chebyshev_distance¶

chebyshev_distance(points_a, points_b)[source]¶: Compute pairwise Chebyshev (L∞) distances between two point sets.

Overview¶

chebyshev_distance(points_a, points_b) computes the full pairwise Chebyshev (L∞) distance matrix between two 2D numeric arrays of shapes (N, D) and (M, D), returning an (N, M) float64 matrix. The Chebyshev distance between vectors x and y is:

\[d_{\infty}(x, y) = \max_{i=1..D} |x_i - y_i|\]

It measures the maximum absolute coordinate difference and is useful when the largest deviation across dimensions dominates similarity (e.g., certain quality thresholds or grid-based neighborhood analyses).

Shape Requirements¶

points_a.ndim == 2
points_b.ndim == 2
Feature dimension matches: points_a.shape[1] == points_b.shape[1]

Parameters (see signature above)¶

points_a: NumPy array (N, D) (any numeric dtype; coerced to float64)
points_b: NumPy array (M, D) (same feature dimension as points_a)

Returns¶

numpy.ndarray of shape (N, M) with out[i, j] = max(abs(points_a[i, k] - points_b[j, k])).

Numerical & Dtype Notes¶

All inputs are coerced to float64 internally for uniform arithmetic.
No special epsilon handling is required (pure absolute differences).
Extremely large values propagate normally; consider prior clipping if needed.

Performance¶

Implemented in Rust; releases the Python GIL.
Outer loops may parallelize for large N * M workloads.
Memory usage is O(N*M) for the output; for very large matrices consider blockwise strategies (not implemented here).

Examples¶

Basic usage:

import numpy as np
from eo_processor import chebyshev_distance

A = np.array([[0.0, 1.0],
              [2.0, 3.5]], dtype=np.float32)   # (2, 2)
B = np.array([[1.0, 2.0],
              [0.0, -1.0],
              [2.0, 3.0]], dtype=np.float64)   # (3, 2)

dist = chebyshev_distance(A, B)
# dist[0, 0] = max(|0-1|, |1-2|) = 1
# dist[1, 2] = max(|2-2|, |3.5-3|) = 0.5
print(dist.shape)  # (2, 3)

Edge Case (single feature dimension):

A = np.array([[0.0], [5.0]])
B = np.array([[2.5], [10.0]])
d = chebyshev_distance(A, B)  # Equivalent to absolute difference

Error Handling¶

Raises ValueError if: - Inputs are not 2D - Feature dimensions differ

Raises TypeError if inputs are non-numeric.

Use Cases¶

Fast max-difference screening
Grid / tile similarity where worst-case deviation matters
Alternative to L2/L1 norms for bounding box or threshold checks