# Coverage for pygeodesy/heights.py : 94%

## 287 statements 270 run 17 missing 31 excluded

Hot-keys on this page

r m x p toggle line displays

j k next/prev highlighted chunk

0 (zero) top of page

1 (one) first highlighted chunk

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 | # -*- coding: utf-8 -*- u'''Classes L{HeightCubic}, L{HeightIDWequirectangular}, L{HeightIDWeuclidean}, L{HeightIDWhaversine}, L{HeightIDWkarney}, L{HeightIDWvincentys}, L{HeightLinear}, L{HeightLSQBiSpline} and L{HeightSmoothBiSpline} to interpolate the height of C{LatLon} locations or separate lat-/longitudes from a set of C{LatLon} points with known heights. Except for L{HeightIDWequirectangular}, L{HeightIDWeuclidean}, L{HeightIDWhaversine} and L{HeightIDWvincentys}, the height interpolators in this module require the packages U{numpy <https://PyPI.org/project/numpy>} and U{scipy<https://SciPy.org>} or U{geographiclib<https://PyPI.org/project/geographiclib>} to be installed. Typical usage is as follows. First create an interpolator from a given set of C{LatLon} points with known heights, called C{knots}. C{hinterpolator = HeightXyz(knots, **options)} Get the interpolated height of other C{LatLon} location(s) with C{h = hinterpolator(ll)} or C{h0, h1, h2, ... = hinterpolator(ll0, ll1, ll2, ...)} or C{hs = hinterpolator(lls)} # C{list, tuple, generator, ...} For separate lat-/longitudes invoke the C{.height} method C{h = hinterpolator.height(lat, lon)} or C{h0, h1, h2, ... = hinterpolator.height(lats, lons)} # C{list, ...} The C{knots} do not need to be ordered for any of the height interpolators. Errors from C{scipy} as raised as L{SciPyError}s. Warnings issued by C{scipy} can be thrown as L{SciPyWarning} exceptions, provided Python C{warnings} are filtered accordingly, see L{SciPyWarning}. @see: U{SciPy<https://docs.SciPy.org/doc/scipy/reference/interpolate.html>}. ''' from pygeodesy.datum import Datum from pygeodesy.fmath import EPS, fidw, hypot2, \ _IsNotError, isscalar, len2, map1, map2 from pygeodesy.formy import euclidean_, haversine_, _scaler, vincentys_ from pygeodesy.lazily import _ALL_LAZY from pygeodesy.named import _Named from pygeodesy.points import LatLon_ from pygeodesy.utily import PI, PI2, PI_2, property_RO, \ radiansPI, radiansPI2, unroll180, unrollPI __all__ = _ALL_LAZY.heights __version__ = '20.02.20' class HeightError(ValueError): # imported by .geoids '''Height interpolator C{Height...} or interpolation issue. ''' pass class SciPyError(HeightError): '''Error raised for C{SciPy} errors. ''' pass class SciPyWarning(HeightError): '''Exception thrown for C{SciPy} warnings. To raise C{SciPy} warnings as L{SciPyWarning} exceptions, Python C{warnings} must be filtered as U{warnings.filterwarnings('error') <https://docs.Python.org/3/library/warnings.html#the-warnings-filter>} I{prior to} C{import scipy} or by setting environment variable U{PYTHONWARNINGS<https://docs.Python.org/3/using/cmdline.html #envvar-PYTHONWARNINGS>} or with C{python} command line option U{-W<https://docs.Python.org/3/using/cmdline.html#cmdoption-w>} as C{error}. ''' pass def _alist(ais): # return tuple of floats, not numpy.float64s return list(map(float, ais)) def _allis2(llis, m=1, Error=HeightError): # imported by .geoids # dtermine return type and convert lli C{LatLon}s to list if not isinstance(llis, tuple): # llis are *args raise AssertionError('type(%s): %r' % ('*llis', llis)) n = len(llis) if n == 1: # convert single lli to 1-item list llis = llis[0] try: n, llis = len2(llis) _as = _alist # return list of interpolated heights except TypeError: # single lli n, llis = 1, [llis] _as = _ascalar # return single interpolated heights else: # of 0, 2 or more llis _as = _atuple # return tuple of interpolated heights if n < m: raise Error('insufficient %s: %s, need %s' % ('llis', n, m)) return _as, llis def _ascalar(ais): # imported by .geoids # return single float, not numpy.float64 ais = list(ais) # np.array, etc. to list if len(ais) != 1: raise AssertionError('len[%r] = %s == 1' % (ais, len(ais))) return float(ais[0]) # remove np.<type> def _atuple(ais): # return tuple of floats, not numpy.float64s return tuple(map(float, ais)) def _axyllis4(atype, llis, m=1, off=True): # convert lli C{LatLon}s to tuples or C{NumPy} arrays of # C{SciPy} sphericals and determine the return type _as, llis = _allis2(llis, m=m) xis, yis, _ = zip(*_xyhs(llis, off=off)) # unzip return _as, atype(xis), atype(yis), llis def _ordedup(ts, lo=EPS, hi=PI2-EPS): # clip, order and remove duplicates p, ks = 0, [] for k in sorted(max(lo, min(hi, t)) for t in ts): if k > p: ks.append(k) p = k return ks def _SciPyIssue(x, *extras): # imported by .geoids t = ' '.join(str(x).strip().split() + map(str, extras)) if isinstance(x, (RuntimeWarning, UserWarning)): return SciPyWarning(t) else: return SciPyError(t) # PYCHOK not really def _xyhs(lls, off=True): # map (lat, lon, h) to (x, y, h) in radians, offset as # x: 0 <= lon <= PI2, y: 0 <= lat <= PI if off is True # else x: -PI <= lon <= PI, y: -PI_2 <= lat <= PI_2 if off: xf = yf = 0.0 else: # undo offset xf, yf = PI, PI_2 try: for ll in lls: yield (max(0.0, radiansPI2(ll.lon + 180.0)) - xf), \ (max(0.0, radiansPI( ll.lat + 90.0)) - yf), ll.height except AttributeError as x: raise HeightError('%s: %r' % (x, ll)) def _xyhs3(atype, m, knots, off=True): # convert knot C{LatLon}s to tuples or C{NumPy} arrays and C{SciPy} sphericals xs, ys, hs = zip(*_xyhs(knots, off=off)) # PYCHOK unzip n = len(hs) if n < m: raise HeightError('insufficient %s: %s, need %s' % ('knots', n, m)) return map1(atype, xs, ys, hs) class _HeightBase(_Named): # imported by .geoids '''(INTERNAL) Interpolator base class. ''' _kmin = 2 # min number of knots _np = None # numpy _np_v = None # version _spi = None # scipy.interpolate _sp_v = None # version def __call__(self, *args): '''(INTERNAL) I{Must be overloaded}. ''' self._notOverloaded('__call__', *args) def _axyllis4(self, llis): return _axyllis4(self._np.array, llis) def _ev(self, *args): '''(INTERNAL) I{Must be overloaded}. ''' self._notOverloaded(self._ev.__name__, *args) def _eval(self, llis): # XXX single arg, not *args _as, xis, yis, _ = self._axyllis4(llis) try: # SciPy .ev signature: y first, then x! return _as(self._ev(yis, xis)) except Exception as x: raise _SciPyIssue(x) def _height(self, lats, lons, Error=HeightError): if isscalar(lats) and isscalar(lons): llis = LatLon_(lats, lons) else: n, lats = len2(lats) m, lons = len2(lons) if n != m: raise Error('non-matching %s: %s vs %s' % ('len', n, m)) llis = [LatLon_(*ll) for ll in zip(lats, lons)] return self(llis) # __call__(lli) or __call__(llis) def _NumSciPy(self, throwarnings=False): '''(INTERNAL) Import C{numpy} and C{scipy}. ''' if throwarnings: # raise SciPyWarnings, but ... # ... not if scipy has been imported already import sys if 'scipy' not in sys.modules: import warnings warnings.filterwarnings('error') import scipy as sp import scipy.interpolate as spi import numpy as np _HeightBase._np = np _HeightBase._np_v = np.__version__ _HeightBase._spi = spi _HeightBase._sp_v = sp.__version__ return np, spi def _xyhs3(self, knots): return _xyhs3(self._np.array, self._kmin, knots) class HeightCubic(_HeightBase): '''Height interpolator based on C{SciPy} U{interp2d<https://docs.SciPy.org/ doc/scipy/reference/generated/scipy.interpolate.interp2d.html>} C{kind='cubic'}. ''' _interp2d = None _kind = 'cubic' _kmin = 16 def __init__(self, knots, name=''): '''New L{HeightCubic} interpolator. @param knots: The points with known height (C{LatLon}s). @keyword name: Optional height interpolator name (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or invalid B{C{knot}}. @raise ImportError: Package C{numpy} or C{scipy} not found or not installed. @raise SciPyError: A C{scipy.interpolate.interp2d} issue. @raise SciPyWarning: A C{scipy.interpolate.interp2d} warning as exception. ''' _, spi = self._NumSciPy() xs, ys, hs = self._xyhs3(knots) try: # SciPy.interpolate.interp2d kind 'linear' or 'cubic' self._interp2d = spi.interp2d(xs, ys, hs, kind=self._kind) except Exception as x: raise _SciPyIssue(x) if name: self.name = name def __call__(self, *llis): '''Interpolate the height for one or several locations. @param llis: The location or locations (C{LatLon}, ... or C{LatLon}s). @return: A single interpolated height (C{float}) or a list or tuple of interpolated heights (C{float}s). @raise HeightError: Insufficient number of B{C{llis}} or invalid B{C{lli}}. @raise SciPyError: A C{scipy.interpolate.interp2d} issue. @raise SciPyWarning: A C{scipy.interpolate.interp2d} warning as exception. ''' return _HeightBase._eval(self, llis) def _ev(self, yis, xis): # PYCHOK expected # to make SciPy .interp2d signature(x, y), single (x, y) # match SciPy .ev signature(ys, xs), flipped multiples return map(self._interp2d, xis, yis) def height(self, lats, lons): '''Interpolate the height for one or several lat-/longitudes. @param lats: Latitude or latitudes (C{degrees} or C{degrees}s). @param lons: Longitude or longitudes (C{degrees} or C{degrees}s). @return: A single interpolated height (C{float}) or a list of interpolated heights (C{float}s). @raise HeightError: Insufficient or non-matching number of B{C{lats}} and B{C{lons}}. @raise SciPyError: A C{scipy.interpolate.interp2d} issue. @raise SciPyWarning: A C{scipy.interpolate.interp2d} warning as exception. ''' return _HeightBase._height(self, lats, lons) class HeightLinear(HeightCubic): '''Height interpolator based on C{SciPy} U{interp2d<https://docs.SciPy.org/ doc/scipy/reference/generated/scipy.interpolate.interp2d.html>} C{kind='linear}. ''' _kind = 'linear' _kmin = 2 def __init__(self, knots, name=''): '''New L{HeightLinear} interpolator. @param knots: The points with known height (C{LatLon}s). @keyword name: Optional height interpolator name (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or invalid B{C{knot}}. @raise ImportError: Package C{numpy} or C{scipy} not found or not installed. @raise SciPyError: A C{scipy.interpolate.interp2d} issue. @raise SciPyWarning: A C{scipy.interpolate.interp2d} warning as exception. ''' HeightCubic.__init__(self, knots, name=name) __call__ = HeightCubic.__call__ # for __doc__ height = HeightCubic.height # for __doc__ class _HeightIDW(_HeightBase): '''(INTERNAL) Base class for U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) height interpolators. ''' _beta = 0 # inverse distance power _hs = () # known heights _xs = () # knot lons _ys = () # knot lats def __init__(self, knots, beta=2, name=''): '''New L{_HeightIDW} interpolator. ''' self._xs, self._ys, self._hs = _xyhs3(tuple, self._kmin, knots, off=False) self.beta = beta if name: self.name = name def __call__(self, *llis): '''Interpolate the height for one or several locations. @param llis: The location or locations (C{LatLon}, ... or C{LatLon}s). @return: A single interpolated height (C{float}) or a list or tuple of interpolated heights (C{float}s). @raise HeightError: Insufficient number of B{C{llis}}, invalid B{C{lli}} or an L{fidw} issue. ''' _as, xis, yis, _ = _axyllis4(tuple, llis, off=False) return _as(map(self._hIDW, xis, yis)) def _distances(self, x, y): # PYCHOK unused (x, y) radians '''Must be overloaded. ''' raise NotImplementedError('method: %s' % ('_distances',)) def _hIDW(self, x, y): # interpolate height at (x, y) radians or degrees try: ds = self._distances(x, y) return fidw(self._hs, ds, beta=self._beta) except ValueError as x: raise HeightError(str(x)) @property def beta(self): '''Get the inverse distance power (C{int}). ''' return self._beta @beta.setter # PYCHOK setter! def beta(self, beta): '''Set the inverse distance power. @param beta: New inverse distance power (C{int} 1, 2, or 3). @raise HeightError: Invalid B{C{beta}}. ''' try: b = int(beta) if b != beta or 1 > b or b > 3: raise ValueError except (TypeError, ValueError): raise HeightError('%s invalid: %r' % ('beta', beta)) self._beta = b def height(self, lats, lons): '''Interpolate the height for one or several lat-/longitudes. @param lats: Latitude or latitudes (C{degrees} or C{degrees}s). @param lons: Longitude or longitudes (C{degrees} or C{degrees}s). @return: A single interpolated height (C{float}) or a list of interpolated heights (C{float}s). @raise HeightError: Insufficient or non-matching number of B{C{lats}} and B{C{lons}} or an L{fidw} issue. ''' return _HeightBase._height(self, lats, lons) class HeightIDWequirectangular(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the C{equirectangular} distance (in radians squared) like function L{equirectangular_}. @see: L{HeightIDWeuclidean}, L{HeightIDWhaversine}, L{HeightIDWvincentys}, U{Inverse distance weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>}, U{IDW<https://www.Geo.FU-Berlin.De/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. ''' _adjust = True _wrap = False def __init__(self, knots, adjust=True, wrap=False, name=''): '''New L{HeightIDWequirectangular} interpolator. @param knots: The points with known height (C{LatLon}s). @keyword adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @keyword name: Optional height interpolator name (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or invalid B{C{knot}}. ''' if not adjust: self._adjust = False if wrap: self._wrap = True _HeightIDW.__init__(self, knots, beta=1, name=name) # distance**2 def _distances(self, x, y): # (x, y) radians for xk, yk in zip(self._xs, self._ys): d, _ = unrollPI(xk, x, wrap=self._wrap) if self._adjust: d *= _scaler(yk, y) yield hypot2(d, yk - y) # like equirectangular_ distance2 __call__ = _HeightIDW.__call__ # for __doc__ height = _HeightIDW.height # for __doc__ class HeightIDWeuclidean(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the C{Euclidean} distance from function L{euclidean_}. @see: L{HeightIDWequirectangular}, L{HeightIDWhaversine}, L{HeightIDWkarney}, L{HeightIDWvincentys}, U{Inverse distance weighting<https://WikiPedia.org/wiki/Inverse_distance_weighting>}, U{IDW<https://www.Geo.FU-Berlin.De/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. ''' _adjust = True def __init__(self, knots, adjust=True, beta=2, name=''): '''New L{HeightIDWeuclidean} interpolator. @param knots: The points with known height (C{LatLon}s). @keyword adjust: Adjust the longitudinal delta by the cosine of the mean latitude for B{C{adjust}}=C{True}. @keyword beta: Inverse distance power (C{int} 1, 2, or 3). @keyword name: Optional height interpolator name (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or invalid B{C{knot}}, B{C{adjust}} or B{C{beta}}. ''' if adjust not in (True, False): raise HeightError('%s=%r invalid' % ('adjust', adjust)) self._adjust = adjust _HeightIDW.__init__(self, knots, beta=beta, name=name) def _distances(self, x, y): # (x, y) radians for xk, yk in zip(self._xs, self._ys): yield euclidean_(yk, y, xk - x, adjust=self._adjust) __call__ = _HeightIDW.__call__ # for __doc__ height = _HeightIDW.height # for __doc__ class HeightIDWhaversine(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} C{Haversine} distance from function L{haversine_}. @note: See note under L{HeightIDWvincentys}. @see: L{HeightIDWequirectangular}, L{HeightIDWeuclidean}, L{HeightIDWkarney}, L{HeightIDWvincentys}, U{Inverse distance weighting<https://WikiPedia.org/wiki/Inverse_distance_weighting>}, U{IDW<https://www.Geo.FU-Berlin.De/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. ''' _wrap = False def __init__(self, knots, beta=2, wrap=False, name=''): '''New L{HeightIDWhaversine} interpolator. @param knots: The points with known height (C{LatLon}s). @keyword beta: Inverse distance power (C{int} 1, 2, or 3). @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @keyword name: Optional height interpolator name (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or invalid B{C{knot}} or B{C{beta}}. ''' if wrap: self._warp = True _HeightIDW.__init__(self, knots, beta=beta, name=name) def _distances(self, x, y): # (x, y) radians for xk, yk in zip(self._xs, self._ys): d, _ = unrollPI(xk, x, wrap=self._wrap) yield haversine_(yk, y, d) __call__ = _HeightIDW.__call__ # for __doc__ height = _HeightIDW.height # for __doc__ class HeightIDWkarney(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} distance from I{Charles F. F. Karney's} U{GeographicLib<https://PyPI.org/project/geographiclib>} U{Geodesic <https://geographiclib.sourceforge.io/1.49/python/code.html>} Inverse method. @see: L{HeightIDWequirectangular}, L{HeightIDWeuclidean}, L{HeightIDWhaversine}, L{HeightIDWvincentys}, U{Inverse distance weighting<https://WikiPedia.org/wiki/Inverse_distance_weighting>}, U{IDW<https://www.Geo.FU-Berlin.De/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. ''' _datum = None _geodesic = None _wrap = False def __init__(self, knots, datum=None, beta=2, wrap=False, name=''): '''New L{HeightIDWhaversine} interpolator. @param knots: The points with known height (C{LatLon}s). @keyword datum: Optional datum (L{Datum} to use, overriding the default C{B{knots}[0].datum} @keyword beta: Inverse distance power (C{int} 1, 2, or 3). @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @keyword name: Optional height interpolator name (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or invalid B{C{knot}}, B{C{datum}} or B{C{beta}}. @raise ImportError: Package U{GeographicLib <https://PyPI.org/project/geographiclib>} missing. @raise TypeError: Invalid B{C{datum}}. ''' n, self._lls = len2(knots) if n < self._kmin: raise HeightError('insufficient %s: %s, need %s' % ('knots', n, self._kmin)) try: self._datum = self._lls[0].datum if datum is None else datum if not isinstance(self.datum, Datum): raise TypeError except (AttributeError, TypeError): raise _IsNotError('valid', datum=self.datum or datum) self._geodesic = self.datum.ellipsoid.geodesic self.beta = beta if wrap: self._warp = True if name: self.name = name def _distances(self, x, y): # (x, y) degrees g = self._geodesic for ll in self._lls: # see .ellipsoidalKarney.LatLon._inverse _, lon = unroll180(x, ll.lon, wrap=self._wrap) # g.LONG_UNROLL # XXX g.DISTANCE needed for 's12', distance in meters? yield abs(g.Inverse(y, x, ll.lat, lon)['a12']) @property_RO def _hs(self): for ll in self._lls: yield ll.height def __call__(self, *llis): '''Interpolate the height for one or several locations. @param llis: The location or locations (C{LatLon}, ... or C{LatLon}s). @return: A single interpolated height (C{float}) or a list or tuple of interpolated heights (C{float}s). @raise HeightError: Insufficient number of B{C{llis}}, invalid B{C{lli}} or an L{fidw} issue. ''' def _xy2(lls): try: # like _xyhs above, but keeping degrees for ll in lls: yield ll.lon, ll.lat except AttributeError as x: raise HeightError('%s: %r' % (x, ll)) _as, llis = _allis2(llis) return _as(map(self._hIDW, *zip(*_xy2(llis)))) @property_RO def datum(self): '''Get the datum of this interpolator (L{Datum}). ''' return self._datum height = _HeightIDW.height # for __doc__ class HeightIDWvincentys(_HeightIDW): '''Height interpolator using U{Inverse Distance Weighting <https://WikiPedia.org/wiki/Inverse_distance_weighting>} (IDW) and the I{angular} C{Vincenty} distance from function L{vincentys_}. @note: See note under L{vincentys_}. @see: L{HeightIDWequirectangular}, L{HeightIDWeuclidean}, L{HeightIDWhaversine}, L{HeightIDWkarney}, U{Inverse distance weighting<https://WikiPedia.org/wiki/Inverse_distance_weighting>}, U{IDW<https://www.Geo.FU-Berlin.De/en/v/soga/Geodata-analysis/ geostatistics/Inverse-Distance-Weighting/index.html>} and U{SHEPARD_INTERP_2D<https://People.SC.FSU.edu/~jburkardt/c_src/ shepard_interp_2d/shepard_interp_2d.html>}. ''' _wrap = False def __init__(self, knots, beta=2, wrap=False, name=''): '''New L{HeightIDWvincentys} interpolator. @param knots: The points with known height (C{LatLon}s). @keyword beta: Inverse distance power (C{int} 1, 2, or 3). @keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). @keyword name: Optional height interpolator name (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or invalid B{C{knot}} or B{C{beta}}. ''' if wrap: self._warp = True _HeightIDW.__init__(self, knots, beta=beta, name=name) def _distances(self, x, y): # (x, y) radians for xk, yk in zip(self._xs, self._ys): d, _ = unrollPI(xk, x, wrap=self._wrap) yield vincentys_(yk, y, d) __call__ = _HeightIDW.__call__ # for __doc__ height = _HeightIDW.height # for __doc__ class HeightLSQBiSpline(_HeightBase): '''Height interpolator using C{SciPy} U{LSQSphereBivariateSpline <https://docs.SciPy.org/doc/scipy/reference/generated/scipy. interpolate.LSQSphereBivariateSpline.html>}. ''' _kmin = 16 # k = 3, always def __init__(self, knots, weight=None, name=''): '''New L{HeightLSQBiSpline} interpolator. @param knots: The points with known height (C{LatLon}s). @keyword weight: Optional weight or weights for each B{C{knot}} (C{scalar} or C{scalar}s). @keyword name: Optional height interpolator name (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or B{C{weight}}s or invalid B{C{knot}} or B{C{weight}}. @raise ImportError: Package C{numpy} or C{scipy} not found or not installed. @raise SciPyError: A C{LSQSphereBivariateSpline} issue. @raise SciPyWarning: A C{LSQSphereBivariateSpline} warning as exception. ''' np, spi = self._NumSciPy() xs, ys, hs = self._xyhs3(knots) n = len(hs) w = weight if isscalar(w): w = float(w) if w <= 0: raise HeightError('%s invalid: %.6f' % ('weight', w)) w = [w] * n elif w is not None: m, w = len2(w) if m != n: raise HeightError('%s invalid: %s, not %s' % ( 'number of weights', m, n)) w = map2(float, w) m = min(w) if m <= 0: raise HeightError('%s[%s] invalid: %.6f' % ( 'weight', w.find(m), m)) try: T = 1.0e-4 # like SciPy example ps = np.array(_ordedup(xs, T, PI2 - T)) ts = np.array(_ordedup(ys, T, PI - T)) self._ev = spi.LSQSphereBivariateSpline(ys, xs, hs, ts, ps, eps=EPS, w=w).ev except Exception as x: raise _SciPyIssue(x) if name: self.name = name def __call__(self, *llis): '''Interpolate the height for one or several locations. @param llis: The location or locations (C{LatLon}, ... or C{LatLon}s). @return: A single interpolated height (C{float}) or a list or tuple of interpolated heights (C{float}s). @raise HeightError: Insufficient number of B{C{llis}} or invalid B{C{lli}}. @raise SciPyError: A C{LSQSphereBivariateSpline} issue. @raise SciPyWarning: A C{LSQSphereBivariateSpline} warning as exception. ''' return _HeightBase._eval(self, llis) def height(self, lats, lons): '''Interpolate the height for one or several lat-/longitudes. @param lats: Latitude or latitudes (C{degrees} or C{degrees}s). @param lons: Longitude or longitudes (C{degrees} or C{degrees}s). @return: A single interpolated height (C{float}) or a list of interpolated heights (C{float}s). @raise HeightError: Insufficient or non-matching number of B{C{lats}} and B{C{lons}}. @raise SciPyError: A C{LSQSphereBivariateSpline} issue. @raise SciPyWarning: A C{LSQSphereBivariateSpline} warning as exception. ''' return _HeightBase._height(self, lats, lons) class HeightSmoothBiSpline(_HeightBase): '''Height interpolator using C{SciPy} U{SmoothSphereBivariateSpline <https://docs.SciPy.org/doc/scipy/reference/generated/scipy. interpolate.SmoothSphereBivariateSpline.html>}. ''' _kmin = 16 # k = 3, always def __init__(self, knots, s=4, name=''): '''New L{HeightSmoothBiSpline} interpolator. @param knots: The points with known height (C{LatLon}s). @keyword s: The spline smoothing factor (C{4}). @keyword name: Optional height interpolator name (C{str}). @raise HeightError: Insufficient number of B{C{knots}} or invalid B{C{knot}} or B{C{s}}. @raise ImportError: Package C{numpy} or C{scipy} not found or not installed. @raise SciPyError: A C{SmoothSphereBivariateSpline} issue. @raise SciPyWarning: A C{SmoothSphereBivariateSpline} warning as exception. ''' _, spi = self._NumSciPy() if s < 4: raise HeightError('%s too small: %s' % ('smoothing', s)) xs, ys, hs = self._xyhs3(knots) try: self._ev = spi.SmoothSphereBivariateSpline(ys, xs, hs, eps=EPS, s=s).ev except Exception as x: raise _SciPyIssue(x) if name: self.name = name def __call__(self, *llis): '''Interpolate the height for one or several locations. @param llis: The location or locations (C{LatLon}, ... or C{LatLon}s). @return: A single interpolated height (C{float}) or a list or tuple of interpolated heights (C{float}s). @raise HeightError: Insufficient number of B{C{llis}} or invalid B{C{lli}}. @raise SciPyError: A C{SmoothSphereBivariateSpline} issue. @raise SciPyWarning: A C{SmoothSphereBivariateSpline} warning as exception. ''' return _HeightBase._eval(self, llis) def height(self, lats, lons): '''Interpolate the height for one or several lat-/longitudes. @param lats: Latitude or latitudes (C{degrees} or C{degrees}s). @param lons: Longitude or longitudes (C{degrees} or C{degrees}s). @return: A single interpolated height (C{float}) or a list of interpolated heights (C{float}s). @raise HeightError: Insufficient or non-matching number of B{C{lats}} and B{C{lons}}. @raise SciPyError: A C{SmoothSphereBivariateSpline} issue. @raise SciPyWarning: A C{SmoothSphereBivariateSpline} warning as exception. ''' return _HeightBase._height(self, lats, lons) # **) MIT License # # Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.