Tree

A fast implementation of trees which can be accessed with a SQL language and perform linear algebra operations on the leaves.

Libraries

tree.network

Expressive language to access networks with hierarchical structure

Node attributes cascade down the descendants of the node. Attributes across the tree are efficiently accessed through Python's hashing, similar to Structured Query Language (SQL), but with Python's snake syntax and slicing. We refer to tree.network as a Hierarchical Structured Query Language (H-SQL).

tree.linalg

Intuitive construction of matrices for physical systems

Constructs a sparse matrix representation of the tree's leaves, and makes use of efficient caching in constructing the dense matrix. This keeps matrix re-initialisation fast as network parameters are varied.

Mathematical Introduction

Graphs

Mathematical objects of the theory of graphs have one-to-one matrix representations, as described by the theory of linear algebra. In general, a graph is a network structure, whose off-diagonal terms in the matrix representation are known to Condensed Matter Physicists as hopping or interaction terms.

Trees

A particular graph, known as a tree, is a network with a hierarchical structure, which we use to index objects in their matrix representation.

Python implementation

The Tree is a Python subclass of a List, which adds the following attributes and methods:

Attributes

• parent : Tree or none (default) children : Tree or none (default)
• ancestors : list of Trees lineage upwards
• root: root of the tree (parent without parent)
• descendants : lists lineage downwards (list of list of Trees)
• buds : lists descendants without descendants

Methods

• set_ids : add an index (id) to the buds of this Tree
• get_ids : get the indices (ids) of the buds of this Tree .attribute : attributes are inherited down the linage

Summary

A graph structure defines a matrix; a tree structure indexes the matrix.

The tree structure adds parents, children, ancestors, descendants and inheritance of attributes.

Installation

Development environment

pip install --editable . --break-system-packages

Build and upload

python3 -m build
twine upload dist/*

Class Diagram

Package Diagram