| tau_bound {ashapesampler} | R Documentation |
tau_bound
Description
This function finds the bound of tau for one shape, which is the maximum length of the fiber bundle off of a shape for determining the density of points necessary to recover the homology from the open cover. See Niyogi et al 2008. Function checks length of edges and distances to circumcenters from each vertex before checking against the rest of the point cloud and finds the minimum length. We then keep the largest tau to account for the possibility of nonuniformity among points.
Usage
tau_bound(v_list, complex, extremes = NULL, cores = 1, sumstat = "mean")
Arguments
v_list |
matrix or data frame of cartesian coordinates of vertices in in point cloud |
complex |
list of each vertex, edge, face, and (in 3D) tetrahedron in a simplicial complex; same form as complex object in TDA package |
extremes |
matrix or data frame of cartesian coordinates of vertices on the boundary of the data frame. If no list given, function will assume all points are extreme and check them all. Inclusion of this parameter speeds up the process both within this function and when calculating alpha because you will get a bigger (but still valid) tau bound. |
cores |
number of cores for parallelizing. Default 1. |
sumstat |
string for summary statistic to be used to get final tau for shape. Default is 'mean'. Options are 'median', 'min', and 'max'. |
Value
tau_vec, vector real nonnegative number. Tau values for each point