sampling.mm.propose_mmphi_corrected_minimizing_point

sampling.mm.propose_mmphi_corrected_minimizing_point(
    X,
    n_candidates=1000,
    q=2.0,
    p=2.0,
    seed=None,
    lower=None,
    upper=None,
    normalize_flag=False,
)

Proposes a new point that minimizes the corrected Morris-Mitchell criterion.

Samples n_candidates points uniformly at random within [lower, upper] and returns the one whose addition to X yields the lowest value of the corrected criterion :math:\hat{\Phi}_q (see :func:mmphi_corrected).

Internally the function pre-computes the base distance cache (J, d) for X once and then evaluates each candidate via :func:mmphi_corrected_update, which only needs to compute the n new distances between the candidate and the existing points rather than all :math:\binom{n+1}{2} pairwise distances. This makes the search :math:O(n) per candidate instead of :math:O(n^2).

Parameters

Name	Type	Description	Default
X	np.ndarray	Existing design points, shape (n_points, n_dim).	required
n_candidates	int	Number of random candidate points to evaluate. Defaults to 1000.	1000
q	float	Exponent for the corrected Morris-Mitchell criterion. Defaults to 2.0.	2.0
p	float	Distance norm (e.g., p=1 Manhattan, p=2 Euclidean). Defaults to 2.0.	2.0
seed	int	Random seed for reproducibility. Defaults to None.	None
lower	np.ndarray	Lower bounds for each dimension, shape (n_dim,). Defaults to np.zeros(n_dim).	None
upper	np.ndarray	Upper bounds for each dimension, shape (n_dim,). Defaults to np.ones(n_dim).	None
normalize_flag	bool	If True, normalizes X and all candidate points to [0, 1] before computing distances. Defaults to False.	False

Returns

Name	Type	Description
	np.ndarray	np.ndarray: The best candidate point found, shape (1, n_dim).

Raises

Name	Type	Description
	ValueError	If any element of lower is greater than or equal to the corresponding element of upper.

Examples

>>> import numpy as np
>>> from spotoptim.sampling.mm import propose_mmphi_corrected_minimizing_point
>>> X = np.array([[0.1, 0.2], [0.5, 0.5], [0.9, 0.8]])
>>> new_point = propose_mmphi_corrected_minimizing_point(
...     X, n_candidates=200, q=2, p=2, seed=0
... )
>>> print(new_point.shape)
(1, 2)