constrainthg 0.1.0a0

Methods for building and simulating constraint hypergraphs.

ConstraintHg

This repository enables usage of hypergraphs to define and execute system models. It is not a rigorous data storage solution. Do not use this as a database. Note that this repo is under active development (no official release yet), therefore changes may occur rapidly. Fork the repository before using it.

Introduction

Hypergraphs are normal graphs but without the constraint that edges must only link between two nodes. Because of this expanded generality, hypergraphs can be used to model more complex relationships. For instance, the relationship A + B = C is a multinodal relationship between three nodes, A, B, and C. You can think of all three nodes being linked by a 2D hyperedge, so that to move along that hyperedge you need at least two of three nodes.

An constraint hypergraph is a hypergraph where the relationships are constraints that can be solved for by some execution engine, generally via API calls. These constraints reveal the behavior of the system. The goal is for the hypergraph to be platform agnostic, while API calls allow for edges to be processed on any available software.

Processing a series of nodes and edges (a "route") is what constitutes a simulation, so one of the uses of an constraint hypergraph is enabling high-level simulation ability from any possible entry point in a system model.

Getting started

Note that this demo is found in demos/demo_basic.py Let's build a basic action hypergraph of the following equations:

• $A + B = C$
• $A = -D$
• $B = -E$
• $D + E = F$
• $F = -C$

First, import the classes.

from constrainthg.hypergraph import Hypergraph
import constrainthg.relations as R

A hypergraph consists of edges that map between a set of nodes to a single node. We provide the mapping by defining a constraint function (many of which are already defined in the relationships module). The two relationships defined in the governing equations are addition and negation. Using the typical syntax, we refer to the functions defined in relationships with R.<name>', in this case R.RsumandR.Rnegate`. To make the hypergraph we'll need to compose the 5 edges (equations) given above.

hg = Hypergraph()
hg.addEdge(['A', 'B'], C, R.Rsum)
hg.addEdge('A', 'D', R.Rnegate)
hg.addEdge('B', 'E', R.Rnegate)
hg.addEdge(['D', 'E'], 'F', R.Rsum)
hg.addEdge('F', 'C', R.Rnegate)

We can verify that the hypergraph was made correctly by tracing all possible paths for generating C using the printPaths function.

print(hg.printPaths('C'))

This should give us the following output. Hyperedges are indicated with a ◯, with the last source separated from other edges with a ●.

└──C, cost=1
   ├◯─A, cost=0
   ├●─B, cost=0
   └──F, cost=3
      ├◯─D, cost=1
      │  └──A, cost=0
      └●─E, cost=1
         └──B, cost=0

Compute the value of $C$ by picking a set of source nodes (inputs), such as $A$ and $B$ or $A$ and $E$. Set values for the inputs and the solver will automatically calulate an optimized route to simulate $C$.

print("**Inputs A and E**")
hg.solve('C', {'A':3, 'E':-7}, toPrint=True)
print("**Inputs A and B**")
hg.solve('C', {'A':3, 'B':7}, toPrint=True)

The output of the above should be:

**Inputs A and E**
└──C= 10, cost=3
   └──F= -10, cost=2
      ├──D= -3, cost=1
      │  └──A= 3, cost=0
      └──E= -7, cost=0

**Inputs A and B**
└──C= 10, cost=1
   ├──A= 3, cost=0
   └──B= 7, cost=0

Check out the demos directory for more examples.

Licensing and Usage

Author: John Morris
Organization: PLM Center at Clemson University
Contact: Reach out to my GitHub profile (jmorris335)
Usage: An official release will likely be provided under the CC BY-NC-SA 4.0 license, but for now all rights are reserved. For usage, please reach out to the author directly.