def test_input_data_size():
# Regression test for #6288
# Previoulsly, a metric requiring a particular input dimension would fail
def custom_metric(x, y):
assert x.shape[0] == 3
return np.sum((x - y) ** 2)
rng = check_random_state(0)
X = rng.rand(10, 3)
pyfunc = DistanceMetric.get_metric("pyfunc", func=dist_func, p=2)
eucl = DistanceMetric.get_metric("euclidean")
assert_array_almost_equal(pyfunc.pairwise(X), eucl.pairwise(X))
def test_pyfunc_metric():
def dist_func(x1, x2, p):
return np.sum((x1 - x2) ** p) ** (1. / p)
X = np.random.random((10, 3))
euclidean = DistanceMetric.get_metric("euclidean")
pyfunc = DistanceMetric.get_metric("pyfunc", func=dist_func, p=2)
D1 = euclidean.pairwise(X)
D2 = pyfunc.pairwise(X)
assert_allclose(D1, D2)
def check_pdist_bool(metric, D_true):
dm = DistanceMetric.get_metric(metric)
D12 = dm.pairwise(X1_bool)
# Based on https://github.com/scipy/scipy/pull/7373
# When comparing two all-zero vectors, scipy>=1.2.0 jaccard metric
# was changed to return 0, instead of nan.
if metric == 'jaccard' and LooseVersion(scipy_version) < '1.2.0':
D_true[np.isnan(D_true)] = 0
assert_array_almost_equal(D12, D_true)
def test_pyfunc_metric():
X = np.random.random((10, 3))
euclidean = DistanceMetric.get_metric("euclidean")
pyfunc = DistanceMetric.get_metric("pyfunc", func=dist_func, p=2)
# Check if both callable metric and predefined metric initialized
# DistanceMetric object is picklable
euclidean_pkl = pickle.loads(pickle.dumps(euclidean))
pyfunc_pkl = pickle.loads(pickle.dumps(pyfunc))
D1 = euclidean.pairwise(X)
D2 = pyfunc.pairwise(X)
D1_pkl = euclidean_pkl.pairwise(X)
D2_pkl = pyfunc_pkl.pairwise(X)
assert_array_almost_equal(D1, D2)
assert_array_almost_equal(D1_pkl, D2_pkl)
def test_kd_tree_two_point(dualtree):
n_samples, n_features = (100, 3)
rng = check_random_state(0)
X = rng.random_sample((n_samples, n_features))
Y = rng.random_sample((n_samples, n_features))
r = np.linspace(0, 1, 10)
kdt = KDTree(X, leaf_size=10)
D = DistanceMetric.get_metric("euclidean").pairwise(Y, X)
counts_true = [(D <= ri).sum() for ri in r]
counts = kdt.two_point_correlation(Y, r=r, dualtree=dualtree)
assert_array_almost_equal(counts, counts_true)
def test_ball_tree_two_point(n_samples=100, n_features=3):
np.random.seed(0)
X = np.random.random((n_samples, n_features))
Y = np.random.random((n_samples, n_features))
r = np.linspace(0, 1, 10)
bt = BallTree(X, leaf_size=10)
D = DistanceMetric.get_metric("euclidean").pairwise(Y, X)
counts_true = [(D <= ri).sum() for ri in r]
def check_two_point(r, dualtree):
counts = bt.two_point_correlation(Y, r=r, dualtree=dualtree)
assert_array_almost_equal(counts, counts_true)
for dualtree in (True, False):
yield check_two_point, r, dualtree
def test_haversine_metric():
def haversine_slow(x1, x2):
return 2 * np.arcsin(np.sqrt(np.sin(0.5 * (x1[0] - x2[0])) ** 2
+ np.cos(x1[0]) * np.cos(x2[0]) *
np.sin(0.5 * (x1[1] - x2[1])) ** 2))
X = np.random.random((10, 2))
haversine = DistanceMetric.get_metric("haversine")
D1 = haversine.pairwise(X)
D2 = np.zeros_like(D1)
for i, x1 in enumerate(X):
for j, x2 in enumerate(X):
D2[i, j] = haversine_slow(x1, x2)
assert_array_almost_equal(D1, D2)
assert_array_almost_equal(haversine.dist_to_rdist(D1),
np.sin(0.5 * D2) ** 2)
def check_pickle(metric, kwargs):
dm = DistanceMetric.get_metric(metric, **kwargs)
D1 = dm.pairwise(X1)
dm2 = pickle.loads(pickle.dumps(dm))
D2 = dm2.pairwise(X1)
assert_array_almost_equal(D1, D2)
def test_pickle_bool_metrics(metric):
dm = DistanceMetric.get_metric(metric)
D1 = dm.pairwise(X1_bool)
dm2 = pickle.loads(pickle.dumps(dm))
D2 = dm2.pairwise(X1_bool)
assert_array_almost_equal(D1, D2)
def check_pdist(self, metric, kwargs, D_true):
if metric == 'canberra' and cmp_version(scipy.__version__, '0.9') <= 0:
raise SkipTest("Canberra distance incorrect in scipy < 0.9")
dm = DistanceMetric.get_metric(metric, **kwargs)
D12 = dm.pairwise(self.X1)
assert_allclose(D12, D_true)
def check_cdist(self, metric, kwargs, D_true):
dm = DistanceMetric.get_metric(metric, **kwargs)
D12 = dm.pairwise(self.X1, self.X2)
assert_array_almost_equal(D12, D_true)
def check_pickle_bool(self, metric):
dm = DistanceMetric.get_metric(metric)
D1 = dm.pairwise(self.X1_bool)
dm2 = pickle.loads(pickle.dumps(dm))
D2 = dm2.pairwise(self.X1_bool)
assert_array_almost_equal(D1, D2)
def check_cdist(self, metric, kwargs, D_true):
if metric == "canberra" and cmp_version(scipy.__version__, "0.9") <= 0:
raise SkipTest("Canberra distance incorrect in scipy < 0.9")
dm = DistanceMetric.get_metric(metric, **kwargs)
D12 = dm.pairwise(self.X1, self.X2)
assert_array_almost_equal(D12, D_true)
def compute_distances():
# Load IXP-GST positions
altitude = 1150
min_elev = 40
orbits = 32
sat_per_orbit = 50
inclination = 53
gst_file = "data/raw/ixp_geolocation.csv"
src_file = "data/raw/WUP2018-F22-Cities_Over_300K_Annual.csv"
# Load geo information
sat_pos, gst_pos, src_pos = load_locations(altitude,
orbits,
sat_per_orbit,
inclination,
gst_file,
src_file,
time=15000)
lon_sort_idx_src = np.argsort(src_pos[:, 1])
src_pos = (src_pos[lon_sort_idx_src])
# Remove SRCs that are too high in latitude
higher = np.where(src_pos[:, 0] > 56)[0]
src_pos = np.delete(src_pos, higher, axis=0)
lon_sort_idx_gst = np.argsort(gst_pos[:, 1])
gst_pos = (gst_pos[lon_sort_idx_gst])
# %%
sat_sat_dist = compute_sat_sat_distance(sat_pos, altitude, orbits,
sat_per_orbit)
# Compute the BallTree for the satellites. This gives nn to satellites.
sat_tree = BallTree(np.deg2rad(sat_pos),
metric=DistanceMetric.get_metric("haversine"))
# Get the satellites that are in reach for the ground stations
# and their distance.
sat_gst_ind_city, sat_gst_dist_city = compute_gst_sat_distance(
altitude, min_elev, src_pos, sat_tree)
src_src_satellite = gsts_optimization(sat_gst_ind_city,
sat_gst_dist_city,
sat_sat_dist,
n_gsts=src_pos.shape[0])
src_src_latency = src_src_satellite / LIGHT_IN_VACUUM
# %%
sat_gst_ind_ixp, sat_gst_dist_ixp = compute_gst_sat_distance(
altitude, min_elev, gst_pos, sat_tree)
gst_gst_satellite = gsts_optimization(sat_gst_ind_ixp,
sat_gst_dist_ixp,
sat_sat_dist,
n_gsts=gst_pos.shape[0])
src_gst_ind, src_gst_dist = src_nearest_gst_distance(src_pos, gst_pos)
n_src = src_pos.shape[0]
src_gst_latency = compute_src_dst_latency(n_src, [], src_gst_ind,
src_gst_dist, [], [],
gst_gst_satellite)
return src_gst_latency, src_src_latency, src_pos
def check_pdist_bool(self, metric, D_true):
dm = DistanceMetric.get_metric(metric)
D12 = dm.pairwise(self.X1_bool)
assert_allclose(D12, D_true)
def check_pdist(metric, kwargs, D_true):
dm = DistanceMetric.get_metric(metric, **kwargs)
D12 = dm.pairwise(X1)
assert_array_almost_equal(D12, D_true)
def plot_absolute(src_gst_latency, src_src_latency, src_pos):
triu = np.triu_indices(src_gst_latency.shape[0], 1)
ixp_routed = np.around(src_gst_latency[triu], 6)
city_gst = np.around(src_src_latency[triu], 6)
SCALING = 1e3
plt.figure(figsize=(8, 6))
pairwise_src = DistanceMetric.pairwise(
DistanceMetric.get_metric("haversine"), np.deg2rad(src_pos),
np.deg2rad(src_pos))
pairwise_src = pairwise_src * EARTH_RADIUS
pairwise = pairwise_src[triu]
vals, avg_c, min_c, max_c, _ = vector_map_statistics(
pairwise, city_gst, 10)
avg_c = np.asarray(avg_c) * SCALING
min_c = np.asarray(min_c) * SCALING
max_c = np.asarray(max_c) * SCALING
plt.plot(vals, avg_c, label="Average city-city", linewidth=3)
plt.xlabel("SRC-DST distance (km)")
plt.ylabel("Latency (s)")
plt.legend(loc=2)
pairwise = pairwise_src[triu]
vals, avg_g, min_g, max_g, _ = vector_map_statistics(
pairwise, ixp_routed, 10)
avg_g = np.asarray(avg_g) * SCALING
min_g = np.asarray(min_g) * SCALING
max_g = np.asarray(max_g) * SCALING
plt.plot(vals, avg_g, label="Average IXP-city", linewidth=3)
plt.plot(vals,
vals / LIGHT_IN_FIBER * SCALING,
':',
linewidth=3,
label="Great-circle in fiber")
plt.plot(vals,
vals / LIGHT_IN_VACUUM * SCALING,
'--',
label="Great-circle in vacuum",
linewidth=3)
plt.plot(vals,
vals * FIBER_PATH_STRETCH / LIGHT_IN_FIBER * SCALING,
'-.',
label="Path-stretch in fiber",
linewidth=3)
plt.ylim(0, 150)
plt.xlim(0, np.max(vals))
plt.xlabel("SRC-DST great-circle distance (km)")
plt.ylabel("One-way latency (s)")
plt.legend(loc=9, ncol=2, mode="expand")
# Save figures
# plt.savefig("figures/latency-distance.pdf")
plt.savefig("figures/latency-distance.png")
def test_pickle_bool_metrics(metric):
dm = DistanceMetric.get_metric(metric)
D1 = dm.pairwise(X1_bool)
dm2 = pickle.loads(pickle.dumps(dm))
D2 = dm2.pairwise(X1_bool)
assert_array_almost_equal(D1, D2)
def check_cdist(self, metric, kwargs, D_true):
dm = DistanceMetric.get_metric(metric, **kwargs)
D12 = dm.pairwise(self.X1, self.X2)
assert_array_almost_equal(D12, D_true)
def check_pickle_bool(self, metric):
dm = DistanceMetric.get_metric(metric)
D1 = dm.pairwise(self.X1_bool)
dm2 = pickle.loads(pickle.dumps(dm))
D2 = dm2.pairwise(self.X1_bool)
assert_array_almost_equal(D1, D2)
def brute_force_neighbors(X, Y, k, metric, **kwargs):
D = DistanceMetric.get_metric(metric, **kwargs).pairwise(Y, X)
ind = np.argsort(D, axis=1)[:, :k]
dist = D[np.arange(Y.shape[0])[:, None], ind]
return dist, ind
# def dist_func(a, b):
# alpha = 1
# return np.sqrt((a.x - b.x)**2 +
# (a.y - b.y)**2 +
# alpha*(a.theta - b.theta)**2)
def dist_func(a, b):
alpha = 1
return np.sqrt((a[0] - b[0])**2 + (a[1] - b[1])**2 + alpha *
(a[2] - b[2])**2)
pyfunc = DistanceMetric.get_metric("pyfunc", func=dist_func)
model_states, X = make_states()
for i in range(X.shape[0]):
print(X[i, :])
print("TREE TIME")
tree = KDTree(X, leaf_size=4, metric="euclidean")
pts = np.array([(0, 0, 0)])
dist, ind = tree.query(pts, k=1)
for i in ind:
print(X[i])
print(np.asscalar(i))
print(model_states[np.asscalar(i)])
# print(dist)
# print(KDTree.valid_metrics)
# a = np.empty((5, 5, 3))
def check_pickle(metric, kwargs):
dm = DistanceMetric.get_metric(metric, **kwargs)
D1 = dm.pairwise(X1)
dm2 = pickle.loads(pickle.dumps(dm))
D2 = dm2.pairwise(X1)
assert_array_almost_equal(D1, D2)
def plot_relative(src_gst_latency, src_src_latency, src_pos):
triu = np.triu_indices(src_gst_latency.shape[0], 1)
ixp_routed = np.around(src_gst_latency[triu], 6)
city_gst = np.around(src_src_latency[triu], 6)
pairwise_src = DistanceMetric.pairwise(
DistanceMetric.get_metric("haversine"), np.deg2rad(src_pos),
np.deg2rad(src_pos))
pairwise_src = pairwise_src * EARTH_RADIUS
percent = (ixp_routed - city_gst) / city_gst * 100
pairwise = pairwise_src[triu]
vals, avg_c, min_c, max_c, percent = vector_map_statistics(
pairwise, percent, 100, [25, 75])
colors = plt.rcParams['axes.prop_cycle'].by_key()['color']
cur_color = colors[0]
plt.figure(figsize=(8, 6))
gs1 = gridspec.GridSpec(2, 1)
gs1.update(wspace=0.01, hspace=0.11) # set the spacing between axes.
axes = [plt.subplot(gs1[0]), plt.subplot(gs1[1])]
axes[0].axhline(0, c='grey', linewidth=0.5)
axes[0].semilogy(vals, avg_c, label="Average", c=cur_color, linewidth=3)
axes[0].semilogy(vals,
percent[25],
"--",
label="Quartiles",
c=cur_color,
linewidth=3)
axes[0].semilogy(vals, percent[75], "--", c=cur_color, linewidth=3)
axes[0].plot(vals,
max_c,
":",
linewidth=3,
label="Min-max variability",
c=cur_color)
axes[0].set_ylim(90, 1000)
axes[0].set_ylabel("log-scale")
axes[0].set_xticks([])
axes[0].legend()
axes[1].axhline(0, c='grey', linewidth=0.5)
axes[1].plot(vals,
avg_c,
label="Average city-city",
c=cur_color,
linewidth=3)
axes[1].plot(vals,
percent[25],
"--",
label="Quartiles",
c=cur_color,
linewidth=3)
axes[1].plot(vals, percent[75], "--", c=cur_color, linewidth=3)
axes[1].plot(vals,
max_c,
":",
linewidth=3,
label="Min-max variability",
c=cur_color)
axes[1].plot(vals,
min_c,
":",
linewidth=3,
label="Min-max variability",
c=cur_color)
axes[1].set_xlabel("SRC-DST great-circle distance (km)")
axes[1].set_ylabel("Loss IXP deployment (%)")
# axes[1].set_ylabel("Latency increase IXP deployment (%)")
axes[1].set_ylim(-50, 90)
plt.savefig("figures/percent-ixp-loss.png")
def check_cdist_bool(metric, D_true):
dm = DistanceMetric.get_metric(metric)
D12 = dm.pairwise(X1_bool, X2_bool)
assert_array_almost_equal(D12, D_true)
def check_cdist_bool(metric, D_true):
dm = DistanceMetric.get_metric(metric)
D12 = dm.pairwise(X1_bool, X2_bool)
assert_array_almost_equal(D12, D_true)
def check_pdist(metric, kwargs, D_true):
dm = DistanceMetric.get_metric(metric, **kwargs)
D12 = dm.pairwise(X1)
assert_array_almost_equal(D12, D_true)
def check_pdist(self, metric, kwargs, D_true):
if metric == 'canberra' and cmp_version(scipy.__version__, '0.9') <= 0:
raise SkipTest("Canberra distance incorrect in scipy < 0.9")
dm = DistanceMetric.get_metric(metric, **kwargs)
D12 = dm.pairwise(self.X1)
assert_array_almost_equal(D12, D_true)
def brute_force_neighbors(X, Y, k, metric, **kwargs):
D = DistanceMetric.get_metric(metric, **kwargs).pairwise(Y, X)
ind = np.argsort(D, axis=1)[:, :k]
dist = D[np.arange(Y.shape[0])[:, None], ind]
return dist, ind
""" Retrieve the row of a condensed matrix from the x index of its corresponding square matrix. """
row = np.empty(shape=(n, ), dtype=cndsd_matrix.dtype)
for y in range(n):
if y == x:
row[y] = 0
continue
row[y] = square_idx_to_condensed(cndsd_matrix, x, y, n)
return row
def square_rows_idx_to_condensed_rows(cndsd_matrix, indexes, n):
""" Retrieve the rows of a condensed matrix from the indexes x indexes of its corresponding square matrix. """
rows = np.empty(shape=(n, len(indexes)), dtype=cndsd_matrix.dtype)
for i, x in enumerate(indexes):
row = square_row_idx_to_condensed_row(cndsd_matrix, x, n)
rows[:, i] = row
return rows
if __name__ == "__main__":
data = load_iris().data[:5, :]
distance_matrix = DistanceMetric.get_metric("euclidean").pairwise(data)
distance_matrix_condensed = scipy.spatial.distance.pdist(data, "euclidean")
x, y = 2, None
print(distance_matrix[x, :])
print(
square_row_idx_to_condensed_row(distance_matrix_condensed,
x,
n=distance_matrix.shape[0]))
