def ex_1():
'''Example 1 of the paper.
A 2-by-20 grid with reflecting boundary condition and an obstacle in the
middle.
'''
N = 20
G = nx.grid_2d_graph(N,N)
n_middle = (N/2, N/2)
# Add reflecting boundary condition
for i,j in G:
if i == 0 or i == N-1 or j == 0 or j == N-1:
G.add_edge((i,j), (i,j))
# Remove edges of the node at the middle
# (keep one edge, to simplify the bookiping
for u,v in sorted(G.edges(n_middle))[:-1]:
G.add_edge(v,v) # Add self loop
G.remove_edge(u, v)
T, _ = get_T(G)
savemat('vf_ex1', {'T':T}, oned_as='column')
return G
def circle(N):
G = nx.cycle_graph(N)
T, L = get_T(G)
fn = 'T_circle_%d.mat' % N
savemat(fn, {'T':T, 'L':L}, oned_as='column')
print 'T saved as %s' % fn
# Add self loops to all nodes
for node in G.nodes():
G.add_edge(node, node)
T_loop, L_loop = get_T(G)
fn = 'T_circle_selfloop_%d.mat' % N
savemat(fn, {'T':T_loop, 'L':L_loop}, oned_as='column')
print 'T saved as %s' % fn
return T, L, T_loop, L_loop
def circle(N):
G = nx.cycle_graph(N)
T, L = get_T(G)
fn = 'T_circle_%d.mat' % N
savemat(fn, {'T': T, 'L': L}, oned_as='column')
print 'T saved as %s' % fn
# Add self loops to all nodes
for node in G.nodes():
G.add_edge(node, node)
T_loop, L_loop = get_T(G)
fn = 'T_circle_selfloop_%d.mat' % N
savemat(fn, {'T': T_loop, 'L': L_loop}, oned_as='column')
print 'T saved as %s' % fn
return T, L, T_loop, L_loop
def make_T(N, add_selfloops=False):
'''Compute the diffusion operator of an N-by-N grid graph.
The difussion operator is defined as
T = D^0.5 * P * D^-0.5, where D is the degree matrix, P=D^-1W is the random
walk matrix, and W is the adjancency matrix.
'''
G = nx.grid_2d_graph(N,N)
if add_selfloops:
for n in G:
G.add_edge(n, n)
T, _ = get_T(G)
L = nx.laplacian(G, nodelist=sorted(G.nodes()))
return T, L
def make_T(N, add_selfloops=False):
'''Compute the diffusion operator of an N-by-N grid graph.
The difussion operator is defined as
T = D^0.5 * P * D^-0.5, where D is the degree matrix, P=D^-1W is the random
walk matrix, and W is the adjancency matrix.
'''
G = nx.grid_2d_graph(N, N)
if add_selfloops:
for n in G:
G.add_edge(n, n)
T, _ = get_T(G)
L = nx.laplacian(G, nodelist=sorted(G.nodes()))
return T, L
