import numpy as np
[docs]
def directed_hausdorff_distance(pred: np.ndarray, reference: np.ndarray):
"""One-sided directed Hausdorff distance between two 1D sets. Useful for computing distances
between estimated eigenvalues
Calculates the directed Hausdorff distance
:math:`\\vec{H}(A, B) = \\max_{a \\in A} \\min_{b \\in B} \\|a - b\\|_p` where :math:`A` is the
set of points in ``pred`` and :math:`B` is the set of points in ``reference``. The current
implementation uses the :math:`L_1` norm: :math:`\\|a - b\\|_1 = |a - b|`.
Parameters
----------
pred : numpy.ndarray
The set of predicted points :math:`A`. Must be a 1D array.
reference : numpy.ndarray
The set of reference points :math:`B`. Must be a 1D array.
Returns
-------
float
The directed Hausdorff distance between ``pred``and ``reference``.
Raises
------
AssertionError
If ``pred`` or ``reference`` are not 1-dimensional arrays.
Examples
--------
.. code-block:: python
import numpy as np
from kooplearn.metrics import directed_hausdorff_distance
pred = np.array([1, 5, 6])
reference = np.array([2, 4, 7])
directed_hausdorff_distance(pred, reference)
# Will print np.float64(1.0)
"""
pred = np.asanyarray(pred)
reference = np.asanyarray(reference)
assert pred.ndim == 1
assert reference.ndim == 1
distances = np.zeros((pred.shape[0], reference.shape[0]), dtype=np.float64)
for pred_idx, pred_pt in enumerate(pred):
for reference_idx, reference_pt in enumerate(reference):
distances[pred_idx, reference_idx] = np.abs(pred_pt - reference_pt)
hausdorff_dist = np.max(np.min(distances, axis=1))
return hausdorff_dist
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