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335 lines
12 KiB
Python
335 lines
12 KiB
Python
import numpy as np
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from numpy.testing import assert_array_almost_equal, assert_array_equal
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from pytest import raises as assert_raises
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from scipy.sparse.csgraph import (shortest_path, dijkstra, johnson,
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bellman_ford, construct_dist_matrix,
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NegativeCycleError)
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import scipy.sparse
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import pytest
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directed_G = np.array([[0, 3, 3, 0, 0],
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[0, 0, 0, 2, 4],
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[0, 0, 0, 0, 0],
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[1, 0, 0, 0, 0],
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[2, 0, 0, 2, 0]], dtype=float)
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undirected_G = np.array([[0, 3, 3, 1, 2],
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[3, 0, 0, 2, 4],
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[3, 0, 0, 0, 0],
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[1, 2, 0, 0, 2],
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[2, 4, 0, 2, 0]], dtype=float)
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unweighted_G = (directed_G > 0).astype(float)
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directed_SP = [[0, 3, 3, 5, 7],
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[3, 0, 6, 2, 4],
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[np.inf, np.inf, 0, np.inf, np.inf],
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[1, 4, 4, 0, 8],
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[2, 5, 5, 2, 0]]
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directed_sparse_zero_G = scipy.sparse.csr_matrix(([0, 1, 2, 3, 1],
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([0, 1, 2, 3, 4],
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[1, 2, 0, 4, 3])),
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shape = (5, 5))
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directed_sparse_zero_SP = [[0, 0, 1, np.inf, np.inf],
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[3, 0, 1, np.inf, np.inf],
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[2, 2, 0, np.inf, np.inf],
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[np.inf, np.inf, np.inf, 0, 3],
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[np.inf, np.inf, np.inf, 1, 0]]
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undirected_sparse_zero_G = scipy.sparse.csr_matrix(([0, 0, 1, 1, 2, 2, 1, 1],
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([0, 1, 1, 2, 2, 0, 3, 4],
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[1, 0, 2, 1, 0, 2, 4, 3])),
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shape = (5, 5))
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undirected_sparse_zero_SP = [[0, 0, 1, np.inf, np.inf],
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[0, 0, 1, np.inf, np.inf],
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[1, 1, 0, np.inf, np.inf],
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[np.inf, np.inf, np.inf, 0, 1],
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[np.inf, np.inf, np.inf, 1, 0]]
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directed_pred = np.array([[-9999, 0, 0, 1, 1],
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[3, -9999, 0, 1, 1],
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[-9999, -9999, -9999, -9999, -9999],
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[3, 0, 0, -9999, 1],
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[4, 0, 0, 4, -9999]], dtype=float)
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undirected_SP = np.array([[0, 3, 3, 1, 2],
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[3, 0, 6, 2, 4],
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[3, 6, 0, 4, 5],
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[1, 2, 4, 0, 2],
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[2, 4, 5, 2, 0]], dtype=float)
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undirected_SP_limit_2 = np.array([[0, np.inf, np.inf, 1, 2],
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[np.inf, 0, np.inf, 2, np.inf],
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[np.inf, np.inf, 0, np.inf, np.inf],
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[1, 2, np.inf, 0, 2],
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[2, np.inf, np.inf, 2, 0]], dtype=float)
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undirected_SP_limit_0 = np.ones((5, 5), dtype=float) - np.eye(5)
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undirected_SP_limit_0[undirected_SP_limit_0 > 0] = np.inf
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undirected_pred = np.array([[-9999, 0, 0, 0, 0],
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[1, -9999, 0, 1, 1],
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[2, 0, -9999, 0, 0],
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[3, 3, 0, -9999, 3],
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[4, 4, 0, 4, -9999]], dtype=float)
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methods = ['auto', 'FW', 'D', 'BF', 'J']
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def test_dijkstra_limit():
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limits = [0, 2, np.inf]
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results = [undirected_SP_limit_0,
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undirected_SP_limit_2,
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undirected_SP]
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def check(limit, result):
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SP = dijkstra(undirected_G, directed=False, limit=limit)
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assert_array_almost_equal(SP, result)
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for limit, result in zip(limits, results):
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check(limit, result)
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def test_directed():
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def check(method):
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SP = shortest_path(directed_G, method=method, directed=True,
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overwrite=False)
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assert_array_almost_equal(SP, directed_SP)
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for method in methods:
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check(method)
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def test_undirected():
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def check(method, directed_in):
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if directed_in:
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SP1 = shortest_path(directed_G, method=method, directed=False,
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overwrite=False)
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assert_array_almost_equal(SP1, undirected_SP)
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else:
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SP2 = shortest_path(undirected_G, method=method, directed=True,
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overwrite=False)
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assert_array_almost_equal(SP2, undirected_SP)
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for method in methods:
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for directed_in in (True, False):
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check(method, directed_in)
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def test_directed_sparse_zero():
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# test directed sparse graph with zero-weight edge and two connected components
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def check(method):
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SP = shortest_path(directed_sparse_zero_G, method=method, directed=True,
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overwrite=False)
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assert_array_almost_equal(SP, directed_sparse_zero_SP)
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for method in methods:
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check(method)
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def test_undirected_sparse_zero():
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def check(method, directed_in):
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if directed_in:
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SP1 = shortest_path(directed_sparse_zero_G, method=method, directed=False,
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overwrite=False)
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assert_array_almost_equal(SP1, undirected_sparse_zero_SP)
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else:
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SP2 = shortest_path(undirected_sparse_zero_G, method=method, directed=True,
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overwrite=False)
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assert_array_almost_equal(SP2, undirected_sparse_zero_SP)
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for method in methods:
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for directed_in in (True, False):
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check(method, directed_in)
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@pytest.mark.parametrize('directed, SP_ans',
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((True, directed_SP),
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(False, undirected_SP)))
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@pytest.mark.parametrize('indices', ([0, 2, 4], [0, 4], [3, 4], [0, 0]))
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def test_dijkstra_indices_min_only(directed, SP_ans, indices):
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SP_ans = np.array(SP_ans)
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indices = np.array(indices, dtype=np.int64)
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min_ind_ans = indices[np.argmin(SP_ans[indices, :], axis=0)]
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min_d_ans = np.zeros(SP_ans.shape[0], SP_ans.dtype)
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for k in range(SP_ans.shape[0]):
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min_d_ans[k] = SP_ans[min_ind_ans[k], k]
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min_ind_ans[np.isinf(min_d_ans)] = -9999
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SP, pred, sources = dijkstra(directed_G,
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directed=directed,
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indices=indices,
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min_only=True,
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return_predecessors=True)
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assert_array_almost_equal(SP, min_d_ans)
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assert_array_equal(min_ind_ans, sources)
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SP = dijkstra(directed_G,
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directed=directed,
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indices=indices,
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min_only=True,
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return_predecessors=False)
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assert_array_almost_equal(SP, min_d_ans)
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@pytest.mark.parametrize('n', (10, 100, 1000))
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def test_shortest_path_min_only_random(n):
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np.random.seed(1234)
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data = scipy.sparse.rand(n, n, density=0.5, format='lil',
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random_state=42, dtype=np.float64)
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data.setdiag(np.zeros(n, dtype=np.bool_))
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# choose some random vertices
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v = np.arange(n)
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np.random.shuffle(v)
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indices = v[:int(n*.1)]
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ds, pred, sources = dijkstra(data,
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directed=False,
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indices=indices,
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min_only=True,
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return_predecessors=True)
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for k in range(n):
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p = pred[k]
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s = sources[k]
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while(p != -9999):
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assert(sources[p] == s)
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p = pred[p]
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def test_shortest_path_indices():
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indices = np.arange(4)
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def check(func, indshape):
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outshape = indshape + (5,)
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SP = func(directed_G, directed=False,
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indices=indices.reshape(indshape))
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assert_array_almost_equal(SP, undirected_SP[indices].reshape(outshape))
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for indshape in [(4,), (4, 1), (2, 2)]:
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for func in (dijkstra, bellman_ford, johnson, shortest_path):
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check(func, indshape)
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assert_raises(ValueError, shortest_path, directed_G, method='FW',
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indices=indices)
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def test_predecessors():
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SP_res = {True: directed_SP,
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False: undirected_SP}
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pred_res = {True: directed_pred,
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False: undirected_pred}
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def check(method, directed):
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SP, pred = shortest_path(directed_G, method, directed=directed,
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overwrite=False,
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return_predecessors=True)
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assert_array_almost_equal(SP, SP_res[directed])
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assert_array_almost_equal(pred, pred_res[directed])
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for method in methods:
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for directed in (True, False):
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check(method, directed)
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def test_construct_shortest_path():
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def check(method, directed):
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SP1, pred = shortest_path(directed_G,
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directed=directed,
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overwrite=False,
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return_predecessors=True)
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SP2 = construct_dist_matrix(directed_G, pred, directed=directed)
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assert_array_almost_equal(SP1, SP2)
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for method in methods:
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for directed in (True, False):
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check(method, directed)
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def test_unweighted_path():
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def check(method, directed):
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SP1 = shortest_path(directed_G,
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directed=directed,
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overwrite=False,
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unweighted=True)
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SP2 = shortest_path(unweighted_G,
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directed=directed,
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overwrite=False,
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unweighted=False)
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assert_array_almost_equal(SP1, SP2)
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for method in methods:
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for directed in (True, False):
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check(method, directed)
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def test_negative_cycles():
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# create a small graph with a negative cycle
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graph = np.ones([5, 5])
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graph.flat[::6] = 0
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graph[1, 2] = -2
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def check(method, directed):
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assert_raises(NegativeCycleError, shortest_path, graph, method,
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directed)
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for method in ['FW', 'J', 'BF']:
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for directed in (True, False):
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check(method, directed)
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def test_masked_input():
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np.ma.masked_equal(directed_G, 0)
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def check(method):
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SP = shortest_path(directed_G, method=method, directed=True,
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overwrite=False)
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assert_array_almost_equal(SP, directed_SP)
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for method in methods:
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check(method)
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def test_overwrite():
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G = np.array([[0, 3, 3, 1, 2],
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[3, 0, 0, 2, 4],
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[3, 0, 0, 0, 0],
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[1, 2, 0, 0, 2],
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[2, 4, 0, 2, 0]], dtype=float)
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foo = G.copy()
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shortest_path(foo, overwrite=False)
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assert_array_equal(foo, G)
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@pytest.mark.parametrize('method', methods)
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def test_buffer(method):
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# Smoke test that sparse matrices with read-only buffers (e.g., those from
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# joblib workers) do not cause::
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#
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# ValueError: buffer source array is read-only
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#
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G = scipy.sparse.csr_matrix([[1.]])
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G.data.flags['WRITEABLE'] = False
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shortest_path(G, method=method)
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def test_NaN_warnings():
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with pytest.warns(None) as record:
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shortest_path(np.array([[0, 1], [np.nan, 0]]))
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for r in record:
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assert r.category is not RuntimeWarning
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def test_sparse_matrices():
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# Test that using lil,csr and csc sparse matrix do not cause error
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G_dense = np.array([[0, 3, 0, 0, 0],
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[0, 0, -1, 0, 0],
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[0, 0, 0, 2, 0],
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[0, 0, 0, 0, 4],
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[0, 0, 0, 0, 0]], dtype=float)
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SP = shortest_path(G_dense)
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G_csr = scipy.sparse.csr_matrix(G_dense)
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G_csc = scipy.sparse.csc_matrix(G_dense)
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G_lil = scipy.sparse.lil_matrix(G_dense)
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assert_array_almost_equal(SP, shortest_path(G_csr))
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assert_array_almost_equal(SP, shortest_path(G_csc))
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assert_array_almost_equal(SP, shortest_path(G_lil))
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