# Cuthill-McKee ordering of matrices
# The reverse Cuthill-McKee algorithm gives a sparse matrix ordering that 
# reduces the matrix bandwidth.
# Requires NumPy
# Copyright (C) 2011 by 
# Aric Hagberg <aric.hagberg@gmail.com>
# BSD License
import networkx as nx
from networkx.utils import reverse_cuthill_mckee_ordering
import numpy as np

# build low-bandwidth numpy matrix
G=nx.grid_2d_graph(3,3)
rcm = list(reverse_cuthill_mckee_ordering(G))    
print("ordering",rcm)

print("unordered Laplacian matrix")
A = nx.laplacian_matrix(G)
x,y = np.nonzero(A)
#print("lower bandwidth:",(y-x).max())
#print("upper bandwidth:",(x-y).max())
print("bandwidth: %d"%((y-x).max()+(x-y).max()+1))
print(A)

B = nx.laplacian_matrix(G,nodelist=rcm)
print("low-bandwidth Laplacian matrix")
x,y = np.nonzero(B)
#print("lower bandwidth:",(y-x).max())
#print("upper bandwidth:",(x-y).max())
print("bandwidth: %d"%((y-x).max()+(x-y).max()+1))
print(B)

