sampling.mm.plot_mmphi_corrected_vs_n_lhs

sampling.mm.plot_mmphi_corrected_vs_n_lhs(
    k_dim,
    seed,
    n_min=10,
    n_max=100,
    n_step=5,
    q_phi=2.0,
    p_phi=2.0,
    plot_only_corrected=False,
)

Generate LHS designs for varying n and plot the Corrected Morris-Mitchell Criterion against the standard criterion.

For each sample size n in range(n_min, n_max + 1, n_step) a fresh Latin Hypercube design is drawn and both the intensive criterion hat_Phi_q^I (normalized by M = n(n-1)/2) and the corrected criterion hat_Phi_q (normalized by n^{1+q/k}) are computed. The two series are displayed on a shared x-axis with independent y-axes so their trends can be compared directly.

When plot_only_corrected is True, the intensive criterion is omitted: only hat_Phi_q is plotted on a single y-axis. This is the preferred form when illustrating the asymptotic size-invariance of the corrected criterion on its own scale.

The corrected criterion is asymptotically size-invariant: for large n its expected value stabilizes at a finite constant that depends only on the spatial distribution of the design, not on n itself. This plot makes that convergence behaviour visible.

Parameters

Name	Type	Description	Default
k_dim	int	Number of dimensions for the LHS design.	required
seed	int	Random seed for reproducibility.	required
n_min	int	Minimum number of samples. Defaults to 10.	10
n_max	int	Maximum number of samples. Defaults to 100.	100
n_step	int	Step size for increasing n. Defaults to 5.	5
q_phi	float	Exponent q for the Morris-Mitchell criteria. Defaults to 2.0.	2.0
p_phi	float	Distance norm p for the Morris-Mitchell criteria. Defaults to 2.0.	2.0
plot_only_corrected	bool	If True, plot only the corrected criterion hat_Phi_q on a single y-axis and skip the intensive criterion entirely. Defaults to False, which preserves the original dual-axis comparison plot.	False

Returns

Name	Type	Description
None	None	Displays the plot. When plot_only_corrected is False the
	None	figure has dual y-axes showing mmphi_intensive and
	None	mmphi_corrected; when True only the corrected curve is shown.

Examples

>>> from spotoptim.sampling.mm import plot_mmphi_corrected_vs_n_lhs
>>> plot_mmphi_corrected_vs_n_lhs(k_dim=3, seed=42, n_min=10, n_max=50, n_step=5, q_phi=2.0, p_phi=2.0)
>>> plot_mmphi_corrected_vs_n_lhs(k_dim=3, seed=42, n_min=10, n_max=50, plot_only_corrected=True)