SimplexTree
This is an internal module used for representing simplicial complexes.
The methods in here allow for low level manipulation of the simplicial structure and may break the representation assumptions made throughout the remainder of the code. Only use these if you know what you are doing (and really need to do that).
Hodge.SimplexTrees.SimplexTree — TypeStore a simplicial complex using the Simplex Tree data structure.
Based on the paper:
- Jean-Daniel Boissonnat, Clément Maria. The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes. [Research Report] RR-7993, 2012, pp.20. hal-00707901v1
Hodge.SimplexTrees.child_from_label — Methodchild_from_label(node, j)Return the child of node whose label is j. If no child has label j, return nothing.
Hodge.SimplexTrees.children_label — Methodchildren_label(node)Return an array containing the labels of node's children.
Hodge.SimplexTrees.foldST — MethodfoldST(st::SimplexTree; basecase, joiner)Fold st applying the function basecase to the leafs and joining siblings using the function joiner.
Hodge.SimplexTrees.foldST_depth — MethodfoldST_depth(st::SimplexTree, depth; basecase, joiner)Fold st until a given depth applying the function basecase to the leafs and joining siblings vi a the function joiner.
See also foldST.
Hodge.SimplexTrees.getnode — Methodgetnode(root, s)Return the node of the SimplexTree rooted at root representing the simplex s. If s is not in the complex, return nothing.
Hodge.SimplexTrees.getsimplices — Methodgetsimplices(st, k)Return all the k-simplices of complex.
Hodge.SimplexTrees.haschild — Methodhaschild(node, j)Test whether node has a child with label j.
Hodge.SimplexTrees.hassimplex — Methodhassimplex(node, s)Test whether the SimplexTree rooted at node contains the simplex s.
Hodge.SimplexTrees.insert! — Methodinsert!(complex, simplex)Insert a simplex and all its faces on an existing simplicial complex.
Hodge.SimplexTrees.isemptyface — Methodisemptyface(node)Test whether node represents an empty simplex.
Hodge.SimplexTrees.isleaf — Methodisleaf(node)Test whether node is a leaf of a SimplexTree.
Hodge.SimplexTrees.numsimplices — Methodnumsimplices(st, k)Return the number of k-simplices of st.
This is a more efficient implementation of length ∘ getsimplices.