NAME

full_ph_tree - Construct a tree structure data for (n-1)-th persistent homology

SYNOPSIS

python3 -m homcloud.full_ph_tree 
    [-h] [-V] -d DEGREE [-j DUMP_JSON] input output

ALIAS

homcloud-full-ph-tree

DESCRIPTION

This program computes a tree structure data for (n-1)-th persistent homology of the alpha filtration diagram of a point cloud in R^n based on the theory of volume optimal cycle.

OPTIONS

-h, --help            show this help message and exit
-V, --version         show program's version number and exit
-d DEGREE, --degree DEGREE
                      degree of PH
-j DUMP_JSON, --dump-json DUMP_JSON
                      json dump output

INPUT

The input file should be the idiagram file computed from a point cloud

OUTPUT

PH-tree format. You can query the output file by

• plot_PD_gui with -p option by GUI
• query_full_ph_tree by CUI

You can also use all tree information in json format with -j option.

OUTPUT JSON FORMAT

# root struct
{
    "dim": int, /* dimension of a point cloud */
    "num-node": int, /* the number of nodes */
    "nodes": dict of (nodeid, node) pairs
}
# Node struct
{
    "index": string, /* id of the node itself */
    "parent": string, /* id of the parent node */
    "birth-time": float, /* birth time */
    "death-time": float, /* death time */
    "simplices": list of Simplex, /* all simplices contained in the volume */
    "birth-simplex": Simplex, /* birth simplex */
    "death-simplex": Simplex, /* death simplex */
    "points": list of Point /* all vertices contianed in the volume */
}
# Simplex
list of Point /* vertices */
# Point
list of float /* coordinate values */

EXAMPLE

# Compute diagram
python3 -m homcloud.pc2diphacomplex -d 3 -I -D sphere_packing.txt sphere_packing.idiagram
# Compute tree structure
python3 -m homcloud.full_ph_tree -d 2 sphere_packing.idiagram sphere_packing.pht -j sphere_packing_tree.json
# See the tree data using plog_PD_gui
python3 -m homcloud.plog_PD_gui -d 2 -p sphere_packing.pht sphere_packing.idiagram

NOTES

The argument of -d option must be n-1 for a point cloud in R^n.