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46 lines
1.4 KiB
Python
46 lines
1.4 KiB
Python
def minkowski_distance(
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point_a: list[float],
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point_b: list[float],
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order: int,
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) -> float:
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"""
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This function calculates the Minkowski distance for a given order between
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two n-dimensional points represented as lists. For the case of order = 1,
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the Minkowski distance degenerates to the Manhattan distance. For
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order = 2, the usual Euclidean distance is obtained.
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https://en.wikipedia.org/wiki/Minkowski_distance
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Note: due to floating point calculation errors the output of this
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function may be inaccurate.
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>>> minkowski_distance([1.0, 1.0], [2.0, 2.0], 1)
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2.0
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>>> minkowski_distance([1.0, 2.0, 3.0, 4.0], [5.0, 6.0, 7.0, 8.0], 2)
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8.0
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>>> import numpy as np
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>>> bool(np.isclose(5.0, minkowski_distance([5.0], [0.0], 3)))
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True
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>>> minkowski_distance([1.0], [2.0], -1)
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Traceback (most recent call last):
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...
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ValueError: The order must be greater than or equal to 1.
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>>> minkowski_distance([1.0], [1.0, 2.0], 1)
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Traceback (most recent call last):
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...
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ValueError: Both points must have the same dimension.
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"""
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if order < 1:
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raise ValueError("The order must be greater than or equal to 1.")
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if len(point_a) != len(point_b):
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raise ValueError("Both points must have the same dimension.")
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return sum(abs(a - b) ** order for a, b in zip(point_a, point_b)) ** (1 / order)
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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