def test_has_edge_undirected(self):
"""Tests the has_edge method for an undirected graph.
"""
undirected = Graph(graph = { 'A' : ['B'], 'B' : ['A'] })
self.assertTrue(undirected.has_edge('A', 'B'), 'There is an edge between A and B.')
self.assertTrue(undirected.has_edge('B', 'A'), 'There is an edge between B and A.')
def task_3(sequence_length, phase_filtering):
polyharmonic_sequence = generate_polyharmonic_sequence(sequence_length)
direct_transformer = DirectFourierTransformer(polyharmonic_sequence)
amplitude_spectrum = direct_transformer.get_amplitude_spectrum()
phase_spectrum = [
x if amplitude_spectrum[i] > phase_filtering else 0
for i, x in enumerate(direct_transformer.get_phase_spectrum())
]
restored_sequence = InverseFourierTransformer(
amplitude_spectrum, phase_spectrum).restore_polyharmonic(True)
restored_sequence_without_phases \
= InverseFourierTransformer(amplitude_spectrum, phase_spectrum).restore_polyharmonic(False)
drawer = GraphDrawer()
drawer.add_plot(
Graph(range(sequence_length), polyharmonic_sequence,
"Original sequence"))
drawer.add_stem(
Graph(range(sequence_length), amplitude_spectrum,
"Amplitude spectrum"))
drawer.add_stem(
Graph(range(sequence_length), phase_spectrum, "Phase spectrum"))
drawer.add_plot(
Graph(range(sequence_length), restored_sequence, "Restored sequence"))
drawer.add_plot(
Graph(range(sequence_length), restored_sequence_without_phases,
"Restored sequence w/o phase spectrum"))
drawer.draw()
drawer.show()
def run(data):
servers = Graph(data, Transformer, " - ", ": ", oriented=True)
res = {}
out = ""
for node in servers.nodes:
if not out:
out = node
best = float("inf")
for neighbour in servers.nodes[node].neighbours():
if neighbour in res.keys():
continue
path, cost = servers.dijkstra(node, neighbour)
if cost < best:
best = cost
res[node] = path
total = 0
to_unpack = len(res)
while to_unpack:
key = out[-1]
direction = res[key].pop()
total += servers.vertex_cost(key, direction)
out = out + " - " + direction
to_unpack -= 1
print(out + ": " + str(total))
def test_has_edge_directed(self):
"""Tests the has_edge method for a directed graph.
"""
directed = Graph(graph = { 'C' : ['D'], 'D' : [] }, is_directed = True)
self.assertTrue(directed.has_edge('C', 'D'), 'There is an edge from C to D.')
self.assertFalse(directed.has_edge('D', 'C'), 'There is no edge from D to C.')
def assessment_page():
""" This is the assessment category page. This method is used to generate
the graphs and talbes that display on the page.
"""
graph = Graph()
# assessment_count = graph.assessment_count()
# assessment_avgtone = graph.assessment_avgtone()
maine_html_table = graph.table_generator("main_nummen_assessment",
"assessment")
student_html_table = graph.table_generator("student_nummen_assessment",
"assessment")
US_html_table = graph.table_generator("US_nummen_assessment", "assessment")
FL_html_table = graph.table_generator("FL_nummen_assessment", "assessment")
return render_template(
'assessment.html',
maine_html_table=maine_html_table,
student_html_table=student_html_table,
US_html_table=US_html_table,
FL_html_table=FL_html_table,
# assessment_avgtone=assessment_avgtone,
# assessment_count=assessment_count
)
def build_graph(code):
graph = Graph()
blocks = [b["name"] for b in code["blocks"]]
edges = [(b["name"], e) for b in code["blocks"] for e in b["next_block"]]
graph.add_nodes(*blocks)
graph.add_edges(*edges)
return graph
def curri_page():
""" This is the curriculum category page. This method is used to generate the
graphs and tables that display on this page.
"""
# The Graph class is instantiated and assigned to the graph variable.
graph = Graph()
# CA_distplot = graph.curri_distplot("ca_avgtone_curri_topstates", "California")
# TX_distplot = graph.curri_distplot("tx_avgtone_curri_topstates", "Texas")
# MA_distplot = graph.curri_distplot("ma_avgtone_curri_topstates", "Massachusetts")
# NY_distplot = graph.curri_distplot("ny_avgtone_curri_topstates", "New York")
CA_html_table = graph.table_generator("ca_curri_topstates", "curriculum")
TX_html_table = graph.table_generator("tx_curri_topstates", "curriculum")
MA_html_table = graph.table_generator("ma_curri_topstates", "curriculum")
NY_html_table = graph.table_generator("ny_curri_topstates", "curriculum")
return render_template(
'curriculum.html',
# CA_distplot=CA_distplot,
# TX_distplot=TX_distplot,
# MA_distplot=MA_distplot,
# NY_distplot=NY_distplot,
CA_html_table=CA_html_table,
TX_html_table=TX_html_table,
MA_html_table=MA_html_table,
NY_html_table=NY_html_table)
def test_has_edge_no_connexion(self):
"""Tests the has_edge method for a graph without connexion.
"""
graph = Graph(graph = {'Z' : []})
self.assertFalse(graph.has_edge('Z', 'A'), 'There is no edge between Z to A.')
self.assertFalse(graph.has_edge('Z', None), 'There is no edge between Z and a None vertex.')
def topsort(G: Graph) -> List[str]:
"""
Topologically sort the graph
"""
i = 0
visited = set()
ft = {v: None for v in G.get_vertices()} # finishing time
def DFS(u):
nonlocal i, visited, ft
visited.add(u)
for v in G[u]:
if v not in visited:
DFS(v)
ft[u] = i
i += 1
for u in G.get_vertices():
if u not in visited:
DFS(u)
return sorted(ft, key=ft.get, reverse=True)
def charter_schools_page():
""" This is the charter school category page. This method is used to generate
the graphs and tables that display on the page.
"""
graph = Graph()
# This line can be used to generate the avgtone/nummention line plot again if needed.
# I left it commented out because there are a lot of data points and it takes a long time
# to load.
# lineplot_url = graph.charter_lineplot()
# top10_us_url = graph.buzzwords_graph("keyword_count")
# I used the highest number of mentions from 2014-2015 to create this table
top_20_20142015 = graph.table_generator("charter_schools_20142015",
"charter-school")
# I used the lowest number of mentions from 2014-2015 to create this table
top_20_20152016 = graph.table_generator("charter_schools_20152016",
"charter-school")
# I used the lowest number of mentions from 2014-2015 to create this table
top_20_2017pres = graph.table_generator("charter_schools_2017pres",
"charter-school")
return render_template(
'charter-schools.html',
# top10_us_url=top10_us_url,
# # lineplot_url=lineplot_url,
top_20_20142015=top_20_20142015,
top_20_20152016=top_20_20152016,
top_20_2017pres=top_20_2017pres)
def test_add_edge_not_valid_vertex(self):
"""Tests the add_edge method in a graph with a non-existing vertex.
"""
graph = Graph(graph = { 'A' : [] })
graph.add_edge('A', 'B')
self.assertFalse(graph.has_edge('A', 'B'), 'No edge between A and non-existing B.')
def setUp(self):
n6 = Node(6)
n5 = Node(5, [n6])
n4 = Node(4, [n6])
n3 = Node(3, [n4, n5])
n2 = Node(2, [n4])
n1 = Node(1, [n2, n3])
self.g = Graph([n1, n2, n3, n4, n5, n6])
def test_get_nodes():
graph = Graph()
graph.add_node('coffee')
graph.add_node('muffin')
Vertex('loner')
expected = 2
actual = len(graph.get_nodes())
assert actual == expected
def test_remove_unexisting_edge(self):
"""Tests the remove_edge method in a graph without edge between two vertex
"""
graph = Graph(graph = { 'A' : [], 'B' : [] })
self.assertFalse(graph.has_edge('A', 'B'), 'There is no edge between A and B.')
graph.remove_edge('A', 'B')
self.assertFalse(graph.has_edge('A', 'B'), 'Nothing changed.')
def test_add_vertex(self):
"""Tests the add_vertex method with an empty graph.
"""
graph = Graph()
self.assertFalse(graph.contains_vertex('A'), 'The graph does not contain A yet.')
graph.add_vertex('A')
self.assertTrue(graph.contains_vertex('A'), 'The graph now contains A.')
def test_contains_vertex(self):
"""Tests the contains_vertex method with a single vertex.
"""
data = { 'A' : [] }
graph = Graph(graph=data)
self.assertTrue(graph.contains_vertex('A'), 'The graph contains A.')
self.assertFalse(graph.contains_vertex('B'), 'The graph does not contain B.')
def test_remove_edge_undirected(self):
"""Tests the remove_edge method in an undirected graph.
"""
graph = Graph(graph = { 'A' : ['B'], 'B' : ['A'] })
self.assertTrue(graph.has_edge('A', 'B'), 'There is an edge between A and B.')
graph.remove_edge('A', 'B')
self.assertFalse(graph.has_edge('A', 'B'), 'No more edge between A and B.')
def __init__(self):
Graph.__init__(self)
# stop to cluster matching
self.stop_to_cluster = {}
# cluster's name to node id matching
self.cluster_id = {}
def test_remove_unexisting_edge_with_unexisting_vertex(self):
"""Tests the remove_edge method in a graph between an existing vertex and a non-existing one.
"""
graph = Graph(graph = { 'A' : [] })
self.assertFalse(graph.has_edge('A', 'C'), 'There cannot be edge between A and C.')
graph.remove_edge('A', 'C')
self.assertFalse(graph.has_edge('A', 'C'), 'Nothing changed.')
def test_degree(self):
"""Tests the degree methods in a graph.
"""
graph = Graph(graph = { 'A' : ['B', 'C'], 'B' : ['A'], 'C' : [] })
self.assertEqual(graph.interior_degree('A'), 1, 'There is 1 edge coming to A.')
self.assertEqual(graph.exterior_degree('A'), 2, 'There are 2 edges extending from A.')
self.assertEqual(graph.degree('A'), 3, 'There are 3 edges from and to A.')
def test_add_edge_interloper_start():
graph = Graph()
start = Vertex('start')
end = graph.add_node('end')
with pytest.raises(KeyError):
graph.add_edge(start, end)
def run(data):
people = Graph(data, Person, " - ")
groups = people.get_groups_a2()
# hax groups
groups = hax_one_member_grp(people.nodes, groups)
for group in sorted(groups):
print(", ".join(g for g in group))
def test_circular_layout(self):
G = Graph.from_edge_pairs([], num_vertices=4)
expected = np.array([[1,0],[0,1],[-1,0],[0,-1]])
assert_array_almost_equal(G.layout_circle(), expected)
# edge cases
for nv in (0, 1):
G = Graph.from_edge_pairs([], num_vertices=nv)
X = G.layout_circle()
self.assertEqual(X.shape, (nv, 2))
def knightsGraph(board_size=8):
g = Graph()
for row in range(board_size):
for col in range(board_size):
currPos = getNormalizedPos(row, col, board_size)
newPos = getPossiblePositions(row, col, board_size)
for pos in newPos:
g.addEdge(currPos, pos)
return g
def test__graph_get_community_labels_sparse_graph():
login, passwd = get_login_password()
from vkwrapper import Vk
from graphs import Graph
v = Vk(cache=FileCache(), login=login, password=passwd)
g = Graph(v, "148907612")
g.get_community_labels()
def test_it_can_topo_sort_a_graph(self):
n5 = Node(105)
n3 = Node(103, [n5])
n4 = Node(104)
n2 = Node(102, [n3, n4, n5])
n1 = Node(101, [n2, n4])
g = Graph([n1, n2, n3, n4, n5])
topoSorted = g.topo_sort()
r = g.min_path(topoSorted)
self.assertEqual(r, [1, 2, 3, 4, 5])
def read_edge_list_graph(infile):
"""Parse an edge-list formatted graph from `infile`."""
num_vertices = int(infile.readline())
graph = Graph(range(num_vertices))
for line in infile:
source, target = line.split(' ')
graph.add_edge(int(source), int(target))
return graph
def test_graph_get_community_labels():
login, passwd = get_login_password()
from vkwrapper import Vk
from graphs import Graph
v = Vk(cache=FileCache(), login=login, password=passwd)
g = Graph(v, "238696131")
g.get_community_labels()
def test_add_edge_undirected(self):
"""Tests the add_edge method for an undirected graph.
"""
graph = Graph(graph = { 'A' : [], 'B' : [] })
self.assertFalse(graph.has_edge('A', 'B'), 'There is no edge between A and B.')
graph.add_edge('A', 'B')
self.assertTrue(graph.has_edge('A', 'B'), 'There is now an edge between A and B.')
def allMoves(bdSize):
ktGraph = Graph()
for row in range(bdSize):
for col in range(bdSize):
nodeId = posToNodeId(row, col, bdSize)
newPositions = genAllMoves(row, col, bdSize)
for e in newPositions:
nid = posToNodeId(e[0], e[1], bdSize)
ktGraph.addEdge(nodeId, nid)
return ktGraph
def roadsAndLibraries(n, c_lib, c_road, cities):
# Complete this function
if not n:
return 0
if c_lib <= c_road:
return n * c_lib
graph = Graph()
# for _n in range(n):
# graph.addVertex(Vertex(str(_n+1)))
for edge in cities:
try:
graph.addVertex(Vertex(str(edge[0])))
except KeyError:
pass
try:
graph.addVertex(Vertex(str(edge[1])))
except KeyError:
pass
graph.createEdge(str(edge[0]), str(edge[1]))
print graph.degree
subgraphs = graph.listSubGraphs()
print subgraphs
libraries = len(subgraphs) + (n - graph.degree)
roads = 0
for g in subgraphs:
roads += len(g) - 1
return (libraries * c_lib) + (roads * c_road)
def setUp(self):
pairs = np.array([[0, 1], [0, 2], [1, 2], [3, 4]])
adj = [[0, 1, 2, 0, 0], [0, 0, 3, 0, 0], [0, 0, 0, 0, 0],
[0, 0, 0, 0, 4], [0, 0, 0, 0, 0]]
self.graphs = [
Graph.from_edge_pairs(pairs),
Graph.from_edge_pairs(pairs, symmetric=True),
Graph.from_adj_matrix(adj),
Graph.from_adj_matrix(csr_matrix(adj)),
]
self.coords = np.random.random((5, 3))
def knight_graph(board_size):
# Build the graph
graph = Graph()
for row in range(board_size):
for col in range(board_size):
node_id = pos_to_node_id(row, col, board_size)
new_positions = generate_legal_moves(row, col, board_size)
for e in new_positions:
nid = pos_to_node_id(e[0], e[1], board_size)
graph.add_edge(node_id, nid)
return graph
def test_kernelize(self):
graphs = [
Graph.from_edge_pairs(PAIRS),
Graph.from_adj_matrix(ADJ),
Graph.from_adj_matrix(coo_matrix(ADJ)),
Graph.from_adj_matrix(csr_matrix(ADJ)),
]
for G in graphs:
for kernel in ('none', 'binary'):
K = G.kernelize(kernel)
assert_array_equal(K.matrix('dense'), ADJ)
self.assertRaises(ValueError, G.kernelize, 'foobar')
def test_greedy_coloring(self):
pairs = np.array([[0, 1], [0, 2], [1, 0], [1, 2], [2, 0], [2, 1],
[3, 4], [4, 3]])
adj = [[0, 1, 1, 0, 0], [1, 0, 1, 0, 0], [1, 1, 0, 0, 0],
[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]]
test_cases = [
Graph.from_edge_pairs(pairs),
Graph.from_adj_matrix(adj),
Graph.from_adj_matrix(coo_matrix(adj)),
]
for G in test_cases:
assert_array_equal([1, 2, 3, 1, 2], G.color_greedy())
def test_remove_connected_vertex(self):
"""Tests the remove_vertex method for a connected vertex.
"""
data = { 'A' : ['B'], 'B' : ['A'] }
graph = Graph(graph=data)
self.assertTrue('B' in graph.connected_vertex('A'), 'There is an edge between A and B.')
self.assertTrue('A' in graph.connected_vertex('B'), 'There is an edge between A and B.')
graph.remove_vertex('A')
self.assertFalse('A' in graph.connected_vertex('B'), 'No more edge between A and B.')
def test_bicolor_spectral(self):
pairs = np.array([[0, 1], [0, 2], [1, 0], [1, 2], [2, 0], [2, 1],
[2, 3], [3, 2]])
adj = [[0, 1, 1, 0], [1, 0, 1, 0], [1, 1, 0, 1], [0, 0, 1, 0]]
test_cases = [
Graph.from_edge_pairs(pairs),
Graph.from_adj_matrix(adj),
Graph.from_adj_matrix(coo_matrix(adj)),
]
expected = np.array([1, 1, 0, 1], dtype=bool)
for G in test_cases:
assert_array_equal(expected, G.bicolor_spectral())
def knightGraph(bdSize):
ktGraph = Graph()
for row in range(bdSize):
for col in range(bdSize):
#import pdb; pdb.set_trace()
nodeId = posToNodeId(row, col, bdSize)
newPositions = genLegalMoves(row, col, bdSize)
for e in newPositions:
nid = posToNodeId(e[0], e[1], bdSize)
ktGraph.addEdge(nodeId, nid)
# import pdb; pdb.set_trace()
return ktGraph
def test_kernelize(self):
graphs = [
Graph.from_edge_pairs(PAIRS),
Graph.from_adj_matrix(ADJ),
Graph.from_adj_matrix(coo_matrix(ADJ)),
Graph.from_adj_matrix(csr_matrix(ADJ)),
]
for G in graphs:
for kernel in ('none', 'binary'):
K = G.kernelize(kernel)
assert_array_equal(K.matrix('dense'), ADJ)
self.assertRaises(ValueError, G.kernelize, 'foobar')
def dijkstra(G: Graph, s: str) -> Dict[str, List[str]]:
L = {s}
R = set([v for v in G.get_vertices() if v != s])
SD = {v: None for v in G.get_vertices()} # Shortest Distances
parent = {v: v for v in G.get_vertices()}
paths = {v: [] for v in G.get_vertices()}
paths[s] = [s]
dSoFar = []
dSoFarDict = {}
i = 0
# Initialization
dSoFarDict[s] = [0, i, s]
heapq.heappush(dSoFar, [0, i, s])
i += 1
for v in G.get_vertices():
if v != s:
dSoFarDict[v] = [inf, i, v]
heapq.heappush(dSoFar, [inf, i, v])
i += 1
for _ in range(len(SD) - 1):
# Extract min
while dSoFar[0][2] is None:
heapq.heappop(dSoFar)
min_d = heapq.heappop(dSoFar)
vprime = min_d[2]
R.discard(vprime)
L.add(vprime)
SD[vprime] = min_d[0]
# Decrement Key
for z in G[vprime]:
if z in R:
newDistToZ = SD[vprime] + G.get_weight(vprime, z)
if newDistToZ < dSoFarDict[z][0]:
# decrease key
dSoFarDict[z][2] = None
entry = [newDistToZ, i, z]
i += 1
dSoFarDict[z] = entry
heapq.heappush(dSoFar, entry)
# set parent
parent[z] = vprime
# record path
paths[z] = paths[vprime] + [z]
return paths
def incremental_neighbor_graph(X,
precomputed=False,
k=None,
epsilon=None,
weighting='none'):
'''See neighbor_graph.'''
assert ((k is not None)
or (epsilon is not None)), "Must provide `k` or `epsilon`"
assert (_issequence(k) ^ _issequence(epsilon)
), "Exactly one of `k` or `epsilon` must be a sequence."
assert weighting in ('binary',
'none'), "Invalid weighting param: " + weighting
is_weighted = weighting == 'none'
if precomputed:
D = X
else:
D = pairwise_distances(X, metric='euclidean')
# pre-sort for efficiency
order = np.argsort(D)[:, 1:]
if k is None:
k = D.shape[0]
# generate the sequence of graphs
# TODO: convert the core of these loops to Cython for speed
W = np.zeros_like(D)
I = np.arange(D.shape[0])
if _issequence(k):
# varied k, fixed epsilon
if epsilon is not None:
D[D > epsilon] = 0
old_k = 0
for new_k in k:
idx = order[:, old_k:new_k]
dist = D[I, idx.T]
W[I, idx.T] = dist if is_weighted else 1
yield Graph.from_adj_matrix(W)
old_k = new_k
else:
# varied epsilon, fixed k
idx = order[:, :k]
dist = D[I, idx.T].T
old_i = np.zeros(D.shape[0], dtype=int)
for eps in epsilon:
for i, row in enumerate(dist):
oi = old_i[i]
ni = oi + np.searchsorted(row[oi:], eps)
rr = row[oi:ni]
W[i, idx[i, oi:ni]] = rr if is_weighted else 1
old_i[i] = ni
yield Graph.from_adj_matrix(W)
def setUp(self):
pairs = np.array([[0,1],[0,2],[1,2],[3,4]])
adj = [[0,1,2,0,0],
[0,0,3,0,0],
[0,0,0,0,0],
[0,0,0,0,4],
[0,0,0,0,0]]
self.graphs = [
Graph.from_edge_pairs(pairs),
Graph.from_edge_pairs(pairs, symmetric=True),
Graph.from_adj_matrix(adj),
Graph.from_adj_matrix(csr_matrix(adj)),
]
self.coords = np.random.random((5, 3))
def test_locality_preserving_projections(self):
X = np.array([[1,2],[2,1],[3,1.5],[4,0.5],[5,1]])
G = Graph.from_adj_matrix([[0, 1, 1, 0, 0],
[1, 0, 1, 0, 0],
[1, 1, 0, 1, 1],
[0, 0, 1, 0, 1],
[0, 0, 1, 1, 0]])
proj = G.locality_preserving_projections(X, num_dims=1)
assert_array_almost_equal(proj, np.array([[-0.95479113],[0.29727749]]))
# test case with bigger d than n
X = np.hstack((X, X))[:3]
G = Graph.from_adj_matrix(G.matrix()[:3,:3])
proj = G.locality_preserving_projections(X, num_dims=1)
assert_array_almost_equal(proj, np.array([[0.9854859,0.1697574,0,0]]).T)
def test_bicolor_spectral(self):
pairs = np.array([[0,1],[0,2],[1,0],[1,2],[2,0],[2,1],[2,3],[3,2]])
adj = [[0,1,1,0],
[1,0,1,0],
[1,1,0,1],
[0,0,1,0]]
test_cases = [
Graph.from_edge_pairs(pairs),
Graph.from_adj_matrix(adj),
Graph.from_adj_matrix(coo_matrix(adj)),
]
expected = np.array([1,1,0,1], dtype=bool)
for G in test_cases:
assert_array_equal(expected, G.bicolor_spectral())
def test_greedy_coloring(self):
pairs = np.array([[0,1],[0,2],[1,0],[1,2],[2,0],[2,1],[3,4],[4,3]])
adj = [[0,1,1,0,0],
[1,0,1,0,0],
[1,1,0,0,0],
[0,0,0,0,1],
[0,0,0,1,0]]
test_cases = [
Graph.from_edge_pairs(pairs),
Graph.from_adj_matrix(adj),
Graph.from_adj_matrix(coo_matrix(adj)),
]
for G in test_cases:
assert_array_equal([1,2,3,1,2], G.color_greedy())
def run(data):
crossroads = Graph(data, Crossroad)
start = "A"
distances, predecessors = crossroads.bellman_ford(start)
successors = invert_dict(predecessors)
path = start + " - " + successors[start][0]
while (path.count(" - ") + 1) != len(crossroads.nodes):
path = path + " - " + successors[path[-1]][0]
bonuses = 0 # get all bonuses
for node in crossroads.nodes:
if crossroads.nodes[node].has_bonus:
bonuses += path.count(node)
print(path + ":", (-distances[path[-1]]) + bonuses)
def run(data):
start = "Vy"
car = Graph(data, Transformer, " - ", ": ")
endpoints = car.nodes.keys()
res = {}
for endpoint in endpoints:
path, cost = car.dijkstra(start, endpoint)
res[endpoint] = 0 - cost
inverted = invert_dict(res)
weights = sorted(inverted)
for weight in reversed(weights):
for endpoint in sorted(inverted[weight]):
print("{}: {}".format(endpoint, weight))
def incremental_neighbor_graph(X, precomputed=False, k=None, epsilon=None,
weighting='none'):
'''See neighbor_graph.'''
assert ((k is not None) or (epsilon is not None)
), "Must provide `k` or `epsilon`"
assert (_issequence(k) ^ _issequence(epsilon)
), "Exactly one of `k` or `epsilon` must be a sequence."
assert weighting in ('binary','none'), "Invalid weighting param: " + weighting
is_weighted = weighting == 'none'
if precomputed:
D = X
else:
D = pairwise_distances(X, metric='euclidean')
# pre-sort for efficiency
order = np.argsort(D)[:,1:]
if k is None:
k = D.shape[0]
# generate the sequence of graphs
# TODO: convert the core of these loops to Cython for speed
W = np.zeros_like(D)
I = np.arange(D.shape[0])
if _issequence(k):
# varied k, fixed epsilon
if epsilon is not None:
D[D > epsilon] = 0
old_k = 0
for new_k in k:
idx = order[:, old_k:new_k]
dist = D[I, idx.T]
W[I, idx.T] = dist if is_weighted else 1
yield Graph.from_adj_matrix(W)
old_k = new_k
else:
# varied epsilon, fixed k
idx = order[:,:k]
dist = D[I, idx.T].T
old_i = np.zeros(D.shape[0], dtype=int)
for eps in epsilon:
for i, row in enumerate(dist):
oi = old_i[i]
ni = oi + np.searchsorted(row[oi:], eps)
rr = row[oi:ni]
W[i, idx[i,oi:ni]] = rr if is_weighted else 1
old_i[i] = ni
yield Graph.from_adj_matrix(W)
def _slow_neighbor_graph(dist, k, epsilon, binary):
num_pts = dist.shape[0]
if k is not None:
k = min(k+1, num_pts)
nn, not_nn = _min_k_indices(dist, k, inv_ind=True)
I = np.arange(num_pts)
if epsilon is not None:
mask = dist <= epsilon
if k is not None:
mask[I, not_nn.T] = False
if binary:
np.fill_diagonal(mask, False)
W = mask.astype(float)
else:
W = np.where(mask, dist, 0)
else:
inv_mask = np.eye(num_pts, dtype=bool)
inv_mask[I, not_nn.T] = True
if binary:
W = 1.0 - inv_mask
else:
W = np.where(inv_mask, 0, dist)
# W = scipy.sparse.csr_matrix(W)
return Graph.from_adj_matrix(W)
def setUp(self): ii = np.array([0, 0, 1, 2, 2, 3, 3, 3, 4, 5]) jj = np.array([1, 2, 3, 4, 5, 6, 7, 8, 7, 7]) adj = np.zeros((9,9), dtype=int) adj[ii,jj] = 1 adj[jj,ii] = 1 self.G = Graph.from_adj_matrix(adj)
def get_node(self, key):
"""
Override parent's get_node function. (Supported to search by
cluster name , key and instance)
@param data The key
@type data db.Key
@type data int
@type data basestring The key of cluster
"""
if isinstance(key, int):
id = key
else:
if isinstance(key, basestring):
# The name of the cluster
if isinstance(key, unicode):
cluster = str(key)
else:
cluster = key
elif isinstance(key, db.Key):
cluster = key().id_or_name()
else:
cluster = key.key().id_or_name()
id = self.cluster_id[cluster]
return Graph.get_node(self, id)
def sparse_regularized_graph(X, positive=False, sparsity_param=None, kmax=None):
'''Sparse Regularized Graph Construction, commonly known as an l1-graph.
positive : bool, optional
When True, computes the Sparse Probability Graph (SPG).
sparsity_param : float, optional
Controls sparsity cost in the LASSO optimization.
When None, uses cross-validation to find sparsity parameters.
This is very slow, but it gets good results.
kmax : int, optional
When None, allow all points to be edges. Otherwise, restrict to kNN set.
l1-graph: "Semi-supervised Learning by Sparse Representation"
Yan & Wang, SDM 2009
http://epubs.siam.org/doi/pdf/10.1137/1.9781611972795.68
SPG: "Nonnegative Sparse Coding for Discriminative Semi-supervised Learning"
He et al., CVPR 2001
'''
clf, X = _l1_graph_setup(X, positive, sparsity_param)
if kmax is None:
W = _l1_graph_solve_full(clf, X)
else:
W = _l1_graph_solve_k(clf, X, kmax)
return Graph.from_adj_matrix(W)
def manifold_spanning_graph(X, embed_dim, num_ccs=1, verbose=False):
G = neighbor_graph(X, k=1, weighting='binary')
G.symmetrize(method='max')
G = grow_trees(X, G, embed_dim, verbose=verbose)
CC_labels, angle_thresh = join_CCs(X, G, embed_dim, num_ccs=num_ccs,
verbose=verbose)
adj = G.matrix('dense')
if num_ccs == 1:
G = flesh_out(X, adj, embed_dim, CC_labels, angle_thresh=angle_thresh,
min_shortcircuit=embed_dim+1, verbose=verbose)
else:
n, labels = G.connected_components(return_labels=True)
for i in range(n):
mask = labels==i
if verbose: # pragma: no cover
print('CC', i, 'has size', np.count_nonzero(mask))
idx = np.ix_(mask, mask)
_, tmp_labels = np.unique(CC_labels[mask], return_inverse=True)
adj[idx] = flesh_out(X[mask], adj[idx], embed_dim, tmp_labels,
angle_thresh=angle_thresh,
min_shortcircuit=embed_dim+1,
verbose=verbose).matrix()
G = Graph.from_adj_matrix(adj)
return G
def permute_graph(G, order): '''Reorder the graph's vertices, returning a copy of the input graph. order : integer array-like, some permutation of range(G.num_vertices()). ''' adj = G.matrix(dense=True) adj = adj[np.ix_(order, order)] return Graph.from_adj_matrix(adj)
def _make_blob_graphs(self, k=11): pts = np.random.random(size=(20, 2)) pts[10:] += 2 labels = np.zeros(20) labels[10:] = 1 G_sparse = neighbor_graph(pts, k=k).symmetrize() G_dense = Graph.from_adj_matrix(G_sparse.matrix(dense=True)) return (G_sparse, G_dense), labels
def test_laplacian_eigenmaps(self): # Test a simple chain graph expected = np.array([0.5, 0.5, 0., -0.5, -0.5]) W = np.zeros((5,5)) + np.diag(np.ones(4), k=1) + np.diag(np.ones(4), k=-1) G = Graph.from_adj_matrix(W) Y = G.laplacian_eigenmaps(num_dims=1) self.assertEqual(Y.shape, (5, 1)) assert_signless_array_almost_equal(Y[:,0], expected) # Test num_dims=None case Y = G.laplacian_eigenmaps() self.assertEqual(Y.shape, (5, 4)) assert_signless_array_almost_equal(Y[:,0], expected) # Test sparse case G = Graph.from_adj_matrix(csr_matrix(W)) Y = G.laplacian_eigenmaps(num_dims=1) self.assertEqual(Y.shape, (5, 1)) assert_signless_array_almost_equal(Y[:,0], expected)
def concat_trajectories(traj_lengths, directed=False):
P = []
last_idx = 0
for tl in traj_lengths:
P.append(last_idx + _traj_pair_idxs(tl))
last_idx += tl
return Graph.from_edge_pairs(np.vstack(P), num_vertices=last_idx,
symmetric=(not directed))
