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
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_, _knots_, \
98 _lat_, _linear_, _lon_, _mean_, _N_, _n_a_, \
99 _not_, _numpy_, _on_, _outside_, _S_, _s_, _scipy_, \
100 _SPACE_, _stdev_, _supported_, _tbd_, _W_, _width_
101from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _FOR_DOCS
102from pygeodesy.named import _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__ = '24.05.13'
123_assert_ = 'assert'
124_bHASH_ = b'#'
125_endian_ = 'endian'
126_format_ = '%s %r'
127_header_ = 'header'
128# temporarily hold a single instance for each int value
129_intCs = {}
130_interp2d_ks = {-2: _linear_,
131 -3: _cubic_,
132 -5: 'quintic'}
133_lli_ = 'lli'
134_non_increasing_ = 'non-increasing'
135_rb_ = 'rb'
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, B{H}=False}.
241 If C{B{wrap} is True}, wrap or I{normalize} all
242 B{C{llis}} locations (C{bool}). If C{B{H} is True},
243 return the I{orthometric} height instead of the
244 I{geoid} height at each location (C{bool}).
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, crop=None, datum=None, # NAD 83 Ellipsoid
757 kind=3, name=NN, smooth=0):
758 '''New L{GeoidG2012B} interpolator.
760 @arg g2012b_bin: A C{GEOID12B} grid file name (C{.bin}).
761 @kwarg crop: Optional crop box, not supported (C{None}).
762 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
763 or L{a_f2Tuple}), default C{WGS84}.
764 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for
765 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/
766 reference/generated/scipy.interpolate.RectBivariateSpline.html>},
767 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/
768 reference/generated/scipy.interpolate.interp2d.html>}, -3
769 for C{interp2d cubic} or -5 for C{interp2d quintic}.
770 @kwarg name: Optional geoid name (C{str}).
771 @kwarg smooth: Smoothing factor for U{RectBivariateSpline
772 <https://docs.SciPy.org/doc/scipy/reference/generated/
773 scipy.interpolate.RectBivariateSpline.html>}
774 only (C{int}).
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
780 not 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 if crop is not None:
795 raise GeoidError(crop=crop, txt=_not_(_supported_))
797 g = self._open(g2012b_bin, datum, kind, name, smooth)
798 _ = self.numpy # import numpy for ._load and
800 try:
801 p = _Gpars()
802 n = (self.sizeB // 4) - 11 # number of f4 heights
803 # U{numpy dtype formats are different from Python struct formats
804 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>}
805 for en_ in ('<', '>'):
806 # skip 4xf8, get 3xi4
807 p.nlat, p.nlon, ien = map(int, self._load(g, en_+'i4', 3, 32))
808 if ien == 1: # correct endian
809 p.knots = p.nlat * p.nlon
810 if p.knots == n and 1 < p.nlat < n \
811 and 1 < p.nlon < n:
812 self._endian = en_+'f4'
813 break
814 else: # couldn't validate endian
815 raise GeoidError(_endian_)
817 # get the first 4xf8
818 p.slat, p.wlon, p.dlat, p.dlon = map(float, self._load(g, en_+'f8', 4))
819 # read all f4 heights, ignoring the first 4xf8 and 3xi4
820 hs = self._load(g, self._endian, n, 44).reshape(p.nlat, p.nlon)
821 p.wlon -= _360_0 # western-most East longitude to earth (..., lon)
822 _GeoidBase.__init__(self, hs, p)
824 except Exception as x:
825 raise _SciPyIssue(x, _in_, repr(g2012b_bin))
826 finally:
827 g.close()
829 def _g2ll2(self, lat, lon):
830 # convert grid (lat, lon) to earth (lat, lon)
831 return lat, lon
833 def _ll2g2(self, lat, lon):
834 # convert earth (lat, lon) to grid (lat, lon)
835 return lat, lon
837 if _FOR_DOCS:
838 __call__ = _GeoidBase.__call__
839 height = _GeoidBase.height
842class GeoidHeight5Tuple(_NamedTuple): # .geoids.py
843 '''5-Tuple C{(lat, lon, egm84, egm96, egm2008)} for U{GeoidHeights.dat
844 <https://SourceForge.net/projects/geographiclib/files/testdata/>}
845 tests with the heights for 3 different EGM grids at C{degrees90}
846 and C{degrees180} degrees (after converting C{lon} from original
847 C{0 <= EasterLon <= 360}).
848 '''
849 _Names_ = (_lat_, _lon_, 'egm84', 'egm96', 'egm2008')
850 _Units_ = ( Lat, Lon, Height, Height, Height)
853def _I(i):
854 '''(INTERNAL) Cache a single C{int} constant.
855 '''
856 return _intCs.setdefault(i, i) # PYCHOK undefined due to del _intCs
859def _T(*cs):
860 '''(INTERNAL) Cache a tuple of single C{int} constants.
861 '''
862 return map1(_I, *cs)
864_T0s12 = (_I(0),) * 12 # PYCHOK _T(0, 0, ..., 0)
867class GeoidKarney(_GeoidBase):
868 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth
869 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/
870 geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/
871 C++/doc/geoid.html#geoidinst>} datasets using bilinear or U{cubic
872 <https://dl.ACM.org/citation.cfm?id=368443>} interpolation and U{caching
873 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidcache>}
874 in pure Python, transcoded from I{Karney}'s U{C++ class Geoid
875 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinterp>}.
877 Use any of the geoid U{egm84-, egm96- or egm2008-*.pgm
878 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>}
879 datasets.
880 '''
881 _C0 = _F(372), _F(240), _F(372) # n, _ and s common denominators
882 # matrices c3n_, c3, c3s_, transposed from GeographicLib/Geoid.cpp
883 _C3 = ((_T(0, 0, 62, 124, 124, 62, 0, 0, 0, 0, 0, 0),
884 _T0s12,
885 _T(-131, 7, -31, -62, -62, -31, 45, 216, 156, -45, -55, -7),
886 _T0s12,
887 _T(138, -138, 0, 0, 0, 0, -183, 33, 153, -3, 48, -48), # PYCHOK indent
888 _T(144, 42, -62, -124, -124, -62, -9, 87, 99, 9, 42, -42),
889 _T0s12,
890 _T(0, 0, 0, 0, 0, 0, 93, -93, -93, 93, 0, 0),
891 _T(-102, 102, 0, 0, 0, 0, 18, 12, -12, -18, -84, 84),
892 _T(-31, -31, 31, 62, 62, 31, 0, -93, -93, 0, 31, 31)), # PYCHOK indent
894 (_T(9, -9, 9, 186, 54, -9, -9, 54, -54, 9, -9, 9),
895 _T(-18, 18, -88, -42, 162, -32, 8, -78, 78, -8, 18, -18),
896 _T(-88, 8, -18, -42, -78, 18, 18, 162, 78, -18, -32, -8),
897 _T(0, 0, 90, -150, 30, 30, 30, -90, 90, -30, 0, 0),
898 _T(96, -96, 96, -96, -24, 24, -96, -24, 144, -24, 24, -24), # PYCHOK indent
899 _T(90, 30, 0, -150, -90, 0, 0, 30, 90, 0, 30, -30),
900 _T(0, 0, -20, 60, -60, 20, -20, 60, -60, 20, 0, 0),
901 _T(0, 0, -60, 60, 60, -60, 60, -60, -60, 60, 0, 0),
902 _T(-60, 60, 0, 60, -60, 0, 0, 60, -60, 0, -60, 60),
903 _T(-20, -20, 0, 60, 60, 0, 0, -60, -60, 0, 20, 20)),
905 (_T(18, -18, 36, 210, 162, -36, 0, 0, 0, 0, -18, 18), # PYCHOK indent
906 _T(-36, 36, -165, 45, 141, -21, 0, 0, 0, 0, 36, -36),
907 _T(-122, -2, -27, -111, -75, 27, 62, 124, 124, 62, -64, 2),
908 _T(0, 0, 93, -93, -93, 93, 0, 0, 0, 0, 0, 0),
909 _T(120, -120, 147, -57, -129, 39, 0, 0, 0, 0, 66, -66), # PYCHOK indent
910 _T(135, 51, -9, -192, -180, 9, 31, 62, 62, 31, 51, -51),
911 _T0s12,
912 _T(0, 0, -93, 93, 93, -93, 0, 0, 0, 0, 0, 0),
913 _T(-84, 84, 18, 12, -12, -18, 0, 0, 0, 0, -102, 102),
914 _T(-31, -31, 0, 93, 93, 0, -31, -62, -62, -31, 31, 31)))
916 _BT = (_T(0, 0), # bilinear 4-tuple [i, j] indices
917 _T(1, 0),
918 _T(0, 1),
919 _T(1, 1))
921 _CM = (_T( 0, -1), # 10x12 cubic matrix [i, j] indices
922 _T( 1, -1),
923 _T(-1, 0),
924 _T( 0, 0),
925 _T( 1, 0),
926 _T( 2, 0),
927 _T(-1, 1),
928 _T( 0, 1),
929 _T( 1, 1),
930 _T( 2, 1),
931 _T( 0, 2),
932 _T( 1, 2))
934 _endian = '>H' # struct.unpack 1 ushort (big endian, unsigned short)
935 _4endian = '>4H' # struct.unpack 4 ushorts
936 _Rendian = NN # struct.unpack a row of ushorts
937# _highest = (-8.4, 147.367, 85.839) if egm2008-1.pgm else (
938# (-8.167, 147.25, 85.422) if egm96-5.pgm else
939# (-4.5, 148.75, 81.33)) # egm84-15.pgm
940# _lowest = (4.7, 78.767, -106.911) if egm2008-1.pgm else (
941# (4.667, 78.833, -107.043) if egm96-5.pgm else
942# (4.75, 79.25, -107.34)) # egm84-15.pgm
943 _mean = _F(-1.317) # from egm2008-1, -1.438 egm96-5, -0.855 egm84-15
944 _nBytes = None # not applicable
945 _nterms = len(_C3[0]) # columns length, number of row
946 _smooth = None # not applicable
947 _stdev = _F(29.244) # from egm2008-1, 29.227 egm96-5, 29.183 egm84-15
948 _u2B = _calcsize(_endian) # pixelsize_ in bytes
949 _4u2B = _calcsize(_4endian) # 4 pixelsize_s in bytes
950 _Ru2B = 0 # row of pixelsize_s in bytes
951 _yxH = () # cache (y, x) indices
952 _yxHt = () # cached 4- or 10-tuple for _ev2H resp. _ev3H
953 _yx_hits = 0 # cache hits
955 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84
956 kind=3, name=NN, smooth=None):
957 '''New L{GeoidKarney} interpolator.
959 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/
960 C++/doc/geoid.html#geoidinst>} file name (C{egm*.pgm}), see
961 note below.
962 @kwarg crop: Optional box to limit geoid locations, a 4-tuple (C{south,
963 west, north, east}), 2-tuple (C{(south, west), (north,
964 east)}) or 2, in C{degrees90} lat- and C{degrees180}
965 longitudes or a 2-tuple (C{LatLonSW, LatLonNE}) of
966 C{LatLon} instances.
967 @kwarg datum: Optional grid datum (C{Datum}, L{Ellipsoid}, L{Ellipsoid2}
968 or L{a_f2Tuple}), default C{WGS84}.
969 @kwarg kind: Interpolation order (C{int}), 2 for C{bilinear} or 3
970 for C{cubic}.
971 @kwarg name: Optional geoid name (C{str}).
972 @kwarg smooth: Smoothing factor, unsupported (C{None}).
974 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid
975 B{C{crop}}, B{C{kind}} or B{C{smooth}}.
977 @raise TypeError: Invalid B{C{datum}}.
979 @see: Class L{GeoidPGM} and function L{egmGeoidHeights}.
981 @note: Geoid file B{C{egm_pgm}} remains open and must be closed
982 by calling the C{close} method or by using this instance
983 in a C{with B{GeoidKarney}(...) as ...} context.
984 '''
985 if smooth is not None:
986 raise GeoidError(smooth=smooth, txt=_not_(_supported_))
988 if kind in (2,):
989 self._evH = self._ev2H
990 elif kind not in (3,):
991 raise GeoidError(kind=kind)
993 self._egm = g = self._open(egm_pgm, datum, kind, name, smooth)
994 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB)
996 self._Rendian = self._4endian.replace(_4_, str(p.nlon))
997 self._Ru2B = _calcsize(self._Rendian)
999 self._knots = p.knots # grid knots
1000 self._lon_of = float(p.flon) # forward offset
1001 self._lon_og = float(p.glon) # reverse offset
1002 # set earth (lat, lon) limits (s, w, n, e)
1003 self._lat_lo, self._lon_lo, \
1004 self._lat_hi, self._lon_hi = self._swne(crop if crop else p.crop4)
1005 self._cropped = True if crop else False
1007 def __call__(self, *llis, **wrap_H):
1008 '''Interpolate the geoid height for one or several locations.
1010 @arg llis: One or more locations (C{LatLon}s), all positional.
1011 @kwarg wrap_H: Keyword arguments C{B{wrap}=False, B{H}=False}.
1012 If C{B{wrap} is True}, wrap or I{normalize} all
1013 B{C{llis}} locations (C{bool}). If C{B{H} is True},
1014 return the I{orthometric} height instead of the
1015 I{geoid} height at each location (C{bool}).
1017 @return: A single interpolated geoid (or orthometric) height
1018 (C{float}) or a list or tuple of interpolated geoid
1019 (or orthometric) heights (C{float}s).
1021 @raise GeoidError: Insufficient number of B{C{llis}}, an
1022 invalid B{C{lli}} or the C{egm*.pgm}
1023 geoid file is closed.
1025 @raise RangeError: An B{C{lli}} is outside this geoid's lat-
1026 or longitude range.
1028 @note: To obtain I{orthometric} heights, each B{C{llis}}
1029 location must have an ellipsoid C{height} or C{h}
1030 attribute, otherwise C{height=0} is used.
1032 @see: Function L{pygeodesy.heightOrthometric}.
1033 '''
1034 return self._called(llis, False, **wrap_H)
1036 def _c0c3v(self, y, x):
1037 # get the common denominator, the 10x12 cubic matrix and
1038 # the 12 cubic v-coefficients around geoid index (y, x)
1039 p = self._pgm
1040 if 0 < x < (p.nlon - 2) and 0 < y < (p.nlat - 2):
1041 # read 4x4 ushorts, drop the 4 corners
1042 g = self._egm
1043 e = self._4endian
1044 n = self._4u2B
1045 R = self._Ru2B
1047 b = self._seek(y - 1, x - 1)
1048 v = _unpack(e, g.read(n))[1:3]
1049 b += R
1050 g.seek(b, _SEEK_SET)
1051 v += _unpack(e, g.read(n))
1052 b += R
1053 g.seek(b, _SEEK_SET)
1054 v += _unpack(e, g.read(n))
1055 b += R
1056 g.seek(b, _SEEK_SET)
1057 v += _unpack(e, g.read(n))[1:3]
1058 j = 1
1060 else: # likely some wrapped y and/or x's
1061 v = self._raws(y, x, GeoidKarney._CM)
1062 j = 0 if y < 1 else (1 if y < (p.nlat - 2) else 2)
1064 return GeoidKarney._C0[j], GeoidKarney._C3[j], v
1066 @Property_RO
1067 def dtype(self):
1068 '''Get the geoid's grid data type (C{str}).
1069 '''
1070 return 'ushort'
1072 def _ev(self, lat, lon): # PYCHOK expected
1073 # interpolate the geoid height at grid (lat, lon)
1074 fy, fx = self._g2yx2(lat, lon)
1075 y, x = int(floor(fy)), int(floor(fx))
1076 fy -= y
1077 fx -= x
1078 H = self._evH(fy, fx, y, x) # ._ev3H or ._ev2H
1079 H *= self._pgm.Scale # H.fmul(self._pgm.Scale)
1080 H += self._pgm.Offset # H.fadd(self._pgm.Offset)
1081 return H.fsum()
1083 def _ev2H(self, fy, fx, *yx):
1084 # compute the bilinear 4-tuple and interpolate raw H
1085 if self._yxH == yx:
1086 t = self._yxHt
1087 self._yx_hits += 1
1088 else:
1089 y, x = self._yxH = yx
1090 self._yxHt = t = self._raws(y, x, GeoidKarney._BT)
1091 v = _1_0, -fx, fx
1092 H = Fdot(v, t[0], t[0], t[1]).fmul(_1_0 - fy) # c = a * (1 - fy)
1093 H += Fdot(v, t[2], t[2], t[3]).fmul(fy) # c += b * fy
1094 return H
1096 def _ev3H(self, fy, fx, *yx):
1097 # compute the cubic 10-tuple and interpolate raw H
1098 if self._yxH == yx:
1099 t = self._yxHt
1100 self._yx_hits += 1
1101 else:
1102 self._yxH = yx
1103 c0, c3, v = self._c0c3v(*yx)
1104 t = [fdot(v, *c3[i]) / c0 for i in range(self._nterms)]
1105 self._yxHt = t = tuple(t)
1106 # GeographicLib/Geoid.cpp Geoid::height(lat, lon) ...
1107 # real h = t[0] + fx * (t[1] + fx * (t[3] + fx * t[6])) +
1108 # fy * (t[2] + fx * (t[4] + fx * t[7]) +
1109 # fy * (t[5] + fx * t[8] + fy * t[9]));
1110 v = _1_0, fx, fy
1111 H = Fdot(v, t[5], t[8], t[9])
1112 H *= fy
1113 H += Fhorner(fx, t[2], t[4], t[7])
1114 H *= fy
1115 H += Fhorner(fx, t[0], t[1], t[3], t[6])
1116 return H
1118 _evH = _ev3H # overriden for kind == 2
1120 def _g2ll2(self, lat, lon):
1121 # convert grid (lat, lon) to earth (lat, lon), uncropped
1122 while lon > _180_0:
1123 lon -= _360_0
1124 return lat, lon
1126 def _g2yx2(self, lat, lon):
1127 # convert grid (lat, lon) to grid (y, x) indices
1128 p = self._pgm
1129 # note, slat = +90, rlat < 0 makes y >=0
1130 return ((lat - p.slat) * p.rlat), ((lon - p.wlon) * p.rlon)
1132 def _gyx2g2(self, y, x):
1133 # convert grid (y, x) indices to grid (lat, lon)
1134 p = self._pgm
1135 return (p.slat + p.dlat * y), (p.wlon + p.dlon * x)
1137 def height(self, lats, lons, **wrap):
1138 '''Interpolate the geoid height for one or several lat-/longitudes.
1140 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s).
1141 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s).
1142 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{lats}}
1143 and B{C{lons}} locations (C{bool}).
1145 @return: A single interpolated geoid height (C{float}) or a
1146 list of interpolated geoid heights (C{float}s).
1148 @raise GeoidError: Insufficient or non-matching number of
1149 B{C{lats}} and B{C{lons}} or the C{egm*.pgm}
1150 geoid file is closed.
1152 @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this
1153 geoid's lat- or longitude range.
1154 '''
1155 return _height_called(self, lats, lons, Error=GeoidError, **wrap)
1157 @Property_RO
1158 def _highest_ltd(self):
1159 '''(INTERNAL) Cache for L{highest} mesthod.
1160 '''
1161 return self._llh3minmax(True, -12, -4)
1163 def highest(self, LatLon=None, full=False): # PYCHOK full
1164 '''Return the location and largest height of this geoid.
1166 @kwarg LatLon: Optional class to return the location and height
1167 (C{LatLon}) or C{None}.
1168 @kwarg full: Search the full or limited latitude range (C{bool}).
1170 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,
1171 lon, height)} otherwise a B{C{LatLon}} instance
1172 with the lat-, longitude and geoid height at the
1173 highest grid location.
1174 '''
1175 llh = self._highest if full or self.cropped else self._highest_ltd
1176 return self._llh3LL(llh, LatLon)
1178 def _lat2y2(self, lat2):
1179 # convert earth lat(s) to min and max grid y indices
1180 ys, m = [], self._pgm.nlat - 1
1181 for lat in lat2:
1182 y, _ = self._g2yx2(*self._ll2g2(lat, 0))
1183 ys.append(max(min(int(y), m), 0))
1184 return min(ys), max(ys) + 1
1186 def _ll2g2(self, lat, lon):
1187 # convert earth (lat, lon) to grid (lat, lon), uncropped
1188 while lon < 0:
1189 lon += _360_0
1190 return lat, lon
1192 def _llh3minmax(self, highest=True, *lat2):
1193 # find highest or lowest, takes 10+ secs for egm2008-1.pgm geoid
1194 # (Python 2.7.16, macOS 10.13.6 High Sierra, iMac 3 GHz Core i3)
1195 y = x = 0
1196 h = self._raw(y, x)
1197 if highest:
1198 for j, r in self._raw2(*lat2):
1199 m = max(r)
1200 if m > h:
1201 h, y, x = m, j, r.index(m)
1202 else: # lowest
1203 for j, r in self._raw2(*lat2):
1204 m = min(r)
1205 if m < h:
1206 h, y, x = m, j, r.index(m)
1207 h *= self._pgm.Scale
1208 h += self._pgm.Offset
1209 return self._g2ll2(*self._gyx2g2(y, x)) + (h,)
1211 @Property_RO
1212 def _lowest_ltd(self):
1213 '''(INTERNAL) Cache for L{lowest}.
1214 '''
1215 return self._llh3minmax(False, 0, 8)
1217 def lowest(self, LatLon=None, full=False): # PYCHOK full
1218 '''Return the location and lowest height of this geoid.
1220 @kwarg LatLon: Optional class to return the location and height
1221 (C{LatLon}) or C{None}.
1222 @kwarg full: Search the full or limited latitude range (C{bool}).
1224 @return: If B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat,
1225 lon, height)} otherwise a B{C{LatLon}} instance
1226 with the lat-, longitude and geoid height of the
1227 lowest grid location.
1228 '''
1229 llh = self._lowest if full or self.cropped else self._lowest_ltd
1230 return self._llh3LL(llh, LatLon)
1232 def _raw(self, y, x):
1233 # get the ushort geoid height at geoid index (y, x),
1234 # like GeographicLib/Geoid.hpp real rawval(is, iy)
1235 p = self._pgm
1236 if x < 0:
1237 x += p.nlon
1238 elif x >= p.nlon:
1239 x -= p.nlon
1240 h = p.nlon // 2
1241 if y < 0:
1242 y = -y
1243 elif y >= p.nlat:
1244 y = (p.nlat - 1) * 2 - y
1245 else:
1246 h = 0
1247 x += h if x < h else -h
1248 self._seek(y, x)
1249 h = _unpack(self._endian, self._egm.read(self._u2B))
1250 return h[0]
1252 def _raws(self, y, x, ijs):
1253 # get bilinear 4-tuple or 10x12 cubic matrix
1254 return tuple(self._raw(y + j, x + i) for i, j in ijs)
1256 def _raw2(self, *lat2):
1257 # yield a 2-tuple (y, ushorts) for each row or for
1258 # the rows between two (or more) earth lat values
1259 p = self._pgm
1260 g = self._egm
1261 e = self._Rendian
1262 n = self._Ru2B
1263 # min(lat2) <= lat <= max(lat2) or 0 <= y < p.nlat
1264 s, t = self._lat2y2(lat2) if lat2 else (0, p.nlat)
1265 self._seek(s, 0) # to start of row s
1266 for y in range(s, t):
1267 yield y, _unpack(e, g.read(n))
1269 def _seek(self, y, x):
1270 # position geoid to grid index (y, x)
1271 p, g = self._pgm, self._egm
1272 if g:
1273 b = p.skip + (y * p.nlon + x) * self._u2B
1274 g.seek(b, _SEEK_SET)
1275 return b # position
1276 raise GeoidError('closed file', txt=repr(p.egm)) # IOError
1279class GeoidPGM(_GeoidBase):
1280 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth
1281 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/
1282 geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/
1283 C++/doc/geoid.html#geoidinst>} datasets but based on C{SciPy}
1284 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/reference/
1285 generated/scipy.interpolate.RectBivariateSpline.html>} or
1286 U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/
1287 scipy.interpolate.interp2d.html>} interpolation.
1289 Use any of the U{egm84-, egm96- or egm2008-*.pgm
1290 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>}
1291 datasets. However, unless cropped, an entire C{egm*.pgm} dataset
1292 is loaded into the C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/
1293 doc/scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>}
1294 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/
1295 scipy.interpolate.interp2d.html>} interpolator and converted from
1296 2-byte C{int} to 8-byte C{dtype float64}. Therefore, internal memory
1297 usage is 4x the U{egm*.pgm<https://GeographicLib.SourceForge.io/C++/doc/
1298 geoid.html#geoidinst>} file size and may exceed the available memory,
1299 especially with 32-bit Python, see properties C{.nBytes} and C{.sizeB}.
1300 '''
1301 _cropped = False
1302 _endian = '>u2'
1304 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84
1305 kind=3, name=NN, smooth=0):
1306 '''New L{GeoidPGM} interpolator.
1308 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/
1309 C++/doc/geoid.html#geoidinst>} file name (C{egm*.pgm}).
1310 @kwarg crop: Optional box to crop B{C{egm_pgm}}, a 4-tuple (C{south, west,
1311 north, east}) or 2-tuple (C{(south, west), (north, east)}),
1312 in C{degrees90} lat- and C{degrees180} longitudes or a
1313 2-tuple (C{LatLonSW, LatLonNE}) of C{LatLon} instances.
1314 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
1315 or L{a_f2Tuple}), default C{WGS84}.
1316 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for
1317 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/
1318 reference/generated/scipy.interpolate.RectBivariateSpline.html>},
1319 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/
1320 reference/generated/scipy.interpolate.interp2d.html>}, -3
1321 for C{interp2d cubic} or -5 for C{interp2d quintic}.
1322 @kwarg name: Optional geoid name (C{str}).
1323 @kwarg smooth: Smoothing factor for U{RectBivariateSpline
1324 <https://docs.SciPy.org/doc/scipy/reference/generated/
1325 scipy.interpolate.RectBivariateSpline.html>}
1326 only (C{int}).
1328 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid B{C{crop}},
1329 B{C{kind}} or B{C{smooth}}.
1331 @raise ImportError: Package C{numpy} or C{scipy} not found or not installed.
1333 @raise LenError: EGM dataset B{C{egm_pgm}} axis mismatch.
1335 @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue.
1337 @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d}
1338 warning as exception.
1340 @raise TypeError: Invalid B{C{datum}}.
1342 @note: C{scipy.interpolate.interp2d} has been C{DEPRECATED}, specify
1343 C{B{kind}=1..5} for C{scipy.interpolate.RectBivariateSpline}.
1345 @note: The U{GeographicLib egm*.pgm<https://GeographicLib.SourceForge.io/
1346 C++/doc/geoid.html#geoidinst>} file sizes are based on a 2-byte
1347 C{int} height converted to 8-byte C{dtype float64} for C{scipy}
1348 interpolators. Therefore, internal memory usage is 4 times the
1349 C{egm*.pgm} file size and may exceed the available memory,
1350 especially with 32-bit Python. To reduce memory usage, set
1351 keyword argument B{C{crop}} to the region of interest. For example
1352 C{B{crop}=(20, -125, 50, -65)} covers the U{conterminous US<https://
1353 www.NGS.NOAA.gov/GEOID/GEOID12B/maps/GEOID12B_CONUS_grids.png>}
1354 (CONUS), less than 3% of the entire C{egm2008-1.pgm} dataset.
1356 @see: Class L{GeoidKarney} and function L{egmGeoidHeights}.
1357 '''
1358 np = self.numpy
1359 self._u2B = np.dtype(self.endian).itemsize
1361 g = self._open(egm_pgm, datum, kind, name, smooth)
1362 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB)
1363 if crop:
1364 g = p._cropped(g, abs(kind) + 1, *self._swne(crop))
1365 if _MODS.internals._version2(np.__version__) < (1, 9):
1366 g = open(g.name, _rb_) # reopen tempfile for numpy 1.8.0-
1367 self._cropped = True
1368 try:
1369 # U{numpy dtype formats are different from Python struct formats
1370 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>}
1371 # read all heights, skipping the PGM header lines, converted to float
1372 hs = self._load(g, self.endian, p.knots, p.skip).reshape(p.nlat, p.nlon) * p.Scale
1373 if p.Offset: # offset
1374 hs = p.Offset + hs
1375 if p.dlat < 0: # flip the rows
1376 hs = np.flipud(hs)
1377 _GeoidBase.__init__(self, hs, p)
1378 except Exception as x:
1379 raise _SciPyIssue(x, _in_, repr(egm_pgm))
1380 finally:
1381 g.close()
1383 def _g2ll2(self, lat, lon):
1384 # convert grid (lat, lon) to earth (lat, lon), un-/cropped
1385 if self._cropped:
1386 lon -= self._lon_of
1387 else:
1388 while lon > _180_0:
1389 lon -= _360_0
1390 return lat, lon
1392 def _ll2g2(self, lat, lon):
1393 # convert earth (lat, lon) to grid (lat, lon), un-/cropped
1394 if self._cropped:
1395 lon += self._lon_of
1396 else:
1397 while lon < 0:
1398 lon += _360_0
1399 return lat, lon
1401 if _FOR_DOCS:
1402 __call__ = _GeoidBase.__call__
1403 height = _GeoidBase.height
1406class _Gpars(_Named):
1407 '''(INTERNAL) Basic geoid parameters.
1408 '''
1409 # interpolator parameters
1410 dlat = 0 # +/- latitude resolution in C{degrees}
1411 dlon = 0 # longitude resolution in C{degrees}
1412 nlat = 1 # number of latitude knots (C{int})
1413 nlon = 0 # number of longitude knots (C{int})
1414 rlat = 0 # +/- latitude resolution in C{float}, 1 / .dlat
1415 rlon = 0 # longitude resolution in C{float}, 1 / .dlon
1416 slat = 0 # nothern- or southern most latitude (C{degrees90})
1417 wlon = 0 # western-most longitude in Eastern lon (C{degrees360})
1419 flon = 0 # forward, earth to grid longitude offset
1420 glon = 0 # reverse, grid to earth longitude offset
1422 knots = 0 # number of knots, nlat * nlon (C{int})
1423 skip = 0 # header bytes to skip (C{int})
1425 def __repr__(self):
1426 t = _COMMASPACE_.join(pairs((a, getattr(self, a)) for
1427 a in dir(self.__class__)
1428 if a[:1].isupper()))
1429 return _COLONSPACE_(self, t)
1431 def __str__(self):
1432 return Fmt.PAREN(self.classname, repr(self.name))
1435class _PGM(_Gpars):
1436 '''(INTERNAL) Parse an C{egm*.pgm} geoid dataset file.
1438 # Geoid file in PGM format for the GeographicLib::Geoid class
1439 # Description WGS84 EGM96, 5-minute grid
1440 # URL https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html
1441 # DateTime 2009-08-29 18:45:03
1442 # MaxBilinearError 0.140
1443 # RMSBilinearError 0.005
1444 # MaxCubicError 0.003
1445 # RMSCubicError 0.001
1446 # Offset -108
1447 # Scale 0.003
1448 # Origin 90N 0E
1449 # AREA_OR_POINT Point
1450 # Vertical_Datum WGS84
1451 <width> <height>
1452 <pixel>
1453 ...
1454 '''
1455 crop4 = () # 4-tuple (C{south, west, north, east}).
1456 egm = None
1457 glon = 180 # reverse offset, uncropped
1458# pgm = NN # name
1459 sizeB = 0
1460 u2B = 2 # item size of grid height (C{int}).
1462 @staticmethod
1463 def _llstr2floats(latlon):
1464 # llstr to (lat, lon) floats
1465 lat, lon = latlon.split()
1466 return _MODS.dms.parseDMS2(lat, lon)
1468 # PGM file attributes, CamelCase but not .istitle()
1469 AREA_OR_POINT = str
1470 DateTime = str
1471 Description = str # 'WGS84 EGM96, 5-minute grid'
1472 Geoid = str # 'file in PGM format for the GeographicLib::Geoid class'
1473 MaxBilinearError = float
1474 MaxCubicError = float
1475 Offset = float
1476 Origin = _llstr2floats
1477 Pixel = 0
1478 RMSBilinearError = float
1479 RMSCubicError = float
1480 Scale = float
1481 URL = str # 'https://Earth-Info.NGA.mil/GandG/wgs84/...'
1482 Vertical_Datum = str
1484 def __init__(self, g, pgm=NN, itemsize=0, sizeB=0): # MCCABE 22
1485 '''(INTERNAL) New C{_PGM} parsed C{egm*.pgm} geoid dataset.
1486 '''
1487 self.name = pgm # geoid file name
1488 if itemsize:
1489 self._u2B = itemsize
1490 if sizeB:
1491 self.sizeB = sizeB
1493 t = g.readline() # make sure newline == '\n'
1494 if t != b'P5\n' and t.strip() != b'P5':
1495 raise self._Errorf(_format_, _header_, t)
1497 while True: # read all # Attr ... lines,
1498 try: # ignore empty ones or comments
1499 t = g.readline().strip()
1500 if t.startswith(_bHASH_):
1501 t = t.lstrip(_bHASH_).lstrip()
1502 a, v = map(_ub2str, t.split(None, 1))
1503 f = getattr(_PGM, a, None)
1504 if callable(f) and a[:1].isupper():
1505 setattr(self, a, f(v))
1506 elif t:
1507 break
1508 except (TypeError, ValueError):
1509 raise self._Errorf(_format_, 'Attr', t)
1510 else: # should never get here
1511 raise self._Errorf(_format_, _header_, g.tell())
1513 try: # must be (even) width and (odd) height
1514 nlon, nlat = map(int, t.split())
1515 if nlon < 2 or nlon > (360 * 60) or isodd(nlon) or \
1516 nlat < 2 or nlat > (181 * 60) or not isodd(nlat):
1517 raise ValueError
1518 except (TypeError, ValueError):
1519 raise self._Errorf(_format_, _SPACE_(_width_, _height_), t)
1521 try: # must be 16 bit pixel height
1522 t = g.readline().strip()
1523 self.Pixel = int(t)
1524 if not 255 < self.Pixel < 65536: # >u2 or >H only
1525 raise ValueError
1526 except (TypeError, ValueError):
1527 raise self._Errorf(_format_, 'pixel', t)
1529 for a in dir(_PGM): # set undefined # Attr ... to None
1530 if a[:1].isupper() and callable(getattr(self, a)):
1531 setattr(self, a, None)
1533 if self.Origin is None:
1534 raise self._Errorf(_format_, 'Origin', self.Origin)
1535 if self.Offset is None or self.Offset > 0:
1536 raise self._Errorf(_format_, 'Offset', self.Offset)
1537 if self.Scale is None or self.Scale < EPS:
1538 raise self._Errorf(_format_, 'Scale', self.Scale)
1540 self.skip = g.tell()
1541 self.knots = nlat * nlon
1543 self.nlat, self.nlon = nlat, nlon
1544 self.slat, self.wlon = self.Origin
1545 # note, negative .dlat and .rlat since rows
1546 # are from .slat 90N down in decreasing lat
1547 self.dlat, self.dlon = _180_0 / (1 - nlat), _360_0 / nlon
1548 self.rlat, self.rlon = (1 - nlat) / _180_0, nlon / _360_0
1550 # grid corners in earth (lat, lon), .slat = 90, .dlat < 0
1551 n = float(self.slat)
1552 s = n + self.dlat * (nlat - 1)
1553 w = self.wlon - self.glon
1554 e = w + self.dlon * nlon
1555 self.crop4 = s, w, n, e
1557 n = self.sizeB - self.skip
1558 if n > 0 and n != (self.knots * self.u2B):
1559 raise self._Errorf('%s(%s x %s != %s)', _assert_, nlat, nlon, n)
1561 def _cropped(self, g, k1, south, west, north, east): # MCCABE 15
1562 '''Crop the geoid to (south, west, north, east) box.
1563 '''
1564 # flon offset for both west and east
1565 f = 360 if west < 0 else 0
1566 # earth (lat, lon) to grid indices (y, x),
1567 # note y is decreasing, i.e. n < s
1568 s, w = self._lle2yx2(south, west, f)
1569 n, e = self._lle2yx2(north, east, f)
1570 s += 1 # s > n
1571 e += 1 # e > w
1573 hi, wi = self.nlat, self.nlon
1574 # handle special cases
1575 if (s - n) > hi:
1576 n, s = 0, hi # entire lat range
1577 if (e - w) > wi:
1578 w, e, f = 0, wi, 180 # entire lon range
1579 if s == hi and w == n == 0 and e == wi:
1580 return g # use entire geoid as-is
1582 if (e - w) < k1 or (s - n) < (k1 + 1):
1583 raise self._Errorf(_format_, 'swne', (north - south, east - west))
1585 if e > wi > w: # wrap around
1586 # read w..wi and 0..e
1587 r, p = (wi - w), (e - wi)
1588 elif e > w:
1589 r, p = (e - w), 0
1590 else:
1591 raise self._Errorf('%s(%s < %s)', _assert_, w, e)
1593 # convert to bytes
1594 r *= self.u2B
1595 p *= self.u2B
1596 q = wi * self.u2B # stride
1597 # number of rows and cols to skip from
1598 # the original (.slat, .wlon) origin
1599 z = self.skip + (n * wi + w) * self.u2B
1600 # sanity check
1601 if r < 2 or p < 0 or q < 2 or z < self.skip \
1602 or z > self.sizeB:
1603 raise self._Errorf(_format_, _assert_, (r, p, q, z))
1605 # can't use _BytesIO since numpy
1606 # needs .fileno attr in .fromfile
1607 t, c = 0, self._tmpfile()
1608 # reading (s - n) rows, forward
1609 for y in range(n, s): # PYCHOK y unused
1610 g.seek(z, _SEEK_SET)
1611 # Python 2 tmpfile.write returns None
1612 t += c.write(g.read(r)) or r
1613 if p: # wrap around to start of row
1614 g.seek(-q, _SEEK_CUR)
1615 # assert(g.tell() == (z - w * self.u2B))
1616 # Python 2 tmpfile.write returns None
1617 t += c.write(g.read(p)) or p
1618 z += q
1619 c.flush()
1620 g.close()
1622 s -= n # nlat
1623 e -= w # nlon
1624 k = s * e # knots
1625 z = k * self.u2B
1626 if t != z:
1627 raise self._Errorf('%s(%s != %s) %s', _assert_, t, z, self)
1629 # update the _Gpars accordingly, note attributes
1630 # .dlat, .dlon, .rlat and .rlon remain unchanged
1631 self.slat += n * self.dlat
1632 self.wlon += w * self.dlon
1633 self.nlat = s
1634 self.nlon = e
1635 self.flon = self.glon = f
1637 self.crop4 = south, west, north, east
1638 self.knots = k
1639 self.skip = 0 # no header lines in c
1641 c.seek(0, _SEEK_SET)
1642 # c = open(c.name, _rb_) # reopen for numpy 1.8.0-
1643 return c
1645 def _Errorf(self, fmt, *args): # PYCHOK no cover
1646 t = fmt % args
1647 e = self.pgm or NN
1648 if e:
1649 t = _SPACE_(t, _in_, repr(e))
1650 return PGMError(t)
1652 def _lle2yx2(self, lat, lon, flon):
1653 # earth (lat, lon) to grid indices (y, x)
1654 # with .dlat decreasing from 90N .slat
1655 lat -= self.slat
1656 lon += flon - self.wlon
1657 return (min(self.nlat - 1, max(0, int(lat * self.rlat))),
1658 max(0, int(lon * self.rlon)))
1660 def _tmpfile(self):
1661 # create a tmpfile to hold the cropped geoid grid
1662 try:
1663 from tempfile import NamedTemporaryFile as tmpfile
1664 except ImportError: # Python 2.7.16-
1665 from os import tmpfile
1666 t = _os_path.splitext(_os_path.basename(self.pgm))[0]
1667 f = tmpfile(mode='w+b', prefix=t or 'egm')
1668 f.seek(0, _SEEK_SET) # force overwrite
1669 return f
1671 @Property_RO
1672 def pgm(self):
1673 '''Get the geoid file name (C{str}).
1674 '''
1675 return self.name
1678class PGMError(GeoidError):
1679 '''Issue parsing or cropping an C{egm*.pgm} geoid dataset.
1680 '''
1681 pass
1684def egmGeoidHeights(GeoidHeights_dat):
1685 '''Generate geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/
1686 C++/doc/geoid.html#geoidinst>} height tests from U{GeoidHeights.dat
1687 <https://SourceForge.net/projects/geographiclib/files/testdata/>}
1688 U{Test data for Geoids<https://GeographicLib.SourceForge.io/C++/doc/
1689 geoid.html#testgeoid>}.
1691 @arg GeoidHeights_dat: The un-gz-ed C{GeoidHeights.dat} file
1692 (C{str} or C{file} handle).
1694 @return: For each test, yield a L{GeoidHeight5Tuple}C{(lat, lon,
1695 egm84, egm96, egm2008)}.
1697 @raise GeoidError: Invalid B{C{GeoidHeights_dat}}.
1699 @note: Function L{egmGeoidHeights} is used to test the geoids
1700 L{GeoidKarney} and L{GeoidPGM}, see PyGeodesy module
1701 C{test/testGeoids.py}.
1702 '''
1703 dat = GeoidHeights_dat
1704 if isinstance(dat, bytes):
1705 dat = _BytesIO(dat)
1707 try:
1708 dat.seek(0, _SEEK_SET) # reset
1709 except AttributeError as x:
1710 raise GeoidError(GeoidHeights_dat=type(dat), cause=x)
1712 for t in dat.readlines():
1713 t = t.strip()
1714 if t and not t.startswith(_bHASH_):
1715 lat, lon, egm84, egm96, egm2008 = map(float, t.split())
1716 while lon > _180_0: # EasternLon to earth lon
1717 lon -= _360_0
1718 yield GeoidHeight5Tuple(lat, lon, egm84, egm96, egm2008)
1721__all__ += _ALL_DOCS(_GeoidBase)
1723if __name__ == '__main__':
1725 from pygeodesy.internals import printf, _sys
1727 _crop = ()
1728 _GeoidEGM = GeoidKarney
1729 _kind = 3
1731 geoids = _sys.argv[1:]
1732 while geoids:
1733 geoid = geoids.pop(0)
1735 if '-crop'.startswith(geoid.lower()):
1736 _crop = 20, -125, 50, -65 # CONUS
1738 elif '-karney'.startswith(geoid.lower()):
1739 _GeoidEGM = GeoidKarney
1741 elif '-kind'.startswith(geoid.lower()):
1742 _kind = int(geoids.pop(0))
1744 elif '-pgm'.startswith(geoid.lower()):
1745 _GeoidEGM = GeoidPGM
1747 elif geoid[-4:].lower() in ('.pgm',):
1748 g = _GeoidEGM(geoid, crop=_crop, kind=_kind)
1749 printf(g.toStr(), nt=1, nl=1)
1750 printf(repr(g.pgm), nt=1)
1751 # <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>:
1752 # The height of the EGM96 geoid at Timbuktu
1753 # echo 16:46:33N 3:00:34W | GeoidEval
1754 # => 28.7068 -0.02e-6 -1.73e-6
1755 # The 1st number is the height of the geoid, the 2nd and
1756 # 3rd are its slopes in northerly and easterly direction
1757 t = 'Timbuktu %s' % (g,)
1758 k = {'egm84-15.pgm': '31.2979',
1759 'egm96-5.pgm': '28.7067',
1760 'egm2008-1.pgm': '28.7880'}.get(g.name.lower(), '28.7880')
1761 ll = _MODS.dms.parseDMS2('16:46:33N', '3:00:34W', sep=':')
1762 for ll in (ll, (16.776, -3.009),):
1763 try:
1764 h, ll = g.height(*ll), fstr(ll, prec=6)
1765 printf('%s.height(%s): %.4F vs %s', t, ll, h, k)
1766 except (GeoidError, RangeError) as x:
1767 printf(_COLONSPACE_(t, str(x)))
1769 elif geoid[-4:].lower() in ('.bin',):
1770 g = GeoidG2012B(geoid, kind=_kind)
1771 printf(g.toStr())
1773 else:
1774 raise GeoidError(grid=repr(geoid))
1776_I = int # PYCHOK unused _I
1777del _intCs # trash ints cache
1779# **) MIT License
1780#
1781# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1782#
1783# Permission is hereby granted, free of charge, to any person obtaining a
1784# copy of this software and associated documentation files (the "Software"),
1785# to deal in the Software without restriction, including without limitation
1786# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1787# and/or sell copies of the Software, and to permit persons to whom the
1788# Software is furnished to do so, subject to the following conditions:
1789#
1790# The above copyright notice and this permission notice shall be included
1791# in all copies or substantial portions of the Software.
1792#
1793# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1794# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1795# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1796# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1797# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1798# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1799# OTHER DEALINGS IN THE SOFTWARE.
1801# <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>
1802# _lowerleft = -90, -179, -30.1500 # egm2008-1.pgm
1803# _lowerleft = -90, -179, -29.5350 # egm96-5.pgm
1804# _lowerleft = -90, -179, -29.7120 # egm84-15.pgm
1806# _center = 0, 0, 17.2260 # egm2008-1.pgm
1807# _center = 0, 0, 17.1630 # egm96-5.pgm
1808# _center = 0, 0, 18.3296 # egm84-15.pgm
1810# _upperright = 90, 180, 14.8980 # egm2008-1.pgm
1811# _upperright = 90, 180, 13.6050 # egm96-5.pgm
1812# _upperright = 90, 180, 13.0980 # egm84-15.pgm
1815# % python3 -m pygeodesy.geoids [-Karney] ../testGeoids/egm*.pgm
1816#
1817# 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)
1818#
1819# _PGM('../testGeoids/egm2008-1.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-31 06:54:00', Description='WGS84 EGM2008, 1-minute grid', Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.025, MaxCubicError=0.003, Offset=-108.0, Origin=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.001, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008', Vertical_Datum='WGS84'
1820#
1821# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880
1822# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880
1823#
1824# 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)
1825#
1826# _PGM('../testGeoids/egm84-15.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-29 18:45:02', Description='WGS84 EGM84, 15-minute grid', Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.413, MaxCubicError=0.02, Offset=-108.0, Origin=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.018, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/wgs84_180/wgs84_180.html', Vertical_Datum='WGS84'
1827#
1828# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979
1829# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979
1830#
1831# 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)
1832#
1833# _PGM('../testGeoids/egm96-5.pgm'): AREA_OR_POINT='Point', DateTime='2009-08-29 18:45:03', Description='WGS84 EGM96, 5-minute grid', Geoid='file in PGM format for the GeographicLib::Geoid class', MaxBilinearError=0.14, MaxCubicError=0.003, Offset=-108.0, Origin=LatLon2Tuple(lat=90.0, lon=0.0), Pixel=65535, RMSBilinearError=0.005, RMSCubicError=0.001, Scale=0.003, URL='http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm96/egm96.html', Vertical_Datum='WGS84'
1834#
1835# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067
1836# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067
1839# % python3 -m pygeodesy.geoids -Karney ../testGeoids/egm*.pgm
1840#
1841# 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)
1842#
1843# _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'
1844#
1845# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880
1846# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880
1847#
1848# 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)
1849#
1850# _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'
1851#
1852# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979
1853# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979
1854#
1855# 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)
1856#
1857# _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'
1858#
1859# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067
1860# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067
1863# % python2 -m pygeodesy.geoids -PGM ../testGeoids/egm*.pgm
1864#
1865# 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)
1866#
1867# _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'
1868#
1869# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880
1870# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880
1871#
1872# 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)
1873#
1874# _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'
1875#
1876# Timbuktu GeoidPGM('egm84-15.pgm').height(16.775833, -3.009444): 31.2979 vs 31.2979
1877# Timbuktu GeoidPGM('egm84-15.pgm').height(16.776, -3.009): 31.2975 vs 31.2979
1878#
1879# 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)
1880#
1881# _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'
1882#
1883# Timbuktu GeoidPGM('egm96-5.pgm').height(16.775833, -3.009444): 28.7065 vs 28.7067
1884# Timbuktu GeoidPGM('egm96-5.pgm').height(16.776, -3.009): 28.7064 vs 28.7067