rigidPy is a library written in python with minimal dependency to compute rigidity properties of a graph/network. The namespace is designed to resemble mathematical terminology unifying the research themes in mathematics, physics and biology. The library can be used to compute the rigidity matrix, vibrational properties, and elastic properties of the spring networks. It also offers a set of tools to find different realizations of a graph for a given topology.

The library consists of three modules:

• Framework: This is the main module which given a set of coordinates and connectivity can compute rigidty matrix, Hessian matrix, vibrarional frequencies,
• Conguration: This module minimizes energy by optimizing the positions of sites given a set of target edge lengths.
• Circuit (experimental): This module allows one to start from a given framework (identified by coordinates of sites and their connectivty) and find another network that satisfies all constraints but with different position of sites (alternative realization of a framework).

Example

import numpy as np
import rigidpy as rp
# position of sites
coordinates = np.array([[-1,0], [1,0], [0,1]])
# list of sites between sites
bonds = np.array([[0,1],[1,2],[0,2]])
# repetition of unit-cell
basis = [[0,0],[0,0]]
# which site is pinned in space
pins = [0]
# create a Framework object
F = rp.framework(coordinates, bonds, basis=basis, pins=pins)
# calculate the rigidity matrix
print ("rigidity matrix:\n",F.rigidityMatrix())
# calculate the eigenvalues of Hessian/dynamical matrix
eigvals, eigvecs = F.eigenSpace(eigvals=(0,3))
print("vibrational eigenvalues:\n",eigvals)
# visualize network (pinned sites are shown as red diamonds)
F.visulize()

Output:

rigidity matrix:
 [[ 1.         -0.          0.          0.        ]
 [ 0.70710678 -0.70710678 -0.70710678  0.70710678]
 [ 0.          0.          0.70710678  0.70710678]]
vibrational eigenvalues:
 [2.22044605e-16 6.33974596e-01 1.00000000e+00 2.36602540e+00]

Requirements

• Python 3.5+
• Numpy (>= 1.20.0)
• Scipy (>= 1.6.0)
• Matplotlib (>= 1.4.3) (only required for plotting)

Authors:

• Varda Faghir Hagh
• Mahdi Sadjadi

Citations

@article{hagh2021rigidpy,
  title={rigidPy: Rigidity Analysis in Python},
  author={Hagh, Varda F and Sadjadi, Mahdi},
  journal={arXiv preprint arXiv:2108.07195},
  year={2021}
}

License

This project is licensed under the MIT License - see the LICENSE.md file for details.