Coverage for pygeodesy/geoids.py: 96%
673 statements
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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__ = '24.06.11'
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 C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,
327 height)} otherwise a B{C{LatLon}} instance with the lat-,
328 longitude and geoid height of the center grid location.
329 '''
330 return self._llh3LL(self._center, LatLon)
332 def close(self):
333 '''Close the C{egm*.pgm} geoid file if open (and applicable).
334 '''
335 if not self.closed:
336 self._egm.close()
337 self._egm = None
339 @property_RO
340 def closed(self):
341 '''Get the C{egm*.pgm} geoid file status.
342 '''
343 return self._egm is None
345 @Property_RO
346 def cropped(self):
347 '''Is geoid cropped (C{bool} or C{None} if crop not supported).
348 '''
349 return self._cropped
351 @Property_RO
352 def dtype(self):
353 '''Get the grid C{scipy} U{dtype<https://docs.SciPy.org/doc/numpy/
354 reference/generated/numpy.ndarray.dtype.html>} (C{numpy.dtype}).
355 '''
356 return self._hs_y_x.dtype
358 @Property_RO
359 def endian(self):
360 '''Get the geoid endianess and U{dtype<https://docs.SciPy.org/
361 doc/numpy/reference/generated/numpy.dtype.html>} (C{str}).
362 '''
363 return self._endian
365 def _ev(self, y, x): # PYCHOK expected
366 # only used for .interpolate.interp2d, but
367 # overwritten for .RectBivariateSpline,
368 # note (y, x) must be flipped!
369 return self._interp2d(x, y)
371 def _gaxis2(self, lo, d, n, name):
372 # build grid axis, hi = lo + (n - 1) * d
373 m, a = len2(frange(lo, n, d))
374 if m != n:
375 raise LenError(self.__class__, grid=m, **{name: n})
376 if d < 0:
377 d, a = -d, list(reversed(a))
378 for i in range(1, m):
379 e = a[i] - a[i-1]
380 if e < EPS: # non-increasing axis
381 i = Fmt.INDEX(name, i)
382 raise GeoidError(i, e, txt=_non_increasing_)
383 return self.numpy.array(a), d
385 def _g2ll2(self, lat, lon): # PYCHOK no cover
386 '''(INTERNAL) I{Must be overloaded}.'''
387 self._notOverloaded(lat, lon)
389 def _gyx2g2(self, y, x):
390 # convert grid (y, x) indices to grid (lat, lon)
391 return ((self._lat_lo + self._lat_d * y),
392 (self._lon_lo + self._lon_of + self._lon_d * x))
394 def height(self, lats, lons, **wrap):
395 '''Interpolate the geoid height for one or several lat-/longitudes.
397 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s).
398 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s).
399 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{lats}}
400 and B{C{lons}} locations (C{bool}).
402 @return: A single interpolated geoid height (C{float}) or a
403 list of interpolated geoid heights (C{float}s).
405 @raise GeoidError: Insufficient or non-matching number of
406 B{C{lats}} and B{C{lons}}.
408 @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this
409 geoid's lat- or longitude range.
411 @raise SciPyError: A C{scipy.interpolate.inter2d} or
412 C{-.RectBivariateSpline} issue.
414 @raise SciPyWarning: A C{scipy.interpolate.inter2d} or
415 C{-.RectBivariateSpline} warning as
416 exception.
417 '''
418 return _height_called(self, lats, lons, Error=GeoidError, **wrap)
420 def _hGeoid(self, lat, lon):
421 out = self.outside(lat, lon)
422 if out:
423 lli = fstr((lat, lon), strepr=repr)
424 raise RangeError(lli=lli, txt=_SPACE_(_outside_, _on_, out))
425 return float(self._ev(*self._ll2g2(lat, lon)))
427 @Property_RO
428 def _highest(self):
429 '''(INTERNAL) Cache for L{highest} method.
430 '''
431 return self._llh3minmax(True)
433 def highest(self, LatLon=None, **unused):
434 '''Return the location and largest height of this geoid.
436 @kwarg LatLon: Optional class to return the location and height
437 (C{LatLon}) or C{None}.
439 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,
440 height)} otherwise a B{C{LatLon}} instance with the lat-,
441 longitude and geoid height of the highest grid location.
442 '''
443 return self._llh3LL(self._highest, LatLon)
445 @Property_RO
446 def hits(self):
447 '''Get the number of cache hits (C{int} or C{None}).
448 '''
449 return self._yx_hits
451 @deprecated_method
452 def _interp2d(self, xs, ys, hs=(), k=0): # overwritten in .__init__ above
453 '''DEPRECATED on 23.01.06, use keyword argument C{B{kind}=1..5}.'''
454 # assert k in _interp2d_ks # and len(hs) == len(xs) == len(ys)
455 try:
456 return self.scipy_interpolate.interp2d(xs, ys, hs, kind=_interp2d_ks[k])
457 except AttributeError as x:
458 raise SciPyError(interp2d=MISSING, kind=k, cause=x)
460 @Property_RO
461 def kind(self):
462 '''Get the interpolator kind and order (C{int}).
463 '''
464 return self._kind
466 @Property_RO
467 def knots(self):
468 '''Get the number of grid knots (C{int}).
469 '''
470 return self._knots
472 def _ll2g2(self, lat, lon): # PYCHOK no cover
473 '''(INTERNAL) I{Must be overloaded}.'''
474 self._notOverloaded(lat, lon)
476 @property_RO
477 def _LL3T(self):
478 '''(INTERNAL) Get L{LatLon3Tuple}, I{once}.
479 '''
480 _GeoidBase._LL3T = T = _MODS.namedTuples.LatLon3Tuple # overwrite poperty_RO
481 return T
483 def _llh3(self, lat, lon):
484 return self._LL3T(lat, lon, self._hGeoid(lat, lon), name=self.name)
486 def _llh3LL(self, llh, LatLon):
487 return llh if LatLon is None else self._xnamed(LatLon(*llh))
489 def _llh3minmax(self, highest=True, *unused):
490 hs, np = self._hs_y_x, self.numpy
491 # <https://docs.SciPy.org/doc/numpy/reference/generated/
492 # numpy.argmin.html#numpy.argmin>
493 arg = np.argmax if highest else np.argmin
494 y, x = np.unravel_index(arg(hs, axis=None), hs.shape)
495 return self._g2ll2(*self._gyx2g2(y, x)) + (float(hs[y, x]),)
497 def _load(self, g, dtype, n, offset=0):
498 # numpy.fromfile, like .frombuffer
499 g.seek(offset, _SEEK_SET)
500 return self.numpy.fromfile(g, dtype, n)
502 @Property_RO
503 def _lowerleft(self):
504 '''(INTERNAL) Cache for L{lowerleft}.
505 '''
506 return self._llh3(self._lat_lo, self._lon_lo)
508 def lowerleft(self, LatLon=None):
509 '''Return the lower-left location and height of this geoid.
511 @kwarg LatLon: Optional class to return the location
512 (C{LatLon}) and height or C{None}.
514 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)}
515 otherwise a B{C{LatLon}} instance with the lat-, longitude and
516 geoid height of the lower-left, SW grid corner.
517 '''
518 return self._llh3LL(self._lowerleft, LatLon)
520 @Property_RO
521 def _loweright(self):
522 '''(INTERNAL) Cache for L{loweright}.
523 '''
524 return self._llh3(self._lat_lo, self._lon_hi)
526 def loweright(self, LatLon=None):
527 '''Return the lower-right location and height of this geoid.
529 @kwarg LatLon: Optional class to return the location and height
530 (C{LatLon}) or C{None}.
532 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)}
533 otherwise a B{C{LatLon}} instance with the lat-, longitude and
534 geoid height of the lower-right, SE grid corner.
535 '''
537 return self._llh3LL(self._loweright, LatLon)
539 lowerright = loweright # synonymous
541 @Property_RO
542 def _lowest(self):
543 '''(INTERNAL) Cache for L{lowest}.
544 '''
545 return self._llh3minmax(False)
547 def lowest(self, LatLon=None, **unused):
548 '''Return the location and lowest height of this geoid.
550 @kwarg LatLon: Optional class to return the location and height
551 (C{LatLon}) or C{None}.
553 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,
554 height)} otherwise a B{C{LatLon}} instance with the lat-,
555 longitude and geoid height of the lowest grid location.
556 '''
557 return self._llh3LL(self._lowest, LatLon)
559 @Property_RO
560 def mean(self):
561 '''Get the mean of this geoid's heights (C{float}).
562 '''
563 if self._mean is None: # see GeoidKarney
564 self._mean = float(self.numpy.mean(self._hs_y_x))
565 return self._mean
567 @property_RO
568 def name(self):
569 '''Get the name of this geoid (C{str}).
570 '''
571 return _HeightsBase.name.fget(self) or self._geoid # recursion
573 @Property_RO
574 def nBytes(self):
575 '''Get the grid in-memory size in bytes (C{int}).
576 '''
577 return self._nBytes
579 def _open(self, geoid, datum, kind, name, smooth):
580 # open the geoid file
581 try:
582 self._geoid = _os_path.basename(geoid)
583 self._sizeB = _os_path.getsize(geoid)
584 g = open(geoid, _rb_)
585 except (IOError, OSError) as x:
586 raise GeoidError(geoid=geoid, cause=x)
588 if datum not in (None, self._datum):
589 self._datum = _ellipsoidal_datum(datum, name=name)
590 self._kind = int(kind)
591 if name:
592 _HeightsBase.name.fset(self, name) # rename
593 if smooth:
594 self._smooth = Int_(smooth=smooth, Error=GeoidError, low=0)
596 return g
598 def outside(self, lat, lon):
599 '''Check whether a location is outside this geoid's
600 lat-/longitude or crop range.
602 @arg lat: The latitude (C{degrees}).
603 @arg lon: The longitude (C{degrees}).
605 @return: A 1- or 2-character C{str} if outside or an
606 empty C{str} if inside.
607 '''
608 return (_S_ if lat < self._lat_lo else
609 (_N_ if lat > self._lat_hi else NN)) + \
610 (_W_ if lon < self._lon_lo else
611 (_E_ if lon > self._lon_hi else NN))
613 @Property_RO
614 def pgm(self):
615 '''Get the PGM attributes (C{_PGM} or C{None} if not available/applicable).
616 '''
617 return self._pgm
619 @Property_RO
620 def sizeB(self):
621 '''Get the geoid grid file size in bytes (C{int}).
622 '''
623 return self._sizeB
625 @Property_RO
626 def smooth(self):
627 '''Get the C{RectBivariateSpline} smoothing (C{int}).
628 '''
629 return self._smooth
631 @Property_RO
632 def stdev(self):
633 '''Get the standard deviation of this geoid's heights (C{float}) or C{None}.
634 '''
635 if self._stdev is None: # see GeoidKarney
636 self._stdev = float(self.numpy.std(self._hs_y_x))
637 return self._stdev
639 def _swne(self, crop):
640 # crop box to 4-tuple (s, w, n, e)
641 try:
642 if len(crop) == 2:
643 try: # sw, ne LatLons
644 swne = (crop[0].lat, crop[0].lon,
645 crop[1].lat, crop[1].lon)
646 except AttributeError: # (s, w), (n, e)
647 swne = tuple(crop[0]) + tuple(crop[1])
648 else: # (s, w, n, e)
649 swne = crop
650 if len(swne) == 4:
651 s, w, n, e = map(float, swne)
652 if -90 <= s <= (n - _1_0) <= 89 and \
653 -180 <= w <= (e - _1_0) <= 179:
654 return s, w, n, e
655 except (IndexError, TypeError, ValueError):
656 pass
657 raise GeoidError(crop=crop)
659 def toStr(self, prec=3, sep=_COMMASPACE_): # PYCHOK signature
660 '''This geoid and all geoid attributes as a string.
662 @kwarg prec: Number of decimal digits (0..9 or C{None} for
663 default). Trailing zero decimals are stripped
664 for B{C{prec}} values of 1 and above, but kept
665 for negative B{C{prec}} values.
666 @kwarg sep: Separator to join (C{str}).
668 @return: Geoid name and attributes (C{str}).
669 '''
670 s = 1 if self.kind < 0 else 2
671 t = tuple(Fmt.PAREN(m.__name__, fstr(m(), prec=prec)) for m in
672 (self.lowerleft, self.upperright,
673 self.center,
674 self.highest, self.lowest)) + \
675 attrs( _mean_, _stdev_, prec=prec, Nones=False) + \
676 attrs((_kind_, 'smooth')[:s], prec=prec, Nones=False) + \
677 attrs( 'cropped', 'dtype', _endian_, 'hits', 'knots', 'nBytes',
678 'sizeB', _scipy_, _numpy_, prec=prec, Nones=False)
679 return _COLONSPACE_(self, sep.join(t))
681 @Property_RO
682 def u2B(self):
683 '''Get the PGM itemsize in bytes (C{int}).
684 '''
685 return self._u2B
687 @Property_RO
688 def _upperleft(self):
689 '''(INTERNAL) Cache for method L{upperleft}.
690 '''
691 return self._llh3(self._lat_hi, self._lon_lo)
693 def upperleft(self, LatLon=None):
694 '''Return the upper-left location and height of this geoid.
696 @kwarg LatLon: Optional class to return the location and height
697 (C{LatLon}) or C{None}.
699 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)}
700 otherwise a B{C{LatLon}} instance with the lat-, longitude and
701 geoid height of the upper-left, NW grid corner.
702 '''
703 return self._llh3LL(self._upperleft, LatLon)
705 @Property_RO
706 def _upperright(self):
707 '''(INTERNAL) Cache for method L{upperright}.
708 '''
709 return self._llh3(self._lat_hi, self._lon_hi)
711 def upperright(self, LatLon=None):
712 '''Return the upper-right location and height of this geoid.
714 @kwarg LatLon: Optional class to return the location and height
715 (C{LatLon}) or C{None}.
717 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)}
718 otherwise a B{C{LatLon}} instance with the lat-, longitude and
719 geoid height of the upper-right, NE grid corner.
720 '''
721 return self._llh3LL(self._upperright, LatLon)
724class GeoidError(HeightError):
725 '''Geoid interpolator C{Geoid...} or interpolation issue.
726 '''
727 pass
730class GeoidG2012B(_GeoidBase):
731 '''Geoid height interpolator for U{GEOID12B Model
732 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/>} grids U{CONUS
733 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_CONUS.shtml>},
734 U{Alaska<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_AK.shtml>},
735 U{Hawaii<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_HI.shtml>},
736 U{Guam and Northern Mariana Islands
737 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_GMNI.shtml>},
738 U{Puerto Rico and U.S. Virgin Islands
739 <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_PRVI.shtml>} and
740 U{American Samoa<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_AS.shtml>}
741 based on C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/doc/
742 scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>}
743 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/
744 scipy.interpolate.interp2d.html>} interpolation.
746 Use any of the binary C{le} (little endian) or C{be} (big endian)
747 C{g2012b*.bin} grid files.
748 '''
749 def __init__(self, g2012b_bin, datum=None, # NAD 83 Ellipsoid
750 kind=3, smooth=0, **name_crop):
751 '''New L{GeoidG2012B} interpolator.
753 @arg g2012b_bin: A C{GEOID12B} grid file name (C{.bin}).
754 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
755 or L{a_f2Tuple}), default C{WGS84}.
756 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for
757 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/
758 reference/generated/scipy.interpolate.RectBivariateSpline.html>},
759 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/
760 reference/generated/scipy.interpolate.interp2d.html>}, -3
761 for C{interp2d cubic} or -5 for C{interp2d quintic}.
762 @kwarg smooth: Smoothing factor for U{RectBivariateSpline
763 <https://docs.SciPy.org/doc/scipy/reference/generated/
764 scipy.interpolate.RectBivariateSpline.html>}
765 only (C{int}).
766 @kwarg name_crop: Optional geoid C{B{name}=NN} (C{str}) and UNSUPPORTED
767 keyword argument C{B{crop}}, use C{B{crop}=None} to ignore.
769 @raise GeoidError: G2012B grid file B{C{g2012b_bin}} issue or invalid
770 B{C{crop}}, B{C{kind}} or B{C{smooth}}.
772 @raise ImportError: Package C{numpy} or C{scipy} not found or not
773 installed.
775 @raise LenError: Grid file B{C{g2012b_bin}} axis mismatch.
777 @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue.
779 @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d}
780 warning as exception.
782 @raise TypeError: Invalid B{C{datum}}.
784 @note: C{scipy.interpolate.interp2d} has been C{DEPRECATED}, specify
785 C{B{kind}=1..5} for C{scipy.interpolate.RectBivariateSpline}.
786 '''
787 crop, name = _xkwds_pop2(name_crop, crop=None)
788 if crop is not None:
789 raise GeoidError(crop=crop, txt_not_=_supported_)
791 g = self._open(g2012b_bin, datum, kind, _name__(**name), smooth)
792 _ = self.numpy # import numpy for ._load and
794 try:
795 p = _Gpars()
796 n = (self.sizeB // 4) - 11 # number of f4 heights
797 # U{numpy dtype formats are different from Python struct formats
798 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>}
799 for en_ in ('<', '>'):
800 # skip 4xf8, get 3xi4
801 p.nlat, p.nlon, ien = map(int, self._load(g, en_+'i4', 3, 32))
802 if ien == 1: # correct endian
803 p.knots = p.nlat * p.nlon
804 if p.knots == n and 1 < p.nlat < n \
805 and 1 < p.nlon < n:
806 self._endian = en_+'f4'
807 break
808 else: # couldn't validate endian
809 raise GeoidError(_endian_)
811 # get the first 4xf8
812 p.slat, p.wlon, p.dlat, p.dlon = map(float, self._load(g, en_+'f8', 4))
813 # read all f4 heights, ignoring the first 4xf8 and 3xi4
814 hs = self._load(g, self._endian, n, 44).reshape(p.nlat, p.nlon)
815 p.wlon -= _360_0 # western-most East longitude to earth (..., lon)
816 _GeoidBase.__init__(self, hs, p)
818 except Exception as x:
819 raise _SciPyIssue(x, _in_, repr(g2012b_bin))
820 finally:
821 g.close()
823 def _g2ll2(self, lat, lon):
824 # convert grid (lat, lon) to earth (lat, lon)
825 return lat, lon
827 def _ll2g2(self, lat, lon):
828 # convert earth (lat, lon) to grid (lat, lon)
829 return lat, lon
831 if _FOR_DOCS:
832 __call__ = _GeoidBase.__call__
833 height = _GeoidBase.height
836class GeoidHeight5Tuple(_NamedTuple): # .geoids.py
837 '''5-Tuple C{(lat, lon, egm84, egm96, egm2008)} for U{GeoidHeights.dat
838 <https://SourceForge.net/projects/geographiclib/files/testdata/>}
839 tests with the heights for 3 different EGM grids at C{degrees90}
840 and C{degrees180} degrees (after converting C{lon} from original
841 C{0 <= EasterLon <= 360}).
842 '''
843 _Names_ = (_lat_, _lon_, 'egm84', 'egm96', 'egm2008')
844 _Units_ = ( Lat, Lon, Height, Height, Height)
847def _I(i):
848 '''(INTERNAL) Cache a single C{int} constant.
849 '''
850 return _intCs.setdefault(i, i) # PYCHOK undefined due to del _intCs
853def _T(*cs):
854 '''(INTERNAL) Cache a tuple of single C{int} constants.
855 '''
856 return map1(_I, *cs)
858_T0s12 = (_I(0),) * 12 # PYCHOK _T(0, 0, ..., 0)
861class GeoidKarney(_GeoidBase):
862 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth
863 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/
864 geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/
865 C++/doc/geoid.html#geoidinst>} datasets using bilinear or U{cubic
866 <https://dl.ACM.org/citation.cfm?id=368443>} interpolation and U{caching
867 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidcache>}
868 in pure Python, transcoded from I{Karney}'s U{C++ class Geoid
869 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinterp>}.
871 Use any of the geoid U{egm84-, egm96- or egm2008-*.pgm
872 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>}
873 datasets.
874 '''
875 _C0 = _F(372), _F(240), _F(372) # n, _ and s common denominators
876 # matrices c3n_, c3, c3s_, transposed from GeographicLib/Geoid.cpp
877 _C3 = ((_T(0, 0, 62, 124, 124, 62, 0, 0, 0, 0, 0, 0),
878 _T0s12,
879 _T(-131, 7, -31, -62, -62, -31, 45, 216, 156, -45, -55, -7),
880 _T0s12,
881 _T(138, -138, 0, 0, 0, 0, -183, 33, 153, -3, 48, -48), # PYCHOK indent
882 _T(144, 42, -62, -124, -124, -62, -9, 87, 99, 9, 42, -42),
883 _T0s12,
884 _T(0, 0, 0, 0, 0, 0, 93, -93, -93, 93, 0, 0),
885 _T(-102, 102, 0, 0, 0, 0, 18, 12, -12, -18, -84, 84),
886 _T(-31, -31, 31, 62, 62, 31, 0, -93, -93, 0, 31, 31)), # PYCHOK indent
888 (_T(9, -9, 9, 186, 54, -9, -9, 54, -54, 9, -9, 9),
889 _T(-18, 18, -88, -42, 162, -32, 8, -78, 78, -8, 18, -18),
890 _T(-88, 8, -18, -42, -78, 18, 18, 162, 78, -18, -32, -8),
891 _T(0, 0, 90, -150, 30, 30, 30, -90, 90, -30, 0, 0),
892 _T(96, -96, 96, -96, -24, 24, -96, -24, 144, -24, 24, -24), # PYCHOK indent
893 _T(90, 30, 0, -150, -90, 0, 0, 30, 90, 0, 30, -30),
894 _T(0, 0, -20, 60, -60, 20, -20, 60, -60, 20, 0, 0),
895 _T(0, 0, -60, 60, 60, -60, 60, -60, -60, 60, 0, 0),
896 _T(-60, 60, 0, 60, -60, 0, 0, 60, -60, 0, -60, 60),
897 _T(-20, -20, 0, 60, 60, 0, 0, -60, -60, 0, 20, 20)),
899 (_T(18, -18, 36, 210, 162, -36, 0, 0, 0, 0, -18, 18), # PYCHOK indent
900 _T(-36, 36, -165, 45, 141, -21, 0, 0, 0, 0, 36, -36),
901 _T(-122, -2, -27, -111, -75, 27, 62, 124, 124, 62, -64, 2),
902 _T(0, 0, 93, -93, -93, 93, 0, 0, 0, 0, 0, 0),
903 _T(120, -120, 147, -57, -129, 39, 0, 0, 0, 0, 66, -66), # PYCHOK indent
904 _T(135, 51, -9, -192, -180, 9, 31, 62, 62, 31, 51, -51),
905 _T0s12,
906 _T(0, 0, -93, 93, 93, -93, 0, 0, 0, 0, 0, 0),
907 _T(-84, 84, 18, 12, -12, -18, 0, 0, 0, 0, -102, 102),
908 _T(-31, -31, 0, 93, 93, 0, -31, -62, -62, -31, 31, 31)))
910 _BT = (_T(0, 0), # bilinear 4-tuple [i, j] indices
911 _T(1, 0),
912 _T(0, 1),
913 _T(1, 1))
915 _CM = (_T( 0, -1), # 10x12 cubic matrix [i, j] indices
916 _T( 1, -1),
917 _T(-1, 0),
918 _T( 0, 0),
919 _T( 1, 0),
920 _T( 2, 0),
921 _T(-1, 1),
922 _T( 0, 1),
923 _T( 1, 1),
924 _T( 2, 1),
925 _T( 0, 2),
926 _T( 1, 2))
928 _endian = '>H' # struct.unpack 1 ushort (big endian, unsigned short)
929 _4endian = '>4H' # struct.unpack 4 ushorts
930 _Rendian = NN # struct.unpack a row of ushorts
931# _highest = (-8.4, 147.367, 85.839) if egm2008-1.pgm else (
932# (-8.167, 147.25, 85.422) if egm96-5.pgm else
933# (-4.5, 148.75, 81.33)) # egm84-15.pgm
934# _lowest = (4.7, 78.767, -106.911) if egm2008-1.pgm else (
935# (4.667, 78.833, -107.043) if egm96-5.pgm else
936# (4.75, 79.25, -107.34)) # egm84-15.pgm
937 _mean = _F(-1.317) # from egm2008-1, -1.438 egm96-5, -0.855 egm84-15
938 _nBytes = None # not applicable
939 _nterms = len(_C3[0]) # columns length, number of row
940 _smooth = None # not applicable
941 _stdev = _F(29.244) # from egm2008-1, 29.227 egm96-5, 29.183 egm84-15
942 _u2B = _calcsize(_endian) # pixelsize_ in bytes
943 _4u2B = _calcsize(_4endian) # 4 pixelsize_s in bytes
944 _Ru2B = 0 # row of pixelsize_s in bytes
945 _yxH = () # cache (y, x) indices
946 _yxHt = () # cached 4- or 10-tuple for _ev2H resp. _ev3H
947 _yx_hits = 0 # cache hits
949 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84
950 kind=3, **name_smooth):
951 '''New L{GeoidKarney} interpolator.
953 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/
954 C++/doc/geoid.html#geoidinst>} file name (C{egm*.pgm}), see
955 note below.
956 @kwarg crop: Optional box to limit geoid locations, a 4-tuple (C{south,
957 west, north, east}), 2-tuple (C{(south, west), (north,
958 east)}) or 2, in C{degrees90} lat- and C{degrees180}
959 longitudes or a 2-tuple (C{LatLonSW, LatLonNE}) of
960 C{LatLon} instances.
961 @kwarg datum: Optional grid datum (C{Datum}, L{Ellipsoid}, L{Ellipsoid2}
962 or L{a_f2Tuple}), default C{WGS84}.
963 @kwarg kind: Interpolation order (C{int}), 2 for C{bilinear} or 3
964 for C{cubic}.
965 @kwarg name_smooth: Optional geoid C{B{name}=NN} (C{str}) and UNSUPPORTED
966 keyword argument C{B{smooth}}, use C{B{smooth}=None} to ignore.
968 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid
969 B{C{crop}}, B{C{kind}} or B{C{smooth}}.
971 @raise TypeError: Invalid B{C{datum}}.
973 @see: Class L{GeoidPGM} and function L{egmGeoidHeights}.
975 @note: Geoid file B{C{egm_pgm}} remains open and must be closed
976 by calling the C{close} method or by using this instance
977 in a C{with B{GeoidKarney}(...) as ...} context.
978 '''
979 smooth, name = _xkwds_pop2(name_smooth, smooth=None)
980 if smooth is not None:
981 raise GeoidError(smooth=smooth, txt_not_=_supported_)
983 if kind in (2,):
984 self._evH = self._ev2H
985 elif kind not in (3,):
986 raise GeoidError(kind=kind)
988 self._egm = g = self._open(egm_pgm, datum, kind, _name__(**name), None)
989 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB)
991 self._Rendian = self._4endian.replace(_4_, str(p.nlon))
992 self._Ru2B = _calcsize(self._Rendian)
994 self._knots = p.knots # grid knots
995 self._lon_of = float(p.flon) # forward offset
996 self._lon_og = float(p.glon) # reverse offset
997 # set earth (lat, lon) limits (s, w, n, e)
998 self._lat_lo, self._lon_lo, \
999 self._lat_hi, self._lon_hi = self._swne(crop if crop else p.crop4)
1000 self._cropped = True if crop else False
1002 def __call__(self, *llis, **wrap_H):
1003 '''Interpolate the geoid height for one or several locations.
1005 @arg llis: One or more locations (C{LatLon}s), all positional.
1006 @kwarg wrap_H: Keyword arguments C{B{wrap}=False, B{H}=False}.
1007 If C{B{wrap} is True}, wrap or I{normalize} all
1008 B{C{llis}} locations (C{bool}). If C{B{H} is True},
1009 return the I{orthometric} height instead of the
1010 I{geoid} height at each location (C{bool}).
1012 @return: A single interpolated geoid (or orthometric) height
1013 (C{float}) or a list or tuple of interpolated geoid
1014 (or orthometric) heights (C{float}s).
1016 @raise GeoidError: Insufficient number of B{C{llis}}, an
1017 invalid B{C{lli}} or the C{egm*.pgm}
1018 geoid file is closed.
1020 @raise RangeError: An B{C{lli}} is outside this geoid's lat-
1021 or longitude range.
1023 @note: To obtain I{orthometric} heights, each B{C{llis}}
1024 location must have an ellipsoid C{height} or C{h}
1025 attribute, otherwise C{height=0} is used.
1027 @see: Function L{pygeodesy.heightOrthometric}.
1028 '''
1029 return self._called(llis, False, **wrap_H)
1031 def _c0c3v(self, y, x):
1032 # get the common denominator, the 10x12 cubic matrix and
1033 # the 12 cubic v-coefficients around geoid index (y, x)
1034 p = self._pgm
1035 if 0 < x < (p.nlon - 2) and 0 < y < (p.nlat - 2):
1036 # read 4x4 ushorts, drop the 4 corners
1037 g = self._egm
1038 e = self._4endian
1039 n = self._4u2B
1040 R = self._Ru2B
1042 b = self._seek(y - 1, x - 1)
1043 v = _unpack(e, g.read(n))[1:3]
1044 b += R
1045 g.seek(b, _SEEK_SET)
1046 v += _unpack(e, g.read(n))
1047 b += R
1048 g.seek(b, _SEEK_SET)
1049 v += _unpack(e, g.read(n))
1050 b += R
1051 g.seek(b, _SEEK_SET)
1052 v += _unpack(e, g.read(n))[1:3]
1053 j = 1
1055 else: # likely some wrapped y and/or x's
1056 v = self._raws(y, x, GeoidKarney._CM)
1057 j = 0 if y < 1 else (1 if y < (p.nlat - 2) else 2)
1059 return GeoidKarney._C0[j], GeoidKarney._C3[j], v
1061 @Property_RO
1062 def dtype(self):
1063 '''Get the geoid's grid data type (C{str}).
1064 '''
1065 return 'ushort'
1067 def _ev(self, lat, lon): # PYCHOK expected
1068 # interpolate the geoid height at grid (lat, lon)
1069 fy, fx = self._g2yx2(lat, lon)
1070 y, x = int(floor(fy)), int(floor(fx))
1071 fy -= y
1072 fx -= x
1073 H = self._evH(fy, fx, y, x) # ._ev3H or ._ev2H
1074 H *= self._pgm.Scale # H.fmul(self._pgm.Scale)
1075 H += self._pgm.Offset # H.fadd(self._pgm.Offset)
1076 return H.fsum()
1078 def _ev2H(self, fy, fx, *yx):
1079 # compute the bilinear 4-tuple and interpolate raw H
1080 if self._yxH == yx:
1081 t = self._yxHt
1082 self._yx_hits += 1
1083 else:
1084 y, x = self._yxH = yx
1085 self._yxHt = t = self._raws(y, x, GeoidKarney._BT)
1086 v = _1_0, -fx, fx
1087 H = Fdot(v, t[0], t[0], t[1]).fmul(_1_0 - fy) # c = a * (1 - fy)
1088 H += Fdot(v, t[2], t[2], t[3]).fmul(fy) # c += b * fy
1089 return H
1091 def _ev3H(self, fy, fx, *yx):
1092 # compute the cubic 10-tuple and interpolate raw H
1093 if self._yxH == yx:
1094 t = self._yxHt
1095 self._yx_hits += 1
1096 else:
1097 self._yxH = yx
1098 c0, c3, v = self._c0c3v(*yx)
1099 t = [fdot(v, *c3[i]) / c0 for i in range(self._nterms)]
1100 self._yxHt = t = tuple(t)
1101 # GeographicLib/Geoid.cpp Geoid::height(lat, lon) ...
1102 # real h = t[0] + fx * (t[1] + fx * (t[3] + fx * t[6])) +
1103 # fy * (t[2] + fx * (t[4] + fx * t[7]) +
1104 # fy * (t[5] + fx * t[8] + fy * t[9]));
1105 v = _1_0, fx, fy
1106 H = Fdot(v, t[5], t[8], t[9])
1107 H *= fy
1108 H += Fhorner(fx, t[2], t[4], t[7])
1109 H *= fy
1110 H += Fhorner(fx, t[0], t[1], t[3], t[6])
1111 return H
1113 _evH = _ev3H # overriden for kind == 2
1115 def _g2ll2(self, lat, lon):
1116 # convert grid (lat, lon) to earth (lat, lon), uncropped
1117 while lon > _180_0:
1118 lon -= _360_0
1119 return lat, lon
1121 def _g2yx2(self, lat, lon):
1122 # convert grid (lat, lon) to grid (y, x) indices
1123 p = self._pgm
1124 # note, slat = +90, rlat < 0 makes y >=0
1125 return ((lat - p.slat) * p.rlat), ((lon - p.wlon) * p.rlon)
1127 def _gyx2g2(self, y, x):
1128 # convert grid (y, x) indices to grid (lat, lon)
1129 p = self._pgm
1130 return (p.slat + p.dlat * y), (p.wlon + p.dlon * x)
1132 def height(self, lats, lons, **wrap):
1133 '''Interpolate the geoid height for one or several lat-/longitudes.
1135 @arg lats: Latitude or latitudes (C{degrees} or C{degrees}s).
1136 @arg lons: Longitude or longitudes (C{degrees} or C{degrees}s).
1137 @kwarg wrap: If C{True}, wrap or I{normalize} all B{C{lats}}
1138 and B{C{lons}} locations (C{bool}).
1140 @return: A single interpolated geoid height (C{float}) or a
1141 list of interpolated geoid heights (C{float}s).
1143 @raise GeoidError: Insufficient or non-matching number of
1144 B{C{lats}} and B{C{lons}} or the C{egm*.pgm}
1145 geoid file is closed.
1147 @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this
1148 geoid's lat- or longitude range.
1149 '''
1150 return _height_called(self, lats, lons, Error=GeoidError, **wrap)
1152 @Property_RO
1153 def _highest_ltd(self):
1154 '''(INTERNAL) Cache for L{highest} mesthod.
1155 '''
1156 return self._llh3minmax(True, -12, -4)
1158 def highest(self, LatLon=None, full=False): # PYCHOK full
1159 '''Return the location and largest height of this geoid.
1161 @kwarg LatLon: Optional class to return the location and height
1162 (C{LatLon}) or C{None}.
1163 @kwarg full: Search the full or limited latitude range (C{bool}).
1165 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,
1166 height)} otherwise a B{C{LatLon}} instance with the lat-,
1167 longitude and geoid height of the highest grid location.
1168 '''
1169 llh = self._highest if full or self.cropped else self._highest_ltd
1170 return self._llh3LL(llh, LatLon)
1172 def _lat2y2(self, lat2):
1173 # convert earth lat(s) to min and max grid y indices
1174 ys, m = [], self._pgm.nlat - 1
1175 for lat in lat2:
1176 y, _ = self._g2yx2(*self._ll2g2(lat, 0))
1177 ys.append(max(min(int(y), m), 0))
1178 return min(ys), max(ys) + 1
1180 def _ll2g2(self, lat, lon):
1181 # convert earth (lat, lon) to grid (lat, lon), uncropped
1182 while lon < 0:
1183 lon += _360_0
1184 return lat, lon
1186 def _llh3minmax(self, highest=True, *lat2):
1187 # find highest or lowest, takes 10+ secs for egm2008-1.pgm geoid
1188 # (Python 2.7.16, macOS 10.13.6 High Sierra, iMac 3 GHz Core i3)
1189 y = x = 0
1190 h = self._raw(y, x)
1191 if highest:
1192 for j, r in self._raw2(*lat2):
1193 m = max(r)
1194 if m > h:
1195 h, y, x = m, j, r.index(m)
1196 else: # lowest
1197 for j, r in self._raw2(*lat2):
1198 m = min(r)
1199 if m < h:
1200 h, y, x = m, j, r.index(m)
1201 h *= self._pgm.Scale
1202 h += self._pgm.Offset
1203 return self._g2ll2(*self._gyx2g2(y, x)) + (h,)
1205 @Property_RO
1206 def _lowest_ltd(self):
1207 '''(INTERNAL) Cache for L{lowest}.
1208 '''
1209 return self._llh3minmax(False, 0, 8)
1211 def lowest(self, LatLon=None, full=False): # PYCHOK full
1212 '''Return the location and lowest height of this geoid.
1214 @kwarg LatLon: Optional class to return the location and height
1215 (C{LatLon}) or C{None}.
1216 @kwarg full: Search the full or limited latitude range (C{bool}).
1218 @return: If C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,
1219 height)} otherwise a B{C{LatLon}} instance with the lat-,
1220 longitude and geoid height of the lowest grid location.
1221 '''
1222 llh = self._lowest if full or self.cropped else self._lowest_ltd
1223 return self._llh3LL(llh, LatLon)
1225 def _raw(self, y, x):
1226 # get the ushort geoid height at geoid index (y, x),
1227 # like GeographicLib/Geoid.hpp real rawval(is, iy)
1228 p = self._pgm
1229 if x < 0:
1230 x += p.nlon
1231 elif x >= p.nlon:
1232 x -= p.nlon
1233 h = p.nlon // 2
1234 if y < 0:
1235 y = -y
1236 elif y >= p.nlat:
1237 y = (p.nlat - 1) * 2 - y
1238 else:
1239 h = 0
1240 x += h if x < h else -h
1241 self._seek(y, x)
1242 h = _unpack(self._endian, self._egm.read(self._u2B))
1243 return h[0]
1245 def _raws(self, y, x, ijs):
1246 # get bilinear 4-tuple or 10x12 cubic matrix
1247 return tuple(self._raw(y + j, x + i) for i, j in ijs)
1249 def _raw2(self, *lat2):
1250 # yield a 2-tuple (y, ushorts) for each row or for
1251 # the rows between two (or more) earth lat values
1252 p = self._pgm
1253 g = self._egm
1254 e = self._Rendian
1255 n = self._Ru2B
1256 # min(lat2) <= lat <= max(lat2) or 0 <= y < p.nlat
1257 s, t = self._lat2y2(lat2) if lat2 else (0, p.nlat)
1258 self._seek(s, 0) # to start of row s
1259 for y in range(s, t):
1260 yield y, _unpack(e, g.read(n))
1262 def _seek(self, y, x):
1263 # position geoid to grid index (y, x)
1264 p, g = self._pgm, self._egm
1265 if g:
1266 b = p.skip + (y * p.nlon + x) * self._u2B
1267 g.seek(b, _SEEK_SET)
1268 return b # position
1269 raise GeoidError('closed file', txt=repr(p.egm)) # IOError
1272class GeoidPGM(_GeoidBase):
1273 '''Geoid height interpolator for I{Karney}'s U{GeographicLib Earth
1274 Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/C++/doc/
1275 geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/
1276 C++/doc/geoid.html#geoidinst>} datasets but based on C{SciPy}
1277 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/reference/
1278 generated/scipy.interpolate.RectBivariateSpline.html>} or
1279 U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/
1280 scipy.interpolate.interp2d.html>} interpolation.
1282 Use any of the U{egm84-, egm96- or egm2008-*.pgm
1283 <https://GeographicLib.SourceForge.io/C++/doc/geoid.html#geoidinst>}
1284 datasets. However, unless cropped, an entire C{egm*.pgm} dataset
1285 is loaded into the C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/
1286 doc/scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>}
1287 or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/
1288 scipy.interpolate.interp2d.html>} interpolator and converted from
1289 2-byte C{int} to 8-byte C{dtype float64}. Therefore, internal memory
1290 usage is 4x the U{egm*.pgm<https://GeographicLib.SourceForge.io/C++/doc/
1291 geoid.html#geoidinst>} file size and may exceed the available memory,
1292 especially with 32-bit Python, see properties C{.nBytes} and C{.sizeB}.
1293 '''
1294 _cropped = False
1295 _endian = '>u2'
1297 def __init__(self, egm_pgm, crop=None, datum=None, # WGS84
1298 kind=3, smooth=0, **name):
1299 '''New L{GeoidPGM} interpolator.
1301 @arg egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/
1302 C++/doc/geoid.html#geoidinst>} file name (C{egm*.pgm}).
1303 @kwarg crop: Optional box to crop B{C{egm_pgm}}, a 4-tuple (C{south, west,
1304 north, east}) or 2-tuple (C{(south, west), (north, east)}),
1305 in C{degrees90} lat- and C{degrees180} longitudes or a
1306 2-tuple (C{LatLonSW, LatLonNE}) of C{LatLon} instances.
1307 @kwarg datum: Optional grid datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
1308 or L{a_f2Tuple}), default C{WGS84}.
1309 @kwarg kind: C{scipy.interpolate} order (C{int}), use 1..5 for
1310 U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/
1311 reference/generated/scipy.interpolate.RectBivariateSpline.html>},
1312 -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/
1313 reference/generated/scipy.interpolate.interp2d.html>}, -3
1314 for C{interp2d cubic} or -5 for C{interp2d quintic}.
1315 @kwarg smooth: Smoothing factor for U{RectBivariateSpline
1316 <https://docs.SciPy.org/doc/scipy/reference/generated/
1317 scipy.interpolate.RectBivariateSpline.html>}
1318 only (C{int}).
1319 @kwarg name: Optional geoid C{B{name}=NN} (C{str}).
1321 @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid B{C{crop}},
1322 B{C{kind}} or B{C{smooth}}.
1324 @raise ImportError: Package C{numpy} or C{scipy} not found or not installed.
1326 @raise LenError: EGM dataset B{C{egm_pgm}} axis mismatch.
1328 @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue.
1330 @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d}
1331 warning as exception.
1333 @raise TypeError: Invalid B{C{datum}} or unexpected argument.
1335 @note: C{scipy.interpolate.interp2d} has been C{DEPRECATED}, specify
1336 C{B{kind}=1..5} for C{scipy.interpolate.RectBivariateSpline}.
1338 @note: The U{GeographicLib egm*.pgm<https://GeographicLib.SourceForge.io/
1339 C++/doc/geoid.html#geoidinst>} file sizes are based on a 2-byte
1340 C{int} height converted to 8-byte C{dtype float64} for C{scipy}
1341 interpolators. Therefore, internal memory usage is 4 times the
1342 C{egm*.pgm} file size and may exceed the available memory,
1343 especially with 32-bit Python. To reduce memory usage, set
1344 keyword argument B{C{crop}} to the region of interest. For example
1345 C{B{crop}=(20, -125, 50, -65)} covers the U{conterminous US<https://
1346 www.NGS.NOAA.gov/GEOID/GEOID12B/maps/GEOID12B_CONUS_grids.png>}
1347 (CONUS), less than 3% of the entire C{egm2008-1.pgm} dataset.
1349 @see: Class L{GeoidKarney} and function L{egmGeoidHeights}.
1350 '''
1351 np = self.numpy
1352 self._u2B = np.dtype(self.endian).itemsize
1354 g = self._open(egm_pgm, datum, kind, _name__(**name), smooth)
1355 self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB)
1356 if crop:
1357 g = p._cropped(g, abs(kind) + 1, *self._swne(crop))
1358 if _MODS.internals._version2(np.__version__) < (1, 9):
1359 g = open(g.name, _rb_) # reopen tempfile for numpy 1.8.0-
1360 self._cropped = True
1361 try:
1362 # U{numpy dtype formats are different from Python struct formats
1363 # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>}
1364 # read all heights, skipping the PGM header lines, converted to float
1365 hs = self._load(g, self.endian, p.knots, p.skip).reshape(p.nlat, p.nlon) * p.Scale
1366 if p.Offset: # offset
1367 hs = p.Offset + hs
1368 if p.dlat < 0: # flip the rows
1369 hs = np.flipud(hs)
1370 _GeoidBase.__init__(self, hs, p)
1371 except Exception as x:
1372 raise _SciPyIssue(x, _in_, repr(egm_pgm))
1373 finally:
1374 g.close()
1376 def _g2ll2(self, lat, lon):
1377 # convert grid (lat, lon) to earth (lat, lon), un-/cropped
1378 if self._cropped:
1379 lon -= self._lon_of
1380 else:
1381 while lon > _180_0:
1382 lon -= _360_0
1383 return lat, lon
1385 def _ll2g2(self, lat, lon):
1386 # convert earth (lat, lon) to grid (lat, lon), un-/cropped
1387 if self._cropped:
1388 lon += self._lon_of
1389 else:
1390 while lon < 0:
1391 lon += _360_0
1392 return lat, lon
1394 if _FOR_DOCS:
1395 __call__ = _GeoidBase.__call__
1396 height = _GeoidBase.height
1399class _Gpars(_Named):
1400 '''(INTERNAL) Basic geoid parameters.
1401 '''
1402 # interpolator parameters
1403 dlat = 0 # +/- latitude resolution in C{degrees}
1404 dlon = 0 # longitude resolution in C{degrees}
1405 nlat = 1 # number of latitude knots (C{int})
1406 nlon = 0 # number of longitude knots (C{int})
1407 rlat = 0 # +/- latitude resolution in C{float}, 1 / .dlat
1408 rlon = 0 # longitude resolution in C{float}, 1 / .dlon
1409 slat = 0 # nothern- or southern most latitude (C{degrees90})
1410 wlon = 0 # western-most longitude in Eastern lon (C{degrees360})
1412 flon = 0 # forward, earth to grid longitude offset
1413 glon = 0 # reverse, grid to earth longitude offset
1415 knots = 0 # number of knots, nlat * nlon (C{int})
1416 skip = 0 # header bytes to skip (C{int})
1418 def __repr__(self):
1419 t = _COMMASPACE_.join(pairs((a, getattr(self, a)) for
1420 a in dir(self.__class__)
1421 if a[:1].isupper()))
1422 return _COLONSPACE_(self, t)
1424 def __str__(self):
1425 return Fmt.PAREN(self.classname, repr(self.name))
1428class _PGM(_Gpars):
1429 '''(INTERNAL) Parse an C{egm*.pgm} geoid dataset file.
1431 # Geoid file in PGM format for the GeographicLib::Geoid class
1432 # Description WGS84 EGM96, 5-minute grid
1433 # URL https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html
1434 # DateTime 2009-08-29 18:45:03
1435 # MaxBilinearError 0.140
1436 # RMSBilinearError 0.005
1437 # MaxCubicError 0.003
1438 # RMSCubicError 0.001
1439 # Offset -108
1440 # Scale 0.003
1441 # Origin 90N 0E
1442 # AREA_OR_POINT Point
1443 # Vertical_Datum WGS84
1444 <width> <height>
1445 <pixel>
1446 ...
1447 '''
1448 crop4 = () # 4-tuple (C{south, west, north, east}).
1449 egm = None
1450 glon = 180 # reverse offset, uncropped
1451# pgm = NN # name
1452 sizeB = 0
1453 u2B = 2 # item size of grid height (C{int}).
1455 @staticmethod
1456 def _llstr2floats(latlon):
1457 # llstr to (lat, lon) floats
1458 lat, lon = latlon.split()
1459 return _MODS.dms.parseDMS2(lat, lon)
1461 # PGM file attributes, CamelCase but not .istitle()
1462 AREA_OR_POINT = str
1463 DateTime = str
1464 Description = str # 'WGS84 EGM96, 5-minute grid'
1465 Geoid = str # 'file in PGM format for the GeographicLib::Geoid class'
1466 MaxBilinearError = float
1467 MaxCubicError = float
1468 Offset = float
1469 Origin = _llstr2floats
1470 Pixel = 0
1471 RMSBilinearError = float
1472 RMSCubicError = float
1473 Scale = float
1474 URL = str # 'https://Earth-Info.NGA.mil/GandG/wgs84/...'
1475 Vertical_Datum = str
1477 def __init__(self, g, pgm=NN, itemsize=0, sizeB=0): # MCCABE 22
1478 '''(INTERNAL) New C{_PGM} parsed C{egm*.pgm} geoid dataset.
1479 '''
1480 self.name = pgm # geoid file name
1481 if itemsize:
1482 self._u2B = itemsize
1483 if sizeB:
1484 self.sizeB = sizeB
1486 t = g.readline() # make sure newline == '\n'
1487 if t != b'P5\n' and t.strip() != b'P5':
1488 raise self._Errorf(_format_, _header_, t)
1490 while True: # read all # Attr ... lines,
1491 try: # ignore empty ones or comments
1492 t = g.readline().strip()
1493 if t.startswith(_bHASH_):
1494 t = t.lstrip(_bHASH_).lstrip()
1495 a, v = map(_ub2str, t.split(None, 1))
1496 f = getattr(_PGM, a, None)
1497 if callable(f) and a[:1].isupper():
1498 setattr(self, a, f(v))
1499 elif t:
1500 break
1501 except (TypeError, ValueError):
1502 raise self._Errorf(_format_, 'Attr', t)
1503 else: # should never get here
1504 raise self._Errorf(_format_, _header_, g.tell())
1506 try: # must be (even) width and (odd) height
1507 nlon, nlat = map(int, t.split())
1508 if nlon < 2 or nlon > (360 * 60) or isodd(nlon) or \
1509 nlat < 2 or nlat > (181 * 60) or not isodd(nlat):
1510 raise ValueError
1511 except (TypeError, ValueError):
1512 raise self._Errorf(_format_, _SPACE_(_width_, _height_), t)
1514 try: # must be 16 bit pixel height
1515 t = g.readline().strip()
1516 self.Pixel = int(t)
1517 if not 255 < self.Pixel < 65536: # >u2 or >H only
1518 raise ValueError
1519 except (TypeError, ValueError):
1520 raise self._Errorf(_format_, 'pixel', t)
1522 for a in dir(_PGM): # set undefined # Attr ... to None
1523 if a[:1].isupper() and callable(getattr(self, a)):
1524 setattr(self, a, None)
1526 if self.Origin is None:
1527 raise self._Errorf(_format_, 'Origin', self.Origin)
1528 if self.Offset is None or self.Offset > 0:
1529 raise self._Errorf(_format_, 'Offset', self.Offset)
1530 if self.Scale is None or self.Scale < EPS:
1531 raise self._Errorf(_format_, 'Scale', self.Scale)
1533 self.skip = g.tell()
1534 self.knots = nlat * nlon
1536 self.nlat, self.nlon = nlat, nlon
1537 self.slat, self.wlon = self.Origin
1538 # note, negative .dlat and .rlat since rows
1539 # are from .slat 90N down in decreasing lat
1540 self.dlat, self.dlon = _180_0 / (1 - nlat), _360_0 / nlon
1541 self.rlat, self.rlon = (1 - nlat) / _180_0, nlon / _360_0
1543 # grid corners in earth (lat, lon), .slat = 90, .dlat < 0
1544 n = float(self.slat)
1545 s = n + self.dlat * (nlat - 1)
1546 w = self.wlon - self.glon
1547 e = w + self.dlon * nlon
1548 self.crop4 = s, w, n, e
1550 n = self.sizeB - self.skip
1551 if n > 0 and n != (self.knots * self.u2B):
1552 raise self._Errorf('%s(%s x %s != %s)', _assert_, nlat, nlon, n)
1554 def _cropped(self, g, k1, south, west, north, east): # MCCABE 15
1555 '''Crop the geoid to (south, west, north, east) box.
1556 '''
1557 # flon offset for both west and east
1558 f = 360 if west < 0 else 0
1559 # earth (lat, lon) to grid indices (y, x),
1560 # note y is decreasing, i.e. n < s
1561 s, w = self._lle2yx2(south, west, f)
1562 n, e = self._lle2yx2(north, east, f)
1563 s += 1 # s > n
1564 e += 1 # e > w
1566 hi, wi = self.nlat, self.nlon
1567 # handle special cases
1568 if (s - n) > hi:
1569 n, s = 0, hi # entire lat range
1570 if (e - w) > wi:
1571 w, e, f = 0, wi, 180 # entire lon range
1572 if s == hi and w == n == 0 and e == wi:
1573 return g # use entire geoid as-is
1575 if (e - w) < k1 or (s - n) < (k1 + 1):
1576 raise self._Errorf(_format_, 'swne', (north - south, east - west))
1578 if e > wi > w: # wrap around
1579 # read w..wi and 0..e
1580 r, p = (wi - w), (e - wi)
1581 elif e > w:
1582 r, p = (e - w), 0
1583 else:
1584 raise self._Errorf('%s(%s < %s)', _assert_, w, e)
1586 # convert to bytes
1587 r *= self.u2B
1588 p *= self.u2B
1589 q = wi * self.u2B # stride
1590 # number of rows and cols to skip from
1591 # the original (.slat, .wlon) origin
1592 z = self.skip + (n * wi + w) * self.u2B
1593 # sanity check
1594 if r < 2 or p < 0 or q < 2 or z < self.skip \
1595 or z > self.sizeB:
1596 raise self._Errorf(_format_, _assert_, (r, p, q, z))
1598 # can't use _BytesIO since numpy
1599 # needs .fileno attr in .fromfile
1600 t, c = 0, self._tmpfile()
1601 # reading (s - n) rows, forward
1602 for y in range(n, s): # PYCHOK y unused
1603 g.seek(z, _SEEK_SET)
1604 # Python 2 tmpfile.write returns None
1605 t += c.write(g.read(r)) or r
1606 if p: # wrap around to start of row
1607 g.seek(-q, _SEEK_CUR)
1608 # assert(g.tell() == (z - w * self.u2B))
1609 # Python 2 tmpfile.write returns None
1610 t += c.write(g.read(p)) or p
1611 z += q
1612 c.flush()
1613 g.close()
1615 s -= n # nlat
1616 e -= w # nlon
1617 k = s * e # knots
1618 z = k * self.u2B
1619 if t != z:
1620 raise self._Errorf('%s(%s != %s) %s', _assert_, t, z, self)
1622 # update the _Gpars accordingly, note attributes
1623 # .dlat, .dlon, .rlat and .rlon remain unchanged
1624 self.slat += n * self.dlat
1625 self.wlon += w * self.dlon
1626 self.nlat = s
1627 self.nlon = e
1628 self.flon = self.glon = f
1630 self.crop4 = south, west, north, east
1631 self.knots = k
1632 self.skip = 0 # no header lines in c
1634 c.seek(0, _SEEK_SET)
1635 # c = open(c.name, _rb_) # reopen for numpy 1.8.0-
1636 return c
1638 def _Errorf(self, fmt, *args): # PYCHOK no cover
1639 t = fmt % args
1640 e = self.pgm or NN
1641 if e:
1642 t = _SPACE_(t, _in_, repr(e))
1643 return PGMError(t)
1645 def _lle2yx2(self, lat, lon, flon):
1646 # earth (lat, lon) to grid indices (y, x)
1647 # with .dlat decreasing from 90N .slat
1648 lat -= self.slat
1649 lon += flon - self.wlon
1650 return (min(self.nlat - 1, max(0, int(lat * self.rlat))),
1651 max(0, int(lon * self.rlon)))
1653 def _tmpfile(self):
1654 # create a tmpfile to hold the cropped geoid grid
1655 try:
1656 from tempfile import NamedTemporaryFile as tmpfile
1657 except ImportError: # Python 2.7.16-
1658 from os import tmpfile
1659 t = _os_path.splitext(_os_path.basename(self.pgm))[0]
1660 f = tmpfile(mode='w+b', prefix=t or 'egm')
1661 f.seek(0, _SEEK_SET) # force overwrite
1662 return f
1664 @Property_RO
1665 def pgm(self):
1666 '''Get the geoid file name (C{str}).
1667 '''
1668 return self.name
1671class PGMError(GeoidError):
1672 '''Issue parsing or cropping an C{egm*.pgm} geoid dataset.
1673 '''
1674 pass
1677def egmGeoidHeights(GeoidHeights_dat):
1678 '''Generate geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/
1679 C++/doc/geoid.html#geoidinst>} height tests from U{GeoidHeights.dat
1680 <https://SourceForge.net/projects/geographiclib/files/testdata/>}
1681 U{Test data for Geoids<https://GeographicLib.SourceForge.io/C++/doc/
1682 geoid.html#testgeoid>}.
1684 @arg GeoidHeights_dat: The un-gz-ed C{GeoidHeights.dat} file
1685 (C{str} or C{file} handle).
1687 @return: For each test, yield a L{GeoidHeight5Tuple}C{(lat, lon,
1688 egm84, egm96, egm2008)}.
1690 @raise GeoidError: Invalid B{C{GeoidHeights_dat}}.
1692 @note: Function L{egmGeoidHeights} is used to test the geoids
1693 L{GeoidKarney} and L{GeoidPGM}, see PyGeodesy module
1694 C{test/testGeoids.py}.
1695 '''
1696 dat = GeoidHeights_dat
1697 if isinstance(dat, bytes):
1698 dat = _BytesIO(dat)
1700 try:
1701 dat.seek(0, _SEEK_SET) # reset
1702 except AttributeError as x:
1703 raise GeoidError(GeoidHeights_dat=type(dat), cause=x)
1705 for t in dat.readlines():
1706 t = t.strip()
1707 if t and not t.startswith(_bHASH_):
1708 lat, lon, egm84, egm96, egm2008 = map(float, t.split())
1709 while lon > _180_0: # EasternLon to earth lon
1710 lon -= _360_0
1711 yield GeoidHeight5Tuple(lat, lon, egm84, egm96, egm2008)
1714__all__ += _ALL_DOCS(_GeoidBase)
1716if __name__ == '__main__':
1718 from pygeodesy.internals import printf, _sys
1720 _crop = ()
1721 _GeoidEGM = GeoidKarney
1722 _kind = 3
1724 geoids = _sys.argv[1:]
1725 while geoids:
1726 geoid = geoids.pop(0)
1728 if '-crop'.startswith(geoid.lower()):
1729 _crop = 20, -125, 50, -65 # CONUS
1731 elif '-karney'.startswith(geoid.lower()):
1732 _GeoidEGM = GeoidKarney
1734 elif '-kind'.startswith(geoid.lower()):
1735 _kind = int(geoids.pop(0))
1737 elif '-pgm'.startswith(geoid.lower()):
1738 _GeoidEGM = GeoidPGM
1740 elif geoid[-4:].lower() in ('.pgm',):
1741 g = _GeoidEGM(geoid, crop=_crop, kind=_kind)
1742 printf(g.toStr(), nt=1, nl=1)
1743 printf(repr(g.pgm), nt=1)
1744 # <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>:
1745 # The height of the EGM96 geoid at Timbuktu
1746 # echo 16:46:33N 3:00:34W | GeoidEval
1747 # => 28.7068 -0.02e-6 -1.73e-6
1748 # The 1st number is the height of the geoid, the 2nd and
1749 # 3rd are its slopes in northerly and easterly direction
1750 t = 'Timbuktu %s' % (g,)
1751 k = {'egm84-15.pgm': '31.2979',
1752 'egm96-5.pgm': '28.7067',
1753 'egm2008-1.pgm': '28.7880'}.get(g.name.lower(), '28.7880')
1754 ll = _MODS.dms.parseDMS2('16:46:33N', '3:00:34W', sep=':')
1755 for ll in (ll, (16.776, -3.009),):
1756 try:
1757 h, ll = g.height(*ll), fstr(ll, prec=6)
1758 printf('%s.height(%s): %.4F vs %s', t, ll, h, k)
1759 except (GeoidError, RangeError) as x:
1760 printf(_COLONSPACE_(t, str(x)))
1762 elif geoid[-4:].lower() in ('.bin',):
1763 g = GeoidG2012B(geoid, kind=_kind)
1764 printf(g.toStr())
1766 else:
1767 raise GeoidError(grid=repr(geoid))
1769_I = int # PYCHOK unused _I
1770del _intCs # trash ints cache
1772# **) MIT License
1773#
1774# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1775#
1776# Permission is hereby granted, free of charge, to any person obtaining a
1777# copy of this software and associated documentation files (the "Software"),
1778# to deal in the Software without restriction, including without limitation
1779# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1780# and/or sell copies of the Software, and to permit persons to whom the
1781# Software is furnished to do so, subject to the following conditions:
1782#
1783# The above copyright notice and this permission notice shall be included
1784# in all copies or substantial portions of the Software.
1785#
1786# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1787# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1788# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1789# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1790# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1791# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1792# OTHER DEALINGS IN THE SOFTWARE.
1794# <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>
1795# _lowerleft = -90, -179, -30.1500 # egm2008-1.pgm
1796# _lowerleft = -90, -179, -29.5350 # egm96-5.pgm
1797# _lowerleft = -90, -179, -29.7120 # egm84-15.pgm
1799# _center = 0, 0, 17.2260 # egm2008-1.pgm
1800# _center = 0, 0, 17.1630 # egm96-5.pgm
1801# _center = 0, 0, 18.3296 # egm84-15.pgm
1803# _upperright = 90, 180, 14.8980 # egm2008-1.pgm
1804# _upperright = 90, 180, 13.6050 # egm96-5.pgm
1805# _upperright = 90, 180, 13.0980 # egm84-15.pgm
1808# % python3 -m pygeodesy.geoids [-Karney] ../testGeoids/egm*.pgm
1809#
1810# 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)
1811#
1812# _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'
1813#
1814# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880
1815# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880
1816#
1817# 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)
1818#
1819# _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'
1820#
1821# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979
1822# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979
1823#
1824# 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)
1825#
1826# _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'
1827#
1828# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067
1829# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067
1832# % python3 -m pygeodesy.geoids -Karney ../testGeoids/egm*.pgm
1833#
1834# 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)
1835#
1836# _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'
1837#
1838# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880
1839# Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880
1840#
1841# 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)
1842#
1843# _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'
1844#
1845# Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979
1846# Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979
1847#
1848# 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)
1849#
1850# _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'
1851#
1852# Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067
1853# Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067
1856# % python2 -m pygeodesy.geoids -PGM ../testGeoids/egm*.pgm
1857#
1858# 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)
1859#
1860# _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'
1861#
1862# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880
1863# Timbuktu GeoidPGM('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880
1864#
1865# 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)
1866#
1867# _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'
1868#
1869# Timbuktu GeoidPGM('egm84-15.pgm').height(16.775833, -3.009444): 31.2979 vs 31.2979
1870# Timbuktu GeoidPGM('egm84-15.pgm').height(16.776, -3.009): 31.2975 vs 31.2979
1871#
1872# 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)
1873#
1874# _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'
1875#
1876# Timbuktu GeoidPGM('egm96-5.pgm').height(16.775833, -3.009444): 28.7065 vs 28.7067
1877# Timbuktu GeoidPGM('egm96-5.pgm').height(16.776, -3.009): 28.7064 vs 28.7067