# Coverage for pygeodesy/geoids.py : 93%

## 650 statements 606 run 44 missing 73 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 | # -*- coding: utf-8 -*- u'''Classes L{GeoidG2012B}, L{GeoidKarney} and L{GeoidPGM} to interpolate the height of various U{geoid<https://WikiPedia.org/wiki/Geoid>}s at C{LatLon} locations or separate lat-/longitudes using different interpolation methods and C{geoid} files. L{GeoidKarney} is a transcription of I{Charles Karney's} C++ class U{Geoid <https://GeographicLib.SourceForge.io/html/geoid.html>} to pure Python. The L{GeoidG2012B} and L{GeoidPGM} interpolators both depend on U{scipy<https://SciPy.org>} and U{numpy<https://PyPI.org/project/numpy>} and require those packages to be installed. In addition, each geoid interpolator needs C{grid knots} to be (down)loaded from a geoid file, specific to the interpolator, more details below. For each interpolator, there are several interpolation choices, like I{linear}, I{cubic}, etc. Typical usage is as follows. First create an interpolator from a geoid file, also referred to as the C{grid knots}. C{ginterpolator = GeoidXyz(grid_file, **options)} Get the interpolated geoid height of C{LatLon} location(s) with C{h = ginterpolator(ll)} or C{h0, h1, h2, ... = ginterpolator(ll0, ll1, ll2, ...)} or C{hs = ginterpolator(lls)} # C{list, tuple, generator, ...} For separate lat-/longitudes invoke the C{.height} method C{h = ginterpolator.height(lat, lon)} or C{h0, h1, h2, ... = ginterpolator.height(lats, lons)} # C{list, ...} Errors from C{scipy} are 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: Charles Karney's U{GeographicLib<https://GeographicLib.SourceForge.io/ html/index.html>}, U{Geoid height<https://GeographicLib.SourceForge.io/ html/geoid.html>} and U{Installing the Geoid datasets <https:// GeographicLib.SourceForge.io/html/geoid.html#geoidinst>}, U{SciPy <https://docs.SciPy.org/doc/scipy/reference/interpolate.html>} interpolation U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/ reference/generated/scipy.interpolate.RectBivariateSpline.html>} and U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/ scipy.interpolate.interp2d.html>} and the functions L{elevations.elevation2} and L{elevations.geoidHeight2}. ''' from pygeodesy.datum import Datum, Datums from pygeodesy.dms import parseDMS2, RangeError from pygeodesy.fmath import EPS, favg, Fdot, fdot, Fhorner, frange, fStr, \ len2, map1, map2 from pygeodesy.heights import _allis2, _ascalar, \ _HeightBase, HeightError, _SciPyIssue from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY from pygeodesy.named import GeoidHeight5Tuple, LatLon3Tuple, _Named from pygeodesy.utily import property_RO from math import floor import os.path as _os_path from os import SEEK_CUR as _SEEK_CUR, SEEK_SET as _SEEK_SET from struct import calcsize as _calcsize, unpack as _unpack try: from StringIO import StringIO as _BytesIO # reads bytes _b2str = str # convert bytes to str except ImportError: # Python 3+ from io import BytesIO as _BytesIO # PYCHOK expected def _b2str(bs): # used only for egm*.pgm text return bs.decode('utf-8') __all__ = _ALL_LAZY.geoids + _ALL_DOCS('_GeoidBase') __version__ = '20.02.24' # temporarily hold a single instance for each int value _intCs = {} _interp2d_ks = {-2: 'linear', -3: 'cubic', -5: 'quintic'} class GeoidError(HeightError): '''Geoid interpolator C{Geoid...} or interpolation issue. ''' pass class PGMError(GeoidError): '''Issue parsing or cropping an C{egm*.pgm} geoid dataset. ''' pass class _GeoidBase(_HeightBase): '''(INTERNAL) Base class for C{Geoid...}s. ''' _cropped = None _datum = Datums.WGS84 _endian = 'tbd' _geoid = 'n/a' _hs_y_x = None # numpy 2darray, row-major order _interp2d = None # interp2d interpolation _kind = 3 # order for interp2d, RectBivariateSpline _knots = 0 # nlat * nlon _mean = None # _name = '' # _Named _nBytes = 0 # numpy size in bytes, float64 _sizeB = 0 # geoid file size in bytes _smooth = 0 # used only for RectBivariateSpline _stdev = None _lat_d = 0.0 # increment, +tive _lat_lo = 0.0 # lower lat, south _lat_hi = 0.0 # upper lat, noth _lon_d = 0.0 # increment, +tive _lon_lo = 0.0 # left lon, west _lon_hi = 0.0 # right lon, east _lon_of = 0.0 # forward lon offset _lon_og = 0.0 # reverse lon offset _center = None # (lat, lon, height) _highest = None # (lat, lon, height) _lowerleft = None # (lat, lon, height) _lowerright = None # (lat, lon, height) _lowest = None # (lat, lon, height) _upperleft = None # (lat, lon, height) _upperright = None # (lat, lon, height) _yx_hits = None # cache hits, ala Karney def __init__(self, hs, p): '''(INTERNAL) Set up the grid axes, the C{SciPy} interpolator and several internal geoid attributes. @param hs: Grid knots with known height (C{numpy 2darray}). @param p: The C{slat, wlon, nlat, nlon, dlat, dlon} and other geoid parameters (C{INTERNAL}). @raise GeoidError: Invalid B{C{kind}}. @raise SciPyError: A C{scipy.interpolate.inter2d} or C{-.RectBivariateSpline} issue. @raise SciPyWarning: A C{scipy.interpolate.inter2d} or C{-.RectBivariateSpline} warning as exception. ''' # for 2d scipy.interpolate.interp2d(xs, ys, hs, ...) and # scipy.interpolate.RectBivariateSpline(ys, xs, hs, ...) # require the shape of hs to be (len(ys), len(xs)), note # the different (xs, ys, ...) and (ys, xs, ...) orders if (p.nlat, p.nlon) != hs.shape: raise GeoidError('%s %s vs %r' % ('shape', hs.shape, (p.nlat, p.nlon))) # both axes and bounding box ys, self._lat_d = self._gaxis2(p.slat, p.dlat, p.nlat, 'lats') xs, self._lon_d = self._gaxis2(p.wlon, p.dlon, p.nlon, 'lons') bb = ys[0], ys[-1], xs[0], xs[-1] + p.dlon # fudge lon_hi # geoid grids are typically stored in row-major order, some # with rows (90..-90) reversed and columns (0..360) wrapped # to Easten longitude, 0 <= east < 180 and 180 <= west < 0 k = self._kind if k in _interp2d_ks: self._interp2d = self._spi.interp2d(xs, ys, hs, kind=_interp2d_ks[k]) elif 1 <= k <= 5: self._ev = self._spi.RectBivariateSpline(ys, xs, hs, bbox=bb, ky=k, kx=k, s=self._smooth).ev else: raise GeoidError('%s invalid: %r' % ('kind', k)) self._hs_y_x = hs # numpy 2darray, row-major self._nBytes = hs.nbytes # numpy size in bytes self._knots = p.knots # grid knots self._lon_of = float(p.flon) # forward offset self._lon_og = float(p.glon) # reverse offset # shrink the box by 1 unit on every side # bb += self._lat_d, -self._lat_d, self._lon_d, -self._lon_d self._lat_lo = float(bb[0]) self._lat_hi = float(bb[1]) self._lon_lo = float(bb[2] - p.glon) self._lon_hi = float(bb[3] - p.glon) def __call__(self, *llis): '''Interpolate the geoid height for one or several locations. @param llis: The location or locations (C{LatLon}, ... or C{LatLon}s). @return: A single interpolated geoid height (C{float}) or a list or tuple of interpolated geoid heights (C{float}s). @raise GeoidError: Insufficient number of B{C{llis}} or an invalid B{C{lli}}. @raise RangeError: An B{C{lli}} is outside this geoid's lat- or longitude range. @raise SciPyError: A C{scipy.interpolate.inter2d} or C{-.RectBivariateSpline} issue. @raise SciPyWarning: A C{scipy.interpolate.inter2d} or C{-.RectBivariateSpline} warning as exception. ''' return self._called(llis, True) def __repr__(self): return self.toStr() def __str__(self): return '%s(%r)' % (self.classname, self.name) def _called(self, llis, scipy): # handle __call__ _as, llis = _allis2(llis, Error=GeoidError) hs = [] for i, lli in enumerate(llis): try: hs.append(self._hGeoid(lli.lat, lli.lon)) except (GeoidError, RangeError) as x: # XXX avoid str(LatLon()) degree symbols i = '' if _as is _ascalar else '[%s]' % (i,) lli = fStr((lli.lat, lli.lon), prec=6) raise x.__class__('location%s (%s) %s' % (i, lli, x)) except Exception as x: if scipy and self.scipy: raise _SciPyIssue(x) else: raise return _as(hs) def _ev(self, y, x): # PYCHOK expected # only used for .interpolate.interp2d, but # overwritten for .RectBivariateSpline, # note (y, x) must be flipped! return self._interp2d(x, y) def _gaxis2(self, lo, d, n, name): # build grid axis, hi = lo + (n - 1) * d m, a = len2(frange(lo, n, d)) if m != n: raise GeoidError('len(%s) = %s != %s' % (name, m, n)) if d < 0: d, a = -d, list(reversed(a)) for i in range(1, m): e = a[i] - a[i-1] if e < EPS: # non-increasing axis raise GeoidError('%s[%s]: %.12f' % (name, i, e)) return self._np.array(a), d def _g2ll2(self, lat, lon): self._notOverloaded(self._g2ll2.__name__, lat, lon) def _gyx2g2(self, y, x): # convert grid (y, x) indices to grid (lat, lon) return ((self._lat_lo + self._lat_d * y), (self._lon_lo + self._lon_of + self._lon_d * x)) def _hGeoid(self, lat, lon): out = self.outside(lat, lon) if out: raise RangeError('outside on %s' % (out,)) return float(self._ev(*self._ll2g2(lat, lon))) def _ll2g2(self, lat, lon): self._notOverloaded(self._ll2g2.__name__, lat, lon) def _llh3(self, lat, lon): r = LatLon3Tuple(lat, lon, self._hGeoid(lat, lon)) return self._xnamed(r) def _llh3LL(self, llh, LatLon): return llh if LatLon is None else LatLon(*llh) def _llh3minmax(self, highest=True, *unused): hs, np = self._hs_y_x, self._np # <https://docs.SciPy.org/doc/numpy/reference/generated/ # numpy.argmin.html#numpy.argmin> arg = self._np.argmax if highest else self._np.argmin y, x = np.unravel_index(arg(hs, axis=None), hs.shape) return self._g2ll2(*self._gyx2g2(y, x)) + (float(hs[y, x]),) def _load(self, g, dtype, n, offset=0): # numpy.fromfile, like .frombuffer g.seek(offset, _SEEK_SET) return self._np.fromfile(g, dtype, n) def _open(self, geoid, datum, kind, name, smooth): # open the geoid file try: self._geoid = _os_path.basename(geoid) self._sizeB = _os_path.getsize(geoid) g = open(geoid, 'rb') except (IOError, OSError) as x: raise GeoidError(str(x)) if datum and isinstance(datum, Datum): self._datum = datum self._kind = int(kind) if name: _HeightBase.name.fset(self, name) # recursion if smooth: if int(smooth) < 0: raise GeoidError('%s invalid: %r' % ('smooth', smooth)) self._smooth = int(smooth) return g def _swne(self, crop): # crop box to 4-tuple (s, w, n, e) try: if len(crop) == 2: try: # sw, ne LatLons swne = (crop[0].lat, crop[0].lon, crop[1].lat, crop[1].lon) except AttributeError: # (s, w), (n, e) swne = tuple(crop[0]) + tuple(crop[1]) else: # (s, w, n, e) swne = crop if len(swne) == 4: s, w, n, e = map(float, swne) if -90 <= s <= (n - 1) <= 89 and \ -180 <= w <= (e - 1) <= 179: return s, w, n, e except (IndexError, TypeError, ValueError): pass raise GeoidError('%s invalid: %r' % ('crop', crop)) def center(self, LatLon=None): '''Return the center location and height of this geoid. @keyword LatLon: Optional (sub-)class to return the location (C{LatLon}) and height or C{None}. @return: A L{LatLon3Tuple}C{(lat, lon, height)} if B{C{LatLon}} is C{None} or a B{C{LatLon}} instance with the lat-, longitude and height of the grid center location. ''' if self._center is None: self._center = self._llh3(favg(self._lat_lo, self._lat_hi), favg(self._lon_lo, self._lon_hi)) return self._llh3LL(self._center, LatLon) @property_RO def cropped(self): '''Is geoid cropped (C{bool} or C{None} if crop not supported). ''' return self._cropped @property_RO def dtype(self): '''Get the grid C{scipy} U{dtype<https://docs.SciPy.org/doc/numpy/ reference/generated/numpy.ndarray.dtype.html>} (C{numpy.dtype}). ''' return self._hs_y_x.dtype @property_RO def endian(self): '''Get the geoid endianess and U{dtype<https://docs.SciPy.org/ doc/numpy/reference/generated/numpy.dtype.html>} (C{str}). ''' return self._endian def height(self, lats, lons): '''Interpolate the geoid 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 geoid height (C{float}) or a list of interpolated geoid heights (C{float}s). @raise GeoidError: Insufficient or non-matching number of B{C{lats}} and B{C{lons}}. @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this geoid's lat- or longitude range. @raise SciPyError: A C{scipy.interpolate.inter2d} or C{-.RectBivariateSpline} issue. @raise SciPyWarning: A C{scipy.interpolate.inter2d} or C{-.RectBivariateSpline} warning as exception. ''' return _HeightBase._height(self, lats, lons, Error=GeoidError) def highest(self, LatLon=None, **unused): '''Return the location and largest height of this geoid. @keyword LatLon: Optional (sub-)class to return the location (C{LatLon}) and height or C{None}. @return: A L{LatLon3Tuple}C{(lat, lon, height)} if B{C{LatLon}} is C{None} or a B{C{LatLon}} instance with the lat-, longitude and height of the highest grid location. ''' if self._highest is None: self._highest = self._llh3minmax(True) return self._llh3LL(self._highest, LatLon) @property_RO def hits(self): '''Get the number of cache hits (C{int} or C{None}). ''' return self._yx_hits @property_RO def kind(self): '''Get the interpolator kind and order (C{int}). ''' return self._kind @property_RO def knots(self): '''Get the number of grid knots (C{int}). ''' return self._knots def lowerleft(self, LatLon=None): '''Return the lower-left location and height of this geoid. @keyword LatLon: Optional (sub-)class to return the location (C{LatLon}) and height or C{None}. @return: A L{LatLon3Tuple}C{(lat, lon, height)} if B{C{LatLon}} is C{None} or a B{C{LatLon}} instance with the lat-, longitude and height of the lower-left, SW grid corner. ''' if self._lowerleft is None: self._lowerleft = self._llh3(self._lat_lo, self._lon_lo) return self._llh3LL(self._lowerleft, LatLon) def lowerright(self, LatLon=None): '''Return the lower-right location and height of this geoid. @keyword LatLon: Optional (sub-)class to return the location (C{LatLon}) and height or C{None}. @return: A L{LatLon3Tuple}C{(lat, lon, height)} if B{C{LatLon}} is C{None} or a B{C{LatLon}} instance with the lat-, longitude and height of the lower-right, SE grid corner. ''' if self._lowerright is None: self._lowerright = self._llh3(self._lat_lo, self._lon_hi) return self._llh3LL(self._lowerright, LatLon) def lowest(self, LatLon=None, **unused): '''Return the location and the lowest height of this geoid. @keyword LatLon: Optional (sub-)class to return the location (C{LatLon}) and height or C{None}. @return: A L{LatLon3Tuple}C{(lat, lon, height)} if B{C{LatLon}} is C{None} or a B{C{LatLon}} instance with the lat-, longitude and height of the lowest grid location. ''' if self._lowest is None: self._lowest = self._llh3minmax(False) return self._llh3LL(self._lowest, LatLon) @property_RO def mean(self): '''Get the mean of this geoid's heights (C{float}). ''' if self._mean is None: self._mean = float(self._np.mean(self._hs_y_x)) return self._mean @property_RO def name(self): '''Get the name of this geoid (C{str}). ''' return _HeightBase.name.fget(self) or self._geoid # recursion @property_RO def nBytes(self): '''Get the grid in-memory size in bytes (C{int}). ''' return self._nBytes @property_RO def numpy(self): '''Get the imported C{numpy} version (C{str}). ''' return self._np_v def outside(self, lat, lon): '''Check whether a location is outside this geoid's lat-/longitude or crop range. @param lat: The latitude (C{degrees}). @param lon: The longitude (C{degrees}). @return: A 1- or 2-character C{str} if outside or an empty C{str} if inside. ''' return ('S' if lat < self._lat_lo else ('N' if lat > self._lat_hi else '')) + \ ('W' if lon < self._lon_lo else ('E' if lon > self._lon_hi else '')) @property_RO def scipy(self): '''Get the imported C{scipy} version (C{str}). ''' return self._sp_v @property_RO def sizeB(self): '''Get the geoid grid file size in bytes (C{int}). ''' return self._sizeB @property_RO def smooth(self): '''Get the C{RectBivariateSpline} smoothing (C{int}). ''' return self._smooth @property_RO def stdev(self): '''Get the standard deviation of this geoid's heights (C{float}). ''' if self._stdev is None: self._stdev = float(self._np.std(self._hs_y_x)) return self._stdev def toStr(self, prec=3, sep=', '): # PYCHOK signature '''This geoid and all geoid attributes as a string. @keyword prec: Optional number of decimal digits (0..9 or C{None} for default). Trailing zero decimals are stripped for B{C{prec}} values of 1 and above, but kept for negative B{C{prec}} values. @keyword sep: Optional separator (C{str}). @return: Geoid name and attributes (C{str}). ''' t = ['%s(%s)' % (m.__name__, fStr(m(), prec=prec)) for m in (self.lowerleft, self.upperright, self.center, self.highest, self.lowest)] for n in ('mean', 'stdev'): v = getattr(self, n) if v is not None: t.append('%s=%s' % (n, fStr(v, prec=prec))) s = 1 if self.kind < 0 else 2 for n in (('kind', 'smooth')[:s] + ('cropped', 'dtype', 'endian', 'hits', 'knots', 'nBytes', 'sizeB', 'scipy', 'numpy')): v = getattr(self, n) if v is not None: t.append('%s=%r' % (n, v)) return '%s: %s' % (self, sep.join(t)) def upperleft(self, LatLon=None): '''Return the upper-left location and height of this geoid. @keyword LatLon: Optional (sub-)class to return the location (C{LatLon}) and height or C{None}. @return: A L{LatLon3Tuple}C{(lat, lon, height)} if B{C{LatLon}} is C{None} or a B{C{LatLon}} instance with the lat-, longitude and height of the upper-left, NW grid corner. ''' if self._upperleft is None: self._upperleft = self._llh3(self._lat_hi, self._lon_lo) return self._llh3LL(self._upperleft, LatLon) def upperright(self, LatLon=None): '''Return the upper-right location and height of this geoid. @keyword LatLon: Optional (sub-)class to return the location (C{LatLon}) and height or C{None}. @return: A L{LatLon3Tuple}C{(lat, lon, height)} if B{C{LatLon}} is C{None} or a B{C{LatLon}} instance with the lat-, longitude and height of the upper-right, NE grid corner. ''' if self._upperright is None: self._upperright = self._llh3(self._lat_hi, self._lon_hi) return self._llh3LL(self._upperright, LatLon) class GeoidG2012B(_GeoidBase): '''Geoid height interpolator for U{GEOID12B Model <https://www.NGS.NOAA.gov/GEOID/GEOID12B/>} grids U{CONUS <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_CONUS.shtml>}, U{Alaska<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_AK.shtml>}, U{Hawaii<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_HI.shtml>}, U{Guam and Northern Mariana Islands <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_GMNI.shtml>}, U{Puerto Rico and U.S. Virgin Islands <https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_PRVI.shtml>} and U{American Samoa<https://www.NGS.NOAA.gov/GEOID/GEOID12B/GEOID12B_AS.shtml>} based on C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/doc/ scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>} or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/ scipy.interpolate.interp2d.html>} interpolation. Use any of the binary C{le} (little endian) or C{be} (big endian) C{g2012b*.bin} grid files. ''' def __init__(self, g2012b_bin, crop=None, datum=None, # NAD 83 Ellipsoid kind=3, name='', smooth=0): '''New L{GeoidG2012B} interpolator. @param g2012b_bin: A C{GEOID12B} grid file name (C{.bin}). @keyword crop: Optional crop box, not supported (C{None}). @keyword datum: Optional grid datum (C{Datum}), default C{WGS84}. @keyword kind: C{scipy.interpolate} order (C{int}), use 1..5 for U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/ reference/generated/scipy.interpolate.RectBivariateSpline.html>}, -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/ reference/generated/scipy.interpolate.interp2d.html>}, -3 for C{interp2d cubic} or -5 for C{interp2d quintic}. @keyword name: Optional geoid name (C{str}). @keyword smooth: Smoothing factor for U{RectBivariateSpline <https://docs.SciPy.org/doc/scipy/reference/generated/ scipy.interpolate.RectBivariateSpline.html>} only (C{int}). @raise GeoidError: G2012B grid file B{C{g2012b_bin}} issue, non-C{None} B{C{crop}} or invalid B{C{kind}} or B{C{smooth}}. @raise ImportError: Package C{numpy} or C{scipy} not found or not installed. @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue. @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d} warning as exception. ''' if crop is not None: raise GeoidError('not supported: %s=%r' % ('crop', crop)) np, _ = self._NumSciPy() g = self._open(g2012b_bin, datum, kind, name, smooth) try: p = _Gpars() n = self.sizeB // 4 - 11 # number of f4 heights # U{numpy dtype formats are different from Python struct formats # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>} for en_f4 in ('<f4', '>f4'): en_ = en_f4[:1] # skip 4xf8, get 3xi4 p.nlat, p.nlon, ien = map(int, self._load(g, en_+'i4', 3, 32)) if ien == 1: # correct endian p.knots = p.nlat * p.nlon if p.knots == n and 1 < p.nlat < n \ and 1 < p.nlon < n: self._endian = en_f4 break else: # couldn't validate endian raise GeoidError('endianess') # get the first 4xf8 p.slat, p.wlon, p.dlat, p.dlon = map(float, self._load(g, en_+'f8', 4)) # read all f4 heights, ignoring the first 4xf8 and 3xi4 hs = self._load(g, en_f4, n, 44).reshape(p.nlat, p.nlon) p.wlon -= 360 # western-most East longitude to earth (..., lon) _GeoidBase.__init__(self, hs, p) except Exception as x: raise _SciPyIssue(x, 'in', repr(g2012b_bin)) finally: g.close() def _g2ll2(self, lat, lon): # convert grid (lat, lon) to earth (lat, lon) return lat, lon def _ll2g2(self, lat, lon): # convert earth (lat, lon) to grid (lat, lon) return lat, lon def _I(i): '''(INTERNAL) Cache a single C{int} constant. ''' return _intCs.setdefault(i, i) # PYCHOK undefined by del _intCs def _T(*cs): '''(INTERNAL) Cache a tuple of single C{int} constants. ''' return map1(_I, *cs) class GeoidKarney(_GeoidBase): '''Geoid height interpolator for Charles Karney's U{GeographicLib Earth Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/ html/geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/ html/geoid.html#geoidinst>} datasets using bilinear or U{cubic <https://dl.ACM.org/citation.cfm?id=368443>} interpolation and U{caching <https://GeographicLib.SourceForge.io/html/geoid.html#geoidcache>} in pure Python transcribed from Karney's U{C++ class Geoid <https://GeographicLib.SourceForge.io/html/geoid.html#geoidinterp>}. Use any of the geoid U{egm84-, egm96- or egm2008-*.pgm <https://GeographicLib.SourceForge.io/html/geoid.html#geoidinst>} datasets. ''' _C0 = (372.0, 240.0, 372.0) # n, _ and s common denominators # matrices c3n_, c3, c3s_, transposed from GeographicLib/Geoid.cpp _C3 = ((_T(0, 0, 62, 124, 124, 62, 0, 0, 0, 0, 0, 0), _T(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), _T(-131, 7, -31, -62, -62, -31, 45, 216, 156, -45, -55, -7), _T(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), _T(138, -138, 0, 0, 0, 0, -183, 33, 153, -3, 48, -48), # PYCHOK indent _T(144, 42, -62, -124, -124, -62, -9, 87, 99, 9, 42, -42), _T(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), _T(0, 0, 0, 0, 0, 0, 93, -93, -93, 93, 0, 0), _T(-102, 102, 0, 0, 0, 0, 18, 12, -12, -18, -84, 84), _T(-31, -31, 31, 62, 62, 31, 0, -93, -93, 0, 31, 31)), # PYCHOK indent (_T(9, -9, 9, 186, 54, -9, -9, 54, -54, 9, -9, 9), _T(-18, 18, -88, -42, 162, -32, 8, -78, 78, -8, 18, -18), _T(-88, 8, -18, -42, -78, 18, 18, 162, 78, -18, -32, -8), _T(0, 0, 90, -150, 30, 30, 30, -90, 90, -30, 0, 0), _T(96, -96, 96, -96, -24, 24, -96, -24, 144, -24, 24, -24), # PYCHOK indent _T(90, 30, 0, -150, -90, 0, 0, 30, 90, 0, 30, -30), _T(0, 0, -20, 60, -60, 20, -20, 60, -60, 20, 0, 0), _T(0, 0, -60, 60, 60, -60, 60, -60, -60, 60, 0, 0), _T(-60, 60, 0, 60, -60, 0, 0, 60, -60, 0, -60, 60), _T(-20, -20, 0, 60, 60, 0, 0, -60, -60, 0, 20, 20)), (_T(18, -18, 36, 210, 162, -36, 0, 0, 0, 0, -18, 18), # PYCHOK indent _T(-36, 36, -165, 45, 141, -21, 0, 0, 0, 0, 36, -36), _T(-122, -2, -27, -111, -75, 27, 62, 124, 124, 62, -64, 2), _T(0, 0, 93, -93, -93, 93, 0, 0, 0, 0, 0, 0), _T(120, -120, 147, -57, -129, 39, 0, 0, 0, 0, 66, -66), # PYCHOK indent _T(135, 51, -9, -192, -180, 9, 31, 62, 62, 31, 51, -51), _T(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), _T(0, 0, -93, 93, 93, -93, 0, 0, 0, 0, 0, 0), _T(-84, 84, 18, 12, -12, -18, 0, 0, 0, 0, -102, 102), _T(-31, -31, 0, 93, 93, 0, -31, -62, -62, -31, 31, 31))) _egm = None # open geoid file _endian = '>H' # struct.unpack 1 ushort (big endian, unsigned short) _4endian = '>4H' # struct.unpack 4 ushorts _Rendian = '' # struct.unpack a row of ushorts # _highest = (-8.4, 147.367, 85.839) if egm2008-1.pgm else ( # (-8.167, 147.25, 85.422) if egm96-5.pgm else # (-4.5, 148.75, 81.33) # egm84-15.pgm) # _lowest = (4.7, 78.767, -106.911) if egm2008-1.pgm else ( # (4.667, 78.833, -107.043) if egm96-5.pgm else # (4.75, 79.25, -107.34) # egm84-15.pgm _mean = -1.317 # from egm2008-1, -1.438 egm96-5, -0.855 egm84-15 _nBytes = None # not applicable _nterms = len(_C3[0]) # columns length, number of row _pgm = None _smooth = None # not applicable _stdev = 29.244 # from egm2008-1, 29.227 egm96-5, 29.183 egm84-15 _u2B = _calcsize(_endian) # pixelsize_ in bytes _4u2B = _calcsize(_4endian) # 4 pixelsize_s in bytes _Ru2B = 0 # row of pixelsize_s in bytes _yxH = () # cache (y, x) indices _yxHt = () # cached 4- or 10-tuple for _ev2H resp. _ev3H _yx_hits = 0 # cache hits def __init__(self, egm_pgm, crop=None, datum=None, # WGS84 kind=3, name='', smooth=None): '''New L{GeoidKarney} interpolator. @param egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/ html/geoid.html#geoidinst>} file name (C{egm*.pgm}). @keyword crop: Optional box to limit geoid locations, a 4-tuple (C{south, west, north, east}), 2-tuple (C{(south, west), (north, east)}) or 2, in C{degrees90} lat- and C{degrees180} longitudes or a 2-tuple (C{LatLonSW, LatLonNE}) of C{LatLon} instances. @keyword datum: Optional grid datum (C{Datum}), default C{WGS84}. @keyword kind: Interpolation order (C{int}), 2 for C{bilinear} or 3 for C{cubic}. @keyword name: Optional geoid name (C{str}). @keyword smooth: Smoothing factor, unsupported (C{None}). @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid B{C{crop}}, B{C{kind}} or B{C{smooth}}. @see: Class L{GeoidPGM} and function L{egmGeoidHeights}. ''' if smooth is not None: raise GeoidError('not supported: %s=%r' % ('smooth', smooth)) if kind in (2,): self._evH = self._ev2H elif kind not in (3,): raise GeoidError('%s invalid: %r' % ('kind', kind)) self._egm = g = self._open(egm_pgm, datum, kind, name, smooth) self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB) self._Rendian = self._4endian.replace('4', str(p.nlon)) self._Ru2B = _calcsize(self._Rendian) self._knots = p.knots # grid knots self._lon_of = float(p.flon) # forward offset self._lon_og = float(p.glon) # reverse offset # set earth (lat, lon) limits (s, w, n, e) self._lat_lo, \ self._lon_lo, \ self._lat_hi, \ self._lon_hi = self._swne(crop if crop else p.crop4) self._cropped = True if crop else False def __call__(self, *llis): '''Interpolate the geoid height for one or several locations. @param llis: The location or locations (C{LatLon}, ... or C{LatLon}s). @return: A single interpolated geoid height (C{float}) or a list or tuple of interpolated geoid heights (C{float}s). @raise GeoidError: Insufficient number of B{C{llis}} or an invalid B{C{lli}}. @raise RangeError: An B{C{lli}} is outside this geoid's lat- or longitude range. ''' return self._called(llis, False) def _c0c3v(self, y, x): # get the common denominator, the 10x12 cubic matrix and # the 12 cubic v-coefficients around geoid index (y, x) p = self._pgm if 0 < x < (p.nlon - 2) and 0 < y < (p.nlat - 2): # read 4x4 ushorts, drop the 4 corners g = self._egm e = self._4endian n = self._4u2B R = self._Ru2B b = self._seek(y - 1, x - 1) v = _unpack(e, g.read(n))[1:3] b += R g.seek(b, _SEEK_SET) v += _unpack(e, g.read(n)) b += R g.seek(b, _SEEK_SET) v += _unpack(e, g.read(n)) b += R g.seek(b, _SEEK_SET) v += _unpack(e, g.read(n))[1:3] j = 1 else: # likely some wrapped y and/or x's v = [self._raw(y + j, x + i) for i, j in (( 0, -1), ( 1, -1), (-1, 0), ( 0, 0), ( 1, 0), ( 2, 0), (-1, 1), ( 0, 1), ( 1, 1), ( 2, 1), ( 0, 2), ( 1, 2))] j = 0 if y < 1 else (1 if y < (p.nlat - 2) else 2) return self._C0[j], self._C3[j], v def _ev(self, lat, lon): # PYCHOK expected # interpolate the geoid height at grid (lat, lon) fy, fx = self._g2yx2(lat, lon) y, x = int(floor(fy)), int(floor(fx)) fy -= y fx -= x H = self._evH(fy, fx, y, x) # ._ev3H or ._ev2H H *= self._pgm.Scale # H.fmul(self._pgm.Scale) H += self._pgm.Offset # H.fadd(self._pgm.Offset) return H.fsum() def _ev2H(self, fy, fx, *yx): # compute the bilinear 4-tuple and interpolate raw H if self._yxH == yx: t = self._yxHt self._yx_hits += 1 else: y, x = self._yxH = yx t = [self._raw(y + j, x + i) for i, j in ((0, 0), (1, 0), (0, 1), (1, 1))] self._yxHt = t = tuple(t) v = 1.0, -fx, fx H = Fdot(v, t[0], t[0], t[1]) # a H -= H * fy # c = (1 - fy) * a H += Fdot(v, t[2], t[2], t[3]) * fy # c += b * fy return H def _ev3H(self, fy, fx, *yx): # compute the cubic 10-tuple and interpolate raw H if self._yxH == yx: t = self._yxHt self._yx_hits += 1 else: self._yxH = yx c0, c3, v = self._c0c3v(*yx) t = [fdot(v, *c3[i]) / c0 for i in range(self._nterms)] self._yxHt = t = tuple(t) # GeographicLib/Geoid.cpp Geoid::height(lat, lon) ... # real h = t[0] + fx * (t[1] + fx * (t[3] + fx * t[6])) + # fy * (t[2] + fx * (t[4] + fx * t[7]) + # fy * (t[5] + fx * t[8] + fy * t[9])); H = Fdot((1, fx, fy), t[5], t[8], t[9]) * fy H = (Fhorner(fx, t[2], t[4], t[7]) + H) * fy H += Fhorner(fx, t[0], t[1], t[3], t[6]) return H _evH = _ev3H # overriden for kind == 2 def _g2ll2(self, lat, lon): # convert grid (lat, lon) to earth (lat, lon), uncropped while lon > 180: lon -= 360 return lat, lon def _g2yx2(self, lat, lon): # convert grid (lat, lon) to grid (y, x) indices p = self._pgm # note, slat = +90, rlat < 0 makes y >=0 return ((lat - p.slat) * p.rlat), ((lon - p.wlon) * p.rlon) def _gyx2g2(self, y, x): # convert grid (y, x) indices to grid (lat, lon) p = self._pgm return (p.slat + p.dlat * y), (p.wlon + p.dlon * x) def _lat2y2(self, lat2): # convert earth lat(s) to min and max grid y indices ys, m = [], self._pgm.nlat - 1 for lat in lat2: y, _ = self._g2yx2(*self._ll2g2(lat, 0)) ys.append(max(min(int(y), m), 0)) return min(ys), max(ys) + 1 def _ll2g2(self, lat, lon): # convert earth (lat, lon) to grid (lat, lon), uncropped while lon < 0: lon += 360 return lat, lon def _llh3minmax(self, highest=True, *lat2): # find highest or lowest, takes 10+ secs for egm2008-1.pgm geoid # (Python 2.7.16, macOS 10.13.6 High Sierra, iMac 3 GHz Core i3) y = x = 0 h = self._raw(y, x) if highest: for j, r in self._raw2(*lat2): m = max(r) if m > h: h, y, x = m, j, r else: # lowest for j, r in self._raw2(*lat2): m = min(r) if m < h: h, y, x = m, j, r try: # min/max index x = x.index(h) except AttributeError: x = 0 h *= self._pgm.Scale h += self._pgm.Offset return self._g2ll2(*self._gyx2g2(y, x)) + (h,) def _raw(self, y, x): # get the ushort geoid height at geoid index (y, x), # like GeographicLib/Geoid.hpp real rawval(is, iy) p = self._pgm if x < 0: x += p.nlon elif x >= p.nlon: x -= p.nlon h = p.nlon // 2 if y < 0: y = -y elif y >= p.nlat: y = (p.nlat - 1) * 2 - y else: h = 0 x += h if x < h else -h self._seek(y, x) h = _unpack(self._endian, self._egm.read(self._u2B)) return h[0] def _raw2(self, *lat2): # yield a 2-tuple (y, ushorts) for each row or for # the rows between two (or more) earth lat values p = self._pgm g = self._egm e = self._Rendian n = self._Ru2B # min(lat2) <= lat <= max(lat2) or 0 <= y < p.nlat s, t = self._lat2y2(lat2) if lat2 else (0, p.nlat) self._seek(s, 0) # to start of row s for y in range(s, t): yield y, _unpack(e, g.read(n)) def _seek(self, y, x): # position geoid to grid index (y, x) p = self._pgm b = p.skip + (y * p.nlon + x) * self._u2B self._egm.seek(b, _SEEK_SET) return b # position @property_RO def dtype(self): '''Get the geoid's grid data type (C{str}). ''' return 'ushort' def height(self, lats, lons): '''Interpolate the geoid 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 geoid height (C{float}) or a list of interpolated geoid heights (C{float}s). @raise GeoidError: Insufficient or non-matching number of B{C{lats}} and B{C{lons}}. @raise RangeError: A B{C{lat}} or B{C{lon}} is outside this geoid's lat- or longitude range. ''' return _HeightBase._height(self, lats, lons, Error=GeoidError) def highest(self, LatLon=None, full=False): # PYCHOK full '''Return the location and largest height of this geoid. @keyword LatLon: Optional (sub-)class to return the location (C{LatLon}) and height or C{None}. @keyword full: Search the full or limited latitude range (C{bool}). @return: A L{LatLon3Tuple}C{(lat, lon, height)} if B{C{LatLon}} is C{None} or a B{C{LatLon}} instance with the lat-, longitude and height of the highest grid location. ''' if self._highest is None: lat2 = () if full or self.cropped else (-12, -4) self._highest = self._llh3minmax(True, *lat2) return self._llh3LL(self._highest, LatLon) def lowest(self, LatLon=None, full=False): # PYCHOK full '''Return the location and the lowest height of this geoid. @keyword LatLon: Optional (sub-)class to return the location (C{LatLon}) and height or C{None}. @keyword full: Search the full or limited latitude range (C{bool}). @return: A L{LatLon3Tuple}C{(lat, lon, height)} if B{C{LatLon}} is C{None} or a B{C{LatLon}} instance with the lat-, longitude and height of the lowest grid location. ''' if self._lowest is None: lat2 = () if full or self.cropped else (0, 8) self._lowest = self._llh3minmax(False, *lat2) return self._llh3LL(self._lowest, LatLon) @property_RO def pgm(self): '''Get the PGM attributes (C{_PGM}). ''' return self._pgm @property_RO def u2B(self): '''Get the PGM itemsize in bytes (C{int}). ''' return self._u2B class GeoidPGM(_GeoidBase): '''Geoid height interpolator for Charles Karney's U{GeographicLib Earth Gravitational Model (EGM)<https://GeographicLib.SourceForge.io/ html/geoid.html>} geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/ html/geoid.html#geoidinst>} datasets but based on C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/reference/ generated/scipy.interpolate.RectBivariateSpline.html>} or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/ scipy.interpolate.interp2d.html>} interpolation. Use any of the U{egm84-, egm96- or egm2008-*.pgm <https://GeographicLib.SourceForge.io/html/geoid.html#geoidinst>} datasets. However, unless cropped, an entire C{egm*.pgm} dataset is loaded into the C{SciPy} U{RectBivariateSpline<https://docs.SciPy.org/ doc/scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html>} or U{interp2d<https://docs.SciPy.org/doc/scipy/reference/generated/ scipy.interpolate.interp2d.html>} interpolator and converted from 2-byte C{int} to 8-byte C{dtype float64}. Therefore, internal memory usage is 4x the U{egm*.pgm<https://GeographicLib.SourceForge.io/html/ geoid.html#geoidinst>} file size and may exceed the available memory, especially with 32-bit Python, see properties C{.nBytes} and C{.sizeB}. ''' _endian = '>u2' _pgm = None _u2B = 0 # np.itemsize def __init__(self, egm_pgm, crop=None, datum=None, # WGS84 kind=3, name='', smooth=0): '''New L{GeoidPGM} interpolator. @param egm_pgm: An U{EGM geoid dataset<https://GeographicLib.SourceForge.io/ html/geoid.html#geoidinst>} file name (C{egm*.pgm}). @keyword crop: Optional box to crop B{C{egm_pgm}}, a 4-tuple (C{south, west, north, east}) or 2-tuple (C{(south, west), (north, east)}), in C{degrees90} lat- and C{degrees180} longitudes or a 2-tuple (C{LatLonSW, LatLonNE}) of C{LatLon} instances. @keyword datum: Optional grid datum (C{Datum}), default C{WGS84}. @keyword kind: C{scipy.interpolate} order (C{int}), use 1..5 for U{RectBivariateSpline<https://docs.SciPy.org/doc/scipy/ reference/generated/scipy.interpolate.RectBivariateSpline.html>}, -2 for U{interp2d linear<https://docs.SciPy.org/doc/scipy/ reference/generated/scipy.interpolate.interp2d.html>}, -3 for C{interp2d cubic} or -5 for C{interp2d quintic}. @keyword name: Optional geoid name (C{str}). @keyword smooth: Smoothing factor for U{RectBivariateSpline <https://docs.SciPy.org/doc/scipy/reference/generated/ scipy.interpolate.RectBivariateSpline.html>} only (C{int}). @raise GeoidError: EGM dataset B{C{egm_pgm}} issue or invalid B{C{crop}}, B{C{kind}} or B{C{smooth}}. @raise ImportError: Package C{numpy} or C{scipy} not found or not installed. @raise SciPyError: A C{RectBivariateSpline} or C{inter2d} issue. @raise SciPyWarning: A C{RectBivariateSpline} or C{inter2d} warning as exception. @note: The U{GeographicLib egm*.pgm<https://GeographicLib.SourceForge.io/ html/geoid.html#geoidinst>} file sizes are based on a 2-byte C{int} height converted to 8-byte C{dtype float64} for C{scipy} interpolators. Therefore, internal memory usage is 4 times the C{egm*.pgm} file size and may exceed the available memory, especially with 32-bit Python. To reduce memory usage, set keyword argument B{C{crop}} to the region of interest. For example B{crop=(20, -125, 50, -65)} covers the U{conterminous US<https:// www.NGS.NOAA.gov/GEOID/GEOID12B/maps/GEOID12B_CONUS_grids.png>} (CONUS), less than 3% of the entire C{egm2008-1.pgm} dataset. @see: Class L{GeoidKarney} and function L{egmGeoidHeights}. ''' np, _ = self._NumSciPy() self._u2B = np.dtype(self.endian).itemsize g = self._open(egm_pgm, datum, kind, name, smooth) self._pgm = p = _PGM(g, pgm=egm_pgm, itemsize=self.u2B, sizeB=self.sizeB) if crop: g = p._cropped(g, abs(kind) + 1, *self._swne(crop)) self._g2ll2 = self._g2ll2_cropped self._ll2g2 = self._ll2g2_cropped if map2(int, self.numpy.split('.')[:2]) < (1, 9): g = open(g.name, 'rb') # reopen tempfile for numpy 1.8.0- self._cropped = True else: self._cropped = False try: # U{numpy dtype formats are different from Python struct formats # <https://docs.SciPy.org/doc/numpy-1.15.0/reference/arrays.dtypes.html>} # read all heights, skipping the PGM header lines, converted to float hs = self._load(g, self.endian, p.knots, p.skip).reshape(p.nlat, p.nlon) * p.Scale if p.Offset: # offset hs = p.Offset + hs if p.dlat < 0: # flip the rows hs = np.flipud(hs) _GeoidBase.__init__(self, hs, p) except Exception as x: raise _SciPyIssue(x, 'in', repr(egm_pgm)) finally: g.close() def _g2ll2(self, lat, lon): # convert grid (lat, lon) to earth (lat, lon), uncropped while lon > 180: lon -= 360 return lat, lon def _g2ll2_cropped(self, lat, lon): # convert cropped grid (lat, lon) to earth (lat, lon) return lat, lon - self._lon_og def _ll2g2(self, lat, lon): # convert earth (lat, lon) to grid (lat, lon), uncropped while lon < 0: lon += 360 return lat, lon def _ll2g2_cropped(self, lat, lon): # convert earth (lat, lon) to cropped grid (lat, lon) return lat, lon + self._lon_of @property_RO def pgm(self): '''Get the PGM attributes (C{_PGM}). ''' return self._pgm @property_RO def u2B(self): '''Get the PGM itemsize in bytes (C{int}). ''' return self._u2B class _Gpars(_Named): '''(INTERNAL) Basic geoid parameters. ''' # interpolator parameters dlat = 0 # +/- latitude resolution in C{degrees}. dlon = 0 # longitude resolution in C{degrees}. nlat = 1 # number of latitude knots (C{int}). nlon = 0 # number of longitude knots (C{int}) rlat = 0 # +/- latitude resolution in C{float}, 1 / .dlat. rlon = 0 # longitude resolution in C{float}, 1 / .dlon. slat = 0 # nothern- or southern most latitude (C{degrees90}). wlon = 0 # western-most longitude in Eastern lon (C{degrees360}). flon = 0 # forward, earth to grid longitude offset glon = 0 # reverse, grid to earth longitude offset knots = 0 # number of knots, nlat * nlon (C{int}). skip = 0 # header bytes to skip (C{int}). def __repr__(self): t = ', '.join('%s=%r' % (a, getattr(self, a)) for a in sorted(dir(self.__class__)) if not a.startswith('_')) return '%s: %s' % (self, t) def __str__(self): return '%s(%r)' % (self.classname, self.name) class _PGM(_Gpars): '''(INTERNAL) Parse an C{egm*.pgm} geoid dataset file. # Geoid file in PGM format for the GeographicLib::Geoid class # Description WGS84 EGM96, 5-minute grid # URL https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html # DateTime 2009-08-29 18:45:03 # MaxBilinearError 0.140 # RMSBilinearError 0.005 # MaxCubicError 0.003 # RMSCubicError 0.001 # Offset -108 # Scale 0.003 # Origin 90N 0E # AREA_OR_POINT Point # Vertical_Datum WGS84 <width> <height> <pixel> ... ''' crop4 = () # 4-tuple (C{south, west, north, east}). egm = None glon = 180 # reverse offset, uncropped # pgm = '' # name sizeB = 0 u2B = 2 # item size of grid height (C{int}). @staticmethod def _llstr2floats(latlon): # llstr to (lat, lon) floats lat, lon = latlon.split() return parseDMS2(lat, lon) # PGM file attributes, CamelCase but not .istitle() AREA_OR_POINT = str DateTime = str Description = str # 'WGS84 EGM96, 5-minute grid' Geoid = str # 'file in PGM format for the GeographicLib::Geoid class' MaxBilinearError = float MaxCubicError = float Offset = float Origin = _llstr2floats Pixel = 0 RMSBilinearError = float RMSCubicError = float Scale = float URL = str # 'https://Earth-Info.NGA.mil/GandG/wgs84/...' Vertical_Datum = str def __init__(self, g, pgm='', itemsize=0, sizeB=0): # MCCABE 22 '''(INTERNAL) New C{_PGM} parsed C{egm*.pgm} geoid dataset. ''' self.name = pgm # geoid file name if itemsize: self._u2B = itemsize if sizeB: self.sizeB = sizeB t = g.readline() # make sure newline == '\n' if t != b'P5\n' or t.strip() != b'P5': raise self._Errorf('header %r', t) while True: # read all # Attr ... lines, try: # ignore empty ones or comments t = g.readline().strip() if t.startswith(b'#'): t = t.lstrip(b'#').lstrip() a, v = map(_b2str, t.split(None, 1)) f = getattr(_PGM, a, None) if callable(f) and a[:1].isupper(): setattr(self, a, f(v)) elif t: break except (TypeError, ValueError): raise self._Errorf('Attr %r', t) else: # should never get here raise self._Errorf('header %r', g.tell()) try: # must be (even) width and (odd) height nlon, nlat = map(int, t.split()) if nlon < 2 or nlon > (360 * 60) or (nlon & 1) != 0 or \ nlat < 2 or nlat > (181 * 60) or (nlat & 1) == 0: raise ValueError except (TypeError, ValueError): raise self._Errorf('width height %r', t) try: # must be 16 bit pixel height t = g.readline().strip() self.Pixel = int(t) if not 255 < self.Pixel < 65536: # >u2 or >H only raise ValueError except (TypeError, ValueError): raise self._Errorf('pixel %r', t) for a in dir(_PGM): # set undefined # Attr ... to None if a[:1].isupper() and callable(getattr(self, a)): setattr(self, a, None) if self.Origin is None: raise self._Errorf('Origin %r', self.Origin) if self.Offset is None or self.Offset > 0: raise self._Errorf('Offset %r', self.Offset) if self.Scale is None or self.Scale < EPS: raise self._Errorf('Scale %r', self.Scale) self.skip = g.tell() self.knots = nlat * nlon self.nlat, self.nlon = nlat, nlon self.slat, self.wlon = self.Origin # note, negative .dlat and .rlat since rows # are from .slat 90N down in decreasing lat self.dlat, self.dlon = 180.0 / (1 - nlat), 360.0 / nlon self.rlat, self.rlon = (1 - nlat) / 180.0, nlon / 360.0 # grid corners in earth (lat, lon), .slat = 90, .dlat < 0 n = float(self.slat) s = n + self.dlat * (nlat - 1) w = self.wlon - self.glon e = w + self.dlon * nlon self.crop4 = s, w, n, e n = self.sizeB - self.skip if n > 0 and n != (self.knots * self.u2B): raise self._Errorf('assert(%s x %s != %s)', nlat, nlon, n) def _cropped(self, g, k1, south, west, north, east): # MCCABE 15 '''Crop the geoid to (south, west, north, east) box. ''' # flon offset for both west and east f = 360 if west < 0 else 0 # earth (lat, lon) to grid indices (y, x), # note y is decreasing, i.e. n < s s, w = self._lle2yx2(south, west, f) n, e = self._lle2yx2(north, east, f) s += 1 # s > n e += 1 # e > w hi, wi = self.nlat, self.nlon # handle special cases if (s - n) > hi: n, s = 0, hi # entire lat range if (e - w) > wi: w, e, f = 0, wi, 180 # entire lon range if s == hi and w == n == 0 and e == wi: return g # use entire geoid as-is if (e - w) < k1 or (s - n) < (k1 + 1): raise self._Errorf('swne %r', (north - south, east - west)) if e > wi > w: # wrap around # read w..wi and 0..e r, p = (wi - w), (e - wi) elif e > w: r, p = (e - w), 0 else: raise self._Errorf('assert(%s < %s)', w, e) # convert to bytes r *= self.u2B p *= self.u2B q = wi * self.u2B # stride # number of rows and cols to skip from # the original (.slat, .wlon) origin z = self.skip + (n * wi + w) * self.u2B # sanity check if r < 2 or p < 0 or q < 2 or z < self.skip \ or z > self.sizeB: raise self._Errorf('assert%r', (r, p, q, z)) # can't use _BytesIO since numpy # needs .fileno attr in .fromfile t, c = 0, self._tmpfile() # reading (s - n) rows, forward for y in range(n, s): # PYCHOK y unused g.seek(z, _SEEK_SET) # Python 2 tmpfile.write returns None t += c.write(g.read(r)) or r if p: # wrap around to start of row g.seek(-q, _SEEK_CUR) # assert(g.tell() == (z - w * self.u2B)) # Python 2 tmpfile.write returns None t += c.write(g.read(p)) or p z += q c.flush() g.close() s -= n # nlat e -= w # nlon k = s * e # knots z = k * self.u2B if t != z: raise self._Errorf('assert(%s != %s) %s', t, z, self) # update the _Gpars accordingly, note attributes # .dlat, .dlon, .rlat and .rlon remain unchanged self.slat += n * self.dlat self.wlon += w * self.dlon self.nlat = s self.nlon = e self.flon = self.glon = f self.crop4 = south, west, north, east self.knots = k self.skip = 0 # no header lines in c c.seek(0, _SEEK_SET) # c = open(c.name, 'rb') # reopen for numpy 1.8.0- return c def _Errorf(self, fmt, *args): # PYCHOK no cover e = self.pgm or '' if e: e = ' in %r' % (e,) return PGMError('%s%s' % ((fmt % args), e)) def _lle2yx2(self, lat, lon, flon): # earth (lat, lon) to grid indices (y, x) # with .dlat decreasing from 90N .slat lat -= self.slat lon += flon - self.wlon return (min(self.nlat - 1, max(0, int(lat * self.rlat))), max(0, int(lon * self.rlon))) def _tmpfile(self): # create a tmpfile to hold the cropped geoid grid try: from tempfile import NamedTemporaryFile as tmpfile except ImportError: # Python 2.7.16- from os import tmpfile t = _os_path.splitext(_os_path.basename(self.pgm))[0] f = tmpfile(mode='w+b', prefix=t or 'egm') f.seek(0, _SEEK_SET) # force overwrite return f @property_RO def pgm(self): '''Get the geoid file name (C{str}). ''' return self.name def egmGeoidHeights(GeoidHeights_dat): '''Generate geoid U{egm*.pgm<https://GeographicLib.SourceForge.io/ html/geoid.html#geoidinst>} height tests from U{GeoidHeights.dat <https://SourceForge.net/projects/geographiclib/files/testdata/>} U{Test data for Geoids <https://GeographicLib.SourceForge.io/html/ geoid.html#testgeoid>}. @param GeoidHeights_dat: The un-gz-ed C{GeoidHeights.dat} file (C{str} or C{file} handle). @return: For each test, yield a L{GeoidHeight5Tuple}C{(lat, lon, egm84, egm96, egm2008)}. @raise GeoidError: Invalid B{C{GeoidHeights_dat}}. @note: Function L{egmGeoidHeights} is used to test the geoids L{GeoidKarney} and L{GeoidPGM}, see PyGeodesy module C{test/testGeoids.py}. ''' dat = GeoidHeights_dat if isinstance(dat, bytes): dat = _BytesIO(dat) try: dat.seek(0, _SEEK_SET) # reset except AttributeError: raise GeoidError('%s invalid: %s' % ('GeoidHeights_dat', type(dat))) for t in dat.readlines(): t = t.strip() if t and not t.startswith(b'#'): lat, lon, egm84, egm96, egm2008 = map(float, t.split()) while lon > 180: # EasternLon to earth lon lon -= 360 yield GeoidHeight5Tuple(lat, lon, egm84, egm96, egm2008) if __name__ == '__main__': import sys _crop = () _GeoidEGM = GeoidKarney _kind = 3 geoids = sys.argv[1:] while geoids: geoid = geoids.pop(0) if '-crop'.startswith(geoid.lower()): _crop = 20, -125, 50, -65 # CONUS elif '-karney'.startswith(geoid.lower()): _GeoidEGM = GeoidKarney elif '-kind'.startswith(geoid.lower()): _kind = int(geoids.pop(0)) elif '-pgm'.startswith(geoid.lower()): _GeoidEGM = GeoidPGM elif geoid[-4:].lower() in ('.pgm',): g = _GeoidEGM(geoid, crop=_crop, kind=_kind) print('\n%s\n' % (g.toStr(),)) print('%r\n' % (g.pgm,)) # <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval>: # The height of the EGM96 geoid at Timbuktu # echo 16:46:33N 3:00:34W | GeoidEval # => 28.7068 -0.02e-6 -1.73e-6 # The 1st number is the height of the geoid, the 2nd and # 3rd are its slopes in northerly and easterly direction t = 'Timbuktu %s' % (g,) k = {'egm84-15.pgm': '31.2979', 'egm96-5.pgm': '28.7067', 'egm2008-1.pgm': '28.7880'}.get(g.name.lower(), '28.7880') ll = parseDMS2('16:46:33N', '3:00:34W', sep=':') for ll in (ll, (16.776, -3.009),): try: h, ll = g.height(*ll), fStr(ll, prec=6) print('%s.height(%s): %.4f vs %s' % (t, ll, h, k)) except (GeoidError, RangeError) as x: print('%s: %s' % (t, x)) elif geoid[-4:].lower() in ('.bin',): g = GeoidG2012B(geoid, kind=_kind) print(g.toStr()) else: raise GeoidError('unknown grid: %r' % (geoid,)) _I = int # PYCHOK unused _I del _intCs # trash ints cache # **) 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. # <https://GeographicLib.SourceForge.io/cgi-bin/GeoidEval> # _lowerleft = -90, -179, -30.1500 # egm2008-1.pgm # _lowerleft = -90, -179, -29.5350 # egm96-5.pgm # _lowerleft = -90, -179, -29.7120 # egm84-15.pgm # _center = 0, 0, 17.2260 # egm2008-1.pgm # _center = 0, 0, 17.1630 # egm96-5.pgm # _center = 0, 0, 18.3296 # egm84-15.pgm # _upperright = 90, 180, 14.8980 # egm2008-1.pgm # _upperright = 90, 180, 13.6050 # egm96-5.pgm # _upperright = 90, 180, 13.0980 # egm84-15.pgm # % python pygeodesy/geoids.py [-Karney] ../geoids/egm*.pgm # # 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, -32.633, 85.839), lowest(4.683, -101.25, -106.911), mean=-1.317, stdev=29.244, # kind=3, dtype='ushort', endian='>H', hits=0, knots=233301600, sizeB=466603604 # _PGM('../geoids/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=(90, 0.0), Pixel=65535, RMSBilinearError=0.001, RMSCubicError=0.001, Scale=0.003, # URL='https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm2008', Vertical_Datum='WGS84', crop4=(-90.0, -180.0, 90.0, 180.0), # dlat=-0.016666666666666666, dlon=0.016666666666666666, egm=None, flon=0, glon=180, knots=233301600, nlat=10801, nlon=21600, # pgm='../geoids/egm2008-1.pgm', rlat=-60.0, rlon=60.0, sizeB=466603604, skip=404, slat=90, u2B=2, wlon=0.0 # Timbuktu GeoidKarney('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880 # Timbuktu GeoidKarney('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880 # # 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(-8.4, -32.633, 85.839), lowest(4.683, -101.25, -106.911), mean=-1.317, stdev=29.244, # kind=3, dtype='ushort', endian='>H', hits=0, knots=1038240, sizeB=2076896 # _PGM('../geoids/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=(90, 0.0), Pixel=65535, RMSBilinearError=0.018, RMSCubicError=0.001, Scale=0.003, # URL='https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/wgs84_180/wgs84_180.html', Vertical_Datum='WGS84', crop4=(-90.0, -180.0, 90.0, 180.0), # dlat=-0.25, dlon=0.25, egm=None, flon=0, glon=180, knots=1038240, nlat=721, nlon=1440, # pgm='../geoids/egm84-15.pgm', rlat=-4.0, rlon=4.0, sizeB=2076896, skip=416, slat=90, u2B=2, wlon=0.0 # Timbuktu GeoidKarney('egm84-15.pgm').height(16.775833, -3.009444): 31.2983 vs 31.2979 # Timbuktu GeoidKarney('egm84-15.pgm').height(16.776, -3.009): 31.2979 vs 31.2979 # # 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(-8.4, -32.633, 85.839), lowest(4.683, -101.25, -106.911), mean=-1.317, stdev=29.244, # kind=3, dtype='ushort', endian='>H', hits=0, knots=9335520, sizeB=18671448 # _PGM('../geoids/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=(90, 0.0), Pixel=65535, RMSBilinearError=0.005, RMSCubicError=0.001, Scale=0.003, # URL='https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html', Vertical_Datum='WGS84', crop4=(), # dlat=-0.08333333333333333, dlon=0.08333333333333333, egm=None, flon=0, glon=180, knots=9335520, nlat=2161, nlon=4320, # pgm='../geoids/egm96-5.pgm', rlat=-12.0, rlon=12.0, sizeB=18671448, skip=408, slat=90, u2B=2, wlon=0.0 # Timbuktu GeoidKarney('egm96-5.pgm').height(16.775833, -3.009444): 28.7068 vs 28.7067 # Timbuktu GeoidKarney('egm96-5.pgm').height(16.776, -3.009): 28.7067 vs 28.7067 # % python pygeodesy/geoids.py -PGM ../geoids/egm*.pgm # # 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), mean=-1.317, stdev=29.244, # kind=3, smooth=0, dtype=dtype('float64'), endian='>u2', knots=233301600, nBytes=1866412800, sizeB=466603604, scipy='1.2.1', numpy='1.16.1' # _PGM('../geoids/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=(90, 0.0), Pixel=65535, RMSBilinearError=0.001, RMSCubicError=0.001, Scale=0.003, # URL='https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm2008', Vertical_Datum='WGS84', crop4=(-90.0, -180.0, 90.0, 180.0), # dlat=-0.016666666666666666, dlon=0.016666666666666666, egm=None, flon=0, glon=180, knots=233301600, nlat=10801, nlon=21600, # pgm='../geoids/egm2008-1.pgm', rlat=-60.0, rlon=60.0, sizeB=466603604, skip=404, slat=90, u2B=2, wlon=0.0 # Timbuktu GeoidPGM('egm2008-1.pgm').height(16.775833, -3.009444): 28.7881 vs 28.7880 # Timbuktu GeoidPGM('egm2008-1.pgm').height(16.776, -3.009): 28.7880 vs 28.7880 # # 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), mean=-0.855, stdev=29.183, # kind=3, smooth=0, dtype=dtype('float64'), endian='>u2', knots=1038240, nBytes=8305920, sizeB=2076896, scipy='1.2.1', numpy='1.16.1' # _PGM('../geoids/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=(90, 0.0), Pixel=65535, RMSBilinearError=0.018, RMSCubicError=0.001, Scale=0.003, # URL='https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/wgs84_180/wgs84_180.html', Vertical_Datum='WGS84', crop4=(-90.0, -180.0, 90.0, 180.0), # dlat=-0.25, dlon=0.25, egm=None, flon=0, glon=180, knots=1038240, nlat=721, nlon=1440, # pgm='../geoids/egm84-15.pgm', rlat=-4.0, rlon=4.0, sizeB=2076896, skip=416, slat=90, u2B=2, wlon=0.0 # Timbuktu GeoidPGM('egm84-15.pgm').height(16.775833, -3.009444): 31.2979 vs 31.2979 # Timbuktu GeoidPGM('egm84-15.pgm').height(16.776, -3.009): 31.2975 vs 31.2979 # # 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), mean=-1.438, stdev=29.227, # kind=3, smooth=0, dtype=dtype('float64'), endian='>u2', knots=9335520, nBytes=74684160, sizeB=18671448, scipy='1.2.1', numpy='1.16.1' # _PGM('../geoids/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=(90, 0.0), Pixel=65535, RMSBilinearError=0.005, RMSCubicError=0.001, Scale=0.003, # URL='https://Earth-Info.NGA.mil/GandG/wgs84/gravitymod/egm96/egm96.html', Vertical_Datum='WGS84', crop4=(-90.0, -180.0, 90.0, 180.0), # dlat=-0.08333333333333333, dlon=0.08333333333333333, egm=None, flon=0, glon=180, knots=9335520, nlat=2161, nlon=4320, # pgm='../geoids/egm96-5.pgm', rlat=-12.0, rlon=12.0, sizeB=18671448, skip=408, slat=90, u2B=2, wlon=0.0 # Timbuktu GeoidPGM('egm96-5.pgm').height(16.775833, -3.009444): 28.7065 vs 28.7067 # Timbuktu GeoidPGM('egm96-5.pgm').height(16.776, -3.009): 28.7064 vs 28.7067