simplex_tree: Simplex Tree
In simplextree: Provides Tools for Working with General Simplicial Complexes

Description Usage Arguments Details Value Fields Properties Methods Author(s) References Examples

Simplex tree class exposed as an Rcpp Module.

1	simplex_tree(simplices = NULL)

simplices

optional simplices to initialize the simplex tree with. See insert.

A simplex tree is an ordered trie-like structure specialized for storing and doing general computation simplicial complexes. Here is figure of a simplex tree, taken from the original paper (see 1):
Figure: simplextree.png
The current implementation provides a subset of the functionality described in the paper.

A queryable simplex tree, as a Rcpp_SimplexTree object (Rcpp module).

n_simplices: A vector, where each index k denotes the number (k-1)-simplices.
dimension: The dimension of the simplicial complex.

Properties are actively bound shortcuts to various methods of the simplex tree that may be thought of as fields. Unlike fields, however, properties are not explicitly stored: they are generated on access.

$id_policy: The policy used to generate new vertex ids. May be assigned "compressed" or "unique". See generate_ids.
$vertices: The 0-simplices of the simplicial complex, as a matrix.
$edges: The 1-simplices of the simplicial complex, as a matrix.
$triangles: The 2-simplices of the simplicial complex, as a matrix.
$quads: The 3-simplices of the simplicial complex, as a matrix.
$connected_components: The connected components of the simplicial complex.

$as_XPtr: Creates an external pointer.
$clear: Clears the simplex tree.
$generate_ids: Generates new vertex ids according to the set policy.
$degree: Returns the degree of each given vertex.
$adjacent: Returns vertices adjacent to a given vertex.
$insert: Inserts a simplex into the trie.
$remove: Removes a simplex from the trie.
$find: Returns whether a simplex exists in the trie.
$collapse: Performs an elementary collapse.
$contract: Performs an edge contraction.
$expand: Performs an k-expansion.
$traverse: Traverses a subset of the simplex tree, applying a function to each simplex.
$ltraverse: Traverses a subset of the simplex tree, applying a function to each simplex and returning the result as a list.
$is_face: Checks for faces.
$is_tree: Checks if the simplicial complex is a tree.
$as_list: Converts the simplicial complex to a list.
$as_adjacency_matrix: Converts the 1-skeleton to an adjacency matrix.
$as_adjacency_list: Converts the 1-skeleton to an adjacency list.
$as_edgelist: Converts the 1-skeleton to an edgelist.

Matt Piekenbrock

Boissonnat, Jean-Daniel, and Clement Maria. "The simplex tree: An efficient data structure for general simplicial complexes." Algorithmica 70.3 (2014): 406-427.

## Recreating simplex tree from figure. 
st <- simplex_tree()
st %>% insert(list(1:3, 2:5, c(6, 7, 9), 7:8, 10))
plot(st)

## Example insertion
st <- simplex_tree(list(1:3, 4:5, 6)) ## Inserts one 2-simplex, one 1-simplex, and one 0-simplex
print(st) 
# Simplex Tree with (6, 4, 1) (0, 1, 2)-simplices

## More detailed look at structure
print_simplices(st, "tree")
# 1 (h = 2): .( 2 3 )..( 3 )
# 2 (h = 1): .( 3 )
# 3 (h = 0): 
# 4 (h = 1): .( 5 )
# 5 (h = 0): 
# 6 (h = 0): 
## Print the set of simplices making up the star of the simplex '2'
print_simplices(st %>% cofaces(2))
# 2, 2 3, 1 2, 1 2 3

## Retrieves list of all simplices in DFS order, starting with the empty face 
dfs_list <- ltraverse(st %>% preorder(empty_face), identity)

## Get connected components 
print(st$connected_components)
# [1] 1 1 1 4 4 5

## Use clone() to make copies of the complex (don't use the assignment `<-`)
new_st <- st %>% clone()

## Other more internal methods available via `$` 
list_of_simplices <- st$as_list()
adj_matrix <- st$as_adjacency_matrix()
# ... see also as_adjacency_list(), as_edge_list(), etc

Attaching package: ‘simplextree’

The following object is masked from ‘package:utils’:

    find

The following objects are masked from ‘package:base’:

    remove, serialize

Simplex Tree with (6, 4, 1) (0, 1, 2)-simplices
1 (h = 2): .( 2 3 )..( 3 )
2 (h = 1): .( 3 )
3 (h = 0): 
4 (h = 1): .( 5 )
5 (h = 0): 
6 (h = 0): 
2, 2 3, 1 2, 1 2 3
[1] 1 1 1 4 4 5