This file is indexed.

/usr/lib/python2.7/dist-packages/geopy/distance.py is in python-geopy 1.3.0-1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  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
"""
.. versionadded:: 0.93

Geopy can calculate geodesic distance between two points using the
[Vincenty distance](https://en.wikipedia.org/wiki/Vincenty's_formulae) or
[great-circle distance](https://en.wikipedia.org/wiki/Great-circle_distance)
formulas, with a default of Vincenty available as the function
`geopy.distance.distance`.

Great-circle distance (:class:`.great_circle`) uses a spherical model of
the earth, using the average great-circle radius of 6372.795 kilometers,
resulting in an error of up to about 0.5%. The radius value is stored in
:const:`distance.EARTH_RADIUS`, so it can be customized
(it should always be in kilometers, however).

Vincenty distance (:class:`.vincenty`) uses a more accurate ellipsoidal model
of the earth. This is the default distance formula, and is thus aliased as
``distance.distance``. There are multiple popular ellipsoidal models, and
which one will be the most accurate depends on where your points are located
on the earth. The default is the WGS-84 ellipsoid, which is the most globally
accurate. geopy includes a few other
models in the distance.ELLIPSOIDS dictionary::

                  model             major (km)   minor (km)     flattening
    ELLIPSOIDS = {'WGS-84':        (6378.137,    6356.7523142,  1 / 298.257223563),
                  'GRS-80':        (6378.137,    6356.7523141,  1 / 298.257222101),
                  'Airy (1830)':   (6377.563396, 6356.256909,   1 / 299.3249646),
                  'Intl 1924':     (6378.388,    6356.911946,   1 / 297.0),
                  'Clarke (1880)': (6378.249145, 6356.51486955, 1 / 293.465),
                  'GRS-67':        (6378.1600,   6356.774719,   1 / 298.25),
                  }

Here's an example usage of distance.vincenty::

    >>> from geopy.distance import vincenty
    >>> newport_ri = (41.49008, -71.312796)
    >>> cleveland_oh = (41.499498, -81.695391)
    >>> vincenty(newport_ri, cleveland_oh).miles
    538.3904451566326

Using great-circle distance::

    >>> from geopy.distance import great_circle
    >>> newport_ri = (41.49008, -71.312796)
    >>> cleveland_oh = (41.499498, -81.695391)
    >>> great_circle(newport_ri, cleveland_oh).miles
    537.1485284062816

You can change the ellipsoid model used by the Vincenty formula like so::

    >>> distance.vincenty(ne, cl, ellipsoid='GRS-80').miles

The above model name will automatically be retrieved from the ELLIPSOIDS dictionary.
Alternatively, you can specify the model values directly::

    >>> distance.vincenty(ne, cl, ellipsoid=(6377., 6356., 1 / 297.)).miles

Distances support simple arithmetic, making it easy to do things like
calculate the length of a path::

    >>> d = distance.distance
    >>> _, wa = g.geocode('Washington, DC')
    >>> _, pa = g.geocode('Palo Alto, CA')
    >>> (d(ne, cl) + d(cl, wa) + d(wa, pa)).miles
    3276.157156868931

"""
from __future__ import division

from math import atan, tan, sin, cos, pi, sqrt, atan2, asin
from geopy.units import radians
from geopy import units, util
from geopy.point import Point
from geopy.compat import string_compare

# Average great-circle radius in kilometers, from Wikipedia.
# Using a sphere with this radius results in an error of up to about 0.5%.
EARTH_RADIUS = 6372.795

# From http://www.movable-type.co.uk/scripts/LatLongVincenty.html:
#   The most accurate and widely used globally-applicable model for the earth
#   ellipsoid is WGS-84, used in this script. Other ellipsoids offering a
#   better fit to the local geoid include Airy (1830) in the UK, International
#   1924 in much of Europe, Clarke (1880) in Africa, and GRS-67 in South
#   America. America (NAD83) and Australia (GDA) use GRS-80, functionally
#   equivalent to the WGS-84 ellipsoid.
ELLIPSOIDS = {
    # model           major (km)   minor (km)     flattening
    'WGS-84':        (6378.137, 6356.7523142, 1 / 298.257223563),
    'GRS-80':        (6378.137, 6356.7523141, 1 / 298.257222101),
    'Airy (1830)':   (6377.563396, 6356.256909, 1 / 299.3249646),
    'Intl 1924':     (6378.388, 6356.911946, 1 / 297.0),
    'Clarke (1880)': (6378.249145, 6356.51486955, 1 / 293.465),
    'GRS-67':        (6378.1600, 6356.774719, 1 / 298.25)
}

class Distance(object):
    """
    Base for :class:`.great_circle` and :class:`.vincenty`.
    """

    def __init__(self, *args, **kwargs):
        kilometers = kwargs.pop('kilometers', 0)
        if len(args) == 1:
            # if we only get one argument we assume
            # it's a known distance instead of
            # calculating it first
            kilometers += args[0]
        elif len(args) > 1:
            for a, b in util.pairwise(args):
                kilometers += self.measure(a, b)

        kilometers += units.kilometers(**kwargs)
        self.__kilometers = kilometers

    def __add__(self, other):
        if isinstance(other, Distance):
            return self.__class__(self.kilometers + other.kilometers)
        else:
            raise TypeError(
                "Distance instance must be added with Distance instance."
            )

    def __neg__(self):
        return self.__class__(-self.kilometers)

    def __sub__(self, other):
        return self + -other

    def __mul__(self, other):
        return self.__class__(self.kilometers * other)

    def __div__(self, other):
        if isinstance(other, Distance):
            return self.kilometers / other.kilometers
        else:
            return self.__class__(self.kilometers / other)

    __truediv__ = __div__

    def __abs__(self):
        return self.__class__(abs(self.kilometers))

    def __nonzero__(self):
        return bool(self.kilometers)

    __bool__ = __nonzero__

    def measure(self, a, b):
        raise NotImplementedError()

    def __repr__(self): # pragma: no cover
        return 'Distance(%s)' % self.kilometers

    def __str__(self): # pragma: no cover
        return '%s km' % self.__kilometers

    def __lt__(self, other):
        if isinstance(other, Distance):
            return self.kilometers < other.kilometers
        else:
            return self.kilometers < other

    def __eq__(self, other):
        if isinstance(other, Distance):
            return self.kilometers == other.kilometers
        else:
            return self.kilometers == other

    @property
    def kilometers(self): # pylint: disable=C0111
        return self.__kilometers

    @property
    def km(self): # pylint: disable=C0111
        return self.kilometers

    @property
    def meters(self): # pylint: disable=C0111
        return units.meters(kilometers=self.kilometers)

    @property
    def m(self): # pylint: disable=C0111
        return self.meters

    @property
    def miles(self): # pylint: disable=C0111
        return units.miles(kilometers=self.kilometers)

    @property
    def mi(self): # pylint: disable=C0111
        return self.miles

    @property
    def feet(self): # pylint: disable=C0111
        return units.feet(kilometers=self.kilometers)

    @property
    def ft(self): # pylint: disable=C0111
        return self.feet

    @property
    def nautical(self): # pylint: disable=C0111
        return units.nautical(kilometers=self.kilometers)

    @property
    def nm(self): # pylint: disable=C0111
        return self.nautical


class great_circle(Distance):
    """
    Use spherical geometry to calculate the surface distance between two
    geodesic points. This formula can be written many different ways,
    including just the use of the spherical law of cosines or the haversine
    formula.

    Set which radius of the earth to use by specifying a 'radius' keyword
    argument. It must be in kilometers. The default is to use the module
    constant `EARTH_RADIUS`, which uses the average great-circle radius.

    Example::

        >>> from geopy.distance import great_circle
        >>> newport_ri = (41.49008, -71.312796)
        >>> cleveland_oh = (41.499498, -81.695391)
        >>> great_circle(newport_ri, cleveland_oh).miles
        537.1485284062816

    """

    def __init__(self, *args, **kwargs):
        self.RADIUS = kwargs.pop('radius', EARTH_RADIUS)
        super(great_circle, self).__init__(*args, **kwargs)

    def measure(self, a, b):
        a, b = Point(a), Point(b)

        lat1, lng1 = radians(degrees=a.latitude), radians(degrees=a.longitude)
        lat2, lng2 = radians(degrees=b.latitude), radians(degrees=b.longitude)

        sin_lat1, cos_lat1 = sin(lat1), cos(lat1)
        sin_lat2, cos_lat2 = sin(lat2), cos(lat2)

        delta_lng = lng2 - lng1
        cos_delta_lng, sin_delta_lng = cos(delta_lng), sin(delta_lng)

        d = atan2(sqrt((cos_lat2 * sin_delta_lng) ** 2 +
                       (cos_lat1 * sin_lat2 -
                        sin_lat1 * cos_lat2 * cos_delta_lng) ** 2),
                  sin_lat1 * sin_lat2 + cos_lat1 * cos_lat2 * cos_delta_lng)

        return self.RADIUS * d

    def destination(self, point, bearing, distance=None): # pylint: disable=W0621
        """
        TODO docs.
        """
        point = Point(point)
        lat1 = units.radians(degrees=point.latitude)
        lng1 = units.radians(degrees=point.longitude)
        bearing = units.radians(degrees=bearing)

        if distance is None:
            distance = self
        if isinstance(distance, Distance):
            distance = distance.kilometers

        d_div_r = float(distance) / self.RADIUS

        lat2 = asin(
            sin(lat1) * cos(d_div_r) +
            cos(lat1) * sin(d_div_r) * cos(bearing)
        )

        lng2 = lng1 + atan2(
            sin(bearing) * sin(d_div_r) * cos(lat1),
            cos(d_div_r) - sin(lat1) * sin(lat2)
        )

        return Point(units.degrees(radians=lat2), units.degrees(radians=lng2))


class vincenty(Distance):
    """
    Calculate the geodesic distance between two points using the formula
    devised by Thaddeus Vincenty, with an accurate ellipsoidal model of the
    earth.

    Set which ellipsoidal model of the earth to use by specifying an
    ``ellipsoid`` keyword argument. The default is 'WGS-84', which is the
    most globally accurate model.  If ``ellipsoid`` is a string, it is
    looked up in the `ELLIPSOIDS` dictionary to obtain the major and minor
    semiaxes and the flattening. Otherwise, it should be a tuple with those
    values.  See the comments above the `ELLIPSOIDS` dictionary for
    more information.

    Example::

        >>> from geopy.distance import vincenty
        >>> newport_ri = (41.49008, -71.312796)
        >>> cleveland_oh = (41.499498, -81.695391)
        >>> vincenty(newport_ri, cleveland_oh).miles
        538.3904451566326

    Note: This implementation of Vincenty distance fails to converge for
    some valid points. In some cases, a result can be obtained by increasing
    the number of iterations (`iterations` keyword argument, given in the
    class `__init__`, with a default of 20). It may be preferable to use
    :class:`.great_circle`, which is marginally less accurate, but always
    produces a result.
    """

    ellipsoid_key = None
    ELLIPSOID = None

    def __init__(self, *args, **kwargs):
        self.set_ellipsoid(kwargs.pop('ellipsoid', 'WGS-84'))
        self.iterations = kwargs.pop('iterations', 20)
        major, minor, f = self.ELLIPSOID # pylint: disable=W0612
        super(vincenty, self).__init__(*args, **kwargs)

    def set_ellipsoid(self, ellipsoid):
        """
        Change the ellipsoid used in the calculation.
        """
        if not isinstance(ellipsoid, (list, tuple)):
            try:
                self.ELLIPSOID = ELLIPSOIDS[ellipsoid]
                self.ellipsoid_key = ellipsoid
            except KeyError:
                raise Exception(
                    "Invalid ellipsoid. See geopy.distance.ELIPSOIDS"
                )
        else:
            self.ELLIPSOID = ellipsoid
            self.ellipsoid_key = None
        return

    def measure(self, a, b):
        a, b = Point(a), Point(b)
        lat1, lng1 = radians(degrees=a.latitude), radians(degrees=a.longitude)
        lat2, lng2 = radians(degrees=b.latitude), radians(degrees=b.longitude)

        if isinstance(self.ELLIPSOID, string_compare):
            major, minor, f = ELLIPSOIDS[self.ELLIPSOID]
        else:
            major, minor, f = self.ELLIPSOID

        delta_lng = lng2 - lng1

        reduced_lat1 = atan((1 - f) * tan(lat1))
        reduced_lat2 = atan((1 - f) * tan(lat2))

        sin_reduced1, cos_reduced1 = sin(reduced_lat1), cos(reduced_lat1)
        sin_reduced2, cos_reduced2 = sin(reduced_lat2), cos(reduced_lat2)

        lambda_lng = delta_lng
        lambda_prime = 2 * pi

        iter_limit = self.iterations

        i = 0
        while abs(lambda_lng - lambda_prime) > 10e-12 and i <= iter_limit:
            i += 1

            sin_lambda_lng, cos_lambda_lng = sin(lambda_lng), cos(lambda_lng)

            sin_sigma = sqrt(
                (cos_reduced2 * sin_lambda_lng) ** 2 +
                (cos_reduced1 * sin_reduced2 -
                 sin_reduced1 * cos_reduced2 * cos_lambda_lng) ** 2
            )

            if sin_sigma == 0:
                return 0 # Coincident points

            cos_sigma = (
                sin_reduced1 * sin_reduced2 +
                cos_reduced1 * cos_reduced2 * cos_lambda_lng
            )

            sigma = atan2(sin_sigma, cos_sigma)

            sin_alpha = (
                cos_reduced1 * cos_reduced2 * sin_lambda_lng / sin_sigma
            )
            cos_sq_alpha = 1 - sin_alpha ** 2

            if cos_sq_alpha != 0:
                cos2_sigma_m = cos_sigma - 2 * (
                    sin_reduced1 * sin_reduced2 / cos_sq_alpha
                )
            else:
                cos2_sigma_m = 0.0 # Equatorial line

            C = f / 16. * cos_sq_alpha * (4 + f * (4 - 3 * cos_sq_alpha))

            lambda_prime = lambda_lng
            lambda_lng = (
                delta_lng + (1 - C) * f * sin_alpha * (
                    sigma + C * sin_sigma * (
                        cos2_sigma_m + C * cos_sigma * (
                            -1 + 2 * cos2_sigma_m ** 2
                        )
                    )
                )
            )

        if i > iter_limit:
            raise ValueError("Vincenty formula failed to converge!")

        u_sq = cos_sq_alpha * (major ** 2 - minor ** 2) / minor ** 2

        A = 1 + u_sq / 16384. * (
            4096 + u_sq * (-768 + u_sq * (320 - 175 * u_sq))
        )

        B = u_sq / 1024. * (256 + u_sq * (-128 + u_sq * (74 - 47 * u_sq)))

        delta_sigma = (
            B * sin_sigma * (
                cos2_sigma_m + B / 4. * (
                    cos_sigma * (
                        -1 + 2 * cos2_sigma_m ** 2
                    ) - B / 6. * cos2_sigma_m * (
                        -3 + 4 * sin_sigma ** 2
                    ) * (
                        -3 + 4 * cos2_sigma_m ** 2
                    )
                )
            )
        )

        s = minor * A * (sigma - delta_sigma)
        return s

    def destination(self, point, bearing, distance=None): # pylint: disable=W0621
        """
        TODO docs.
        """
        point = Point(point)
        lat1 = units.radians(degrees=point.latitude)
        lng1 = units.radians(degrees=point.longitude)
        bearing = units.radians(degrees=bearing)

        if distance is None:
            distance = self
        if isinstance(distance, Distance):
            distance = distance.kilometers

        ellipsoid = self.ELLIPSOID
        if isinstance(ellipsoid, string_compare):
            ellipsoid = ELLIPSOIDS[ellipsoid]

        major, minor, f = ellipsoid

        tan_reduced1 = (1 - f) * tan(lat1)
        cos_reduced1 = 1 / sqrt(1 + tan_reduced1 ** 2)
        sin_reduced1 = tan_reduced1 * cos_reduced1
        sin_bearing, cos_bearing = sin(bearing), cos(bearing)
        sigma1 = atan2(tan_reduced1, cos_bearing)
        sin_alpha = cos_reduced1 * sin_bearing
        cos_sq_alpha = 1 - sin_alpha ** 2
        u_sq = cos_sq_alpha * (major ** 2 - minor ** 2) / minor ** 2

        A = 1 + u_sq / 16384. * (
            4096 + u_sq * (-768 + u_sq * (320 - 175 * u_sq))
        )
        B = u_sq / 1024. * (256 + u_sq * (-128 + u_sq * (74 - 47 * u_sq)))

        sigma = distance / (minor * A)
        sigma_prime = 2 * pi

        while abs(sigma - sigma_prime) > 10e-12:
            cos2_sigma_m = cos(2 * sigma1 + sigma)
            sin_sigma, cos_sigma = sin(sigma), cos(sigma)
            delta_sigma = B * sin_sigma * (
                cos2_sigma_m + B / 4. * (
                    cos_sigma * (
                        -1 + 2 * cos2_sigma_m
                    ) - B / 6. * cos2_sigma_m * (
                        -3 + 4 * sin_sigma ** 2) * (
                        -3 + 4 * cos2_sigma_m ** 2
                    )
                )
            )
            sigma_prime = sigma
            sigma = distance / (minor * A) + delta_sigma

        sin_sigma, cos_sigma = sin(sigma), cos(sigma)

        lat2 = atan2(
            sin_reduced1 * cos_sigma + cos_reduced1 * sin_sigma * cos_bearing,
            (1 - f) * sqrt(
                sin_alpha ** 2 + (
                    sin_reduced1 * sin_sigma -
                    cos_reduced1 * cos_sigma * cos_bearing
                ) ** 2
            )
        )

        lambda_lng = atan2(
            sin_sigma * sin_bearing,
            cos_reduced1 * cos_sigma - sin_reduced1 * sin_sigma * cos_bearing
        )

        C = f / 16. * cos_sq_alpha * (4 + f * (4 - 3 * cos_sq_alpha))

        delta_lng = (
            lambda_lng - (1 - C) * f * sin_alpha * (
                sigma + C * sin_sigma * (
                    cos2_sigma_m + C * cos_sigma * (
                        -1 + 2 * cos2_sigma_m ** 2
                    )
                )
            )
        )

        lng2 = lng1 + delta_lng

        return Point(units.degrees(radians=lat2), units.degrees(radians=lng2))


# Set the default distance formula to the most generally accurate.

distance = VincentyDistance = vincenty
GreatCircleDistance = great_circle