, lat, lon): # PYCHOK no cover
475 '''(INTERNAL) I{Must be overloaded}.'''
476 self._notOverloaded(lat, lon)
478 @property_RO
479 def _LL3T(self):
480 '''(INTERNAL) Get L{LatLon3Tuple}, I{once}.
481 '''
482 _GeoidBase._LL3T = T = _MODS.namedTuples.LatLon3Tuple # overwrite poperty_RO
483 return T
485 def _llh3(self, lat, lon):
486 return self._LL3T(lat, lon, self._hGeoid(lat, lon), name=self.name)
488 def _llh3LL(self, llh, LatLon):
489 return llh if LatLon is None else self._xnamed(LatLon(*llh))
491 def _llh3minmax(self, highest=True, *unused):
492 hs, np = self._hs_y_x, self.numpy
493 # <https://docs.SciPy.org/doc/numpy/reference/generated/
494 # numpy.argmin.html#numpy.argmin>
495 arg = np.argmax if highest else np.argmin
496 y, x = np.unravel_index(arg(hs, axis=None), hs.shape)
497 return self._g2ll2(*self._gyx2g2(y, x)) + (float(hs[y, x]),)
499 def _load(self, g, dtype, n, offset=0):
500 # numpy.fromfile, like .frombuffer
501 g.seek(offset, _SEEK_SET)
502 return self.numpy.fromfile(g, dtype, n)
504 @Property_RO
505 def _lowerleft(self):
506 '''(INTERNAL) Cache for L{lowerleft}.
507 '''
508 return self._llh3(self._lat_lo, self._lon_lo)
510 def lowerleft(self, LatLon=None):
511 '''Return the lower-left location and height of this geoid.
513 @kwarg LatLon: Optional class to return the location
514 (C{LatLon}) and height or C{None}.
516 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,
517 lon, height)} otherwise a B{C{LatLon}} instance
518 with the lat-, longitude and geoid height of the
519 lower-left, SW grid corner.
520 '''
521 return self._llh3LL(self._lowerleft, LatLon)
523 @Property_RO
524 def _loweright(self):
525 '''(INTERNAL) Cache for L{loweright}.
526 '''
527 return self._llh3(self._lat_lo, self._lon_hi)
529 def loweright(self, LatLon=None):
530 '''Return the lower-right location and height of this geoid.
532 @kwarg LatLon: Optional class to return the location and height
533 (C{LatLon}) or C{None}.
535 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,
536 lon, height)} otherwise a B{C{LatLon}} instance
537 with the lat-, longitude and geoid height of the
538 lower-right, SE grid corner.
539 '''
541 return self._llh3LL(self._loweright, LatLon)
543 lowerright = loweright # synonymous
545 @Property_RO
546 def _lowest(self):
547 '''(INTERNAL) Cache for L{lowest}.
548 '''
549 return self._llh3minmax(False)
551 def lowest(self, LatLon=None, **unused):
552 '''Return the location and lowest height of this geoid.
554 @kwarg LatLon: Optional class to return the location and height
555 (C{LatLon}) or C{None}.
557 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,
558 lon, height)} otherwise a B{C{LatLon}} instance
559 with the lat-, longitude and geoid height of the
560 lowest grid location.
561 '''
562 return self._llh3LL(self._lowest, LatLon)
564 @Property_RO
565 def mean(self):
566 '''Get the mean of this geoid's heights (C{float}).
567 '''
568 if self._mean is None: # see GeoidKarney
569 self._mean = float(self.numpy.mean(self._hs_y_x))
570 return self._mean
572 @property_RO
573 def name(self):
574 '''Get the name of this geoid (C{str}).
575 '''
576 return _HeightsBase.name.fget(self) or self._geoid # recursion
578 @Property_RO
579 def nBytes(self):
580 '''Get the grid in-memory size in bytes (C{int}).
581 '''
582 return self._nBytes
584 def _open(self, geoid, datum, kind, name, smooth):
585 # open the geoid file
586 try:
587 self._geoid = _os_path.basename(geoid)
588 self._sizeB = _os_path.getsize(geoid)
589 g = open(geoid, _rb_)
590 except (IOError, OSError) as x:
591 raise GeoidError(geoid=geoid, cause=x)
593 if datum not in (None, self._datum):
594 self._datum = _ellipsoidal_datum(datum, name=name)
595 self._kind = int(kind)
596 if name:
597 _HeightsBase.name.fset(self, name) # rename
598 if smooth:
599 self._smooth = Int_(smooth=smooth, Error=GeoidError, low=0)
601 return g
603 def outside(self, lat, lon):
604 '''Check whether a location is outside this geoid's
605 lat-/longitude or crop range.
607 @arg lat: The latitude (C{degrees}).
608 @arg lon: The longitude (C{degrees}).
610 @return: A 1- or 2-character C{str} if outside or an
611 empty C{str} if inside.
612 '''
613 return (_S_ if lat < self._lat_lo else
614 (_N_ if lat > self._lat_hi else NN)) + \
615 (_W_ if lon < self._lon_lo else
616 (_E_ if lon > self._lon_hi else NN))
618 @Property_RO
619 def pgm(self):
620 '''Get the PGM attributes (C{_PGM} or C{None} if not available/applicable).
621 '''
622 return self._pgm
624 @Property_RO
625 def sizeB(self):
626 '''Get the geoid grid file size in bytes (C{int}).
627 '''
628 return self._sizeB
630 @Property_RO
631 def smooth(self):
632 '''Get the C{RectBivariateSpline} smoothing (C{int}).
633 '''
634 return self._smooth
636 @Property_RO
637 def stdev(self):
638 '''Get the standard deviation of this geoid's heights (C{float}) or C{None}.
639 '''
640 if self._stdev is None: # see GeoidKarney
641 self._stdev = float(self.numpy.std(self._hs_y_x))
642 return self._stdev
644 def _swne(self, crop):
645 # crop box to 4-tuple (s, w, n, e)
646 try:
647 if len(crop) == 2:
648 try: # sw, ne LatLons
649 swne = (crop[0].lat, crop[0].lon,
650 crop[1].lat, crop[1].lon)
651 except AttributeError: # (s, w), (n, e)
652 swne = tuple(crop[0]) + tuple(crop[1])
653 else: # (s, w, n, e)
654 swne = crop
655 if len(swne) == 4:
656 s, w, n, e = map(float, swne)
657 if -90 <= s <= (n - _1_0) <= 89 and \
658 -180 <= w <= (e - _1_0) <= 179:
659 return s, w, n, e
660 except (IndexError, TypeError, ValueError):
661 pass
662 raise GeoidError(crop=crop)
664 def toStr(self, prec=3, sep=_COMMASPACE_): # PYCHOK signature
665 '''This geoid and all geoid attributes as a string.
667 @kwarg prec: Number of decimal digits (0..9 or C{None} for
668 default). Trailing zero decimals are stripped
669 for B{C{prec}} values of 1 and above, but kept
670 for negative B{C{prec}} values.
671 @kwarg sep: Separator to join (C{str}).
673 @return: Geoid name and attributes (C{str}).
674 '''
675 s = 1 if self.kind < 0 else 2
676 t = tuple(Fmt.PAREN(m.__name__, fstr(m(), prec=prec)) for m in
677 (self.lowerleft, self.upperright,
678 self.center,
679 self.highest, self.lowest)) + \
680 attrs( _mean_, _stdev_, prec=prec, Nones=False) + \
681 attrs((_kind_, 'smooth')[:s], prec=prec, Nones=False) + \
682 attrs( 'cropped', 'dtype', _endian_, 'hits', 'knots', 'nBytes',
683 'sizeB', _scipy_, _numpy_, prec=prec, Nones=False)
684 return _COLONSPACE_(self, sep.join(t))
686 @Property_RO
687 def u2B(self):
688 '''Get the PGM itemsize in bytes (C{int}).
689 '''
690 return self._u2B
692 @Property_RO
693 def _upperleft(self):
694 '''(INTERNAL) Cache for method L{upperleft}.
695 '''
696 return self._llh3(self._lat_hi, self._lon_lo)
698 def upperleft(self, LatLon=None):
699 '''Return the upper-left location and height of this geoid.
701 @kwarg LatLon: Optional class to return the location and height
702 (C{LatLon}) or C{None}.
704 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,
705 lon, height)} otherwise a B{C{LatLon}} instance
706 with the lat-, longitude and geoid height of the
707 upper-left, NW grid corner.
708 '''
709 return self._llh3LL(self._upperleft, LatLon)
711 @Property_RO
712 def _upperright(self):
713 '''(INTERNAL) Cache for method L{upperright}.
714 '''
715 return self._llh3(self._lat_hi, self._lon_hi)
717 def upperright(self, LatLon=None):
718 '''Return the upper-right location and height of this geoid.
720 @kwarg LatLon: Optional class to return the location and height
721 (C{LatLon}) or C{None}.
723 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,
724 lon, height)} otherwise a B{C{LatLon}} instance
725 with the lat-, longitude and geoid height of the
726 upper-right, NE grid corner.
727 '''
728 return self._llh3LL(self._upperright, LatLon)
731class GeoidError(HeightError):
732 '''Geoid interpolator C{Geoid...} or interpolation issue.
733 '''
734 pass
737class GeoidG2012B(_GeoidBase):
738 '''Geoid height interpolator for U{GEOID12B Model
739 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/>} grids U{CONUS
740 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_CONUS.shtml>},
741 U{Alaska<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_AK.shtml>},
742 U{Hawaii<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_HI.shtml>},
743 U{Guam and Northern Mariana Islands
744 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_GMNI.shtml>},
745 U{Puerto Rico and U.S. Virgin Islands
746 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_PRVI.shtml>} and
747 U{American Samoa<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_AS.shtml>}
748 based on C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/doc/
749 scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>}
750 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/
751 scipy.interpolate.interp2d.html>} interpolation.
753 Use any of the binary C{le} (little endian) or C{be} (big endian)
754 C{g2012b*.bin} grid files.
755 '''
756 def __init__(self, g2012b_bin, datum=None, # NAD 83 Ellipsoid
757 kind=3, smooth=0, **name_crop):
758 '''New L{GeoidG2012B} interpolator.
760 @arg g2012b_bin: A C{GEOID12B} grid file name (C{.bin}).
761 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
762 or L{a_f2Tuple}), default C{WGS84}.
763 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for
764 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/
765 reference/generated/scipy.interpolate.RectBivariateSpline.html>},
766 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/
767 reference/generated/scipy.interpolate.interp2d.html>}, -3
768 for C{interp2d cubic} or -5 for C{interp2d quintic}.
769 @kwarg smooth: Smoothing factor for U{RectBivariateSpline
770 <https://docs.SciPy.org/doc/scipy/reference/generated/
771 scipy.interpolate.RectBivariateSpline.html>}
772 only (C{int}).
773 @kwarg name_crop: Optional geoid C{B{name}=NN} (C{str}) and UNSUPPORTED
774 keyword argument C{B{crop}}, use C{B{crop}=None} to ignore.
776 @raise GeoidError: G2012B grid file B{C{g2012b_bin}} issue or invalid
777 B{C{crop}}, B{C{kind}} or B{C{smooth}}.
779 @raise ImportError: Package C{numpy} or C{scipy} not found or not
780 installed.
782 @raise LenError: Grid file B{C{g2012b_bin}} axis mismatch.
784 @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue.
786 @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d}
787 warning as exception.
789 @raise TypeError: Invalid B{C{datum}}.
791 @note: C{scipy.interpolate.interp2d} has been C{DEPRECATED}, specify
792 C{B{kind}=1..5} for C{scipy.interpolate.RectBivariateSpline}.
793 '''
794 crop, name = _xkwds_pop2(name_crop, crop=None)
795 if crop is not None:
796 raise GeoidError(crop=crop, txt_not_=_supported_)
798 g = self._open(g2012b_bin, datum, kind, _name__(**name), smooth)
799 _ = self.numpy # import numpy for ._load and
801 try:
802 p = _Gpars()
803 n = (self.sizeB // 4) - 11 # number of f4 heights
804 # U{numpy dtype formats are different from Python struct formats
805 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>}
806 for en_ in ('<', '>'):
807 # skip 4xf8, get 3xi4
808 p.nlat, p.nlon, ien = map(int, self._load(g, en_+'i4', 3, 32))
809 if ien == 1: # correct endian
810 p.knots = p.nlat * p.nlon
811 if p.knots == n and 1 < p.nlat < n \
812 and 1 < p.nlon < n:
813 self._endian = en_+'f4'
814 break
815 else: # couldn't validate endian
816 raise GeoidError(_endian_)
818 # get the first 4xf8
819 p.slat, p.wlon, p.dlat, p.dlon = map(float, self._load(g, en_+'f8', 4))
820 # read all f4 heights, ignoring the first 4xf8 and 3xi4
821 hs = self._load(g, self._endian, n, 44).reshape(p.nlat, p.nlon)
822 p.wlon -= _360_0 # western-most East longitude to earth (..., lon)
823 _GeoidBase.__init__(self, hs, p)
825 except Exception as x:
826 raise _SciPyIssue(x, _in_, repr(g2012b_bin))
827 finally:
828 g.close()
830 def _g2ll2(self, lat, lon):
831 # convert grid (lat, lon) to earth (lat, lon)
832 return lat, lon
834 def _ll2g2(self, lat, lon):
835 # convert earth (lat, lon) to grid (lat, lon)
836 return lat, lon
838 if _FOR_DOCS:
839 __call__ = _GeoidBase.__call__
840 height = _GeoidBase.height
843class GeoidHeight5Tuple(_NamedTuple): # .geoids.py
844 '''5-Tuple C{(lat, lon, egm84, egm96, egm2008)} for U{GeoidHeights.dat
845 <https://SourceForge.net/projects/geographiclib/files/testdata/>}
846 tests with the heights for 3 different EGM grids at C{degrees90}
847 and C{degrees180} degrees (after converting C{lon} from original
848 C{0 <= EasterLon <= 360}).
849 '''
850 _Names_ = (_lat_, _lon_, 'egm84', 'egm96', 'egm2008')
851 _Units_ = ( Lat, Lon, Height, Height, Height)
854def _I(i):
855 '''(INTERNAL) Cache a single C{int} constant.
856 '''
857 return _intCs.setdefault(i, i) # PYCHOK undefined due to del _intCs
860def _T(*cs):
861 '''(INTERNAL) Cache a tuple of single C{int} constants.
862 '''
863 return map1(_I, *cs)
865_T0s12 = (_I(0),) * 12 # PYCHOK _T(0, 0, ..., 0)
868class GeoidKarney(_GeoidBase):
869 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth
870 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/
871 geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/
872 C++/doc/geoid.html#geoidinst>} datasets using bilinear or U{cubic
873 <https://dl.ACM.org/citation.cfm?id=368443>} interpolation and U{caching
874 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidcache>}
875 in pure Python, transcoded from I{Karney}'s U{C++ class Geoid
876 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinterp>}.
878 Use any of the geoid U{egm84-, egm96- or egm2008-*.pgm
879 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>}
880 datasets.
881 '''
882 _C0 = _F(372), _F(240), _F(372) # n, _ and s common denominators
883 # matrices c3n_, c3, c3s_, transposed from GeographicLib/Geoid.cpp
884 _C3 = ((_T(0, 0, 62, 124, 124, 62, 0, 0, 0, 0, 0, 0),
885 _T0s12,
886 _T(-131, 7, -31, -62, -62, -31, 45, 216, 156, -45, -55, -7),
887 _T0s12,
888 _T(138, -138, 0, 0, 0, 0, -183, 33, 153, -3, 48, -48), # PYCHOK indent
889 _T(144, 42, -62, -124, -124, -62, -9, 87, 99, 9, 42, -42),
890 _T0s12,
891 _T(0, 0, 0, 0, 0, 0, 93, -93, -93, 93, 0, 0),
892 _T(-102, 102, 0, 0, 0, 0, 18, 12, -12, -18, -84, 84),
893 _T(-31, -31, 31, 62, 62, 31, 0, -93, -93, 0, 31, 31)), # PYCHOK indent
895 (_T(9, -9, 9, 186, 54, -9, -9, 54, -54, 9, -9, 9),
896 _T(-18, 18, -88, -42, 162, -32, 8, -78, 78, -8, 18, -18),
897 _T(-88, 8, -18, -42, -78, 18, 18, 162, 78, -18, -32, -8),
898 _T(0, 0, 90, -150, 30, 30, 30, -90, 90, -30, 0, 0),
899 _T(96, -96, 96, -96, -24, 24, -96, -24, 144, -24, 24, -24), # PYCHOK indent
900 _T(90, 30, 0, -150, -90, 0, 0, 30, 90, 0, 30, -30),
901 _T(0, 0, -20, 60, -60, 20, -20, 60, -60, 20, 0, 0),
902 _T(0, 0, -60, 60, 60, -60, 60, -60, -60, 60, 0, 0),
903 _T(-60, 60, 0, 60, -60, 0, 0, 60, -60, 0, -60, 60),
904 _T(-20, -20, 0, 60, 60, 0, 0, -60, -60, 0, 20, 20)),
906 (_T(18, -18, 36, 210, 162, -36, 0, 0, 0, 0, -18, 18), # PYCHOK indent
907 _T(-36, 36, -165, 45, 141, -21, 0, 0, 0, 0, 36, -36),
908 _T(-122, -2, -27, -111, -75, 27, 62, 124, 124, 62, -64, 2),
909 _T(0, 0, 93, -93, -93, 93, 0, 0, 0, 0, 0, 0),
910 _T(120, -120, 147, -57, -129, 39, 0, 0, 0, 0, 66, -66), # PYCHOK indent
911 _T(135, 51, -9, -192, -180, 9, 31, 62, 62, 31, 51, -51),
912 _T0s12,
913 _T(0, 0, -93, 93, 93, -93, 0, 0, 0, 0, 0, 0),
914 _T(-84, 84, 18, 12, -12, -18, 0, 0, 0, 0, -102, 102),
915 _T(-31, -31, 0, 93, 93, 0, -31, -62, -62, -31, 31, 31)))
917 _BT = (_T(0, 0), # bilinear 4-tuple [i, j] indices
918 _T(1, 0),
919 _T(0, 1),
920 _T(1, 1))
922 _CM = (_T( 0, -1), # 10x12 cubic matrix [i, j] indices
923 _T( 1, -1),
924 _T(-1, 0),
925 _T( 0, 0),
926 _T( 1, 0),
927 _T( 2, 0),
928 _T(-1, 1),
929 _T( 0, 1),
930 _T( 1, 1),
931 _T( 2, 1),
932 _T( 0, 2),
933 _T( 1, 2))
935 _endian = '>H' # struct.unpack 1 ushort (big endian, unsigned short)
936 _4endian = '>4H' # struct.unpack 4 ushorts
937 _Rendian = NN # struct.unpack a row of ushorts
938# _highest = (-8.4, 147.367, 85.839) if egm2008-1.pgm else (
939# (-8.167, 147.25, 85.422) if egm96-5.pgm else
940# (-4.5, 148.75, 81.33)) # egm84-15.pgm
941# _lowest = (4.7, 78.767, -106.911) if egm2008-1.pgm else (
942# (4.667, 78.833, -107.043) if egm96-5.pgm else
943# (4.75, 79.25, -107.34)) # egm84-15.pgm
944 _mean = _F(-1.317) # from egm2008-1, -1.438 egm96-5, -0.855 egm84-15
945 _nBytes = None # not applicable
946 _nterms = len(_C3[0]) # columns length, number of row
947 _smooth = None # not applicable
948 _stdev = _F(29.244) # from egm2008-1, 29.227 egm96-5, 29.183 egm84-15
949 _u2B = _calcsize(_endian) # pixelsize_ in bytes
950 _4u2B = _calcsize(_4endian) # 4 pixelsize_s in bytes
951 _Ru2B = 0 # row of pixelsize_s in bytes
952 _yxH = () # cache (y, x) indices
953 _yxHt = () # cached 4- or 10-tuple for _ev2H resp. _ev3H
954 _yx_hits = 0 # cache hits
956 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84
957 kind=3, **name_smooth):
958 '''New L{GeoidKarney} interpolator.
960 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/
961 C++/doc/geoid.html#geoidinst>} file name (C{egm*.pgm}), see
962 note below.
963 @kwarg crop: Optional box to limit geoid locations, a 4-tuple (C{south,
964 west, north, east}), 2-tuple (C{(south, west), (north,
965 east)}) or 2, in C{degrees90} lat- and C{degrees180}
966 longitudes or a 2-tuple (C{LatLonSW, LatLonNE}) of
967 C{LatLon} instances.
968 @kwarg datum: Optional grid datum (C{Datum}, L{Ellipsoid}, L{Ellipsoid2}
969 or L{a_f2Tuple}), default C{WGS84}.
970 @kwarg kind: Interpolation order (C{int}), 2 for C{bilinear} or 3
971 for C{cubic}.
972 @kwarg name_smooth: Optional geoid C{B{name}=NN} (C{str}) and UNSUPPORTED
973 keyword argument C{B{smooth}}, use C{B{smooth}=None} to ignore.
975 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid
976 B{C{crop}}, B{C{kind}} or B{C{smooth}}.
978 @raise TypeError: Invalid B{C{datum}}.
980 @see: Class L{GeoidPGM} and function L{egmGeoidHeights}.
982 @note: Geoid file B{C{egm_pgm}} remains open and must be closed
983 by calling the C{close} method or by using this instance
984 in a C{with B{GeoidKarney}(...) as ...} context.
985 '''
986 smooth, name = _xkwds_pop2(name_smooth, smooth=None)
987 if smooth is not None:
988 raise GeoidError(smooth=smooth, txt_not_=_supported_)
990 if kind in (2,):
991 self._evH = self._ev2H
992 elif kind not in (3,):
993 raise GeoidError(kind=kind)
995 self._egm = g = self._open(egm_pgm, datum, kind, _name__(**name), None)
996 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB)
998 self._Rendian = self._4endian.replace(_4_, str(p.nlon))
999 self._Ru2B = _calcsize(self._Rendian)
1001 self._knots = p.knots # grid knots
1002 self._lon_of = float(p.flon) # forward offset
1003 self._lon_og = float(p.glon) # reverse offset
1004 # set earth (lat, lon) limits (s, w, n, e)
1005 self._lat_lo, self._lon_lo, \
1006 self._lat_hi, self._lon_hi = self._swne(crop if crop else p.crop4)
1007 self._cropped = True if crop else False
1009 def __call__(self, *llis, **wrap_H):
1010 '''Interpolate the geoid height for one or several locations.
1012 @arg llis: One or more locations (C{LatLon}s), all positional.
1013 @kwarg wrap_H: Keyword arguments C{B{wrap}=False, B{H}=False}.
1014 If C{B{wrap} is True}, wrap or I{normalize} all
1015 B{C{llis}} locations (C{bool}). If C{B{H} is True},
1016 return the I{orthometric} height instead of the
1017 I{geoid} height at each location (C{bool}).
1019 @return: A single interpolated geoid (or orthometric) height
1020 (C{float}) or a list or tuple of interpolated geoid
1021 (or orthometric) heights (C{float}s).
1023 @raise GeoidError: Insufficient number of B{C{llis}}, an
1024 invalid B{C{lli}} or the C{egm*.pgm}
1025 geoid file is closed.
1027 @raise RangeError: An B{C{lli}} is outside this geoid's lat-
1028 or longitude range.
1030 @note: To obtain I{orthometric} heights, each B{C{llis}}
1031 location must have an ellipsoid C{height} or C{h}
1032 attribute, otherwise C{height=0} is used.
1034 @see: Function L{pygeodesy.heightOrthometric}.
1035 '''
1036 return self._called(llis, False, **wrap_H)
1038 def _c0c3v(self, y, x):
1039 # get the common denominator, the 10x12 cubic matrix and
1040 # the 12 cubic v-coefficients around geoid index (y, x)
1041 p = self._pgm
1042 if 0 < x < (p.nlon - 2) and 0 < y < (p.nlat - 2):
1043 # read 4x4 ushorts, drop the 4 corners
1044 g = self._egm
1045 e = self._4endian
1046 n = self._4u2B
1047 R = self._Ru2B
1049 b = self._seek(y - 1, x - 1)
1050 v = _unpack(e, g.read(n))[1:3]
1051 b += R
1052 g.seek(b, _SEEK_SET)
1053 v += _unpack(e, g.read(n))
1054 b += R
1055 g.seek(b, _SEEK_SET)
1056 v += _unpack(e, g.read(n))
1057 b += R
1058 g.seek(b, _SEEK_SET)
1059 v += _unpack(e, g.read(n))[1:3]
1060 j = 1
1062 else: # likely some wrapped y and/or x's
1063 v = self._raws(y, x, GeoidKarney._CM)
1064 j = 0 if y < 1 else (1 if y < (p.nlat - 2) else 2)
1066 return GeoidKarney._C0[j], GeoidKarney._C3[j], v
1068 @Property_RO
1069 def dtype(self):
1070 '''Get the geoid's grid data type (C{str}).
1071 '''
1072 return 'ushort'
1074 def _ev(self, lat, lon): # PYCHOK expected
1075 # interpolate the geoid height at grid (lat, lon)
1076 fy, fx = self._g2yx2(lat, lon)
1077 y, x = int(floor(fy)), int(floor(fx))
1078 fy -= y
1079 fx -= x
1080 H = self._evH(fy, fx, y, x) # ._ev3H or ._ev2H
1081 H *= self._pgm.Scale # H.fmul(self._pgm.Scale)
1082 H += self._pgm.Offset # H.fadd(self._pgm.Offset)
1083 return H.fsum()
1085 def _ev2H(self, fy, fx, *yx):
1086 # compute the bilinear 4-tuple and interpolate raw H
1087 if self._yxH == yx:
1088 t = self._yxHt
1089 self._yx_hits += 1
1090 else:
1091 y, x = self._yxH = yx
1092 self._yxHt = t = self._raws(y, x, GeoidKarney._BT)
1093 v = _1_0, -fx, fx
1094 H = Fdot(v, t[0], t[0], t[1]).fmul(_1_0 - fy) # c = a * (1 - fy)
1095 H += Fdot(v, t[2], t[2], t[3]).fmul(fy) # c += b * fy
1096 return H
1098 def _ev3H(self, fy, fx, *yx):
1099 # compute the cubic 10-tuple and interpolate raw H
1100 if self._yxH == yx:
1101 t = self._yxHt
1102 self._yx_hits += 1
1103 else:
1104 self._yxH = yx
1105 c0, c3, v = self._c0c3v(*yx)
1106 t = [fdot(v, *c3[i]) / c0 for i in range(self._nterms)]
1107 self._yxHt = t = tuple(t)
1108 # GeographicLib/Geoid.cpp Geoid::height(lat, lon) ...
1109 # real h = t[0] + fx * (t[1] + fx * (t[3] + fx * t[6])) +
1110 # fy * (t[2] + fx * (t[4] + fx * t[7]) +
1111 # fy * (t[5] + fx * t[8] + fy * t[9]));
1112 v = _1_0, fx, fy
1113 H = Fdot(v, t[5], t[8], t[9])
1114 H *= fy
1115 H += Fhorner(fx, t[2], t[4], t[7])
1116 H *= fy
1117 H += Fhorner(fx, t[0], t[1], t[3], t[6])
1118 return H
1120 _evH = _ev3H # overriden for kind == 2
1122 def _g2ll2(self, lat, lon):
1123 # convert grid (lat, lon) to earth (lat, lon), uncropped
1124 while lon > _180_0:
1125 lon -= _360_0
1126 return lat, lon
1128 def _g2yx2(self, lat, lon):
1129 # convert grid (lat, lon) to grid (y, x) indices
1130 p = self._pgm
1131 # note, slat = +90, rlat < 0 makes y >=0
1132 return ((lat - p.slat) * p.rlat), ((lon - p.wlon) * p.rlon)
1134 def _gyx2g2(self, y, x):
1135 # convert grid (y, x) indices to grid (lat, lon)
1136 p = self._pgm
1137 return (p.slat + p.dlat * y), (p.wlon + p.dlon * x)
1139 def height(self, lats, lons, **wrap):
1140 '''Interpolate the geoid height for one or several lat-/longitudes.
1142 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s).
1143 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s).
1144 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{lats}}
1145 and B{C{lons}} locations (C{bool}).
1147 @return: A single interpolated geoid height (C{float}) or a
1148 list of interpolated geoid heights (C{float}s).
1150 @raise GeoidError: Insufficient or non-matching number of
1151 B{C{lats}} and B{C{lons}} or the C{egm*.pgm}
1152 geoid file is closed.
1154 @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this
1155 geoid's lat- or longitude range.
1156 '''
1157 return _height_called(self, lats, lons, Error=GeoidError, **wrap)
1159 @Property_RO
1160 def _highest_ltd(self):
1161 '''(INTERNAL) Cache for L{highest} mesthod.
1162 '''
1163 return self._llh3minmax(True, -12, -4)
1165 def highest(self, LatLon=None, full=False): # PYCHOK full
1166 '''Return the location and largest height of this geoid.
1168 @kwarg LatLon: Optional class to return the location and height
1169 (C{LatLon}) or C{None}.
1170 @kwarg full: Search the full or limited latitude range (C{bool}).
1172 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,
1173 lon, height)} otherwise a B{C{LatLon}} instance
1174 with the lat-, longitude and geoid height at the
1175 highest grid location.
1176 '''
1177 llh = self._highest if full or self.cropped else self._highest_ltd
1178 return self._llh3LL(llh, LatLon)
1180 def _lat2y2(self, lat2):
1181 # convert earth lat(s) to min and max grid y indices
1182 ys, m = [], self._pgm.nlat - 1
1183 for lat in lat2:
1184 y, _ = self._g2yx2(*self._ll2g2(lat, 0))
1185 ys.append(max(min(int(y), m), 0))
1186 return min(ys), max(ys) + 1
1188 def _ll2g2(self, lat, lon):
1189 # convert earth (lat, lon) to grid (lat, lon), uncropped
1190 while lon < 0:
1191 lon += _360_0
1192 return lat, lon
1194 def _llh3minmax(self, highest=True, *lat2):
1195 # find highest or lowest, takes 10+ secs for egm2008-1.pgm geoid
1196 # (Python 2.7.16, macOS 10.13.6 High Sierra, iMac 3 GHz Core i3)
1197 y = x = 0
1198 h = self._raw(y, x)
1199 if highest:
1200 for j, r in self._raw2(*lat2):
1201 m = max(r)
1202 if m > h:
1203 h, y, x = m, j, r.index(m)
1204 else: # lowest
1205 for j, r in self._raw2(*lat2):
1206 m = min(r)
1207 if m < h:
1208 h, y, x = m, j, r.index(m)
1209 h *= self._pgm.Scale
1210 h += self._pgm.Offset
1211 return self._g2ll2(*self._gyx2g2(y, x)) + (h,)
1213 @Property_RO
1214 def _lowest_ltd(self):
1215 '''(INTERNAL) Cache for L{lowest}.
1216 '''
1217 return self._llh3minmax(False, 0, 8)
1219 def lowest(self, LatLon=None, full=False): # PYCHOK full
1220 '''Return the location and lowest height of this geoid.
1222 @kwarg LatLon: Optional class to return the location and height
1223 (C{LatLon}) or C{None}.
1224 @kwarg full: Search the full or limited latitude range (C{bool}).
1226 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,
1227 lon, height)} otherwise a B{C{LatLon}} instance
1228 with the lat-, longitude and geoid height of the
1229 lowest grid location.
1230 '''
1231 llh = self._lowest if full or self.cropped else self._lowest_ltd
1232 return self._llh3LL(llh, LatLon)
1234 def _raw(self, y, x):
1235 # get the ushort geoid height at geoid index (y, x),
1236 # like GeographicLib/Geoid.hpp real rawval(is, iy)
1237 p = self._pgm
1238 if x < 0:
1239 x += p.nlon
1240 elif x >= p.nlon:
1241 x -= p.nlon
1242 h = p.nlon // 2
1243 if y < 0:
1244 y = -y
1245 elif y >= p.nlat:
1246 y = (p.nlat - 1) * 2 - y
1247 else:
1248 h = 0
1249 x += h if x < h else -h
1250 self._seek(y, x)
1251 h = _unpack(self._endian, self._egm.read(self._u2B))
1252 return h[0]
1254 def _raws(self, y, x, ijs):
1255 # get bilinear 4-tuple or 10x12 cubic matrix
1256 return tuple(self._raw(y + j, x + i) for i, j in ijs)
1258 def _raw2(self, *lat2):
1259 # yield a 2-tuple (y, ushorts) for each row or for
1260 # the rows between two (or more) earth lat values
1261 p = self._pgm
1262 g = self._egm
1263 e = self._Rendian
1264 n = self._Ru2B
1265 # min(lat2) <= lat <= max(lat2) or 0 <= y < p.nlat
1266 s, t = self._lat2y2(lat2) if lat2 else (0, p.nlat)
1267 self._seek(s, 0) # to start of row s
1268 for y in range(s, t):
1269 yield y, _unpack(e, g.read(n))
1271 def _seek(self, y, x):
1272 # position geoid to grid index (y, x)
1273 p, g = self._pgm, self._egm
1274 if g:
1275 b = p.skip + (y * p.nlon + x) * self._u2B
1276 g.seek(b, _SEEK_SET)
1277 return b # position
1278 raise GeoidError('closed file', txt=repr(p.egm)) # IOError
1281class GeoidPGM(_GeoidBase):
1282 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth
1283 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/
1284 geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/
1285 C++/doc/geoid.html#geoidinst>} datasets but based on C{SciPy}
1286 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/reference/
1287 generated/scipy.interpolate.RectBivariateSpline.html>} or
1288 U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/
1289 scipy.interpolate.interp2d.html>} interpolation.
1291 Use any of the U{egm84-, egm96- or egm2008-*.pgm
1292 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>}
1293 datasets. However, unless cropped, an entire C{egm*.pgm} dataset
1294 is loaded into the C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/
1295 doc/scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>}
1296 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/
1297 scipy.interpolate.interp2d.html>} interpolator and converted from
1298 2-byte C{int} to 8-byte C{dtype float64}. Therefore, internal memory
1299 usage is 4x the U{egm*.pgm<https://GeographicLib.SourceForge.io/C++/doc/
1300 geoid.html#geoidinst>} file size and may exceed the available memory,
1301 especially with 32-bit Python, see properties C{.nBytes} and C{.sizeB}.
1302 '''
1303 _cropped = False
1304 _endian = '>u2'
1306 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84
1307 kind=3, smooth=0, **name):
1308 '''New L{GeoidPGM} interpolator.
1310 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/
1311 C++/doc/geoid.html#geoidinst>} file name (C{egm*.pgm}).
1312 @kwarg crop: Optional box to crop B{C{egm_pgm}}, a 4-tuple (C{south, west,
1313 north, east}) or 2-tuple (C{(south, west), (north, east)}),
1314 in C{degrees90} lat- and C{degrees180} longitudes or a
1315 2-tuple (C{LatLonSW, LatLonNE}) of C{LatLon} instances.
1316 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
1317 or L{a_f2Tuple}), default C{WGS84}.
1318 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for
1319 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/
1320 reference/generated/scipy.interpolate.RectBivariateSpline.html>},
1321 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/
1322 reference/generated/scipy.interpolate.interp2d.html>}, -3
1323 for C{interp2d cubic} or -5 for C{interp2d quintic}.
1324 @kwarg smooth: Smoothing factor for U{RectBivariateSpline
1325 <https://docs.SciPy.org/doc/scipy/reference/generated/
1326 scipy.interpolate.RectBivariateSpline.html>}
1327 only (C{int}).
1328 @kwarg name: Optional geoid C{B{name}=NN} (C{str}).
1330 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid B{C{crop}},
1331 B{C{kind}} or B{C{smooth}}.
1333 @raise ImportError: Package C{numpy} or C{scipy} not found or not installed.
1335 @raise LenError: EGM dataset B{C{egm_pgm}} axis mismatch.
1337 @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue.
1339 @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d}
1340 warning as exception.
1342 @raise TypeError: Invalid B{C{datum}} or unexpected argument.
1344 @note: C{scipy.interpolate.interp2d} has been C{DEPRECATED}, specify
1345 C{B{kind}=1..5} for C{scipy.interpolate.RectBivariateSpline}.
1347 @note: The U{GeographicLib egm*.pgm<https://GeographicLib.SourceForge.io/
1348 C++/doc/geoid.html#geoidinst>} file sizes are based on a 2-byte
1349 C{int} height converted to 8-byte C{dtype float64} for C{scipy}
1350 interpolators. Therefore, internal memory usage is 4 times the
1351 C{egm*.pgm} file size and may exceed the available memory,
1352 especially with 32-bit Python. To reduce memory usage, set
1353 keyword argument B{C{crop}} to the region of interest. For example
1354 C{B{crop}=(20, -125, 50, -65)} covers the U{conterminous US<https://
1355 www.NGS.NOAA.gov/GEOID/GEOID12B/maps/GEOID12B_CONUS_grids.png>}
1356 (CONUS), less than 3% of the entire C{egm2008-1.pgm} dataset.
1358 @see: Class L{GeoidKarney} and function L{egmGeoidHeights}.
1359 '''
1360 np = self.numpy
1361 self._u2B = np.dtype(self.endian).itemsize
1363 g = self._open(egm_pgm, datum, kind, _name__(**name), smooth)
1364 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB)
1365 if crop:
1366 g = p._cropped(g, abs(kind) + 1, *self._swne(crop))
1367 if _MODS.internals._version2(np.__version__) < (1, 9):
1368 g = open(g.name, _rb_) # reopen tempfile for numpy 1.8.0-
1369 self._cropped = True
1370 try:
1371 # U{numpy dtype formats are different from Python struct formats
1372 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>}
1373 # read all heights, skipping the PGM header lines, converted to float
1374 hs = self._load(g, self.endian, p.knots, p.skip).reshape(p.nlat, p.nlon) * p.Scale
1375 if p.Offset: # offset
1376 hs = p.Offset + hs
1377 if p.dlat < 0: # flip the rows
1378 hs = np.flipud(hs)
1379 _GeoidBase.__init__(self, hs, p)
1380 except Exception as x:
1381 raise _SciPyIssue(x, _in_, repr(egm_pgm))
1382 finally:
1383 g.close()
1385 def _g2ll2(self, lat, lon):
1386 # convert grid (lat, lon) to earth (lat, lon), un-/cropped
1387 if self._cropped:
1388 lon -= self._lon_of
1389 else:
1390 while lon > _180_0:
1391 lon -= _360_0
1392 return lat, lon
1394 def _ll2g2(self, lat, lon):
1395 # convert earth (lat, lon) to grid (lat, lon), un-/cropped
1396 if self._cropped:
1397 lon += self._lon_of
1398 else:
1399 while lon < 0:
1400 lon += _360_0
1401 return lat, lon
1403 if _FOR_DOCS:
1404 __call__ = _GeoidBase.__call__
1405 height = _GeoidBase.height
1408class _Gpars(_Named):
1409 '''(INTERNAL) Basic geoid parameters.
1410 '''
1411 # interpolator parameters
1412 dlat = 0 # +/- latitude resolution in C{degrees}
1413 dlon = 0 # longitude resolution in C{degrees}
1414 nlat = 1 # number of latitude knots (C{int})
1415 nlon = 0 # number of longitude knots (C{int})
1416 rlat = 0 # +/- latitude resolution in C{float}, 1 / .dlat
1417 rlon = 0 # longitude resolution in C{float}, 1 / .dlon
1418 slat = 0 # nothern- or southern most latitude (C{degrees90})
1419 wlon = 0 # western-most longitude in Eastern lon (C{degrees360})
1421 flon = 0 # forward, earth to grid longitude offset
1422 glon = 0 # reverse, grid to earth longitude offset
1424 knots = 0 # number of knots, nlat * nlon (C{int})
1425 skip = 0 # header bytes to skip (C{int})
1427 def __repr__(self):
1428 t = _COMMASPACE_.join(pairs((a, getattr(self, a)) for
1429 a in dir(self.__class__)
1430 if a[:1].isupper()))
1431 return _COLONSPACE_(self, t)
1433 def __str__(self):
1434 return Fmt.PAREN(self.classname, repr(self.name))
1437class _PGM(_Gpars):
1438 '''(INTERNAL) Parse an C{egm*.pgm} geoid dataset file.
1440 # Geoid file in PGM format for the GeographicLib::Geoid class
1441 # Description WGS84 EGM96, 5-minute grid
1442 # URL https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html
1443 # DateTime 2009-08-29 18:45:03
1444 # MaxBilinearError 0.140
1445 # RMSBilinearError 0.005
1446 # MaxCubicError 0.003
1447 # RMSCubicError 0.001
1448 # Offset -108
1449 # Scale 0.003
1450 # Origin 90N 0E
1451 # AREA_OR_POINT Point
1452 # Vertical_Datum WGS84
1453 <width> <height>
1454 <pixel>
1455 ...
1456 '''
1457 crop4 = () # 4-tuple (C{south, west, north, east}).
1458 egm = None
1459 glon = 180 # reverse offset, uncropped
1460# pgm = NN # name
1461 sizeB = 0
1462 u2B = 2 # item size of grid height (C{int}).
1464 @staticmethod
1465 def _llstr2floats(latlon):
1466 # llstr to (lat, lon) floats
1467 lat, lon = latlon.split()
1468 return _MODS.dms.parseDMS2(lat, lon)
1470 # PGM file attributes, CamelCase but not .istitle()
1471 AREA_OR_POINT = str
1472 DateTime = str
1473 Description = str # 'WGS84 EGM96, 5-minute grid'
1474 Geoid = str # 'file in PGM format for the GeographicLib::Geoid class'
1475 MaxBilinearError = float
1476 MaxCubicError = float
1477 Offset = float
1478 Origin = _llstr2floats
1479 Pixel = 0
1480 RMSBilinearError = float
1481 RMSCubicError = float
1482 Scale = float
1483 URL = str # 'https://Earth-Info.NGA.mil/GandG/wgs84/...'
1484 Vertical_Datum = str
1486 def __init__(self, g, pgm=NN, itemsize=0, sizeB=0): # MCCABE 22
1487 '''(INTERNAL) New C{_PGM} parsed C{egm*.pgm} geoid dataset.
1488 '''
1489 self.name = pgm # geoid file name
1490 if itemsize:
1491 self._u2B = itemsize
1492 if sizeB:
1493 self.sizeB = sizeB
1495 t = g.readline() # make sure newline == '\n'
1496 if t != b'P5\n' and t.strip() != b'P5':
1497 raise self._Errorf(_format_, _header_, t)
1499 while True: # read all # Attr ... lines,
1500 try: # ignore empty ones or comments
1501 t = g.readline().strip()
1502 if t.startswith(_bHASH_):
1503 t = t.lstrip(_bHASH_).lstrip()
1504 a, v = map(_ub2str, t.split(None, 1))
1505 f = getattr(_PGM, a, None)
1506 if callable(f) and a[:1].isupper():
1507 setattr(self, a, f(v))
1508 elif t:
1509 break
1510 except (TypeError, ValueError):
1511 raise self._Errorf(_format_, 'Attr', t)
1512 else: # should never get here
1513 raise self._Errorf(_format_, _header_, g.tell())
1515 try: # must be (even) width and (odd) height
1516 nlon, nlat = map(int, t.split())
1517 if nlon < 2 or nlon > (360 * 60) or isodd(nlon) or \
1518 nlat < 2 or nlat > (181 * 60) or not isodd(nlat):
1519 raise ValueError
1520 except (TypeError, ValueError):
1521 raise self._Errorf(_format_, _SPACE_(_width_, _height_), t)
1523 try: # must be 16 bit pixel height
1524 t = g.readline().strip()
1525 self.Pixel = int(t)
1526 if not 255 < self.Pixel < 65536: # >u2 or >H only
1527 raise ValueError
1528 except (TypeError, ValueError):
1529 raise self._Errorf(_format_, 'pixel', t)
1531 for a in dir(_PGM): # set undefined # Attr ... to None
1532 if a[:1].isupper() and callable(getattr(self, a)):
1533 setattr(self, a, None)
1535 if self.Origin is None:
1536 raise self._Errorf(_format_, 'Origin', self.Origin)
1537 if self.Offset is None or self.Offset > 0:
1538 raise self._Errorf(_format_, 'Offset', self.Offset)
1539 if self.Scale is None or self.Scale < EPS:
1540 raise self._Errorf(_format_, 'Scale', self.Scale)
1542 self.skip = g.tell()
1543 self.knots = nlat * nlon
1545 self.nlat, self.nlon = nlat, nlon
1546 self.slat, self.wlon = self.Origin
1547 # note, negative .dlat and .rlat since rows
1548 # are from .slat 90N down in decreasing lat
1549 self.dlat, self.dlon = _180_0 / (1 - nlat), _360_0 / nlon
1550 self.rlat, self.rlon = (1 - nlat) / _180_0, nlon / _360_0
1552 # grid corners in earth (lat, lon), .slat = 90, .dlat < 0
1553 n = float(self.slat)
1554 s = n + self.dlat * (nlat - 1)
1555 w = self.wlon - self.glon
1556 e = w + self.dlon * nlon
1557 self.crop4 = s, w, n, e
1559 n = self.sizeB - self.skip
1560 if n > 0 and n != (self.knots * self.u2B):
1561 raise self._Errorf('%s(%s x %s != %s)', _assert_, nlat, nlon, n)
1563 def _cropped(self, g, k1, south, west, north, east): # MCCABE 15
1564 '''Crop the geoid to (south, west, north, east) box.
1565 '''
1566 # flon offset for both west and east
1567 f = 360 if west < 0 else 0
1568 # earth (lat, lon) to grid indices (y, x),
1569 # note y is decreasing, i.e. n < s
1570 s, w = self._lle2yx2(south, west, f)
1571 n, e = self._lle2yx2(north, east, f)
1572 s += 1 # s > n
1573 e += 1 # e > w
1575 hi, wi = self.nlat, self.nlon
1576 # handle special cases
1577 if (s - n) > hi:
1578 n, s = 0, hi # entire lat range
1579 if (e - w) > wi:
1580 w, e, f = 0, wi, 180 # entire lon range
1581 if s == hi and w == n == 0 and e == wi:
1582 return g # use entire geoid as-is
1584 if (e - w) < k1 or (s - n) < (k1 + 1):
1585 raise self._Errorf(_format_, 'swne', (north - south, east - west))
1587 if e > wi > w: # wrap around
1588 # read w..wi and 0..e
1589 r, p = (wi - w), (e - wi)
1590 elif e > w:
1591 r, p = (e - w), 0
1592 else:
1593 raise self._Errorf('%s(%s < %s)', _assert_, w, e)
1595 # convert to bytes
1596 r *= self.u2B
1597 p *= self.u2B
1598 q = wi * self.u2B # stride
1599 # number of rows and cols to skip from
1600 # the original (.slat, .wlon) origin
1601 z = self.skip + (n * wi + w) * self.u2B
1602 # sanity check
1603 if r < 2 or p < 0 or q < 2 or z < self.skip \
1604 or z > self.sizeB:
1605 raise self._Errorf(_format_, _assert_, (r, p, q, z))
1607 # can't use _BytesIO since numpy
1608 # needs .fileno attr in .fromfile
1609 t, c = 0, self._tmpfile()
1610 # reading (s - n) rows, forward
1611 for y in range(n, s): # PYCHOK y unused
1612 g.seek(z, _SEEK_SET)
1613 # Python 2 tmpfile.write returns None
1614 t += c.write(g.read(r)) or r
1615 if p: # wrap around to start of row
1616 g.seek(-q, _SEEK_CUR)
1617 # assert(g.tell() == (z - w * self.u2B))
1618 # Python 2 tmpfile.write returns None
1619 t += c.write(g.read(p)) or p
1620 z += q
1621 c.flush()
1622 g.close()
1624 s -= n # nlat
1625 e -= w # nlon
1626 k = s * e # knots
1627 z = k * self.u2B
1628 if t != z:
1629 raise self._Errorf('%s(%s != %s) %s', _assert_, t, z, self)
1631 # update the _Gpars accordingly, note attributes
1632 # .dlat, .dlon, .rlat and .rlon remain unchanged
1633 self.slat += n * self.dlat
1634 self.wlon += w * self.dlon
1635 self.nlat = s
1636 self.nlon = e
1637 self.flon = self.glon = f
1639 self.crop4 = south, west, north, east
1640 self.knots = k
1641 self.skip = 0 # no header lines in c
1643 c.seek(0, _SEEK_SET)
1644 # c = open(c.name, _rb_) # reopen for numpy 1.8.0-
1645 return c
1647 def _Errorf(self, fmt, *args): # PYCHOK no cover
1648 t = fmt % args
1649 e = self.pgm or NN
1650 if e:
1651 t = _SPACE_(t, _in_, repr(e))
1652 return PGMError(t)
1654 def _lle2yx2(self, lat, lon, flon):
1655 # earth (lat, lon) to grid indices (y, x)
1656 # with .dlat decreasing from 90N .slat
1657 lat -= self.slat
1658 lon += flon - self.wlon
1659 return (min(self.nlat - 1, max(0, int(lat * self.rlat))),
1660 max(0, int(lon * self.rlon)))
1662 def _tmpfile(self):
1663 # create a tmpfile to hold the cropped geoid grid
1664 try:
1665 from tempfile import NamedTemporaryFile as tmpfile
1666 except ImportError: # Python 2.7.16-
1667 from os import tmpfile
1668 t = _os_path.splitext(_os_path.basename(self.pgm))[0]
1669 f = tmpfile(mode='w+b', prefix=t or 'egm')
1670 f.seek(0, _SEEK_SET) # force overwrite
1671 return f
1673 @Property_RO
1674 def pgm(self):
1675 '''Get the geoid file name (C{str}).
1676 '''
1677 return self.name
1680class PGMError(GeoidError):
1681 '''Issue parsing or cropping an C{egm*.pgm} geoid dataset.
1682 '''
1683 pass
1686def egmGeoidHeights(GeoidHeights_dat):
1687 '''Generate geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/
1688 C++/doc/geoid.html#geoidinst>} height tests from U{GeoidHeights.dat
1689 <https://SourceForge.net/projects/geographiclib/files/testdata/>}
1690 U{Test data for Geoids<https://GeographicLib.SourceForge.io/C++/doc/
1691 geoid.html#testgeoid>}.
1693 @arg GeoidHeights_dat: The un-gz-ed C{GeoidHeights.dat} file
1694 (C{str} or C{file} handle).
1696 @return: For each test, yield a L{GeoidHeight5Tuple}C{(lat, lon,
1697 egm84, egm96, egm2008)}.
1699 @raise GeoidError: Invalid B{C{GeoidHeights_dat}}.
1701 @note: Function L{egmGeoidHeights} is used to test the geoids
1702 L{GeoidKarney} and L{GeoidPGM}, see PyGeodesy module
1703 C{test/testGeoids.py}.
1704 '''
1705 dat = GeoidHeights_dat
1706 if isinstance(dat, bytes):
1707 dat = _BytesIO(dat)
1709 try:
1710 dat.seek(0, _SEEK_SET) # reset
1711 except AttributeError as x:
1712 raise GeoidError(GeoidHeights_dat=type(dat), cause=x)
1714 for t in dat.readlines():
1715 t = t.strip()
1716 if t and not t.startswith(_bHASH_):
1717 lat, lon, egm84, egm96, egm2008 = map(float, t.split())
1718 while lon > _180_0: # EasternLon to earth lon
1719 lon -= _360_0
1720 yield GeoidHeight5Tuple(lat, lon, egm84, egm96, egm2008)
1723__all__ += _ALL_DOCS(_GeoidBase)
1725if __name__ == '__main__':
1727 from pygeodesy.internals import printf, _sys
1729 _crop = ()
1730 _GeoidEGM = GeoidKarney
1731 _kind = 3
1733 geoids = _sys.argv[1:]
1734 while geoids:
1735 geoid = geoids.pop(0)
1737 if '-crop'.startswith(geoid.lower()):
1738 _crop = 20, -125, 50, -65 # CONUS
1740 elif '-karney'.startswith(geoid.lower()):
1741 _GeoidEGM = GeoidKarney
1743 elif '-kind'.startswith(geoid.lower()):
1744 _kind = int(geoids.pop(0))
1746 elif '-pgm'.startswith(geoid.lower()):
1747 _GeoidEGM = GeoidPGM
1749 elif geoid[-4:].lower() in ('.pgm',):
1750 g = _GeoidEGM(geoid, crop=_crop, kind=_kind)
1751 printf(g.toStr(), nt=1, nl=1)
1752 printf(repr(g.pgm), nt=1)
1753 # <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>:
1754 # The height of the EGM96 geoid at Timbuktu
1755 # echo 16:46:33N 3:00:34W | GeoidEval
1756 # => 28.7068 -0.02e-6 -1.73e-6
1757 # The 1st number is the height of the geoid, the 2nd and
1758 # 3rd are its slopes in northerly and easterly direction
1759 t = 'Timbuktu %s' % (g,)
1760 k = {'egm84-15.pgm': '31.2979',
1761 'egm96-5.pgm': '28.7067',
1762 'egm2008-1.pgm': '28.7880'}.get(g.name.lower(), '28.7880')
1763 ll = _MODS.dms.parseDMS2('16:46:33N', '3:00:34W', sep=':')
1764 for ll in (ll, (16.776, -3.009),):
1765 try:
1766 h, ll = g.height(*ll), fstr(ll, prec=6)
1767 printf('%s.height(%s): %.4F vs %s', t, ll, h, k)
1768 except (GeoidError, RangeError) as x:
1769 printf(_COLONSPACE_(t, str(x)))
1771 elif geoid[-4:].lower() in ('.bin',):
1772 g = GeoidG2012B(geoid, kind=_kind)
1773 printf(g.toStr())
1775 else:
1776 raise GeoidError(grid=repr(geoid))
1778_I = int # PYCHOK unused _I
1779del _intCs # trash ints cache
1781# **) MIT License
1782#
1783# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1784#
1785# Permission is hereby granted, free of charge, to any person obtaining a
1786# copy of this software and associated documentation files (the "Software"),
1787# to deal in the Software without restriction, including without limitation
1788# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1789# and/or sell copies of the Software, and to permit persons to whom the
1790# Software is furnished to do so, subject to the following conditions:
1791#
1792# The above copyright notice and this permission notice shall be included
1793# in all copies or substantial portions of the Software.
1794#
1795# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1796# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1797# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1798# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1799# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1800# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1801# OTHER DEALINGS IN THE SOFTWARE.
1803# <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>
1804# _lowerleft = -90, -179, -30.1500 # egm2008-1.pgm
1805# _lowerleft = -90, -179, -29.5350 # egm96-5.pgm
1806# _lowerleft = -90, -179, -29.7120 # egm84-15.pgm
1808# _center = 0, 0, 17.2260 # egm2008-1.pgm
1809# _center = 0, 0, 17.1630 # egm96-5.pgm
1810# _center = 0, 0, 18.3296 # egm84-15.pgm
1812# _upperright = 90, 180, 14.8980 # egm2008-1.pgm
1813# _upperright = 90, 180, 13.6050 # egm96-5.pgm
1814# _upperright = 90, 180, 13.0980 # egm84-15.pgm
1817# % python3 -m pygeodesy.geoids [-Karney] ../testGeoids/egm*.pgm
1818#
1819# 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)
1820#
1821# _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'
1822#
1823# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880
1824# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880
1825#
1826# 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)
1827#
1828# _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'
1829#
1830# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979
1831# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979
1832#
1833# 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)
1834#
1835# _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'
1836#
1837# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067
1838# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067
1841# % python3 -m pygeodesy.geoids -Karney ../testGeoids/egm*.pgm
1842#
1843# 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)
1844#
1845# _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'
1846#
1847# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880
1848# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880
1849#
1850# 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)
1851#
1852# _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'
1853#
1854# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979
1855# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979
1856#
1857# 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)
1858#
1859# _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'
1860#
1861# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067
1862# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067
1865# % python2 -m pygeodesy.geoids -PGM ../testGeoids/egm*.pgm
1866#
1867# 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)
1868#
1869# _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'
1870#
1871# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880
1872# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880
1873#
1874# 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)
1875#
1876# _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'
1877#
1878# Timbuktu GeoidPGM('egm84-15.pgm').height(16.775833, -3.009444): 31.2979 vs 31.2979
1879# Timbuktu GeoidPGM('egm84-15.pgm').height(16.776, -3.009): 31.2975 vs 31.2979
1880#
1881# 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)
1882#
1883# _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'
1884#
1885# Timbuktu GeoidPGM('egm96-5.pgm').height(16.775833, -3.009444): 28.7065 vs 28.7067
1886# Timbuktu GeoidPGM('egm96-5.pgm').height(16.776, -3.009): 28.7064 vs 28.7067