Source code for psdr.geometry.fill

from __future__ import print_function, division

import numpy as np
from scipy.spatial.distance import cdist

from .vertex import voronoi_vertex

[docs]def fill_distance_estimate(domain, Xhat, L = None, Nsamp = int(1e3), X0 = None ): r""" Estimate the fill distance of the points Xhat in the domain The *fill distance* (Def. 1.4 of [Wen04]_) or *dispersion* [LC05]_ is the furthest distance between any point :math:`\mathbf{x} \in \mathcal{D}` and a set of points :math:`\lbrace \widehat{\mathbf{x}}_j \rbrace_{j=1}^m \subset \mathcal{D}`: .. math:: \sup_{\mathbf{x} \in \mathcal{D}} \min_{j=1,\ldots,M} \|\mathbf{L}(\mathbf{x} - \widehat{\mathbf{x}}_j)\|_2. Similar to :meth:`psdr.seq_maximin_sample`, this uses :meth:`psdr.voronoi_vertex` to find a subset of local maximizers and returns the best of these. Parameters ---------- domain: Domain Domain on which to compute the dispersion Xhat: array-like (?, m) Existing samples on the domain L: array-like (?, m) optional Matrix defining the distance metric on the domain Nsamp: int, default 1e4 Number of samples to use for vertex sampling X0: array-like (?, m) Samples from the domain to use in :meth:`psdr.voronoi_vertex` Returns ------- d: float Fill distance lower bound References ---------- .. [Wen04] Scattered Data Approximation. Holger Wendland. Cambridge University Press, 2004. https://doi.org/10.1017/CBO9780511617539 .. [LC05] Iteratively Locating Voronoi Vertices for Dispersion Estimation Stephen R. Lindemann and Peng Cheng Proceedings of the 2005 Interational Conference on Robotics and Automation """ if L is None: L = np.eye(len(domain)) if X0 is None: from ..sample import initial_sample X0 = initial_sample(domain, L, Nsamp = Nsamp) # Since we only care about distance in L, we can terminate early if L is rank-deficient # and hence we turn off the randomization Xcan = voronoi_vertex(domain, Xhat, X0, L = L, randomize = False) # Euclidean distance D = cdist(L.dot(Xcan.T).T, L.dot(Xhat.T).T) d = np.min(D, axis = 1) return float(np.max(d))