This commit is contained in:
ton
2023-10-05 00:01:27 +07:00
parent 1541297f6d
commit 4a987d90c5
12169 changed files with 502 additions and 2656459 deletions

View File

@@ -1,45 +0,0 @@
import numpy as np
import skimage.graph.mcp as mcp
from skimage._shared.testing import assert_array_equal
a = np.ones((8, 8), dtype=np.float32)
horizontal_ramp = np.array([[ 0., 1., 2., 3., 4., 5., 6., 7.,],
[ 0., 1., 2., 3., 4., 5., 6., 7.,],
[ 0., 1., 2., 3., 4., 5., 6., 7.,],
[ 0., 1., 2., 3., 4., 5., 6., 7.,],
[ 0., 1., 2., 3., 4., 5., 6., 7.,],
[ 0., 1., 2., 3., 4., 5., 6., 7.,],
[ 0., 1., 2., 3., 4., 5., 6., 7.,],
[ 0., 1., 2., 3., 4., 5., 6., 7.,]])
vertical_ramp = np.array( [[ 0., 0., 0., 0., 0., 0., 0., 0.,],
[ 1., 1., 1., 1., 1., 1., 1., 1.,],
[ 2., 2., 2., 2., 2., 2., 2., 2.,],
[ 3., 3., 3., 3., 3., 3., 3., 3.,],
[ 4., 4., 4., 4., 4., 4., 4., 4.,],
[ 5., 5., 5., 5., 5., 5., 5., 5.,],
[ 6., 6., 6., 6., 6., 6., 6., 6.,],
[ 7., 7., 7., 7., 7., 7., 7., 7.,]])
def test_anisotropy():
# Create seeds; vertical seeds create a horizonral ramp
seeds_for_horizontal = [(i, 0) for i in range(8)]
seeds_for_vertcal = [(0, i) for i in range(8)]
for sy in range(1, 5):
for sx in range(1, 5):
sampling = sy, sx
# Trace horizontally
m1 = mcp.MCP_Geometric(a, sampling=sampling, fully_connected=True)
costs1, traceback = m1.find_costs(seeds_for_horizontal)
# Trace vertically
m2 = mcp.MCP_Geometric(a, sampling=sampling, fully_connected=True)
costs2, traceback = m2.find_costs(seeds_for_vertcal)
# Check
assert_array_equal(costs1, horizontal_ramp * sx)
assert_array_equal(costs2, vertical_ramp * sy)

View File

@@ -1,75 +0,0 @@
import numpy as np
import skimage.graph.mcp as mcp
# import stentseg.graph._mcp as mcp
from skimage._shared.testing import assert_array_equal
a = np.ones((8, 8), dtype=np.float32)
count = 0
class MCP(mcp.MCP_Connect):
def _reset(self):
""" Reset the id map.
"""
mcp.MCP_Connect._reset(self)
self._conn = {}
self._bestconn = {}
def create_connection(self, id1, id2, pos1, pos2, cost1, cost2):
# Process data
hash = min(id1, id2), max(id1, id2)
val = min(pos1, pos2), max(pos1, pos2)
cost = min(cost1, cost2)
# Add to total list
self._conn.setdefault(hash, []).append(val)
# Keep track of connection with lowest cost
curcost = self._bestconn.get(hash, (np.inf,))[0]
if cost < curcost:
self._bestconn[hash] = (cost,) + val
def test_connections():
# Create MCP object with three seed points
mcp = MCP(a)
costs, traceback = mcp.find_costs([(1, 1), (7, 7), (1, 7)])
# Test that all three seed points are connected
connections = set(mcp._conn.keys())
assert (0, 1) in connections
assert (1, 2) in connections
assert (0, 2) in connections
# Test that any two neighbors have only been connected once
for position_tuples in mcp._conn.values():
n1 = len(position_tuples)
n2 = len(set(position_tuples))
assert n1 == n2
# For seed 0 and 1
cost, pos1, pos2 = mcp._bestconn[(0, 1)]
# Test meeting points
assert (pos1, pos2) == ((3, 3), (4, 4))
# Test the whole path
path = mcp.traceback(pos1) + list(reversed(mcp.traceback(pos2)))
assert_array_equal(
path, [(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (7, 7)])
# For seed 1 and 2
cost, pos1, pos2 = mcp._bestconn[(1, 2)]
# Test meeting points
assert (pos1, pos2) == ((3, 7), (4, 7))
# Test the whole path
path = mcp.traceback(pos1) + list(reversed(mcp.traceback(pos2)))
assert_array_equal(
path, [(1, 7), (2, 7), (3, 7), (4, 7), (5, 7), (6, 7), (7, 7)])
# For seed 0 and 2
cost, pos1, pos2 = mcp._bestconn[(0, 2)]
# Test meeting points
assert (pos1, pos2) == ((1, 3), (1, 4))
# Test the whole path
path = mcp.traceback(pos1) + list(reversed(mcp.traceback(pos2)))
assert_array_equal(
path, [(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7)])

View File

@@ -1,53 +0,0 @@
import numpy as np
import skimage.graph.mcp as mcp
from skimage._shared.testing import assert_array_equal
a = np.ones((8, 8), dtype=np.float32)
a[1::2] *= 2.0
class FlexibleMCP(mcp.MCP_Flexible):
""" Simple MCP subclass that allows the front to travel
a certain distance from the seed point, and uses a constant
cost factor that is independent of the cost array.
"""
def _reset(self):
mcp.MCP_Flexible._reset(self)
self._distance = np.zeros((8, 8), dtype=np.float32).ravel()
def goal_reached(self, index, cumcost):
if self._distance[index] > 4:
return 2
else:
return 0
def travel_cost(self, index, new_index, offset_length):
return 1.0 # fixed cost
def examine_neighbor(self, index, new_index, offset_length):
pass # We do not test this
def update_node(self, index, new_index, offset_length):
self._distance[new_index] = self._distance[index] + 1
def test_flexible():
# Create MCP and do a traceback
mcp = FlexibleMCP(a)
costs, traceback = mcp.find_costs([(0, 0)])
# Check that inner part is correct. This basically
# tests whether travel_cost works.
assert_array_equal(costs[:4, :4], [[1, 2, 3, 4],
[2, 2, 3, 4],
[3, 3, 3, 4],
[4, 4, 4, 4]])
# Test that the algorithm stopped at the right distance.
# Note that some of the costs are filled in but not yet frozen,
# so we take a bit of margin
assert np.all(costs[-2:, :] == np.inf)
assert np.all(costs[:, -2:] == np.inf)

View File

@@ -1,50 +0,0 @@
import time
import random
import skimage.graph.heap as heap
from skimage._shared.testing import test_parallel
@test_parallel()
def test_heap():
_test_heap(100000, True)
_test_heap(100000, False)
def _test_heap(n, fast_update):
# generate random numbers with duplicates
random.seed(0)
a = [random.uniform(1.0, 100.0) for i in range(n // 2)]
a = a + a
t0 = time.perf_counter()
# insert in heap with random removals
if fast_update:
h = heap.FastUpdateBinaryHeap(128, n)
else:
h = heap.BinaryHeap(128)
for i in range(len(a)):
h.push(a[i], i)
if a[i] < 25:
# double-push same ref sometimes to test fast update codepaths
h.push(2 * a[i], i)
if 25 < a[i] < 50:
# pop some to test random removal
h.pop()
# pop from heap
b = []
while True:
try:
b.append(h.pop()[0])
except IndexError:
break
t1 = time.perf_counter()
# verify
for i in range(1, len(b)):
assert(b[i] >= b[i - 1])
return t1 - t0

View File

@@ -1,163 +0,0 @@
import numpy as np
import skimage.graph.mcp as mcp
from skimage._shared.testing import (assert_array_equal, assert_almost_equal,
parametrize)
from skimage._shared._warnings import expected_warnings
np.random.seed(0)
a = np.ones((8, 8), dtype=np.float32)
a[1:-1, 1] = 0
a[1, 1:-1] = 0
warning_optional = r'|\A\Z'
def test_basic():
with expected_warnings(['Upgrading NumPy' + warning_optional]):
m = mcp.MCP(a, fully_connected=True)
costs, traceback = m.find_costs([(1, 6)])
return_path = m.traceback((7, 2))
assert_array_equal(costs,
[[1., 1., 1., 1., 1., 1., 1., 1.],
[1., 0., 0., 0., 0., 0., 0., 1.],
[1., 0., 1., 1., 1., 1., 1., 1.],
[1., 0., 1., 2., 2., 2., 2., 2.],
[1., 0., 1., 2., 3., 3., 3., 3.],
[1., 0., 1., 2., 3., 4., 4., 4.],
[1., 0., 1., 2., 3., 4., 5., 5.],
[1., 1., 1., 2., 3., 4., 5., 6.]])
assert_array_equal(return_path,
[(1, 6),
(1, 5),
(1, 4),
(1, 3),
(1, 2),
(2, 1),
(3, 1),
(4, 1),
(5, 1),
(6, 1),
(7, 2)])
def test_neg_inf():
expected_costs = np.where(a == 1, np.inf, 0)
expected_path = [(1, 6),
(1, 5),
(1, 4),
(1, 3),
(1, 2),
(2, 1),
(3, 1),
(4, 1),
(5, 1),
(6, 1)]
test_neg = np.where(a == 1, -1, 0)
test_inf = np.where(a == 1, np.inf, 0)
with expected_warnings(['Upgrading NumPy' + warning_optional]):
m = mcp.MCP(test_neg, fully_connected=True)
costs, traceback = m.find_costs([(1, 6)])
return_path = m.traceback((6, 1))
assert_array_equal(costs, expected_costs)
assert_array_equal(return_path, expected_path)
with expected_warnings(['Upgrading NumPy' + warning_optional]):
m = mcp.MCP(test_inf, fully_connected=True)
costs, traceback = m.find_costs([(1, 6)])
return_path = m.traceback((6, 1))
assert_array_equal(costs, expected_costs)
assert_array_equal(return_path, expected_path)
def test_route():
with expected_warnings(['Upgrading NumPy' + warning_optional]):
return_path, cost = mcp.route_through_array(a, (1, 6), (7, 2),
geometric=True)
assert_almost_equal(cost, np.sqrt(2) / 2)
assert_array_equal(return_path,
[(1, 6),
(1, 5),
(1, 4),
(1, 3),
(1, 2),
(2, 1),
(3, 1),
(4, 1),
(5, 1),
(6, 1),
(7, 2)])
def test_no_diagonal():
with expected_warnings(['Upgrading NumPy' + warning_optional]):
m = mcp.MCP(a, fully_connected=False)
costs, traceback = m.find_costs([(1, 6)])
return_path = m.traceback((7, 2))
assert_array_equal(costs,
[[2., 1., 1., 1., 1., 1., 1., 2.],
[1., 0., 0., 0., 0., 0., 0., 1.],
[1., 0., 1., 1., 1., 1., 1., 2.],
[1., 0., 1., 2., 2., 2., 2., 3.],
[1., 0., 1., 2., 3., 3., 3., 4.],
[1., 0., 1., 2., 3., 4., 4., 5.],
[1., 0., 1., 2., 3., 4., 5., 6.],
[2., 1., 2., 3., 4., 5., 6., 7.]])
assert_array_equal(return_path,
[(1, 6),
(1, 5),
(1, 4),
(1, 3),
(1, 2),
(1, 1),
(2, 1),
(3, 1),
(4, 1),
(5, 1),
(6, 1),
(7, 1),
(7, 2)])
def test_offsets():
offsets = [(1, i) for i in range(10)] + [(1, -i) for i in range(1, 10)]
with expected_warnings(['Upgrading NumPy' + warning_optional]):
m = mcp.MCP(a, offsets=offsets)
costs, traceback = m.find_costs([(1, 6)])
assert_array_equal(traceback,
[[-2, -2, -2, -2, -2, -2, -2, -2],
[-2, -2, -2, -2, -2, -2, -1, -2],
[15, 14, 13, 12, 11, 10, 0, 1],
[10, 0, 1, 2, 3, 4, 5, 6],
[10, 0, 1, 2, 3, 4, 5, 6],
[10, 0, 1, 2, 3, 4, 5, 6],
[10, 0, 1, 2, 3, 4, 5, 6],
[10, 0, 1, 2, 3, 4, 5, 6]])
assert hasattr(m, "offsets")
assert_array_equal(offsets, m.offsets)
@parametrize("shape", [(100, 100), (5, 8, 13, 17)] * 5)
def test_crashing(shape):
_test_random(shape)
def _test_random(shape):
# Just tests for crashing -- not for correctness.
a = np.random.rand(*shape).astype(np.float32)
starts = [[0] * len(shape), [-1] * len(shape),
(np.random.rand(len(shape)) * shape).astype(int)]
ends = [(np.random.rand(len(shape)) * shape).astype(int)
for i in range(4)]
with expected_warnings(['Upgrading NumPy' + warning_optional]):
m = mcp.MCP(a, fully_connected=True)
costs, offsets = m.find_costs(starts)
for point in [(np.random.rand(len(shape)) * shape).astype(int)
for i in range(4)]:
m.traceback(point)
m._reset()
m.find_costs(starts, ends)
for end in ends:
m.traceback(end)
return a, costs, offsets

View File

@@ -1,52 +0,0 @@
import numpy as np
from skimage.graph._graph import pixel_graph, central_pixel
mask = np.array([[1, 0, 0], [0, 1, 1], [0, 1, 0]], dtype=bool)
image = np.random.default_rng().random(mask.shape)
def test_small_graph():
g, n = pixel_graph(mask, connectivity=2)
assert g.shape == (4, 4)
assert len(g.data) == 8
np.testing.assert_allclose(np.unique(g.data), [1, np.sqrt(2)])
np.testing.assert_array_equal(n, [0, 4, 5, 7])
def test_central_pixel():
g, n = pixel_graph(mask, connectivity=2)
px, ds = central_pixel(g, n, shape=mask.shape)
np.testing.assert_array_equal(px, (1, 1))
s2 = np.sqrt(2)
np.testing.assert_allclose(ds, [s2*3 + 2, s2 + 2, s2*2 + 2, s2*2 + 2])
# test raveled coordinate
px, _ = central_pixel(g, n)
assert px == 4
# test no nodes given
px, _ = central_pixel(g)
assert px == 1
def test_edge_function():
def edge_func(values_src, values_dst, distances):
return np.abs(values_src - values_dst) + distances
g, n = pixel_graph(
image, mask=mask, connectivity=2, edge_function=edge_func
)
s2 = np.sqrt(2)
np.testing.assert_allclose(g[0, 1], np.abs(image[0, 0] - image[1, 1]) + s2)
np.testing.assert_allclose(g[1, 2], np.abs(image[1, 1] - image[1, 2]) + 1)
np.testing.assert_array_equal(n, [0, 4, 5, 7])
def test_default_edge_func():
g, n = pixel_graph(image, spacing=np.array([0.78, 0.78]))
num_edges = len(g.data) // 2 # each edge appears in both directions
assert num_edges == 12 # lattice in a (3, 3) grid
np.testing.assert_almost_equal(
g[0, 1], 0.78 * np.abs(image[0, 0] - image[0, 1])
)
np.testing.assert_array_equal(n, np.arange(image.size))

View File

@@ -1,256 +0,0 @@
import pytest
from numpy.testing import assert_array_equal
import numpy as np
from skimage import graph
from skimage import segmentation, data
from skimage._shared import testing
def max_edge(g, src, dst, n):
default = {'weight': -np.inf}
w1 = g[n].get(src, default)['weight']
w2 = g[n].get(dst, default)['weight']
return {'weight': max(w1, w2)}
def test_rag_merge():
g = graph.RAG()
for i in range(5):
g.add_node(i, {'labels': [i]})
g.add_edge(0, 1, {'weight': 10})
g.add_edge(1, 2, {'weight': 20})
g.add_edge(2, 3, {'weight': 30})
g.add_edge(3, 0, {'weight': 40})
g.add_edge(0, 2, {'weight': 50})
g.add_edge(3, 4, {'weight': 60})
gc = g.copy()
# We merge nodes and ensure that the minimum weight is chosen
# when there is a conflict.
g.merge_nodes(0, 2)
assert g.adj[1][2]['weight'] == 10
assert g.adj[2][3]['weight'] == 30
# We specify `max_edge` as `weight_func` as ensure that maximum
# weight is chosen in case on conflict
gc.merge_nodes(0, 2, weight_func=max_edge)
assert gc.adj[1][2]['weight'] == 20
assert gc.adj[2][3]['weight'] == 40
g.merge_nodes(1, 4)
g.merge_nodes(2, 3)
n = g.merge_nodes(3, 4, in_place=False)
assert sorted(g.nodes[n]['labels']) == list(range(5))
assert list(g.edges()) == []
@pytest.mark.parametrize(
"in_place", [True, False],
)
def test_rag_merge_gh5360(in_place):
# Add another test case covering the gallery example plot_rag.py.
# See bug report at gh-5360.
g = graph.RAG()
g.add_edge(1, 2, weight=10)
g.add_edge(2, 3, weight=20)
g.add_edge(3, 4, weight=30)
g.add_edge(4, 1, weight=40)
g.add_edge(1, 3, weight=50)
for n in g.nodes():
g.nodes[n]['labels'] = [n]
gc = g.copy()
# New node ID is chosen if in_place=False
merged_id = 3 if in_place is True else 5
g.merge_nodes(1, 3, in_place=in_place)
assert g.adj[merged_id][2]['weight'] == 10
assert g.adj[merged_id][4]['weight'] == 30
gc.merge_nodes(1, 3, weight_func=max_edge, in_place=in_place)
assert gc.adj[merged_id][2]['weight'] == 20
assert gc.adj[merged_id][4]['weight'] == 40
def test_threshold_cut():
img = np.zeros((100, 100, 3), dtype='uint8')
img[:50, :50] = 255, 255, 255
img[:50, 50:] = 254, 254, 254
img[50:, :50] = 2, 2, 2
img[50:, 50:] = 1, 1, 1
labels = np.zeros((100, 100), dtype='uint8')
labels[:50, :50] = 0
labels[:50, 50:] = 1
labels[50:, :50] = 2
labels[50:, 50:] = 3
rag = graph.rag_mean_color(img, labels)
new_labels = graph.cut_threshold(labels, rag, 10, in_place=False)
# Two labels
assert new_labels.max() == 1
new_labels = graph.cut_threshold(labels, rag, 10)
# Two labels
assert new_labels.max() == 1
def test_cut_normalized():
img = np.zeros((100, 100, 3), dtype='uint8')
img[:50, :50] = 255, 255, 255
img[:50, 50:] = 254, 254, 254
img[50:, :50] = 2, 2, 2
img[50:, 50:] = 1, 1, 1
labels = np.zeros((100, 100), dtype='uint8')
labels[:50, :50] = 0
labels[:50, 50:] = 1
labels[50:, :50] = 2
labels[50:, 50:] = 3
rag = graph.rag_mean_color(img, labels, mode='similarity')
new_labels = graph.cut_normalized(labels, rag, in_place=False)
new_labels, _, _ = segmentation.relabel_sequential(new_labels)
# Two labels
assert new_labels.max() == 1
new_labels = graph.cut_normalized(labels, rag)
new_labels, _, _ = segmentation.relabel_sequential(new_labels)
assert new_labels.max() == 1
def test_rag_error():
img = np.zeros((10, 10, 3), dtype='uint8')
labels = np.zeros((10, 10), dtype='uint8')
labels[:5, :] = 0
labels[5:, :] = 1
with testing.raises(ValueError):
graph.rag_mean_color(img, labels,
2, 'non existent mode')
def _weight_mean_color(graph, src, dst, n):
diff = graph.nodes[dst]['mean color'] - graph.nodes[n]['mean color']
diff = np.linalg.norm(diff)
return {'weight': diff}
def _pre_merge_mean_color(graph, src, dst):
graph.nodes[dst]['total color'] += graph.nodes[src]['total color']
graph.nodes[dst]['pixel count'] += graph.nodes[src]['pixel count']
graph.nodes[dst]['mean color'] = (graph.nodes[dst]['total color'] /
graph.nodes[dst]['pixel count'])
def merge_hierarchical_mean_color(labels, rag, thresh, rag_copy=True,
in_place_merge=False):
return graph.merge_hierarchical(labels, rag, thresh, rag_copy,
in_place_merge, _pre_merge_mean_color,
_weight_mean_color)
def test_rag_hierarchical():
img = np.zeros((8, 8, 3), dtype='uint8')
labels = np.zeros((8, 8), dtype='uint8')
img[:, :, :] = 31
labels[:, :] = 1
img[0:4, 0:4, :] = 10, 10, 10
labels[0:4, 0:4] = 2
img[4:, 0:4, :] = 20, 20, 20
labels[4:, 0:4] = 3
g = graph.rag_mean_color(img, labels)
g2 = g.copy()
thresh = 20 # more than 11*sqrt(3) but less than
result = merge_hierarchical_mean_color(labels, g, thresh)
assert(np.all(result[:, :4] == result[0, 0]))
assert(np.all(result[:, 4:] == result[-1, -1]))
result = merge_hierarchical_mean_color(labels, g2, thresh,
in_place_merge=True)
assert(np.all(result[:, :4] == result[0, 0]))
assert(np.all(result[:, 4:] == result[-1, -1]))
result = graph.cut_threshold(labels, g, thresh)
assert np.all(result == result[0, 0])
def test_ncut_stable_subgraph():
""" Test to catch an error thrown when subgraph has all equal edges. """
img = np.zeros((100, 100, 3), dtype='uint8')
labels = np.zeros((100, 100), dtype='uint8')
labels[:50, :50] = 1
labels[:50, 50:] = 2
rag = graph.rag_mean_color(img, labels, mode='similarity')
new_labels = graph.cut_normalized(labels, rag, in_place=False)
new_labels, _, _ = segmentation.relabel_sequential(new_labels)
assert new_labels.max() == 0
def test_reproducibility():
"""ensure cut_normalized returns the same output for the same input,
when specifying random_state
"""
img = data.coffee()
labels1 = segmentation.slic(
img, compactness=30, n_segments=400, start_label=0)
g = graph.rag_mean_color(img, labels1, mode='similarity')
results = [None] * 4
for i in range(len(results)):
results[i] = graph.cut_normalized(
labels1, g, in_place=False, thresh=1e-3, random_state=1234)
for i in range(len(results) - 1):
assert_array_equal(results[i], results[i + 1])
def test_generic_rag_2d():
labels = np.array([[1, 2], [3, 4]], dtype=np.uint8)
g = graph.RAG(labels)
assert g.has_edge(1, 2) and g.has_edge(2, 4) and not g.has_edge(1, 4)
h = graph.RAG(labels, connectivity=2)
assert h.has_edge(1, 2) and h.has_edge(1, 4) and h.has_edge(2, 3)
def test_generic_rag_3d():
labels = np.arange(8, dtype=np.uint8).reshape((2, 2, 2))
g = graph.RAG(labels)
assert g.has_edge(0, 1) and g.has_edge(1, 3) and not g.has_edge(0, 3)
h = graph.RAG(labels, connectivity=2)
assert h.has_edge(0, 1) and h.has_edge(0, 3) and not h.has_edge(0, 7)
k = graph.RAG(labels, connectivity=3)
assert k.has_edge(0, 1) and k.has_edge(1, 2) and k.has_edge(2, 5)
def test_rag_boundary():
labels = np.zeros((16, 16), dtype='uint8')
edge_map = np.zeros_like(labels, dtype=float)
edge_map[8, :] = 0.5
edge_map[:, 8] = 1.0
labels[:8, :8] = 1
labels[:8, 8:] = 2
labels[8:, :8] = 3
labels[8:, 8:] = 4
g = graph.rag_boundary(labels, edge_map, connectivity=1)
assert set(g.nodes()) == {1, 2, 3, 4}
assert set(g.edges()) == {(1, 2), (1, 3), (2, 4), (3, 4)}
assert g[1][3]['weight'] == 0.25
assert g[2][4]['weight'] == 0.34375
assert g[1][3]['count'] == 16

View File

@@ -1,32 +0,0 @@
import numpy as np
import skimage.graph.spath as spath
from skimage._shared.testing import assert_equal, assert_array_equal
def test_basic():
x = np.array([[1, 1, 3],
[0, 2, 0],
[4, 3, 1]])
path, cost = spath.shortest_path(x)
assert_array_equal(path, [0, 0, 1])
assert_equal(cost, 1)
def test_reach():
x = np.array([[1, 1, 3],
[0, 2, 0],
[4, 3, 1]])
path, cost = spath.shortest_path(x, reach=2)
assert_array_equal(path, [0, 0, 2])
assert_equal(cost, 0)
def test_non_square():
x = np.array([[1, 1, 1, 1, 5, 5, 5],
[5, 0, 0, 5, 9, 1, 1],
[0, 5, 1, 0, 5, 5, 0],
[6, 1, 1, 5, 0, 0, 1]])
path, cost = spath.shortest_path(x, reach=2)
assert_array_equal(path, [2, 1, 1, 2, 3, 3, 2])
assert_equal(cost, 0)