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from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.testing import assert_array_almost_equal, assert_array_equal
from pytest import raises as assert_raises
from scipy.sparse.csgraph import (shortest_path, dijkstra, johnson,
bellman_ford, construct_dist_matrix, NegativeCycleError)
directed_G = np.array([[0, 3, 3, 0, 0],
[0, 0, 0, 2, 4],
[0, 0, 0, 0, 0],
[1, 0, 0, 0, 0],
[2, 0, 0, 2, 0]], dtype=float)
undirected_G = np.array([[0, 3, 3, 1, 2],
[3, 0, 0, 2, 4],
[3, 0, 0, 0, 0],
[1, 2, 0, 0, 2],
[2, 4, 0, 2, 0]], dtype=float)
unweighted_G = (directed_G > 0).astype(float)
directed_SP = [[0, 3, 3, 5, 7],
[3, 0, 6, 2, 4],
[np.inf, np.inf, 0, np.inf, np.inf],
[1, 4, 4, 0, 8],
[2, 5, 5, 2, 0]]
directed_pred = np.array([[-9999, 0, 0, 1, 1],
[3, -9999, 0, 1, 1],
[-9999, -9999, -9999, -9999, -9999],
[3, 0, 0, -9999, 1],
[4, 0, 0, 4, -9999]], dtype=float)
undirected_SP = np.array([[0, 3, 3, 1, 2],
[3, 0, 6, 2, 4],
[3, 6, 0, 4, 5],
[1, 2, 4, 0, 2],
[2, 4, 5, 2, 0]], dtype=float)
undirected_SP_limit_2 = np.array([[0, np.inf, np.inf, 1, 2],
[np.inf, 0, np.inf, 2, np.inf],
[np.inf, np.inf, 0, np.inf, np.inf],
[1, 2, np.inf, 0, 2],
[2, np.inf, np.inf, 2, 0]], dtype=float)
undirected_SP_limit_0 = np.ones((5, 5), dtype=float) - np.eye(5)
undirected_SP_limit_0[undirected_SP_limit_0 > 0] = np.inf
undirected_pred = np.array([[-9999, 0, 0, 0, 0],
[1, -9999, 0, 1, 1],
[2, 0, -9999, 0, 0],
[3, 3, 0, -9999, 3],
[4, 4, 0, 4, -9999]], dtype=float)
methods = ['auto', 'FW', 'D', 'BF', 'J']
def test_dijkstra_limit():
limits = [0, 2, np.inf]
results = [undirected_SP_limit_0,
undirected_SP_limit_2,
undirected_SP]
def check(limit, result):
SP = dijkstra(undirected_G, directed=False, limit=limit)
assert_array_almost_equal(SP, result)
for limit, result in zip(limits, results):
check(limit, result)
def test_directed():
def check(method):
SP = shortest_path(directed_G, method=method, directed=True,
overwrite=False)
assert_array_almost_equal(SP, directed_SP)
for method in methods:
check(method)
def test_undirected():
def check(method, directed_in):
if directed_in:
SP1 = shortest_path(directed_G, method=method, directed=False,
overwrite=False)
assert_array_almost_equal(SP1, undirected_SP)
else:
SP2 = shortest_path(undirected_G, method=method, directed=True,
overwrite=False)
assert_array_almost_equal(SP2, undirected_SP)
for method in methods:
for directed_in in (True, False):
check(method, directed_in)
def test_shortest_path_indices():
indices = np.arange(4)
def check(func, indshape):
outshape = indshape + (5,)
SP = func(directed_G, directed=False,
indices=indices.reshape(indshape))
assert_array_almost_equal(SP, undirected_SP[indices].reshape(outshape))
for indshape in [(4,), (4, 1), (2, 2)]:
for func in (dijkstra, bellman_ford, johnson, shortest_path):
check(func, indshape)
assert_raises(ValueError, shortest_path, directed_G, method='FW',
indices=indices)
def test_predecessors():
SP_res = {True: directed_SP,
False: undirected_SP}
pred_res = {True: directed_pred,
False: undirected_pred}
def check(method, directed):
SP, pred = shortest_path(directed_G, method, directed=directed,
overwrite=False,
return_predecessors=True)
assert_array_almost_equal(SP, SP_res[directed])
assert_array_almost_equal(pred, pred_res[directed])
for method in methods:
for directed in (True, False):
check(method, directed)
def test_construct_shortest_path():
def check(method, directed):
SP1, pred = shortest_path(directed_G,
directed=directed,
overwrite=False,
return_predecessors=True)
SP2 = construct_dist_matrix(directed_G, pred, directed=directed)
assert_array_almost_equal(SP1, SP2)
for method in methods:
for directed in (True, False):
check(method, directed)
def test_unweighted_path():
def check(method, directed):
SP1 = shortest_path(directed_G,
directed=directed,
overwrite=False,
unweighted=True)
SP2 = shortest_path(unweighted_G,
directed=directed,
overwrite=False,
unweighted=False)
assert_array_almost_equal(SP1, SP2)
for method in methods:
for directed in (True, False):
check(method, directed)
def test_negative_cycles():
# create a small graph with a negative cycle
graph = np.ones([5, 5])
graph.flat[::6] = 0
graph[1, 2] = -2
def check(method, directed):
assert_raises(NegativeCycleError, shortest_path, graph, method,
directed)
for method in ['FW', 'J', 'BF']:
for directed in (True, False):
check(method, directed)
def test_masked_input():
G = np.ma.masked_equal(directed_G, 0)
def check(method):
SP = shortest_path(directed_G, method=method, directed=True,
overwrite=False)
assert_array_almost_equal(SP, directed_SP)
for method in methods:
check(method)
def test_overwrite():
G = np.array([[0, 3, 3, 1, 2],
[3, 0, 0, 2, 4],
[3, 0, 0, 0, 0],
[1, 2, 0, 0, 2],
[2, 4, 0, 2, 0]], dtype=float)
foo = G.copy()
shortest_path(foo, overwrite=False)
assert_array_equal(foo, G)
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