| nerve {simplextree} | R Documentation |
nerve
Description
Compute the nerve of a given cover.
Usage
nerve(st, cover, k = st$dimension, threshold = 1L, neighborhood = NULL)
Arguments
st |
a simplex tree. |
cover |
list of integers indicating set membership. See details. |
k |
max simplex dimension to consider. |
threshold |
the number of elements in common for |
neighborhood |
which combinations of sets to check. See details. |
Details
This computes the nerve of a given cover, adding a k-simplex for each combination of k+1 sets
in the given cover that have at least threshold elements in their common intersection.
If neighborhood is supplied, it can be either 1) a matrix, 2) a list, or 3) a function. Each
type parameterizes which sets in the cover need be checked for to see if they have at least threshold
elements in their common intersection. If a matrix is supplied, the columns should indicate the indices
of the cover to check (e.g if neighborhood = matrix(c(1,2), nrow = 2), then only the first two sets of cover
are tested.). Similarly, if a list is supplied, each element in the list should give the indices to test.
The most flexible option is supplying a function to neighborhood. If a function is passed, it's assumed to
accept an integer vector of k indices (of the cover) and return a boolean indicating whether or not to
test if they have at least threshold elements in their common intersection. This can be used
to filter out subsets of the cover the user knows are The indices are
generated using the same code that performs expand.