238 lines
7.7 KiB
Python
238 lines
7.7 KiB
Python
import numpy as np
|
|
from numpy.testing import assert_array_almost_equal
|
|
from sklearn.neighbors.kd_tree import (KDTree, NeighborsHeap,
|
|
simultaneous_sort, kernel_norm,
|
|
nodeheap_sort, DTYPE, ITYPE)
|
|
from sklearn.neighbors.dist_metrics import DistanceMetric
|
|
from sklearn.utils.testing import SkipTest, assert_allclose
|
|
|
|
V = np.random.random((3, 3))
|
|
V = np.dot(V, V.T)
|
|
|
|
DIMENSION = 3
|
|
|
|
METRICS = {'euclidean': {},
|
|
'manhattan': {},
|
|
'chebyshev': {},
|
|
'minkowski': dict(p=3)}
|
|
|
|
|
|
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 test_kd_tree_query():
|
|
np.random.seed(0)
|
|
X = np.random.random((40, DIMENSION))
|
|
Y = np.random.random((10, DIMENSION))
|
|
|
|
def check_neighbors(dualtree, breadth_first, k, metric, kwargs):
|
|
kdt = KDTree(X, leaf_size=1, metric=metric, **kwargs)
|
|
dist1, ind1 = kdt.query(Y, k, dualtree=dualtree,
|
|
breadth_first=breadth_first)
|
|
dist2, ind2 = brute_force_neighbors(X, Y, k, metric, **kwargs)
|
|
|
|
# don't check indices here: if there are any duplicate distances,
|
|
# the indices may not match. Distances should not have this problem.
|
|
assert_array_almost_equal(dist1, dist2)
|
|
|
|
for (metric, kwargs) in METRICS.items():
|
|
for k in (1, 3, 5):
|
|
for dualtree in (True, False):
|
|
for breadth_first in (True, False):
|
|
yield (check_neighbors,
|
|
dualtree, breadth_first,
|
|
k, metric, kwargs)
|
|
|
|
|
|
def test_kd_tree_query_radius(n_samples=100, n_features=10):
|
|
np.random.seed(0)
|
|
X = 2 * np.random.random(size=(n_samples, n_features)) - 1
|
|
query_pt = np.zeros(n_features, dtype=float)
|
|
|
|
eps = 1E-15 # roundoff error can cause test to fail
|
|
kdt = KDTree(X, leaf_size=5)
|
|
rad = np.sqrt(((X - query_pt) ** 2).sum(1))
|
|
|
|
for r in np.linspace(rad[0], rad[-1], 100):
|
|
ind = kdt.query_radius([query_pt], r + eps)[0]
|
|
i = np.where(rad <= r + eps)[0]
|
|
|
|
ind.sort()
|
|
i.sort()
|
|
|
|
assert_array_almost_equal(i, ind)
|
|
|
|
|
|
def test_kd_tree_query_radius_distance(n_samples=100, n_features=10):
|
|
np.random.seed(0)
|
|
X = 2 * np.random.random(size=(n_samples, n_features)) - 1
|
|
query_pt = np.zeros(n_features, dtype=float)
|
|
|
|
eps = 1E-15 # roundoff error can cause test to fail
|
|
kdt = KDTree(X, leaf_size=5)
|
|
rad = np.sqrt(((X - query_pt) ** 2).sum(1))
|
|
|
|
for r in np.linspace(rad[0], rad[-1], 100):
|
|
ind, dist = kdt.query_radius([query_pt], r + eps, return_distance=True)
|
|
|
|
ind = ind[0]
|
|
dist = dist[0]
|
|
|
|
d = np.sqrt(((query_pt - X[ind]) ** 2).sum(1))
|
|
|
|
assert_array_almost_equal(d, dist)
|
|
|
|
|
|
def compute_kernel_slow(Y, X, kernel, h):
|
|
d = np.sqrt(((Y[:, None, :] - X) ** 2).sum(-1))
|
|
norm = kernel_norm(h, X.shape[1], kernel)
|
|
|
|
if kernel == 'gaussian':
|
|
return norm * np.exp(-0.5 * (d * d) / (h * h)).sum(-1)
|
|
elif kernel == 'tophat':
|
|
return norm * (d < h).sum(-1)
|
|
elif kernel == 'epanechnikov':
|
|
return norm * ((1.0 - (d * d) / (h * h)) * (d < h)).sum(-1)
|
|
elif kernel == 'exponential':
|
|
return norm * (np.exp(-d / h)).sum(-1)
|
|
elif kernel == 'linear':
|
|
return norm * ((1 - d / h) * (d < h)).sum(-1)
|
|
elif kernel == 'cosine':
|
|
return norm * (np.cos(0.5 * np.pi * d / h) * (d < h)).sum(-1)
|
|
else:
|
|
raise ValueError('kernel not recognized')
|
|
|
|
|
|
def test_kd_tree_kde(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))
|
|
kdt = KDTree(X, leaf_size=10)
|
|
|
|
for kernel in ['gaussian', 'tophat', 'epanechnikov',
|
|
'exponential', 'linear', 'cosine']:
|
|
for h in [0.01, 0.1, 1]:
|
|
dens_true = compute_kernel_slow(Y, X, kernel, h)
|
|
|
|
def check_results(kernel, h, atol, rtol, breadth_first):
|
|
dens = kdt.kernel_density(Y, h, atol=atol, rtol=rtol,
|
|
kernel=kernel,
|
|
breadth_first=breadth_first)
|
|
assert_allclose(dens, dens_true, atol=atol,
|
|
rtol=max(rtol, 1e-7))
|
|
|
|
for rtol in [0, 1E-5]:
|
|
for atol in [1E-6, 1E-2]:
|
|
for breadth_first in (True, False):
|
|
yield (check_results, kernel, h, atol, rtol,
|
|
breadth_first)
|
|
|
|
|
|
def test_gaussian_kde(n_samples=1000):
|
|
# Compare gaussian KDE results to scipy.stats.gaussian_kde
|
|
from scipy.stats import gaussian_kde
|
|
np.random.seed(0)
|
|
x_in = np.random.normal(0, 1, n_samples)
|
|
x_out = np.linspace(-5, 5, 30)
|
|
|
|
for h in [0.01, 0.1, 1]:
|
|
kdt = KDTree(x_in[:, None])
|
|
try:
|
|
gkde = gaussian_kde(x_in, bw_method=h / np.std(x_in))
|
|
except TypeError:
|
|
raise SkipTest("Old scipy, does not accept explicit bandwidth.")
|
|
|
|
dens_kdt = kdt.kernel_density(x_out[:, None], h) / n_samples
|
|
dens_gkde = gkde.evaluate(x_out)
|
|
|
|
assert_array_almost_equal(dens_kdt, dens_gkde, decimal=3)
|
|
|
|
|
|
def test_kd_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)
|
|
kdt = KDTree(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 = kdt.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_kd_tree_pickle():
|
|
import pickle
|
|
np.random.seed(0)
|
|
X = np.random.random((10, 3))
|
|
kdt1 = KDTree(X, leaf_size=1)
|
|
ind1, dist1 = kdt1.query(X)
|
|
|
|
def check_pickle_protocol(protocol):
|
|
s = pickle.dumps(kdt1, protocol=protocol)
|
|
kdt2 = pickle.loads(s)
|
|
ind2, dist2 = kdt2.query(X)
|
|
assert_array_almost_equal(ind1, ind2)
|
|
assert_array_almost_equal(dist1, dist2)
|
|
|
|
for protocol in (0, 1, 2):
|
|
yield check_pickle_protocol, protocol
|
|
|
|
|
|
def test_neighbors_heap(n_pts=5, n_nbrs=10):
|
|
heap = NeighborsHeap(n_pts, n_nbrs)
|
|
|
|
for row in range(n_pts):
|
|
d_in = np.random.random(2 * n_nbrs).astype(DTYPE)
|
|
i_in = np.arange(2 * n_nbrs, dtype=ITYPE)
|
|
for d, i in zip(d_in, i_in):
|
|
heap.push(row, d, i)
|
|
|
|
ind = np.argsort(d_in)
|
|
d_in = d_in[ind]
|
|
i_in = i_in[ind]
|
|
|
|
d_heap, i_heap = heap.get_arrays(sort=True)
|
|
|
|
assert_array_almost_equal(d_in[:n_nbrs], d_heap[row])
|
|
assert_array_almost_equal(i_in[:n_nbrs], i_heap[row])
|
|
|
|
|
|
def test_node_heap(n_nodes=50):
|
|
vals = np.random.random(n_nodes).astype(DTYPE)
|
|
|
|
i1 = np.argsort(vals)
|
|
vals2, i2 = nodeheap_sort(vals)
|
|
|
|
assert_array_almost_equal(i1, i2)
|
|
assert_array_almost_equal(vals[i1], vals2)
|
|
|
|
|
|
def test_simultaneous_sort(n_rows=10, n_pts=201):
|
|
dist = np.random.random((n_rows, n_pts)).astype(DTYPE)
|
|
ind = (np.arange(n_pts) + np.zeros((n_rows, 1))).astype(ITYPE)
|
|
|
|
dist2 = dist.copy()
|
|
ind2 = ind.copy()
|
|
|
|
# simultaneous sort rows using function
|
|
simultaneous_sort(dist, ind)
|
|
|
|
# simultaneous sort rows using numpy
|
|
i = np.argsort(dist2, axis=1)
|
|
row_ind = np.arange(n_rows)[:, None]
|
|
dist2 = dist2[row_ind, i]
|
|
ind2 = ind2[row_ind, i]
|
|
|
|
assert_array_almost_equal(dist, dist2)
|
|
assert_array_almost_equal(ind, ind2)
|