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"""
===
Rcm
===
Cuthill-McKee ordering of matrices
The reverse Cuthill-McKee algorithm gives a sparse matrix ordering that
reduces the matrix bandwidth.
"""
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(f"lower bandwidth: {(y - x).max()}")
# print(f"upper bandwidth: {(x - y).max()}")
print(f"bandwidth: {(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(f"lower bandwidth: {(y - x).max()}")
# print(f"upper bandwidth: {(x - y).max()}")
print(f"bandwidth: {(y - x).max() + (x - y).max() + 1}")
print(B)