def reference_bellman_ford(G, seeds):
"""
G : sparse matrix
seeds : array
"""
G = G.tocoo()
N = G.shape[0]
seeds = np.asarray(seeds, dtype='intc')
distances = np.inf * np.ones(N, dtype=G.dtype)
distances[seeds] = 0
nearest_seed = -1 * np.ones(N, dtype='intc')
nearest_seed[seeds] = seeds
while True:
update = False
for (i, j, w) in zip(G.row, G.col, G.data):
if distances[j] + w < distances[i]:
update = True
distances[i] = distances[j] + w
nearest_seed[i] = nearest_seed[j]
if not update:
break
# temporary: swap infs for max_value()
distances[np.where(distances == np.inf)[0]] = max_value(G.dtype)
return (distances, nearest_seed)
def reference_bellman_ford(G, seeds):
G = G.tocoo()
N = G.shape[0]
seeds = asarray(seeds, dtype='intc')
distances = empty(N, dtype=G.dtype)
distances[:] = max_value(G.dtype)
distances[seeds] = 0
nearest_seed = empty(N, dtype='intc')
nearest_seed[:] = -1
nearest_seed[seeds] = seeds
while True:
update = False
for (i, j, v) in zip(G.row, G.col, G.data):
if distances[j] + v < distances[i]:
update = True
distances[i] = distances[j] + v
nearest_seed[i] = nearest_seed[j]
if not update:
break
return (distances, nearest_seed)
def reference_bellman_ford(G, seeds):
G = G.tocoo()
N = G.shape[0]
seeds = asarray(seeds, dtype='intc')
distances = empty(N, dtype=G.dtype)
distances[:] = max_value(G.dtype)
distances[seeds] = 0
nearest_seed = empty(N, dtype='intc')
nearest_seed[:] = -1
nearest_seed[seeds] = seeds
while True:
update = False
for (i, j, v) in zip(G.row, G.col, G.data):
if distances[j] + v < distances[i]:
update = True
distances[i] = distances[j] + v
nearest_seed[i] = nearest_seed[j]
if not update:
break
return (distances, nearest_seed)
def test_bellman_ford_reference(self):
Edges = np.array([[1, 4], [3, 1], [1, 3], [0, 1], [0, 2], [3, 2],
[1, 2], [4, 3]])
w = np.array([2, 1, 2, -1, 4, 5, 3, -3], dtype=float)
G = sparse.coo_matrix((w, (Edges[:, 0], Edges[:, 1])))
# distance
# seed 0 : [ 0. -1. 2. -2. 1.]
# seed 1 : [inf 0. 3. -1. 2.]
# seed 2 : [inf inf 0. inf inf]
# seed 3 : [inf 1. 4. 0. 3.]
# seed 4 : [inf -2. 1. -3. 0.]
distances_FROM_seed = np.array([[0., -1., 2., -2., 1.],
[np.inf, 0., 3., -1., 2.],
[np.inf, np.inf, 0., np.inf, np.inf],
[np.inf, 1., 4., 0., 3.],
[np.inf, -2., 1., -3., 0.]])
distances_FROM_seed[np.where(
distances_FROM_seed == np.inf)] = max_value(G.dtype)
for seed in range(5):
distance, nearest = reference_bellman_ford(G.T, [seed])
assert_equal(distance, distances_FROM_seed[seed])
distance, nearest = bellman_ford(G.T, [seed])
assert_equal(distance, distances_FROM_seed[seed])
# seeds [0,1,2,3,4]
# distance to closest: [-2. -1. 0. 0. -3.]
# closest: [3 3 2 3 3]
distance_TO_closest = np.array([-2., -1., 0., 0., -3.])
ref_closest = np.array([3, 3, 2, 3, 3])
distance, closest = reference_bellman_ford(G, [0, 1, 2, 3, 4])
assert_equal(distance, distance_TO_closest)
assert_equal(closest, ref_closest)
distance, closest = bellman_ford(G, [0, 1, 2, 3, 4])
assert_equal(distance, distance_TO_closest)
assert_equal(closest, ref_closest)