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* ci(pre-commit): Add pep8-naming to `pre-commit` hooks (#7038) * refactor: Fix naming conventions (#7038) * Update arithmetic_analysis/lu_decomposition.py Co-authored-by: Christian Clauss <cclauss@me.com> * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * refactor(lu_decomposition): Replace `NDArray` with `ArrayLike` (#7038) * chore: Fix naming conventions in doctests (#7038) * fix: Temporarily disable project euler problem 104 (#7069) * chore: Fix naming conventions in doctests (#7038) Co-authored-by: Christian Clauss <cclauss@me.com> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
57 lines
2.4 KiB
Python
57 lines
2.4 KiB
Python
from math import asin, atan, cos, radians, sin, sqrt, tan
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def haversine_distance(lat1: float, lon1: float, lat2: float, lon2: float) -> float:
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"""
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Calculate great circle distance between two points in a sphere,
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given longitudes and latitudes https://en.wikipedia.org/wiki/Haversine_formula
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We know that the globe is "sort of" spherical, so a path between two points
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isn't exactly a straight line. We need to account for the Earth's curvature
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when calculating distance from point A to B. This effect is negligible for
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small distances but adds up as distance increases. The Haversine method treats
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the earth as a sphere which allows us to "project" the two points A and B
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onto the surface of that sphere and approximate the spherical distance between
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them. Since the Earth is not a perfect sphere, other methods which model the
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Earth's ellipsoidal nature are more accurate but a quick and modifiable
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computation like Haversine can be handy for shorter range distances.
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Args:
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lat1, lon1: latitude and longitude of coordinate 1
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lat2, lon2: latitude and longitude of coordinate 2
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Returns:
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geographical distance between two points in metres
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>>> from collections import namedtuple
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>>> point_2d = namedtuple("point_2d", "lat lon")
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>>> SAN_FRANCISCO = point_2d(37.774856, -122.424227)
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>>> YOSEMITE = point_2d(37.864742, -119.537521)
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>>> f"{haversine_distance(*SAN_FRANCISCO, *YOSEMITE):0,.0f} meters"
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'254,352 meters'
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"""
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# CONSTANTS per WGS84 https://en.wikipedia.org/wiki/World_Geodetic_System
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# Distance in metres(m)
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AXIS_A = 6378137.0 # noqa: N806
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AXIS_B = 6356752.314245 # noqa: N806
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RADIUS = 6378137 # noqa: N806
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# Equation parameters
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# Equation https://en.wikipedia.org/wiki/Haversine_formula#Formulation
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flattening = (AXIS_A - AXIS_B) / AXIS_A
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phi_1 = atan((1 - flattening) * tan(radians(lat1)))
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phi_2 = atan((1 - flattening) * tan(radians(lat2)))
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lambda_1 = radians(lon1)
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lambda_2 = radians(lon2)
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# Equation
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sin_sq_phi = sin((phi_2 - phi_1) / 2)
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sin_sq_lambda = sin((lambda_2 - lambda_1) / 2)
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# Square both values
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sin_sq_phi *= sin_sq_phi
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sin_sq_lambda *= sin_sq_lambda
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h_value = sqrt(sin_sq_phi + (cos(phi_1) * cos(phi_2) * sin_sq_lambda))
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return 2 * RADIUS * asin(h_value)
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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