# Source code for obspy.geodetics.base

# -*- coding: utf-8 -*-
"""
Various geodetic utilities for ObsPy.

The ObsPy Development Team (devs@obspy.org)
GNU Lesser General Public License, Version 3
(https://www.gnu.org/copyleft/lesser.html)
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
from future.builtins import *  # NOQA

import math
import warnings

import numpy as np
from scipy.stats import circmean

from obspy.core.util.misc import to_int_or_zero

# checking for geographiclib
try:
import geographiclib  # @UnusedImport # NOQA
from geographiclib.geodesic import Geodesic
HAS_GEOGRAPHICLIB = True
try:
GEOGRAPHICLIB_VERSION_AT_LEAST_1_34 = [1, 34] <= list(map(
to_int_or_zero, geographiclib.__version__.split(".")))
except AttributeError:
GEOGRAPHICLIB_VERSION_AT_LEAST_1_34 = False
except ImportError:
HAS_GEOGRAPHICLIB = False
GEOGRAPHICLIB_VERSION_AT_LEAST_1_34 = False

WGS84_A = 6378137.0
WGS84_F = 1 / 298.257223563

[docs]def _isclose(a, b, rel_tol=1e-09, abs_tol=0.0):
"""
Equivalent of the :meth:math.isclose method compatible with python 2.7.
"""
return abs(a - b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)

[docs]def _check_latitude(latitude, variable_name='latitude'):
"""
Check whether latitude is in the -90 to +90 range.
"""
if latitude is None:
return
if latitude > 90 or latitude < -90:
msg = '{} out of bounds! (-90 <= {} <=90)'.format(
variable_name, variable_name)
raise ValueError(msg)

[docs]def _normalize_longitude(longitude):
"""
Normalize longitude in the -180 to +180 range.
"""
if longitude is None:
return
while longitude > 180:
longitude -= 360
while longitude < -180:
longitude += 360
return longitude

[docs]def calc_vincenty_inverse(lat1, lon1, lat2, lon2, a=WGS84_A, f=WGS84_F):
"""
Vincenty Inverse Solution of Geodesics on the Ellipsoid.

Computes the distance between two geographic points on the WGS84
ellipsoid and the forward and backward azimuths between these points.

:param lat1: Latitude of point A in degrees (positive for northern,
negative for southern hemisphere)
:param lon1: Longitude of point A in degrees (positive for eastern,
negative for western hemisphere)
:param lat2: Latitude of point B in degrees (positive for northern,
negative for southern hemisphere)
:param lon2: Longitude of point B in degrees (positive for eastern,
negative for western hemisphere)
:param a: Radius of Earth in m. Uses the value for WGS84 by default.
:param f: Flattening of Earth. Uses the value for WGS84 by default.
:return: (Great circle distance in m, azimuth A->B in degrees,
azimuth B->A in degrees)
:raises: This method may have no solution between two nearly antipodal
points; an iteration limit traps this case and a StopIteration
exception will be raised.

.. note::
This code is based on an implementation incorporated in
Matplotlib Basemap Toolkit 0.9.5 http://sourceforge.net/projects/\
matplotlib/files/matplotlib-toolkits/basemap-0.9.5/
(matplotlib/toolkits/basemap/greatcircle.py)

Algorithm from Geocentric Datum of Australia Technical Manual.

* http://www.icsm.gov.au/gda/
* http://www.icsm.gov.au/gda/gdatm/gdav2.3.pdf, pp. 15

It states::

Computations on the Ellipsoid

There are a number of formulae that are available to calculate
accurate geodetic positions, azimuths and distances on the
ellipsoid.

Vincenty's formulae (Vincenty, 1975) may be used for lines ranging
from a few cm to nearly 20,000 km, with millimetre accuracy. The
formulae have been extensively tested for the Australian region, by
comparison with results from other formulae (Rainsford, 1955 &
Sodano, 1965).

* Inverse problem: azimuth and distance from known latitudes and
longitudes
* Direct problem: Latitude and longitude from known position,
azimuth and distance.
"""
# Check inputs
_check_latitude(lat1, 'lat1')
lon1 = _normalize_longitude(lon1)
_check_latitude(lat2, 'lat2')
lon2 = _normalize_longitude(lon2)

b = a * (1 - f)  # semiminor axis

if _isclose(lat1, lat2) and _isclose(lon1, lon2):
return 0.0, 0.0, 0.0

# convert latitudes and longitudes to radians:

tan_u1 = (1 - f) * math.tan(lat1)
tan_u2 = (1 - f) * math.tan(lat2)

u_1 = math.atan(tan_u1)
u_2 = math.atan(tan_u2)

dlon = lon2 - lon1
last_dlon = -4000000.0  # an impossible value
omega = dlon

# Iterate until no significant change in dlon or iterlimit has been
# reached (http://www.movable-type.co.uk/scripts/latlong-vincenty.html)
iterlimit = 100
try:
while (last_dlon < -3000000.0 or dlon != 0 and
abs((last_dlon - dlon) / dlon) > 1.0e-9):
sqr_sin_sigma = pow(math.cos(u_2) * math.sin(dlon), 2) + \
pow((math.cos(u_1) * math.sin(u_2) - math.sin(u_1) *
math.cos(u_2) * math.cos(dlon)), 2)
sin_sigma = math.sqrt(sqr_sin_sigma)

cos_sigma = math.sin(u_1) * math.sin(u_2) + math.cos(u_1) * \
math.cos(u_2) * math.cos(dlon)
sigma = math.atan2(sin_sigma, cos_sigma)
sin_alpha = math.cos(u_1) * math.cos(u_2) * math.sin(dlon) / \
sin_sigma

sqr_cos_alpha = 1 - sin_alpha * sin_alpha
if _isclose(sqr_cos_alpha, 0):
# Equatorial line
cos2sigma_m = 0
else:
cos2sigma_m = cos_sigma - \
(2 * math.sin(u_1) * math.sin(u_2) / sqr_cos_alpha)

c = (f / 16) * sqr_cos_alpha * (4 + f * (4 - 3 * sqr_cos_alpha))
last_dlon = dlon
dlon = omega + (1 - c) * f * sin_alpha * \
(sigma + c * sin_sigma *
(cos2sigma_m + c * cos_sigma *
(-1 + 2 * pow(cos2sigma_m, 2))))

iterlimit -= 1
if iterlimit < 0:
# iteration limit reached
raise StopIteration
except ValueError:
# usually "math domain error"
raise StopIteration

u2 = sqr_cos_alpha * (a * a - b * b) / (b * b)
_a = 1 + (u2 / 16384) * (4096 + u2 * (-768 + u2 * (320 - 175 * u2)))
_b = (u2 / 1024) * (256 + u2 * (-128 + u2 * (74 - 47 * u2)))
delta_sigma = _b * sin_sigma * \
(cos2sigma_m + (_b / 4) *
(cos_sigma * (-1 + 2 * pow(cos2sigma_m, 2)) - (_b / 6) *
cos2sigma_m * (-3 + 4 * sqr_sin_sigma) *
(-3 + 4 * pow(cos2sigma_m, 2))))

dist = b * _a * (sigma - delta_sigma)
alpha12 = math.atan2(
(math.cos(u_2) * math.sin(dlon)),
(math.cos(u_1) * math.sin(u_2) -
math.sin(u_1) * math.cos(u_2) * math.cos(dlon)))
alpha21 = math.atan2(
(math.cos(u_1) * math.sin(dlon)),
(-math.sin(u_1) * math.cos(u_2) +
math.cos(u_1) * math.sin(u_2) * math.cos(dlon)))

if alpha12 < 0.0:
alpha12 = alpha12 + (2.0 * math.pi)
if alpha12 > (2.0 * math.pi):
alpha12 = alpha12 - (2.0 * math.pi)

alpha21 = alpha21 + math.pi

if alpha21 < 0.0:
alpha21 = alpha21 + (2.0 * math.pi)
if alpha21 > (2.0 * math.pi):
alpha21 = alpha21 - (2.0 * math.pi)

# convert to degrees:
alpha12 = alpha12 * 360 / (2.0 * math.pi)
alpha21 = alpha21 * 360 / (2.0 * math.pi)

return dist, alpha12, alpha21

[docs]def gps2dist_azimuth(lat1, lon1, lat2, lon2, a=WGS84_A, f=WGS84_F):
"""
Computes the distance between two geographic points on the WGS84
ellipsoid and the forward and backward azimuths between these points.

:param lat1: Latitude of point A in degrees (positive for northern,
negative for southern hemisphere)
:param lon1: Longitude of point A in degrees (positive for eastern,
negative for western hemisphere)
:param lat2: Latitude of point B in degrees (positive for northern,
negative for southern hemisphere)
:param lon2: Longitude of point B in degrees (positive for eastern,
negative for western hemisphere)
:param a: Radius of Earth in m. Uses the value for WGS84 by default.
:param f: Flattening of Earth. Uses the value for WGS84 by default.
:return: (Great circle distance in m, azimuth A->B in degrees,
azimuth B->A in degrees)

.. note::
This function will check if you have installed the Python module
geographiclib <http://geographiclib.sf.net>_ - a very fast module
for converting between geographic, UTM, UPS, MGRS, and geocentric
coordinates, for geoid calculations, and for solving geodesic problems.
Otherwise the locally implemented Vincenty's Inverse formulae
(:func:obspy.core.util.geodetics.calc_vincenty_inverse) is used which
has known limitations for two nearly antipodal points and is ca. 4x
slower.
"""
if HAS_GEOGRAPHICLIB:
_check_latitude(lat1, 'lat1')
_check_latitude(lat2, 'lat2')
result = Geodesic(a=a, f=f).Inverse(lat1, lon1, lat2, lon2)
azim = result['azi1']
if azim < 0:
azim += 360
bazim = result['azi2'] + 180
return (result['s12'], azim, bazim)
else:
try:
values = calc_vincenty_inverse(lat1, lon1, lat2, lon2, a, f)
if np.alltrue(np.isnan(values)):
raise StopIteration
return values
except StopIteration:
msg = ("Catching unstable calculation on antipodes. "
"The currently used Vincenty's Inverse formulae "
"has known limitations for two nearly antipodal points. "
"Install the Python module 'geographiclib' to solve this "
"issue.")
warnings.warn(msg)
return (20004314.5, 0.0, 0.0)
except ValueError as e:
raise e

"""
Convenience function to convert kilometers to degrees assuming a perfectly
spherical Earth.

:type kilometer: float
:param kilometer: Distance in kilometers
:rtype: float
:return: Distance in degrees as a floating point number.

.. rubric:: Example

>>> from obspy.geodetics import kilometers2degrees
>>> kilometers2degrees(300)
2.6979648177561915
"""
return kilometer / (2.0 * radius * math.pi / 360.0)

kilometer2degrees = kilometers2degrees

"""
Convenience function to convert (great circle) degrees to kilometers
assuming a perfectly spherical Earth.

:type degrees: float
:param degrees: Distance in (great circle) degrees
:rtype: float
:return: Distance in kilometers as a floating point number.

.. rubric:: Example

>>> from obspy.geodetics import degrees2kilometers
>>> degrees2kilometers(1)
111.19492664455873
"""
return degrees * (2.0 * radius * math.pi / 360.0)

[docs]def locations2degrees(lat1, long1, lat2, long2):
"""
Convenience function to calculate the great circle distance between two
points on a spherical Earth.

This method uses the Vincenty formula in the special case of a spherical
Earth. For more accurate values use the geodesic distance calculations of
geopy (https://github.com/geopy/geopy).

:type lat1: float or :class:numpy.ndarray
:param lat1: Latitude(s) of point 1 in degrees
:type long1: float or :class:numpy.ndarray
:param long1: Longitude(s) of point 1 in degrees
:type lat2: float or :class:numpy.ndarray
:param lat2: Latitude(s) of point 2 in degrees
:type long2: float or :class:numpy.ndarray
:param long2: Longitude(s) of point 2 in degrees
:rtype: float or :class:numpy.ndarray
:return: Distance in degrees as a floating point number,
or numpy array of element-wise distances in degrees

.. rubric:: Example

>>> from obspy.geodetics import locations2degrees
>>> locations2degrees(5, 5, 10, 10)
7.0397014191753815
"""
# broadcast explicitly here so it raises once instead of somewhere in the
# middle if things can't be broadcast
lat1, lat2, long1, long2 = np.broadcast_arrays(lat1, lat2, long1, long2)

long_diff = long2 - long1
gd = np.degrees(
np.arctan2(
np.sqrt((
np.cos(lat2) * np.sin(long_diff)) ** 2 +
(np.cos(lat1) * np.sin(lat2) - np.sin(lat1) *
np.cos(lat2) * np.cos(long_diff)) ** 2),
np.sin(lat1) * np.sin(lat2) + np.cos(lat1) * np.cos(lat2) *
np.cos(long_diff)))
return gd

[docs]def mean_longitude(longitudes):
"""
Compute sample mean longitude, assuming longitude in degrees from -180 to
180.

>>> lons = (-170.5, -178.3, 166)
>>> np.mean(lons)  # doctest: +SKIP
-60.933
>>> mean_longitude(lons)  # doctest: +ELLIPSIS
179.08509...

:type longitudes: :class:~numpy.ndarray (or list, ..)
:param longitudes: Geographical longitude values ranging from -180 to 180
in degrees.
"""
mean_longitude = circmean(np.array(longitudes), low=-180, high=180)
mean_longitude = _normalize_longitude(mean_longitude)
return mean_longitude

[docs]def inside_geobounds(obj, minlatitude=None, maxlatitude=None,
minlongitude=None, maxlongitude=None,
latitude=None, longitude=None,
"""
Check whether an object is within a given latitude and/or longitude range,
or within a given distance range from a reference geographic point.

The object must have latitude and longitude attributes, expressed
in degrees.

:type obj: object
:param obj: An object with latitude and longitude attributes.
:type minlatitude: float
:param minlatitude: Minimum latitude in degrees.
:type maxlatitude: float
:param maxlatitude: Maximum latitude in degrees. If this value is smaller
than minlatitude, then 360 degrees are added to this value (i.e.,
wrapping around latitude of +/- 180 degrees)
:type minlongitude: float
:param minlongitude: Minimum longitude in degrees.
:type maxlongitude: float
:param maxlongitude: Minimum longitude in degrees.
:type latitude: float
:param latitude: Latitude of the reference point, in degrees, for distance
range selection.
:type longitude: float
:param longitude: Longitude of the reference point, in degrees, for
distance range selection.
:param minradius: Minimum distance, in degrees, from the reference
geographic point defined by the latitude and longitude parameters.
:param maxradius: Maximum distance, in degrees, from the reference
geographic point defined by the latitude and longitude parameters.
:return: True if the object is within the given range, False
otherwise.

.. rubric:: Example

>>> from obspy.geodetics import inside_geobounds
>>> orig = ev.origins[0]
>>> inside_geobounds(orig, minlatitude=40, maxlatitude=42)
True
>>> inside_geobounds(orig, minlatitude=40, maxlatitude=42,
...                  minlongitude=78, maxlongitude=79)
False
>>> inside_geobounds(orig, latitude=40, longitude=80,
True
"""
if not hasattr(obj, 'latitude') or not hasattr(obj, 'longitude'):
raise AttributeError(
'Object must have "latitude" and "longitude" attributes.')
olatitude = obj.latitude
_check_latitude(olatitude, 'obj.latitude')
_check_latitude(minlatitude, 'minlatitude')
_check_latitude(maxlatitude, 'maxlatitude')
_check_latitude(latitude, 'latitude')
# Make sure longitudes are between -180 to 180 degrees
olongitude = _normalize_longitude(obj.longitude)
minlongitude = _normalize_longitude(minlongitude)
maxlongitude = _normalize_longitude(maxlongitude)
longitude = _normalize_longitude(longitude)
if minlatitude is not None:
if olatitude is None or olatitude < minlatitude:
return False
if maxlatitude is not None:
if olatitude is None or olatitude > maxlatitude:
return False
# Wrap longitude around +/- 180°, if necessary
if None not in [minlongitude, maxlongitude] \
and maxlongitude < minlongitude:
maxlongitude += 360
if olongitude is not None and olongitude < minlongitude:
olongitude += 360
if minlongitude is not None:
if olongitude is None or olongitude < minlongitude:
return False
if maxlongitude is not None:
if olongitude is None or olongitude > maxlongitude:
return False
if all([l is not None for l in
(latitude, longitude, olatitude, olongitude)]):
distance = locations2degrees(latitude, longitude,
olatitude, olongitude)