minkowski_distance¶

minkowski_distance(points_a, points_b, p)[source]¶

Compute pairwise Minkowski distances (order p) between two point sets.

Parameters:

points_a (numpy.ndarray (N, D)) – First point set.
points_b (numpy.ndarray (M, D)) – Second point set.
p (float) – Norm order (must be >= 1). p=1 → Manhattan, p=2 → Euclidean, large p → approximates Chebyshev (L∞).

Returns:

Distance matrix.

Return type:

numpy.ndarray (N, M)

Raises:

ValueError – If p < 1.0 (propagated from the Rust implementation).

Overview¶

Computes the full pairwise Minkowski distance matrix between two 2D point sets points_a (N, D) and points_b (M, D) for a given order p (p ≥ 1).

The Minkowski distance of order p between vectors x and y is:

\[d_p(x, y) = \left( \sum_{i=1}^{D} |x_i - y_i|^p \right)^{1/p}\]

Special cases: - p = 1 → Manhattan (L1) distance - p = 2 → Euclidean (L2) distance - p → ∞ (large p) approximates Chebyshev (L∞) distance

Input Requirements¶

points_a and points_b must be 2-dimensional NumPy arrays with the same feature dimension D.
Any numeric dtype is accepted; values are coerced to float64 internally.
Raises ValueError if p < 1.0.

Output¶

Returns a float64 NumPy array of shape (N, M) where element (i, j) is the Minkowski distance between points_a[i] and points_b[j].

Performance Notes¶

For large N*M products, consider memory implications of a full matrix.
Internally, parallelization may occur for sufficiently large workloads; small matrices avoid parallel overhead.
If you need only nearest neighbors, building a spatial index (not provided here) can be more efficient than computing the full matrix.

Examples¶

import numpy as np
from eo_processor import minkowski_distance

A = np.random.rand(5, 3)   # (N=5, D=3)
B = np.random.rand(7, 3)   # (M=7, D=3)

dist_p2 = minkowski_distance(A, B, p=2.0)  # Euclidean
dist_p3 = minkowski_distance(A, B, p=3.0)

print(dist_p2.shape)  # (5, 7)

Error Handling¶

ValueError if shapes are incompatible (different D).
ValueError if p < 1.0.