# Copyright Anne M. Archibald 2008
# Released under the scipy license
from numpy.testing import (assert_equal, assert_array_equal, assert_,
assert_almost_equal, assert_array_almost_equal)
from pytest import raises as assert_raises
import pytest
from platform import python_implementation
import numpy as np
from scipy.spatial import KDTree, Rectangle, distance_matrix, cKDTree
from scipy.spatial.ckdtree import cKDTreeNode
from scipy.spatial import minkowski_distance
import itertools
def distance_box(a, b, p, boxsize):
diff = a - b
diff[diff > 0.5 * boxsize] -= boxsize
diff[diff < -0.5 * boxsize] += boxsize
d = minkowski_distance(diff, 0, p)
return d
class ConsistencyTests:
def distance(self, a, b, p):
return minkowski_distance(a, b, p)
def test_nearest(self):
x = self.x
d, i = self.kdtree.query(x, 1)
assert_almost_equal(d**2,np.sum((x-self.data[i])**2))
eps = 1e-8
assert_(np.all(np.sum((self.data-x[np.newaxis,:])**2,axis=1) > d**2-eps))
def test_m_nearest(self):
x = self.x
m = self.m
dd, ii = self.kdtree.query(x, m)
d = np.amax(dd)
i = ii[np.argmax(dd)]
assert_almost_equal(d**2,np.sum((x-self.data[i])**2))
eps = 1e-8
assert_equal(np.sum(np.sum((self.data-x[np.newaxis,:])**2,axis=1) < d**2+eps),m)
def test_points_near(self):
x = self.x
d = self.d
dd, ii = self.kdtree.query(x, k=self.kdtree.n, distance_upper_bound=d)
eps = 1e-8
hits = 0
for near_d, near_i in zip(dd,ii):
if near_d == np.inf:
continue
hits += 1
assert_almost_equal(near_d**2,np.sum((x-self.data[near_i])**2))
assert_(near_d < d+eps, "near_d=%g should be less than %g" % (near_d,d))
assert_equal(np.sum(self.distance(self.data,x,2) < d**2+eps),hits)
def test_points_near_l1(self):
x = self.x
d = self.d
dd, ii = self.kdtree.query(x, k=self.kdtree.n, p=1, distance_upper_bound=d)
eps = 1e-8
hits = 0
for near_d, near_i in zip(dd,ii):
if near_d == np.inf:
continue
hits += 1
assert_almost_equal(near_d,self.distance(x,self.data[near_i],1))
assert_(near_d < d+eps, "near_d=%g should be less than %g" % (near_d,d))
assert_equal(np.sum(self.distance(self.data,x,1) < d+eps),hits)
def test_points_near_linf(self):
x = self.x
d = self.d
dd, ii = self.kdtree.query(x, k=self.kdtree.n, p=np.inf, distance_upper_bound=d)
eps = 1e-8
hits = 0
for near_d, near_i in zip(dd,ii):
if near_d == np.inf:
continue
hits += 1
assert_almost_equal(near_d,self.distance(x,self.data[near_i],np.inf))
assert_(near_d < d+eps, "near_d=%g should be less than %g" % (near_d,d))
assert_equal(np.sum(self.distance(self.data,x,np.inf) < d+eps),hits)
def test_approx(self):
x = self.x
k = self.k
eps = 0.1
d_real, i_real = self.kdtree.query(x, k)
d, i = self.kdtree.query(x, k, eps=eps)
assert_(np.all(d <= d_real*(1+eps)))
class Test_random(ConsistencyTests):
def setup_method(self):
self.n = 100
self.m = 4
np.random.seed(1234)
self.data = np.random.randn(self.n, self.m)
self.kdtree = KDTree(self.data,leafsize=2)
self.x = np.random.randn(self.m)
self.d = 0.2
self.k = 10
class Test_random_far(Test_random):
def setup_method(self):
Test_random.setup_method(self)
self.x = np.random.randn(self.m)+10
class Test_small(ConsistencyTests):
def setup_method(self):
self.data = np.array([[0,0,0],
[0,0,1],
[0,1,0],
[0,1,1],
[1,0,0],
[1,0,1],
[1,1,0],
[1,1,1]])
self.kdtree = KDTree(self.data)
self.n = self.kdtree.n
self.m = self.kdtree.m
np.random.seed(1234)
self.x = np.random.randn(3)
self.d = 0.5
self.k = 4
def test_nearest(self):
assert_array_equal(
self.kdtree.query((0,0,0.1), 1),
(0.1,0))
def test_nearest_two(self):
assert_array_equal(
self.kdtree.query((0,0,0.1), 2),
([0.1,0.9],[0,1]))
class Test_small_nonleaf(Test_small):
def setup_method(self):
Test_small.setup_method(self)
self.kdtree = KDTree(self.data,leafsize=1)
class Test_small_compiled(Test_small):
def setup_method(self):
Test_small.setup_method(self)
self.kdtree = cKDTree(self.data)
class Test_small_nonleaf_compiled(Test_small):
def setup_method(self):
Test_small.setup_method(self)
self.kdtree = cKDTree(self.data,leafsize=1)
class Test_random_compiled(Test_random):
def setup_method(self):
Test_random.setup_method(self)
self.kdtree = cKDTree(self.data)
class Test_random_far_compiled(Test_random_far):
def setup_method(self):
Test_random_far.setup_method(self)
self.kdtree = cKDTree(self.data)
class Test_vectorization:
def setup_method(self):
self.data = np.array([[0,0,0],
[0,0,1],
[0,1,0],
[0,1,1],
[1,0,0],
[1,0,1],
[1,1,0],
[1,1,1]])
self.kdtree = KDTree(self.data)
def test_single_query(self):
d, i = self.kdtree.query(np.array([0,0,0]))
assert_(isinstance(d,float))
assert_(np.issubdtype(i, np.signedinteger))
def test_vectorized_query(self):
d, i = self.kdtree.query(np.zeros((2,4,3)))
assert_equal(np.shape(d),(2,4))
assert_equal(np.shape(i),(2,4))
def test_single_query_multiple_neighbors(self):
s = 23
kk = self.kdtree.n+s
d, i = self.kdtree.query(np.array([0,0,0]),k=kk)
assert_equal(np.shape(d),(kk,))
assert_equal(np.shape(i),(kk,))
assert_(np.all(~np.isfinite(d[-s:])))
assert_(np.all(i[-s:] == self.kdtree.n))
def test_vectorized_query_multiple_neighbors(self):
s = 23
kk = self.kdtree.n+s
d, i = self.kdtree.query(np.zeros((2,4,3)),k=kk)
assert_equal(np.shape(d),(2,4,kk))
assert_equal(np.shape(i),(2,4,kk))
assert_(np.all(~np.isfinite(d[:,:,-s:])))
assert_(np.all(i[:,:,-s:] == self.kdtree.n))
def test_single_query_all_neighbors(self):
d, i = self.kdtree.query([0,0,0],k=None,distance_upper_bound=1.1)
assert_(isinstance(d,list))
assert_(isinstance(i,list))
def test_vectorized_query_all_neighbors(self):
d, i = self.kdtree.query(np.zeros((2,4,3)),k=None,distance_upper_bound=1.1)
assert_equal(np.shape(d),(2,4))
assert_equal(np.shape(i),(2,4))
assert_(isinstance(d[0,0],list))
assert_(isinstance(i[0,0],list))
class Test_vectorization_compiled:
def setup_method(self):
self.data = np.array([[0,0,0],
[0,0,1],
[0,1,0],
[0,1,1],
[1,0,0],
[1,0,1],
[1,1,0],
[1,1,1]])
self.kdtree = cKDTree(self.data)
def test_single_query(self):
d, i = self.kdtree.query([0,0,0])
assert_(isinstance(d,float))
assert_(isinstance(i,int))
def test_vectorized_query(self):
d, i = self.kdtree.query(np.zeros((2,4,3)))
assert_equal(np.shape(d),(2,4))
assert_equal(np.shape(i),(2,4))
def test_vectorized_query_noncontiguous_values(self):
np.random.seed(1234)
qs = np.random.randn(3,1000).T
ds, i_s = self.kdtree.query(qs)
for q, d, i in zip(qs,ds,i_s):
assert_equal(self.kdtree.query(q),(d,i))
def test_single_query_multiple_neighbors(self):
s = 23
kk = self.kdtree.n+s
d, i = self.kdtree.query([0,0,0],k=kk)
assert_equal(np.shape(d),(kk,))
assert_equal(np.shape(i),(kk,))
assert_(np.all(~np.isfinite(d[-s:])))
assert_(np.all(i[-s:] == self.kdtree.n))
def test_vectorized_query_multiple_neighbors(self):
s = 23
kk = self.kdtree.n+s
d, i = self.kdtree.query(np.zeros((2,4,3)),k=kk)
assert_equal(np.shape(d),(2,4,kk))
assert_equal(np.shape(i),(2,4,kk))
assert_(np.all(~np.isfinite(d[:,:,-s:])))
assert_(np.all(i[:,:,-s:] == self.kdtree.n))
class ball_consistency:
tol = 0.0
def distance(self, a, b, p):
return minkowski_distance(a * 1.0, b * 1.0, p)
def test_in_ball(self):
x = np.atleast_2d(self.x)
d = np.broadcast_to(self.d, x.shape[:-1])
l = self.T.query_ball_point(x, self.d, p=self.p, eps=self.eps)
for i, ind in enumerate(l):
dist = self.distance(self.data[ind], x[i],self.p) - d[i]*(1.+self.eps)
norm = self.distance(self.data[ind], x[i],self.p) + d[i]*(1.+self.eps)
assert_array_equal(dist < self.tol * norm, True)
def test_found_all(self):
x = np.atleast_2d(self.x)
d = np.broadcast_to(self.d, x.shape[:-1])
l = self.T.query_ball_point(x, self.d, p=self.p, eps=self.eps)
for i, ind in enumerate(l):
c = np.ones(self.T.n, dtype=bool)
c[ind] = False
dist = self.distance(self.data[c], x[i],self.p) - d[i]/(1.+self.eps)
norm = self.distance(self.data[c], x[i],self.p) + d[i]/(1.+self.eps)
assert_array_equal(dist > -self.tol * norm, True)
class Test_random_ball(ball_consistency):
def setup_method(self):
n = 100
m = 4
np.random.seed(1234)
self.data = np.random.randn(n,m)
self.T = KDTree(self.data,leafsize=2)
self.x = np.random.randn(m)
self.p = 2.
self.eps = 0
self.d = 0.2
class Test_random_ball_compiled(ball_consistency):
def setup_method(self):
n = 100
m = 4
np.random.seed(1234)
self.data = np.random.randn(n,m)
self.T = cKDTree(self.data,leafsize=2)
self.x = np.random.randn(m)
self.p = 2.
self.eps = 0
self.d = 0.2
class Test_random_ball_compiled_periodic(ball_consistency):
def distance(self, a, b, p):
return distance_box(a, b, p, 1.0)
def setup_method(self):
n = 10000
m = 4
np.random.seed(1234)
self.data = np.random.uniform(size=(n,m))
self.T = cKDTree(self.data,leafsize=2, boxsize=1)
self.x = np.full(m, 0.1)
self.p = 2.
self.eps = 0
self.d = 0.2
def test_in_ball_outside(self):
l = self.T.query_ball_point(self.x + 1.0, self.d, p=self.p, eps=self.eps)
for i in l:
assert_(self.distance(self.data[i],self.x,self.p) <= self.d*(1.+self.eps))
l = self.T.query_ball_point(self.x - 1.0, self.d, p=self.p, eps=self.eps)
for i in l:
assert_(self.distance(self.data[i],self.x,self.p) <= self.d*(1.+self.eps))
def test_found_all_outside(self):
c = np.ones(self.T.n,dtype=bool)
l = self.T.query_ball_point(self.x + 1.0, self.d, p=self.p, eps=self.eps)
c[l] = False
assert_(np.all(self.distance(self.data[c],self.x,self.p) >= self.d/(1.+self.eps)))
l = self.T.query_ball_point(self.x - 1.0, self.d, p=self.p, eps=self.eps)
c[l] = False
assert_(np.all(self.distance(self.data[c],self.x,self.p) >= self.d/(1.+self.eps)))
class Test_random_ball_compiled_largep_issue9890(ball_consistency):
# allow some roundoff errors due to numerical issues
tol = 1e-13
def setup_method(self):
n = 1000
m = 2
np.random.seed(123)
self.data = np.random.randint(100, 1000, size=(n, m))
self.T = cKDTree(self.data)
self.x = self.data
self.p = 100
self.eps = 0
self.d = 10
class Test_random_ball_approx(Test_random_ball):
def setup_method(self):
Test_random_ball.setup_method(self)
self.eps = 0.1
class Test_random_ball_approx_compiled(Test_random_ball_compiled):
def setup_method(self):
Test_random_ball_compiled.setup_method(self)
self.eps = 0.1
class Test_random_ball_approx_compiled_periodic(Test_random_ball_compiled_periodic):
def setup_method(self):
Test_random_ball_compiled_periodic.setup_method(self)
self.eps = 0.1
class Test_random_ball_far(Test_random_ball):
def setup_method(self):
Test_random_ball.setup_method(self)
self.d = 2.
class Test_random_ball_far_compiled(Test_random_ball_compiled):
def setup_method(self):
Test_random_ball_compiled.setup_method(self)
self.d = 2.
class Test_random_ball_far_compiled_periodic(Test_random_ball_compiled_periodic):
def setup_method(self):
Test_random_ball_compiled_periodic.setup_method(self)
self.d = 2.
class Test_random_ball_l1(Test_random_ball):
def setup_method(self):
Test_random_ball.setup_method(self)
self.p = 1
class Test_random_ball_l1_compiled(Test_random_ball_compiled):
def setup_method(self):
Test_random_ball_compiled.setup_method(self)
self.p = 1
class Test_random_ball_l1_compiled_periodic(Test_random_ball_compiled_periodic):
def setup_method(self):
Test_random_ball_compiled_periodic.setup_method(self)
self.p = 1
class Test_random_ball_linf(Test_random_ball):
def setup_method(self):
Test_random_ball.setup_method(self)
self.p = np.inf
class Test_random_ball_linf_compiled_periodic(Test_random_ball_compiled_periodic):
def setup_method(self):
Test_random_ball_compiled_periodic.setup_method(self)
self.p = np.inf
def test_random_ball_vectorized():
n = 20
m = 5
T = KDTree(np.random.randn(n,m))
r = T.query_ball_point(np.random.randn(2,3,m),1)
assert_equal(r.shape,(2,3))
assert_(isinstance(r[0,0],list))
def test_random_ball_vectorized_compiled():
n = 20
m = 5
np.random.seed(1234)
T = cKDTree(np.random.randn(n,m))
r = T.query_ball_point(np.random.randn(2,3,m),1)
assert_equal(r.shape,(2,3))
assert_(isinstance(r[0,0],list))
def test_query_ball_point_multithreading():
np.random.seed(0)
n = 5000
k = 2
points = np.random.randn(n,k)
T = cKDTree(points)
l1 = T.query_ball_point(points,0.003,n_jobs=1)
l2 = T.query_ball_point(points,0.003,n_jobs=64)
l3 = T.query_ball_point(points,0.003,n_jobs=-1)
for i in range(n):
if l1[i] or l2[i]:
assert_array_equal(l1[i],l2[i])
for i in range(n):
if l1[i] or l3[i]:
assert_array_equal(l1[i],l3[i])
class two_trees_consistency:
def distance(self, a, b, p):
return minkowski_distance(a, b, p)
def test_all_in_ball(self):
r = self.T1.query_ball_tree(self.T2, self.d, p=self.p, eps=self.eps)
for i, l in enumerate(r):
for j in l:
assert_(self.distance(self.data1[i],self.data2[j],self.p) <= self.d*(1.+self.eps))
def test_found_all(self):
r = self.T1.query_ball_tree(self.T2, self.d, p=self.p, eps=self.eps)
for i, l in enumerate(r):
c = np.ones(self.T2.n,dtype=bool)
c[l] = False
assert_(np.all(self.distance(self.data2[c],self.data1[i],self.p) >= self.d/(1.+self.eps)))
class Test_two_random_trees(two_trees_consistency):
def setup_method(self):
n = 50
m = 4
np.random.seed(1234)
self.data1 = np.random.randn(n,m)
self.T1 = KDTree(self.data1,leafsize=2)
self.data2 = np.random.randn(n,m)
self.T2 = KDTree(self.data2,leafsize=2)
self.p = 2.
self.eps = 0
self.d = 0.2
class Test_two_random_trees_compiled(two_trees_consistency):
def setup_method(self):
n = 50
m = 4
np.random.seed(1234)
self.data1 = np.random.randn(n,m)
self.T1 = cKDTree(self.data1,leafsize=2)
self.data2 = np.random.randn(n,m)
self.T2 = cKDTree(self.data2,leafsize=2)
self.p = 2.
self.eps = 0
self.d = 0.2
class Test_two_random_trees_compiled_periodic(two_trees_consistency):
def distance(self, a, b, p):
return distance_box(a, b, p, 1.0)
def setup_method(self):
n = 50
m = 4
np.random.seed(1234)
self.data1 = np.random.uniform(size=(n,m))
self.T1 = cKDTree(self.data1,leafsize=2, boxsize=1.0)
self.data2 = np.random.uniform(size=(n,m))
self.T2 = cKDTree(self.data2,leafsize=2, boxsize=1.0)
self.p = 2.
self.eps = 0
self.d = 0.2
class Test_two_random_trees_far(Test_two_random_trees):
def setup_method(self):
Test_two_random_trees.setup_method(self)
self.d = 2
class Test_two_random_trees_far_compiled(Test_two_random_trees_compiled):
def setup_method(self):
Test_two_random_trees_compiled.setup_method(self)
self.d = 2
class Test_two_random_trees_far_compiled_periodic(Test_two_random_trees_compiled_periodic):
def setup_method(self):
Test_two_random_trees_compiled_periodic.setup_method(self)
self.d = 2
class Test_two_random_trees_linf(Test_two_random_trees):
def setup_method(self):
Test_two_random_trees.setup_method(self)
self.p = np.inf
class Test_two_random_trees_linf_compiled(Test_two_random_trees_compiled):
def setup_method(self):
Test_two_random_trees_compiled.setup_method(self)
self.p = np.inf
class Test_two_random_trees_linf_compiled_periodic(Test_two_random_trees_compiled_periodic):
def setup_method(self):
Test_two_random_trees_compiled_periodic.setup_method(self)
self.p = np.inf
class Test_rectangle:
def setup_method(self):
self.rect = Rectangle([0,0],[1,1])
def test_min_inside(self):
assert_almost_equal(self.rect.min_distance_point([0.5,0.5]),0)
def test_min_one_side(self):
assert_almost_equal(self.rect.min_distance_point([0.5,1.5]),0.5)
def test_min_two_sides(self):
assert_almost_equal(self.rect.min_distance_point([2,2]),np.sqrt(2))
def test_max_inside(self):
assert_almost_equal(self.rect.max_distance_point([0.5,0.5]),1/np.sqrt(2))
def test_max_one_side(self):
assert_almost_equal(self.rect.max_distance_point([0.5,1.5]),np.hypot(0.5,1.5))
def test_max_two_sides(self):
assert_almost_equal(self.rect.max_distance_point([2,2]),2*np.sqrt(2))
def test_split(self):
less, greater = self.rect.split(0,0.1)
assert_array_equal(less.maxes,[0.1,1])
assert_array_equal(less.mins,[0,0])
assert_array_equal(greater.maxes,[1,1])
assert_array_equal(greater.mins,[0.1,0])
def test_distance_l2():
assert_almost_equal(minkowski_distance([0,0],[1,1],2),np.sqrt(2))
def test_distance_l1():
assert_almost_equal(minkowski_distance([0,0],[1,1],1),2)
def test_distance_linf():
assert_almost_equal(minkowski_distance([0,0],[1,1],np.inf),1)
def test_distance_vectorization():
np.random.seed(1234)
x = np.random.randn(10,1,3)
y = np.random.randn(1,7,3)
assert_equal(minkowski_distance(x,y).shape,(10,7))
class count_neighbors_consistency:
def test_one_radius(self):
r = 0.2
assert_equal(self.T1.count_neighbors(self.T2, r),
np.sum([len(l) for l in self.T1.query_ball_tree(self.T2,r)]))
def test_large_radius(self):
r = 1000
assert_equal(self.T1.count_neighbors(self.T2, r),
np.sum([len(l) for l in self.T1.query_ball_tree(self.T2,r)]))
def test_multiple_radius(self):
rs = np.exp(np.linspace(np.log(0.01),np.log(10),3))
results = self.T1.count_neighbors(self.T2, rs)
assert_(np.all(np.diff(results) >= 0))
for r,result in zip(rs, results):
assert_equal(self.T1.count_neighbors(self.T2, r), result)
class Test_count_neighbors(count_neighbors_consistency):
def setup_method(self):
n = 50
m = 2
np.random.seed(1234)
self.T1 = KDTree(np.random.randn(n,m),leafsize=2)
self.T2 = KDTree(np.random.randn(n,m),leafsize=2)
class Test_count_neighbors_compiled(count_neighbors_consistency):
def setup_method(self):
n = 50
m = 2
np.random.seed(1234)
self.T1 = cKDTree(np.random.randn(n,m),leafsize=2)
self.T2 = cKDTree(np.random.randn(n,m),leafsize=2)
class sparse_distance_matrix_consistency:
def distance(self, a, b, p):
return minkowski_distance(a, b, p)
def test_consistency_with_neighbors(self):
M = self.T1.sparse_distance_matrix(self.T2, self.r)
r = self.T1.query_ball_tree(self.T2, self.r)
for i,l in enumerate(r):
for j in l:
assert_almost_equal(M[i,j],
self.distance(self.T1.data[i], self.T2.data[j], self.p),
decimal=14)
for ((i,j),d) in M.items():
assert_(j in r[i])
def test_zero_distance(self):
# raises an exception for bug 870 (FIXME: Does it?)
self.T1.sparse_distance_matrix(self.T1, self.r)
class Test_sparse_distance_matrix(sparse_distance_matrix_consistency):
def setup_method(self):
n = 50
m = 4
np.random.seed(1234)
data1 = np.random.randn(n,m)
data2 = np.random.randn(n,m)
self.T1 = cKDTree(data1,leafsize=2)
self.T2 = cKDTree(data2,leafsize=2)
self.r = 0.5
self.p = 2
self.data1 = data1
self.data2 = data2
self.n = n
self.m = m
class Test_sparse_distance_matrix_compiled(sparse_distance_matrix_consistency):
def setup_method(self):
n = 50
m = 4
np.random.seed(0)
data1 = np.random.randn(n,m)
data2 = np.random.randn(n,m)
self.T1 = cKDTree(data1,leafsize=2)
self.T2 = cKDTree(data2,leafsize=2)
self.ref_T1 = KDTree(data1, leafsize=2)
self.ref_T2 = KDTree(data2, leafsize=2)
self.r = 0.5
self.n = n
self.m = m
self.data1 = data1
self.data2 = data2
self.p = 2
def test_consistency_with_python(self):
M1 = self.T1.sparse_distance_matrix(self.T2, self.r)
M2 = self.ref_T1.sparse_distance_matrix(self.ref_T2, self.r)
assert_array_almost_equal(M1.todense(), M2.todense(), decimal=14)
def test_against_logic_error_regression(self):
# regression test for gh-5077 logic error
np.random.seed(0)
too_many = np.array(np.random.randn(18, 2), dtype=int)
tree = cKDTree(too_many, balanced_tree=False, compact_nodes=False)
d = tree.sparse_distance_matrix(tree, 3).todense()
assert_array_almost_equal(d, d.T, decimal=14)
def test_ckdtree_return_types(self):
# brute-force reference
ref = np.zeros((self.n,self.n))
for i in range(self.n):
for j in range(self.n):
v = self.data1[i,:] - self.data2[j,:]
ref[i,j] = np.dot(v,v)
ref = np.sqrt(ref)
ref[ref > self.r] = 0.
# test return type 'dict'
dist = np.zeros((self.n,self.n))
r = self.T1.sparse_distance_matrix(self.T2, self.r, output_type='dict')
for i,j in r.keys():
dist[i,j] = r[(i,j)]
assert_array_almost_equal(ref, dist, decimal=14)
# test return type 'ndarray'
dist = np.zeros((self.n,self.n))
r = self.T1.sparse_distance_matrix(self.T2, self.r,
output_type='ndarray')
for k in range(r.shape[0]):
i = r['i'][k]
j = r['j'][k]
v = r['v'][k]
dist[i,j] = v
assert_array_almost_equal(ref, dist, decimal=14)
# test return type 'dok_matrix'
r = self.T1.sparse_distance_matrix(self.T2, self.r,
output_type='dok_matrix')
assert_array_almost_equal(ref, r.todense(), decimal=14)
# test return type 'coo_matrix'
r = self.T1.sparse_distance_matrix(self.T2, self.r,
output_type='coo_matrix')
assert_array_almost_equal(ref, r.todense(), decimal=14)
def test_distance_matrix():
m = 10
n = 11
k = 4
np.random.seed(1234)
xs = np.random.randn(m,k)
ys = np.random.randn(n,k)
ds = distance_matrix(xs,ys)
assert_equal(ds.shape, (m,n))
for i in range(m):
for j in range(n):
assert_almost_equal(minkowski_distance(xs[i],ys[j]),ds[i,j])
def test_distance_matrix_looping():
m = 10
n = 11
k = 4
np.random.seed(1234)
xs = np.random.randn(m,k)
ys = np.random.randn(n,k)
ds = distance_matrix(xs,ys)
dsl = distance_matrix(xs,ys,threshold=1)
assert_equal(ds,dsl)
def check_onetree_query(T,d):
r = T.query_ball_tree(T, d)
s = set()
for i, l in enumerate(r):
for j in l:
if i < j:
s.add((i,j))
assert_(s == T.query_pairs(d))
def test_onetree_query():
np.random.seed(0)
n = 50
k = 4
points = np.random.randn(n,k)
T = KDTree(points)
check_onetree_query(T, 0.1)
points = np.random.randn(3*n,k)
points[:n] *= 0.001
points[n:2*n] += 2
T = KDTree(points)
check_onetree_query(T, 0.1)
check_onetree_query(T, 0.001)
check_onetree_query(T, 0.00001)
check_onetree_query(T, 1e-6)
def test_onetree_query_compiled():
np.random.seed(0)
n = 100
k = 4
points = np.random.randn(n,k)
T = cKDTree(points)
check_onetree_query(T, 0.1)
points = np.random.randn(3*n,k)
points[:n] *= 0.001
points[n:2*n] += 2
T = cKDTree(points)
check_onetree_query(T, 0.1)
check_onetree_query(T, 0.001)
check_onetree_query(T, 0.00001)
check_onetree_query(T, 1e-6)
def test_query_pairs_single_node():
tree = KDTree([[0, 1]])
assert_equal(tree.query_pairs(0.5), set())
def test_query_pairs_single_node_compiled():
tree = cKDTree([[0, 1]])
assert_equal(tree.query_pairs(0.5), set())
def test_ckdtree_query_pairs():
np.random.seed(0)
n = 50
k = 2
r = 0.1
r2 = r**2
points = np.random.randn(n,k)
T = cKDTree(points)
# brute force reference
brute = set()
for i in range(n):
for j in range(i+1,n):
v = points[i,:] - points[j,:]
if np.dot(v,v) <= r2:
brute.add((i,j))
l0 = sorted(brute)
# test default return type
s = T.query_pairs(r)
l1 = sorted(s)
assert_array_equal(l0,l1)
# test return type 'set'
s = T.query_pairs(r, output_type='set')
l1 = sorted(s)
assert_array_equal(l0,l1)
# test return type 'ndarray'
s = set()
arr = T.query_pairs(r, output_type='ndarray')
for i in range(arr.shape[0]):
s.add((int(arr[i,0]),int(arr[i,1])))
l2 = sorted(s)
assert_array_equal(l0,l2)
def test_ball_point_ints():
# Regression test for #1373.
x, y = np.mgrid[0:4, 0:4]
points = list(zip(x.ravel(), y.ravel()))
tree = KDTree(points)
assert_equal(sorted([4, 8, 9, 12]),
sorted(tree.query_ball_point((2, 0), 1)))
points = np.asarray(points, dtype=float)
tree = KDTree(points)
assert_equal(sorted([4, 8, 9, 12]),
sorted(tree.query_ball_point((2, 0), 1)))
def test_kdtree_comparisons():
# Regression test: node comparisons were done wrong in 0.12 w/Py3.
nodes = [KDTree.node() for _ in range(3)]
assert_equal(sorted(nodes), sorted(nodes[::-1]))
def test_ckdtree_build_modes():
# check if different build modes for cKDTree give
# similar query results
np.random.seed(0)
n = 5000
k = 4
points = np.random.randn(n, k)
T1 = cKDTree(points).query(points, k=5)[-1]
T2 = cKDTree(points, compact_nodes=False).query(points, k=5)[-1]
T3 = cKDTree(points, balanced_tree=False).query(points, k=5)[-1]
T4 = cKDTree(points, compact_nodes=False, balanced_tree=False).query(points, k=5)[-1]
assert_array_equal(T1, T2)
assert_array_equal(T1, T3)
assert_array_equal(T1, T4)
def test_ckdtree_pickle():
# test if it is possible to pickle
# a cKDTree
try:
import cPickle as pickle
except ImportError:
import pickle
np.random.seed(0)
n = 50
k = 4
points = np.random.randn(n, k)
T1 = cKDTree(points)
tmp = pickle.dumps(T1)
T2 = pickle.loads(tmp)
T1 = T1.query(points, k=5)[-1]
T2 = T2.query(points, k=5)[-1]
assert_array_equal(T1, T2)
def test_ckdtree_pickle_boxsize():
# test if it is possible to pickle a periodic
# cKDTree
try:
import cPickle as pickle
except ImportError:
import pickle
np.random.seed(0)
n = 50
k = 4
points = np.random.uniform(size=(n, k))
T1 = cKDTree(points, boxsize=1.0)
tmp = pickle.dumps(T1)
T2 = pickle.loads(tmp)
T1 = T1.query(points, k=5)[-1]
T2 = T2.query(points, k=5)[-1]
assert_array_equal(T1, T2)
def test_ckdtree_copy_data():
# check if copy_data=True makes the kd-tree
# impervious to data corruption by modification of
# the data arrray
np.random.seed(0)
n = 5000
k = 4
points = np.random.randn(n, k)
T = cKDTree(points, copy_data=True)
q = points.copy()
T1 = T.query(q, k=5)[-1]
points[...] = np.random.randn(n, k)
T2 = T.query(q, k=5)[-1]
assert_array_equal(T1, T2)
def test_ckdtree_parallel():
# check if parallel=True also generates correct
# query results
np.random.seed(0)
n = 5000
k = 4
points = np.random.randn(n, k)
T = cKDTree(points)
T1 = T.query(points, k=5, n_jobs=64)[-1]
T2 = T.query(points, k=5, n_jobs=-1)[-1]
T3 = T.query(points, k=5)[-1]
assert_array_equal(T1, T2)
assert_array_equal(T1, T3)
def test_ckdtree_view():
# Check that the nodes can be correctly viewed from Python.
# This test also sanity checks each node in the cKDTree, and
# thus verifies the internal structure of the kd-tree.
np.random.seed(0)
n = 100
k = 4
points = np.random.randn(n, k)
kdtree = cKDTree(points)
# walk the whole kd-tree and sanity check each node
def recurse_tree(n):
assert_(isinstance(n, cKDTreeNode))
if n.split_dim == -1:
assert_(n.lesser is None)
assert_(n.greater is None)
assert_(n.indices.shape[0] <= kdtree.leafsize)
else:
recurse_tree(n.lesser)
recurse_tree(n.greater)
x = n.lesser.data_points[:, n.split_dim]
y = n.greater.data_points[:, n.split_dim]
assert_(x.max() < y.min())
recurse_tree(kdtree.tree)
# check that indices are correctly retrieved
n = kdtree.tree
assert_array_equal(np.sort(n.indices), range(100))
# check that data_points are correctly retrieved
assert_array_equal(kdtree.data[n.indices, :], n.data_points)
# cKDTree is specialized to type double points, so no need to make
# a unit test corresponding to test_ball_point_ints()
def test_ckdtree_list_k():
# check ckdtree periodic boundary
n = 200
m = 2
klist = [1, 2, 3]
kint = 3
np.random.seed(1234)
data = np.random.uniform(size=(n, m))
kdtree = cKDTree(data, leafsize=1)
# check agreement between arange(1,k+1) and k
dd, ii = kdtree.query(data, klist)
dd1, ii1 = kdtree.query(data, kint)
assert_equal(dd, dd1)
assert_equal(ii, ii1)
# now check skipping one element
klist = np.array([1, 3])
kint = 3
dd, ii = kdtree.query(data, kint)
dd1, ii1 = kdtree.query(data, klist)
assert_equal(dd1, dd[..., klist - 1])
assert_equal(ii1, ii[..., klist - 1])
# check k == 1 special case
# and k == [1] non-special case
dd, ii = kdtree.query(data, 1)
dd1, ii1 = kdtree.query(data, [1])
assert_equal(len(dd.shape), 1)
assert_equal(len(dd1.shape), 2)
assert_equal(dd, np.ravel(dd1))
assert_equal(ii, np.ravel(ii1))
def test_ckdtree_box():
# check ckdtree periodic boundary
n = 2000
m = 3
k = 3
np.random.seed(1234)
data = np.random.uniform(size=(n, m))
kdtree = cKDTree(data, leafsize=1, boxsize=1.0)
# use the standard python KDTree for the simulated periodic box
kdtree2 = cKDTree(data, leafsize=1)
for p in [1, 2, 3.0, np.inf]:
dd, ii = kdtree.query(data, k, p=p)
dd1, ii1 = kdtree.query(data + 1.0, k, p=p)
assert_almost_equal(dd, dd1)
assert_equal(ii, ii1)
dd1, ii1 = kdtree.query(data - 1.0, k, p=p)
assert_almost_equal(dd, dd1)
assert_equal(ii, ii1)
dd2, ii2 = simulate_periodic_box(kdtree2, data, k, boxsize=1.0, p=p)
assert_almost_equal(dd, dd2)
assert_equal(ii, ii2)
def test_ckdtree_box_0boxsize():
# check ckdtree periodic boundary that mimics non-periodic
n = 2000
m = 2
k = 3
np.random.seed(1234)
data = np.random.uniform(size=(n, m))
kdtree = cKDTree(data, leafsize=1, boxsize=0.0)
# use the standard python KDTree for the simulated periodic box
kdtree2 = cKDTree(data, leafsize=1)
for p in [1, 2, np.inf]:
dd, ii = kdtree.query(data, k, p=p)
dd1, ii1 = kdtree2.query(data, k, p=p)
assert_almost_equal(dd, dd1)
assert_equal(ii, ii1)
def test_ckdtree_box_upper_bounds():
data = np.linspace(0, 2, 10).reshape(-1, 2)
data[:, 1] += 10
assert_raises(ValueError, cKDTree, data, leafsize=1, boxsize=1.0)
assert_raises(ValueError, cKDTree, data, leafsize=1, boxsize=(0.0, 2.0))
# skip a dimension.
cKDTree(data, leafsize=1, boxsize=(2.0, 0.0))
def test_ckdtree_box_lower_bounds():
data = np.linspace(-1, 1, 10)
assert_raises(ValueError, cKDTree, data, leafsize=1, boxsize=1.0)
def simulate_periodic_box(kdtree, data, k, boxsize, p):
dd = []
ii = []
x = np.arange(3 ** data.shape[1])
nn = np.array(np.unravel_index(x, [3] * data.shape[1])).T
nn = nn - 1.0
for n in nn:
image = data + n * 1.0 * boxsize
dd2, ii2 = kdtree.query(image, k, p=p)
dd2 = dd2.reshape(-1, k)
ii2 = ii2.reshape(-1, k)
dd.append(dd2)
ii.append(ii2)
dd = np.concatenate(dd, axis=-1)
ii = np.concatenate(ii, axis=-1)
result = np.empty([len(data), len(nn) * k], dtype=[
('ii', 'i8'),
('dd', 'f8')])
result['ii'][:] = ii
result['dd'][:] = dd
result.sort(order='dd')
return result['dd'][:, :k], result['ii'][:,:k]
@pytest.mark.skipif(python_implementation() == 'PyPy',
reason="Fails on PyPy CI runs. See #9507")
def test_ckdtree_memuse():
# unit test adaptation of gh-5630
# NOTE: this will fail when run via valgrind,
# because rss is no longer a reliable memory usage indicator.
try:
import resource
except ImportError:
# resource is not available on Windows
return
# Make some data
dx, dy = 0.05, 0.05
y, x = np.mgrid[slice(1, 5 + dy, dy),
slice(1, 5 + dx, dx)]
z = np.sin(x)**10 + np.cos(10 + y*x) * np.cos(x)
z_copy = np.empty_like(z)
z_copy[:] = z
# Place FILLVAL in z_copy at random number of random locations
FILLVAL = 99.
mask = np.random.randint(0, z.size, np.random.randint(50) + 5)
z_copy.flat[mask] = FILLVAL
igood = np.vstack(np.nonzero(x != FILLVAL)).T
ibad = np.vstack(np.nonzero(x == FILLVAL)).T
mem_use = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss
# burn-in
for i in range(10):
tree = cKDTree(igood)
# count memleaks while constructing and querying cKDTree
num_leaks = 0
for i in range(100):
mem_use = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss
tree = cKDTree(igood)
dist, iquery = tree.query(ibad, k=4, p=2)
new_mem_use = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss
if new_mem_use > mem_use:
num_leaks += 1
# ideally zero leaks, but errors might accidentally happen
# outside cKDTree
assert_(num_leaks < 10)
def test_ckdtree_weights():
data = np.linspace(0, 1, 4).reshape(-1, 1)
tree1 = cKDTree(data, leafsize=1)
weights = np.ones(len(data), dtype='f4')
nw = tree1._build_weights(weights)
assert_array_equal(nw, [4, 2, 1, 1, 2, 1, 1])
assert_raises(ValueError, tree1._build_weights, weights[:-1])
for i in range(10):
# since weights are uniform, these shall agree:
c1 = tree1.count_neighbors(tree1, np.linspace(0, 10, i))
c2 = tree1.count_neighbors(tree1, np.linspace(0, 10, i),
weights=(weights, weights))
c3 = tree1.count_neighbors(tree1, np.linspace(0, 10, i),
weights=(weights, None))
c4 = tree1.count_neighbors(tree1, np.linspace(0, 10, i),
weights=(None, weights))
tree1.count_neighbors(tree1, np.linspace(0, 10, i),
weights=weights)
assert_array_equal(c1, c2)
assert_array_equal(c1, c3)
assert_array_equal(c1, c4)
for i in range(len(data)):
# this tests removal of one data point by setting weight to 0
w1 = weights.copy()
w1[i] = 0
data2 = data[w1 != 0]
tree2 = cKDTree(data2)
c1 = tree1.count_neighbors(tree1, np.linspace(0, 10, 100),
weights=(w1, w1))
# "c2 is correct"
c2 = tree2.count_neighbors(tree2, np.linspace(0, 10, 100))
assert_array_equal(c1, c2)
#this asserts for two different trees, singular weights
# crashes
assert_raises(ValueError, tree1.count_neighbors,
tree2, np.linspace(0, 10, 100), weights=w1)
def test_ckdtree_count_neighbous_multiple_r():
n = 2000
m = 2
np.random.seed(1234)
data = np.random.normal(size=(n, m))
kdtree = cKDTree(data, leafsize=1)
r0 = [0, 0.01, 0.01, 0.02, 0.05]
i0 = np.arange(len(r0))
n0 = kdtree.count_neighbors(kdtree, r0)
nnc = kdtree.count_neighbors(kdtree, r0, cumulative=False)
assert_equal(n0, nnc.cumsum())
for i, r in zip(itertools.permutations(i0),
itertools.permutations(r0)):
# permute n0 by i and it shall agree
n = kdtree.count_neighbors(kdtree, r)
assert_array_equal(n, n0[list(i)])
def test_len0_arrays():
# make sure len-0 arrays are handled correctly
# in range queries (gh-5639)
np.random.seed(1234)
X = np.random.rand(10,2)
Y = np.random.rand(10,2)
tree = cKDTree(X)
# query_ball_point (single)
d,i = tree.query([.5, .5], k=1)
z = tree.query_ball_point([.5, .5], 0.1*d)
assert_array_equal(z, [])
# query_ball_point (multiple)
d,i = tree.query(Y, k=1)
mind = d.min()
z = tree.query_ball_point(Y, 0.1*mind)
y = np.empty(shape=(10,), dtype=object)
y.fill([])
assert_array_equal(y, z)
# query_ball_tree
other = cKDTree(Y)
y = tree.query_ball_tree(other, 0.1*mind)
assert_array_equal(10*[[]], y)
# count_neighbors
y = tree.count_neighbors(other, 0.1*mind)
assert_(y == 0)
# sparse_distance_matrix
y = tree.sparse_distance_matrix(other, 0.1*mind, output_type='dok_matrix')
assert_array_equal(y == np.zeros((10,10)), True)
y = tree.sparse_distance_matrix(other, 0.1*mind, output_type='coo_matrix')
assert_array_equal(y == np.zeros((10,10)), True)
y = tree.sparse_distance_matrix(other, 0.1*mind, output_type='dict')
assert_equal(y, {})
y = tree.sparse_distance_matrix(other,0.1*mind, output_type='ndarray')
_dtype = [('i',np.intp), ('j',np.intp), ('v',np.float64)]
res_dtype = np.dtype(_dtype, align=True)
z = np.empty(shape=(0,), dtype=res_dtype)
assert_array_equal(y, z)
# query_pairs
d,i = tree.query(X, k=2)
mind = d[:,-1].min()
y = tree.query_pairs(0.1*mind, output_type='set')
assert_equal(y, set())
y = tree.query_pairs(0.1*mind, output_type='ndarray')
z = np.empty(shape=(0,2), dtype=np.intp)
assert_array_equal(y, z)
def test_ckdtree_duplicated_inputs():
# check ckdtree with duplicated inputs
n = 1024
for m in range(1, 8):
data = np.concatenate([
np.full((n // 2, m), 1),
np.full((n // 2, m), 2)], axis=0)
# it shall not divide more than 3 nodes.
# root left (1), and right (2)
kdtree = cKDTree(data, leafsize=1)
assert_equal(kdtree.size, 3)
kdtree = cKDTree(data)
assert_equal(kdtree.size, 3)
# if compact_nodes are disabled, the number
# of nodes is n (per leaf) + (m - 1)* 2 (splits per dimension) + 1
# and the root
kdtree = cKDTree(data, compact_nodes=False, leafsize=1)
assert_equal(kdtree.size, n + m * 2 - 1)
def test_ckdtree_noncumulative_nondecreasing():
# check ckdtree with duplicated inputs
# it shall not divide more than 3 nodes.
# root left (1), and right (2)
kdtree = cKDTree([[0]], leafsize=1)
assert_raises(ValueError, kdtree.count_neighbors,
kdtree, [0.1, 0], cumulative=False)
def test_short_knn():
# The test case is based on github: #6425 by @SteveDoyle2
xyz = np.array([
[0., 0., 0.],
[1.01, 0., 0.],
[0., 1., 0.],
[0., 1.01, 0.],
[1., 0., 0.],
[1., 1., 0.],],
dtype='float64')
ckdt = cKDTree(xyz)
deq, ieq = ckdt.query(xyz, k=4, distance_upper_bound=0.2)
assert_array_almost_equal(deq,
[[0., np.inf, np.inf, np.inf],
[0., 0.01, np.inf, np.inf],
[0., 0.01, np.inf, np.inf],
[0., 0.01, np.inf, np.inf],
[0., 0.01, np.inf, np.inf],
[0., np.inf, np.inf, np.inf]])
def test_query_ball_point_vector_r():
np.random.seed(1234)
data = np.random.normal(size=(100, 3))
query = np.random.normal(size=(100, 3))
tree = cKDTree(data)
d = np.random.uniform(0, 0.3, size=len(query))
rvector = tree.query_ball_point(query, d)
rscalar = [tree.query_ball_point(qi, di) for qi, di in zip(query, d)]
for a, b in zip(rvector, rscalar):
assert_array_equal(sorted(a), sorted(b))
def test_query_ball_point_length():
np.random.seed(1234)
data = np.random.normal(size=(100, 3))
query = np.random.normal(size=(100, 3))
tree = cKDTree(data)
d = 0.3
length = tree.query_ball_point(query, d, return_length=True)
length2 = [len(ind) for ind in tree.query_ball_point(query, d, return_length=False)]
length3 = [len(tree.query_ball_point(qi, d)) for qi in query]
length4 = [tree.query_ball_point(qi, d, return_length=True) for qi in query]
assert_array_equal(length, length2)
assert_array_equal(length, length3)
assert_array_equal(length, length4)
def test_discontiguous():
np.random.seed(1234)
data = np.random.normal(size=(100, 3))
d_contiguous = np.arange(100) * 0.04
d_discontiguous = np.ascontiguousarray(
np.arange(100)[::-1] * 0.04)[::-1]
query_contiguous = np.random.normal(size=(100, 3))
query_discontiguous = np.ascontiguousarray(query_contiguous.T).T
assert query_discontiguous.strides[-1] != query_contiguous.strides[-1]
assert d_discontiguous.strides[-1] != d_contiguous.strides[-1]
tree = cKDTree(data)
length1 = tree.query_ball_point(query_contiguous,
d_contiguous, return_length=True)
length2 = tree.query_ball_point(query_discontiguous,
d_discontiguous, return_length=True)
assert_array_equal(length1, length2)
d1, i1 = tree.query(query_contiguous, 1)
d2, i2 = tree.query(query_discontiguous, 1)
assert_array_equal(d1, d2)
assert_array_equal(i1, i2)
@pytest.mark.parametrize("balanced_tree, compact_nodes",
[(True, False),
(True, True),
(False, False),
(False, True)])
def test_cdktree_empty_input(balanced_tree, compact_nodes):
# https://github.com/scipy/scipy/issues/5040
np.random.seed(1234)
empty_v3 = np.empty(shape=(0, 3))
query_v3 = np.ones(shape=(1, 3))
query_v2 = np.ones(shape=(2, 3))
tree = cKDTree(empty_v3, balanced_tree=balanced_tree, compact_nodes=compact_nodes)
length = tree.query_ball_point(query_v3, 0.3, return_length=True)
assert length == 0
dd, ii = tree.query(query_v2, 2)
assert ii.shape == (2, 2)
assert dd.shape == (2, 2)
assert np.isinf(dd).all()
N = tree.count_neighbors(tree, [0, 1])
assert_array_equal(N, [0, 0])
M = tree.sparse_distance_matrix(tree, 0.3)
assert M.shape == (0, 0)
class Test_sorted_query_ball_point(object):
def setup_method(self):
np.random.seed(1234)
self.x = np.random.randn(100, 1)
self.ckdt = cKDTree(self.x)
def test_return_sorted_True(self):
idxs_list = self.ckdt.query_ball_point(self.x, 1., return_sorted=True)
for idxs in idxs_list:
assert_array_equal(idxs, sorted(idxs))
for xi in self.x:
idxs = self.ckdt.query_ball_point(xi, 1., return_sorted=True)
assert_array_equal(idxs, sorted(idxs))
def test_return_sorted_None(self):
"""Previous behavior was to sort the returned indices if there were
multiple points per query but not sort them if there was a single point
per query."""
idxs_list = self.ckdt.query_ball_point(self.x, 1.)
for idxs in idxs_list:
assert_array_equal(idxs, sorted(idxs))
idxs_list_single = [self.ckdt.query_ball_point(xi, 1.) for xi in self.x]
idxs_list_False = self.ckdt.query_ball_point(self.x, 1., return_sorted=False)
for idxs0, idxs1 in zip(idxs_list_False, idxs_list_single):
assert_array_equal(idxs0, idxs1)
def test_kdtree_complex_data():
# Test that KDTree rejects complex input points (gh-9108)
points = np.random.rand(10, 2).view(complex)
with pytest.raises(TypeError, match="complex data"):
t = KDTree(points)
t = KDTree(points.real)
with pytest.raises(TypeError, match="complex data"):
t.query(points)
with pytest.raises(TypeError, match="complex data"):
t.query_ball_point(points, r=1)