sampling.mm.plot_mmphi_corrected_vs_points

sampling.mm.plot_mmphi_corrected_vs_points(
    X_base,
    x_min,
    x_max,
    p_min=10,
    p_max=100,
    p_step=10,
    n_repeats=5,
    q=2.0,
    p_norm=2.0,
    figsize=(10, 6),
)

Plot the Corrected Morris-Mitchell Criterion versus the number of added points.

For each point count in range(p_min, p_max + 1, p_step) a set of uniformly random points is appended to X_base and the corrected criterion hat_Phi_q is evaluated on the extended design. This is repeated n_repeats times per point count to capture stochastic variability. The resulting mean ± std curve is compared to the baseline criterion of X_base alone.

Unlike plot_mmphi_vs_points, which uses the intensive criterion (normalized by M = n(n-1)/2), this function uses the corrected criterion (normalized by n^{1+q/k}), which is asymptotically size-invariant and therefore provides a more reliable comparison across designs of different sizes.

Parameters

Name	Type	Description	Default
X_base	np.ndarray	Base design matrix of shape (n, k).	required
x_min	np.ndarray	Lower bounds for each dimension, shape (k,).	required
x_max	np.ndarray	Upper bounds for each dimension, shape (k,).	required
p_min	int	Minimum number of points to add. Defaults to 10.	10
p_max	int	Maximum number of points to add. Defaults to 100.	100
p_step	int	Step size for the number of added points. Defaults to 10.	10
n_repeats	int	Number of repetitions per point count. Defaults to 5.	5
q	float	Exponent q for the corrected Morris-Mitchell criterion. Defaults to 2.0.	2.0
p_norm	float	Distance norm p. Defaults to 2.0.	2.0
figsize	tuple	Size of the plot (width, height). Defaults to (10, 6).	(10, 6)

Returns

Name	Type	Description
	pd.DataFrame	pd.DataFrame: Summary DataFrame with columns n_points,
	pd.DataFrame	(mmphi_corrected, mean), and (mmphi_corrected, std) for each
	pd.DataFrame	number of added points.

Examples

>>> import numpy as np
>>> from spotoptim.sampling.mm import plot_mmphi_corrected_vs_points
>>> X_base = np.array([[0.1, 0.2], [0.4, 0.5], [0.7, 0.8]])
>>> x_min = np.array([0.0, 0.0])
>>> x_max = np.array([1.0, 1.0])
>>> df_summary = plot_mmphi_corrected_vs_points(X_base, x_min, x_max, p_min=10, p_max=50, p_step=10, n_repeats=3)